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padding-bottom: 1em; text-align: center;} + table.toc td.pagenr {text-align: right; vertical-align: bottom; width: 2em;} + table.toc td.subjects {text-align: justify; vertical-align: top;} + td.blankabove {padding-top: 1.5em;} + td.highline {line-height: 2em;} + td.narrow {width: .25em;} + td.thinrow {line-height: .01em;} + th {font-weight: normal; font-size: .8em; text-decoration: none; text-align: center; padding-left: .5em; padding-right: .5em;} + .tnbox {border: solid 2px; background: #999966; margin: 1em 20%; padding: 1em;} + .top {vertical-align: top;} + ul.index {list-style: none; margin-left: 1em;} + ul.index li.first {margin-top: 1em;} + .wrappable {white-space: normal;} + + @media handheld, print + {.noilloblock, + .caption_b, + .largeimg {display: none;} + .caption_e {text-align: center;} + } + + </style> + </head> +<body> +<div>*** START OF THE PROJECT GUTENBERG EBOOK 44371 ***</div> + +<div class="tnbox"> +<p class="center">Please see the <a href="#TN">Transcriber’s Notes</a> at the end of this text.</p> +</div> + +<hr class="chap" /> + +<div class="noilloblock"> +<div class="figcenter"> +<img src="images/cover-b.jpg" alt="cover" width="366" height="550" /> +</div> +<hr class="chap" /> +</div> + +<p><span class="pagenum"><a name="Page_v" id="Page_v"></a></span></p> +<h1>THE<br /> +ANATOMY OF BRIDGEWORK</h1> + +<hr class="chap" /> + +<p class="center highline blankabove"><span class="fsize125">THE</span><br /> +<span class="fsize175">ANATOMY OF BRIDGEWORK</span></p> + +<p class="center highline">BY</p> + +<p class="center blankabove"><span class="fsize150">WILLIAM HENRY THORPE</span><br /> +ASSOC. M. INST. C. E.</p> + +<p class="center highline blankabove blankbelow sstype">WITH 103 ILLUSTRATIONS</p> + +<div class="figcenter"> +<img src="images/illo003.png" alt="logo" width="150" height="176" /> +</div> + +<p class="center blankabove"><span class="oldtype">London</span><br /> +E. & F. N. SPON, <span class="smcap">Limited</span>, 57 HAYMARKET<br /> +<span class="oldtype">New York</span><br /> +SPON & CHAMBERLAIN, 123 LIBERTY STREET<br /> +1906</p> + +<hr class="chap" /> + +<h2>PREFACE</h2> + +<p>In offering this little book to the reader interested in +Bridgework, the author desires to express his acknowledgments +to the proprietors of “Engineering,” in which journal +the papers first appeared, for their courtesy in facilitating +the production in book form.</p> + +<p>It may possibly happen that the scanning of these pages +will induce others to observe and collect information extending +our knowledge of this subject—information which, +while familiar to maintenance engineers of experience, has +not been so readily available as is desirable.</p> + +<p>No theory which fails to stand the test of practical +working can maintain its claims to regard; the study of +the behaviour of old work has, therefore, a high educational +value, and tends to the occasional correction of views which +might otherwise be complacently retained.</p> + +<p><span class="padl2">60 <span class="smcap">Winsham Street</span>,</span><br /> +<span class="padl4"><span class="smcap">Clapham Common, London, S.W.</span></span><br /> +<span class="padl6"><i>October</i>, 1906.</span></p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_vi" id="Page_vi"></a><br /><a name="Page_vii" id="Page_vii">[vii]</a></span></p> + +<h2>CONTENTS</h2> + +<table class="toc" summary="ToC"> + +<tr> +<td colspan="2" class="chapnr">CHAPTER I.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">INTRODUCTION—GIRDER BEARINGS.</td> +</tr> + +<tr> +<td colspan="2" class="right fsize80">PAGE</td> +</tr> + +<tr> +<td class="subjects">Pressure distribution—Square and skew bearings—Fixed bearings—Knuckles—Rollers—Yield of supports</td> +<td class="pagenr"><a href="#Page_1">1</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER II.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">MAIN GIRDERS.</td> +</tr> + +<tr> +<td class="subjects"><i>Plate webs</i>: Improper loading of flanges—Twisting of girders—Remedial measures—Cracks in webs—Stiffening of webs—<span class="lettsymb">T</span> stiffeners</td> +<td class="pagenr"><a href="#Page_9">9</a></td> +</tr> + +<tr> +<td class="subjects"><i>Open webs</i>: Common faults—Top booms—Buckling of bottom booms—Counterbracing—Flat members</td> +<td class="pagenr"><a href="#Page_17">17</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER III.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">BRIDGE FLOORS.</td> +</tr> + +<tr> +<td class="subjects">Liability to defects—Impact—Ends of cross and longitudinal girders—Awkward riveting—Fixed ends to cross girders—Plated floor—Liberal depths desirable—Type connections—Effect of “skew” on floor—Water-tightness—Drainage—Timber floors—Jack arches—Corrugated sheeting—Ballast—Rail joints—Effect of main girders on floors</td> +<td class="pagenr"><a href="#Page_20">20</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER IV.<span class="pagenum"><a name="Page_viii" id="Page_viii">[viii]</a></span></td> +</tr> + +<tr> +<td colspan="2" class="chapname">BRACING.</td> +</tr> + +<tr> +<td class="subjects">Effect of bracing on girders—Influence of skew on bracing—Flat bars—Overhead girders—Main girders stiffened from floor—Stiffening of light girders—Incomplete bracing—Tall piers—Sea piers</td> +<td class="pagenr"><a href="#Page_34">34</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER V.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">RIVETED CONNECTIONS.</td> +</tr> + +<tr> +<td class="subjects">Latitude in practice—Laboratory experiments—Care in considering practical instances—Main girder web rivets—Lattice girders investigated—Rivets in small girders—Faulty bridge floor—Stresses in rivets—Cross girder connections—Tension in rivets—Defective rivets—Loose rivets—Table of actual rivet stresses—Bearing pressure—Permissible stresses—Proposed table—Immunity of road bridges from loose rivets—Rivet spacing</td> +<td class="pagenr"><a href="#Page_45">45</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER VI.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">HIGH STRESS.</td> +</tr> + +<tr> +<td class="subjects">Elastic limit—Care in calculation—Impact—Examples of high stress—Early examples of high stress in steel girders—Tabulated examples—General remarks</td> +<td class="pagenr"><a href="#Page_61">61</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER VII.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">DEFORMATIONS.</td> +</tr> + +<tr> +<td class="subjects">Various kinds—Flexing of girder flanges—Examples—Settlement deformations—Creeping—Temperature changes—Local distortions—Imperfect workmanship—Deformation of cast-iron arches</td> +<td class="pagenr"><a href="#Page_73">73</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER VIII.<span class="pagenum"><a name="Page_ix" id="Page_ix">[ix]</a></span></td> +</tr> + +<tr> +<td colspan="2" class="chapname">DEFLECTIONS.</td> +</tr> + +<tr> +<td class="subjects">Differences as between new work and old—Influence of booms and web structure on deflection—Yield of rivets and stiffness of connections—Working formulæ—Set—Effect of floor system—Deflection diagrams—Loads quickly applied—“Drop” loads—Flexible girders—Measuring deflections—New method of observing deflections—Effect of running load</td> +<td class="pagenr"><a href="#Page_85">85</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER IX.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">DECAY AND PAINTING.</td> +</tr> + +<tr> +<td class="subjects">Examples of rusting of wrought-iron girders—Girder over sea-water—Rate of rusting—Steelwork—Precautions—Red-lead—Repainting—Scraping—Girders built into masonry—Cast iron—Effect of sea-water on cast iron—Examples—Tabulated observations—Percentage of submersion—Quality of metal</td> +<td class="pagenr"><a href="#Page_96">96</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER X.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.</td> +</tr> + +<tr> +<td class="subjects">Purpose—Methods of examination—Calculations—Stress in old work—Methods of reducing stress—Repair—Loose rivets—Replacing wasted flange plates—Adding new to old sections—Principles governing additions—Example—Strengthening lattice girder bracings—Bracing between girders—Strengthening floors—Distributing girders</td> +<td class="pagenr"><a href="#Page_107">107</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER XI.<span class="pagenum"><a name="Page_x" id="Page_x">[x]</a></span></td> +</tr> + +<tr> +<td colspan="2" class="chapname">STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.</td> +</tr> + +<tr> +<td class="subjects">Principal methods in use—Method of calculation—Adjustments—Connections—Method of execution—Checks—Effect of skew on method considered—Results of calculation for a typical case—Probable error—Practical examples—Special case—Method of determining flexure curves</td> +<td class="pagenr"><a href="#Page_122">122</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER XII.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">CAST-IRON BRIDGES.</td> +</tr> + +<tr> +<td class="subjects">Limitations of cast iron—Stress examples—Advantages and disadvantages—Foundry stresses—Examples—Want of ductility of cast iron—Repairs—Restricted possibilities</td> +<td class="pagenr"><a href="#Page_141">141</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER XIII.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">TIMBER BRIDGES.</td> +</tr> + +<tr> +<td class="subjects">Perishable nature—Causes of decay—Sag—Lateral bracing—Piles—Uncertainty respecting decay—Examples—Conditions and practice favourable to durability—Bracing—Protection—Repair—Piles—Cost</td> +<td class="pagenr"><a href="#Page_149">149</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER XIV.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">MASONRY BRIDGES.</td> +</tr> + +<tr> +<td class="subjects">Definition—Cause of defects or failure—Spreading of abutments—Closing in—Example—Stop piers—Example of failure—Strength of rubble arch—Equilibrium of arches—Effect of vibration on masonry—Safety centring—Methods of repair—Pointing—Rough dressed stonework</td> +<td class="pagenr"><a href="#Page_157">157</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER XV.<span class="pagenum"><a name="Page_xi" id="Page_xi">[xi]</a></span></td> +</tr> + +<tr> +<td colspan="2" class="chapname">LIFE OF BRIDGES—RELATIVE MERITS.</td> +</tr> + +<tr> +<td class="subjects">Previous history—Causes of limited life—Tabulated examples of short-lived metallic bridges—Timber and masonry bridges—Durability—Maintenance charges—First cost—Comparative merits—Choice of material</td> +<td class="pagenr"><a href="#Page_165">165</a></td> +</tr> + +<tr> +<td colspan="2" class="chapnr">CHAPTER XVI.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">RECONSTRUCTION AND WIDENING OF BRIDGES.</td> +</tr> + +<tr> +<td colspan="2" class="chapname">CONCLUSION.</td> +</tr> + +<tr> +<td class="subjects">Measuring up—Railway under-bridges—Methods of reconstruction in common use—Reconstruction of bridges of many openings—Timber staging—Traffic arrangements—Sunday work—Railway over-bridges—Widenings—Junction of new and old work—Concluding remarks—Study of old bridgework</td> +<td class="pagenr"><a href="#Page_172">172</a></td> +</tr> + +<tr> +<td class="left blankabove">INDEX</td> +<td class="pagenr"><a href="#Page_187">187</a></td> +</tr> + +</table> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_1" id="Page_1">[1]</a></span></p> + +<p class="center highline blankabove blankbelow"><b><span class="fsize125">THE</span><br /> +<span class="fsize175">ANATOMY OF BRIDGEWORK.</span></b></p> + +<hr class="chap" /> + +<h2>CHAPTER I.<br /> +<span class="chaptitle">INTRODUCTION.</span></h2> + +<p>No book has, so far as the author is aware, been written +upon that aspect of bridgework to be treated in the following +pages. No excuse need, therefore, be given for adding to +the already large amount of published matter dealing with +bridges. Indeed, as it too often happens that the designing +of such constructions, and their after-maintenance, are in +this country entirely separated, it cannot but be useful to +give such results of the behaviour of bridges, whether new +or old, as have come under observation.</p> + +<p>In the early days of metallic bridges there was of necessity +no experience available to guide the engineer in his +endeavour to avoid objectionable features in design, and he +was, as a result, compelled to rely upon his own foresight +and judgment in any attempt to anticipate the effects of +those influences to which his work might later be subject. +How heavily handicapped he must have been under these +conditions is evident from the mass of information since +acquired by the experimental study of the behaviour of +metals under stress, and the growth of the literature of +bridgework during the last forty years. That many mistakes +were made is little occasion for surprise; rather is it a cause<span class="pagenum"><a name="Page_2" id="Page_2">[2]</a></span> +for admiration that some very fine bridges, still in use, were +the product of that time. Much may be learned from the +study of defects and failures, even though they be of such a +character that no experienced designer would now furnish +like examples.</p> + +<p>Modern instances may, none the less, be found, with +faults repeated, which should long since have disappeared +from all bridgework, and are only to be accounted for by +the unnatural divorce of design and maintenance already +referred to. As the reader proceeds, it may appear that +details are occasionally touched upon of a character altogether +too crude and objectionable to need comment; but the +consideration of these cases is none the less interesting, and, +so far as the author’s observation goes, not altogether unnecessary.</p> + +<p>Most of the instances cited are of bridges, or parts of +bridges, of quite small dimensions; but it is these which +most commonly give trouble, both because the effects of impact +are in such cases most severely felt, and possibly because +the smaller class of bridges is very generally designed by men +of less experience, than large and imposing structures.</p> + +<p>The particulars given relate in all cases to bridges of +wrought iron, unless otherwise described.</p> + +<p>An endeavour has been made to secure some kind of +order in dealing with the subject, but it has been found +difficult to avoid a somewhat disjointed treatment, inseparable, +perhaps, from the nature of the matter. Finally, +the reader may be assured that every case quoted has come +under the writer’s personal notice.</p> + +<h3><span class="smcap">Girder Bearings.</span></h3> + +<p>In girder-work generally, and more particularly in plate-girders, +considerable latitude obtains in the amount of bearing +allowed. Clearly, the surface over which the pressure<span class="pagenum"><a name="Page_3" id="Page_3">[3]</a></span> +is distributed should be sufficiently ample to avoid overloading +and possible crushing or fracture of bedstones where +these exist; but if no knuckles are introduced, this is an +extremely difficult matter to insure. A long bearing may +deliver the load at the extreme end of the surface on which +it rests, or, more probably, near the face.</p> + +<p>If the girder is made with truly level bearings, and the +beds set level, it will certainly, when under load, throw an +extreme pressure upon that part of the bearing surface +immediately under the forward edge of the bearing-plate. +These considerations probably account for bedstones frequently +cracking, in addition to which possibility there is +the disadvantage that the designer does not know where the +girder will rest, and cannot truly define the span. The +variation of flange-stress due to this cause may, in a girder +of ordinary proportions, having bearings equal in length to +the girder’s depth, be as much as 15 per cent. above or +below that intended.</p> + +<p>If great care be taken in setting beds, in the first instance, +to dip toward the centre of the span an amount depending +upon the anticipated girder deflection, it may be possible to +insure that when under full load the girder bearing shall +rest equally upon its seat; but this is evidently a difficult +condition to obtain practically, is good only for one degree of +loading, and may at any time be nullified by a disturbance +of the supports, as, for instance, the very common occurrence +of a slight leaning forward of abutment walls.</p> + +<p>Double or treble thicknesses of hair-felt are sometimes +placed beneath girder bearings, with the object of securing +a better distribution of pressure, no doubt with advantage; +but this practice, though it may be quite satisfactory as +applied to girders carrying an unchangeable load, hardly +meets the case for loads which are variable. Notwithstanding +the faulty nature of the plain bearing ordinarily used<span class="pagenum"><a name="Page_4" id="Page_4">[4]</a></span> +for girders of moderate span, its extreme simplicity commends +it to most engineers. It must be admitted that no serious +inconvenience need be anticipated in the majority of cases, +particularly if the bearings are limited in length, do not +approach nearer than 3 inches to the face of bedstones, and +are furnished with hair-felt or similar packing.</p> + +<div class="figcenter"><a name="Fig1" id="Fig1"></a> +<img src="images/illo016.png" alt="" width="450" height="216" /> +<p class="caption"><span class="smcap">Fig.</span> 1.</p> +</div> + +<p>Whether with long or short bearings, the forward edge +should be at right angles to the girder’s length. In skew +bridges it is sometimes seen that this edge follows the angle +of skew. The effect on the girder is to twist it, as will be +clear from a little consideration. In evidence of this the +case may be quoted of a lattice girder of 95 feet effective +span and 7 feet deep, which, resting on a skew abutment +right up to the masonry face at a rather bad angle (about +15 degrees), was, after twenty years, found canted over at +the top to the extent of 4 inches, with the further result of +springing a joint in the top flange at about the middle of +the girder, causing some rivets to loosen. The bedstone +was also very badly broken at the face, and had to be +replaced in the course of repairs (<a href="#Fig1">Fig. 1</a>). This girder had, +in addition to the canting from the upright position at its +end, and the distortion of the top flange, a curvature in the +same direction, though less in amount, at the bottom—an<span class="pagenum"><a name="Page_5" id="Page_5">[5]</a></span> +effect very common in the main girders of skew bridges, and +possibly accounted for in part by a tendency of the girder +end to creep along the abutment away from the point at +which it bears hardest, under frequent applications and +removals of the live load, and accompanying deflections.</p> + +<p>This tendency to travel may be aggravated in bridges +carrying a ballasted road, in which there may be a considerable +thickness of ballast near the bearings, by the compacting +and spreading of this material taking effect upon the +girder end, tending to push it outwards, being tied only by +a few light cross-girders badly placed for useful effect. +The movement may be prevented in new work for moderate +angles of skew by carrying the end cross-girders well back, +and securing them in some efficient manner; or by the +introduction of a diagonal tie following the skew face, and +attached to cross and main girder flanges (<a href="#Fig2">Fig. 2</a>)—a method +which may be applied to existing work also.</p> + +<div class="figcenter"><a name="Fig2" id="Fig2"></a> +<img src="images/illo017.png" alt="" width="350" height="232" /> +<p class="caption"><span class="smcap">Fig.</span> 2.</p> +</div> + +<p>For such a case as that cited it is imperative that ballast +pressure at the girder end should be altogether eliminated.</p> + +<p>The fixing of girder ends by bolts—a practice at one +time usual—hardly calls for remark, as it is now seldom +resorted to unless for special reasons; but it may be well to +point out the weakening effect of holes for any purpose in<span class="pagenum"><a name="Page_6" id="Page_6">[6]</a></span> +bedstones. Bed-plates commonly need no fixing; the weight +carried keeps them in position, or if, in the case of very +light girders upon separate plates, it is considered well to +secure these from shifting, it may best be done by letting +the plate in bodily a small amount, or by means of a very +shallow feather sunk into a chase.</p> + +<div class="figcenter"><a name="Fig3" id="Fig3"></a> +<img src="images/illo018.png" alt="" width="450" height="298" /> +<p class="caption"><span class="smcap">Fig.</span> 3.</p> +</div> + +<p>As an improvement upon the plain bearing usually +adopted, it is an easy matter so to design girder-ends as to +deliver the load by a narrow strip of bearing-plate carried +across the bottom flange, distributing the pressure upon the +stone, if there be one, by means of a simple rectangular plate +of sufficient stoutness (<a href="#Fig3">Fig. 3</a>). An imperfect knuckle will +by this means result, with freedom to slide, and the girder +span be defined within narrow limits. A true knuckle is, of +course, the best means of securing imposition of the load +always in the same place; but this by itself is not sufficient +where the girder is of a length to make temperature and +stress variations important, in which case rollers, or freedom +to slide, become necessary. Bridges exist in which roller-bearings +have been adopted without the knuckle, or its<span class="pagenum"><a name="Page_7" id="Page_7">[7]</a></span> +equivalent, but this is wholly indefensible, as it is obvious +that the forward roller will in all probability take the whole +load, and cannot be expected to keep its shape and roll freely +under this mal-treatment. It is sometimes asserted that +rollers are never effective after some years’ use; that they +become clogged with dirt, and refuse to perform their office.</p> + +<p>There is no reason why rollers should not be boxed in to +exclude dirt by a casing easily removed, some attention being +given to them, and any possible accumulation of dirt removed +each time the bridge is painted.</p> + +<p>To test the behaviour of rollers under somewhat unfavourable +conditions for their proper action—that of the +bearings of main roof trusses of crescent form, 190 feet span—the +author, some thirty years since, took occasion to make +the necessary observations, and found evidence of a moderate +roller movement, though there was in this case no direct +horizontal member to communicate motion. With girders +resting upon columns, particularly if of cast iron, a roller +and knuckle arrangement is most desirable for any but very +small spans, as, if not adopted, the result will be a canting +of the columns from side to side—a very small amount, it is +true, but sufficient to throw the load upon the extreme edges +of the base, though the knuckle alone will relieve the top of +this danger. The author at one time took the trouble to +examine, so far as it could be done superficially and without +opening out the ground to make a complete inspection +possible, a number of bridges crossing streets, in which +girders rested upon and were secured to cast-iron columns +standing in the line of kerb; and he found cracks, either at +the top or bottom, in about one of every four columns.</p> + +<p>When girders passing over columns are not continuous, +it may be difficult to find room for a double roller and +knuckle arrangement; but this inconvenience may be overcome +by carrying one girder-end wholly across the column-top,<span class="pagenum"><a name="Page_8" id="Page_8">[8]</a></span> +and securing the next girder-end to it in a manner +which a little care and ingenuity will render satisfactory, +one free bearing then serving to carry the load from both +girders.</p> + +<p>Though the wisdom of using rollers is apparent in spans +exceeding some moderate length, say 80 feet—as to which +engineers do not seem quite decided—and varying with the +conditions, it need not be overlooked that in some cases +masonry will be sufficiently accommodating to render them +unnecessary; piers, if sufficiently tall and slender, will +yield a small amount without injury, and though shorter, if +resting upon a bottom not absolutely rigid, will rock and +give the necessary relief; but it is obvious, if the resistance +to movement is sufficiently great, and the girder cannot slide +or roll on its bearings, bedstones will probably loosen, as, +indeed, frequently happens.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_9" id="Page_9">[9]</a></span></p> + +<h2>CHAPTER II.<br /> +<span class="chaptitle">MAIN GIRDERS; PLATE-WEBS.</span></h2> + +<p>It is seldom that girders of this description—or, indeed, of +any other—show signs of failure from mere defect of strength +in the principal parts, even though somewhat highly stressed; +and instances tending to support this statement will be given +in a later chapter. For the present, it is proposed to indicate +peculiarities of behaviour only, generally, but not always, +harmless.</p> + +<p>Though now less often done, it was at one time common +practice to load plate-girders on the bottom flange by simply +resting floor timbers, rails, troughs, or cross-girders upon +them. In outside girders one result of this is to cause the +top flange to take a curve in plan, convex towards the road, +every time the live load comes upon the floor of the bridge, +upon the passing of which the flange resumes its figure, though +still affected by that part of the load which is constant.</p> + +<p>A bridge of 47 feet span, carrying two lines of way, +having one centre and two outside girders, with a floor consisting +of old Barlow rails, resting upon the bottom flanges, +showed the peculiarity named in a marked degree.</p> + +<p>The outside girders, under dead load only, were, as to +the top flanges (see <a href="#Fig4">Figs. 4</a> and <a href="#Fig5">5</a>), 1<sup>1</sup>⁄<sub>4</sub> inch and 1<sup>1</sup>⁄<sub>16</sub> inch +respectively out of straight in their length, but upon the +passing of a goods engine and train curved an additional 1<sup>1</sup>⁄<sub>8</sub> +inch, or 2<sup>3</sup>⁄<sub>8</sub> inches in all, for one outside girder, and 2<sup>3</sup>⁄<sub>16</sub> +inches for the other.</p> + +<p>The centre girder, having a broader and heavier top<span class="pagenum"><a name="Page_10" id="Page_10">[10]</a></span> +flange, curved <sup>5</sup>⁄<sub>8</sub> inch towards whichever road might be +loaded. The effect of such horizontal +flexure is clearly to induce stresses of +tension and compression in the flanges, +which, being (for the top flange) compounded +with the normal compressive +stress due to load carried, results in a +considerable want of uniformity across +the section.</p> + +<div class="figcenter"><a name="Fig4" id="Fig4"></a> +<img src="images/illo022.png" alt="" width="600" height="149" /> +<p class="caption"><span class="smcap">Fig.</span> 4.</p> +</div> + +<p>In the case under notice, the writer +estimates the stresses for an outer +girder top flange at 4·5 tons per +square inch compression for simple +loading, and 5·5 tons per square inch +of tension and compression, on the +inner and outer edges, due to flexure, +resulting when compounded in a stress +of 1 ton per square inch tension on +the inside, and 10 tons per square inch +compression on the outside edge. In +this rather extreme case the stress on +the inner edge, or that nearest the +load, is reversed in character.</p> + +<p>The effect described appears to be +not wholly due to the twisting moment. +It is apparent that whatever curvature +may be induced by twisting alone +must be aggravated in the compression +flange by its being put out of line.</p> + +<p>The writer does not attempt here to +apportion the two effects in any other +way than to say that the greater part +of the flexure appears to be due to the secondary cause. Consistent +with this view of the matter is the fact that the inclination<span class="pagenum"><a name="Page_11" id="Page_11">[11]</a></span> +of the girder towards the rails greatly exceeded the +calculated slope of the Barlow rail-ends when under load, +being about five times as great. The inference is that the +floor rails bore hard at their extreme ends, at which point of +bearing the calculated twisting moment accounts for less +than one-half of the flexure observed in the flanges.</p> + +<div class="figcenter"><a name="Fig5" id="Fig5"></a> +<img src="images/illo023.png" alt="" width="400" height="321" /> +<p class="caption"><span class="smcap">Fig.</span> 5.</p> +</div> + +<p>The girders upon removal in the course of reconstruction +again took the straight form, showing that the very +frequent development of the stresses named had not sensibly +injured the metal, though the bridge carried as many as +three hundred trains daily in each direction, and had done so +for very many years.</p> + +<p>The deformation of the top flange only has been noticed, +yet the same tendency exists in the bottom, though the actual +amount is much less, both because the lower flanges are in +tension, and are also in great degree confined by the frictional +contact of the cross bearers, even where no proper ties +are used. In the case dealt with the bottom flanges of +the outer girders curved <sup>1</sup>⁄<sub>8</sub> inch outwards only.</p> + +<p><span class="pagenum"><a name="Page_12" id="Page_12">[12]</a></span></p> + +<p>With the broad flanges commonly adopted in English +practice, twisting of the girders, under conditions similar to +the above, will not generally be a serious matter; but with +narrow flanges possessing little lateral stiffness it might be a +source of danger.</p> + +<div class="figc450"><a name="Fig6" id="Fig6"></a><a name="Fig7" id="Fig7"></a> +<img src="images/illo024.png" alt="" width="450" height="282" /> +<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 6.</span> +<span class="right49"><span class="smcap">Fig.</span> 7.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 6. and <span class="smcap">Fig.</span> 7.</p> +</div> + +<p>The twisting may be limited in amount by introducing +a cross-frame between the girders, from which they are +stiffened; by strutting the girders immediately from the floor +itself, in which case they cannot cant to a greater extent +than that which corresponds to the floor deflection; or by +designing the top flange to be unsymmetrical with reference +to the web, as in <a href="#Fig6">Figs. 6 and 7</a>, with the object of insuring +that under the joint effect of vertical loading and twisting, +the stress in the flange shall at maximum loads be uniform +across the section, and allow it to remain straight. This +may be secured by making the eccentricity of the flange +section equal to that of the loading. For instance, if the load +be applied 3 inches away from the web centre, the flange +should have its centre of gravity 3 inches on the other side +of the centre line. It can be shown that this is true +throughout the length of the girder, and irrespective of the +depth. An instance in which flange eccentricity being in +excess, curvature outwards resulted, will be found in a later<span class="pagenum"><a name="Page_13" id="Page_13">[13]</a></span> +chapter on deformations, etc. It will not generally be +necessary to make the bottom flange eccentric, as it is +commonly tied in some way; but if done, the eccentricity +should be on the same side as for the top. The flanges +remaining straight under these conditions are not subject to +the complications of stress referred to in the case first quoted. +The author has adopted both the last named details in bridges +where he has been obliged to accept unfair loading of the +kind discussed.</p> + +<p>It should be remarked that by the two first methods, if +the stiffening frames are wide apart and attached direct to +the web, there is a liability for this to tear, under distress, +rather than keep the girder in line.</p> + +<p>There is one other possible consequence of throwing load +upon the flanges of a girder of a much more alarming nature. +In girders not very well stiffened, it may happen that the +frequent application of load in this manner finally so injures +the web-plate, just above the top edge of the bottom angle-bars, +as to cause it to rip in a horizontal direction. More +likely is this to happen with a centre girder taking load first +on one side, then on the other, and again on both together. +Cases may be cited in which cracks right through the webs +3 feet or more in length have resulted from this cause. It +is very probable, however, that in some of these cases the +matter was aggravated by the use of a poor iron in the webs, +as at one time engineers, from mistaken notions of the +extreme tenuity permissible in webs near the centre of a +girder, would, if they could not be made thin enough, even +encourage the use of an indifferent metal as being quite good +enough for that part of the work.</p> + +<p>An instance of web-fracture from somewhat similar causes +may be here given.</p> + +<p>In a bridge of 31 feet 6 inches effective span, and consisting +of twin girders carrying rails between, as shown in <a href="#Fig8">Figs. +8</a> and <a href="#Fig9">9</a>, the load resting upon the inner ledges, formed by<span class="pagenum"><a name="Page_14" id="Page_14">[14]</a></span> +the bottom flange, induced such a bending and tearing action +along the web just above the angle-bars, +as to cause a rip in one of the girders, well +open for some distance, and which could +be traced for 14 feet as a continuous crack.</p> + +<div class="figcenter"><a name="Fig8" id="Fig8"></a> +<img src="images/illo026.png" alt="" width="600" height="101" /> +<p class="caption"><span class="smcap">Fig.</span> 8.</p> +</div> + +<div class="figcenter"><a name="Fig9" id="Fig9"></a> +<img src="images/illo027.png" alt="" width="450" height="309" /> +<p class="caption"><span class="smcap">Fig.</span> 9.</p> +</div> + +<p>It will be noticed in the figure that the +<span class="lettsymb">T</span> stiffeners occur only at the outer face of +the web, and that the inner vertical strips +stop short at the top edge of the angles, +the result being that under load the flange +would tend to twist around some point, say +A, at each stiffener, inducing a serious stress +in the thin web at that place, while away +from these stiffeners the web would be +more free to yield without tearing. The +fact that at a number of the stiffeners +incipient cracks were observed, some only +a few inches long, suggests this view of +the matter.</p> + +<p>A case of web-failure from other influences +coming under notice showed breaks +at the upper part of the web extending +downwards.</p> + +<p>In this bridge, of 32 feet span, which +had been in existence thirty-two years, +the webs—originally <sup>1</sup>⁄<sub>4</sub> inch thick—were, +largely because of cinder ballast in contact +with them, so badly wasted as to be generally +little thicker than a crown-piece, and +in places were eaten through; in addition +to which, the road being on a sharp curve, +the rail-balks had been strutted from the +webs to keep them in position, the effect +of which would be to exert a hammering thrust upon the<span class="pagenum"><a name="Page_15" id="Page_15">[15]</a></span> +face of the web at the abutting ends, and assist in starting +cracks in webs already much corroded. A feature of this case, +tending to show that the breaks resulted as the joint effect of +waste and ill-usage by the strut members, rather than by excessive +stress in the web as reduced, is to be found in the fact that +the girders when removed were observed to be in remarkably +good shape—i.e. the camber, marked on the original drawings +to be 1<sup>1</sup>⁄<sub>2</sub> inch, still showed as a perfectly even curve of that +rise, which would hardly have been the case if the lower +flange had been let down by web-rupture, the result of +excessive web-stresses.</p> + +<p>Occasionally webs will crack through the solid unwasted +plate, in a line nearly vertical; not where shear stress is +greatest, but generally at some other place, and from no +apparent cause, either of stress or ill-usage. The writer has +observed this only in the case of small girders not exceeding +2 feet in depth; and, for want of any better reason, attributes +these cracks to poor material, coupled with some latent defect. +In a bridge having some thirty cross-girders, each 26 feet +long, about every other one had a web cracked in this +manner after many years’ use.</p> + +<p><span class="pagenum"><a name="Page_16" id="Page_16">[16]</a></span></p> + +<p>Web-cracks of the kind first indicated, are perhaps, the +most probable source of danger in plate-girders, of any which +are likely to occur. The fault is insidious, difficult to detect +when first developed, and perhaps not seen at all till the +bridge, condemned for some other reason, has the girders +freely exposed and brought into broad light. The manner +in which old girders are sometimes partly concealed by +timberwork, or covered by ballast, makes the detection of +these defects an uncertain matter, unless sufficient trouble is +occasionally taken to render inspection complete.</p> + +<p>The manner in which girders with wasted and fractured +webs will still hang together under heavy loading seems to +warrant the deduction that, in designing new work, it can +hardly be necessary to provide such a considerable amount of +web-stiffening as is sometimes seen; experience showing that +defects of the web-structure do not commonly occur in the +stiffening so frequently as in the plate, and then in the form +of cracks.</p> + +<p>A case of web-buckling lies, so far, without the author’s +experience. There is no need to introduce, for web-stresses +alone, more stiffening than that which corresponds to making +the stiffeners do duty as vertical struts in an openwork +girder; in which case it is sufficient to insure that the +stiffeners occurring in a length equal to the girder’s depth +shall, as struts, be strong enough in the aggregate to take +the whole shear force at the section considered, in no case +exceeding this amount on one stiffener. For thin webs in +which the free breadth is greater than one hundred and +twenty times the thickness, the diagonal compressive stress +may be completely ignored, and the thickness determined +with reference to the diagonal tension stress only.</p> + +<p>There is one fault which frequently shows itself in +stiffeners though not the result of web-stresses, and when +performing an additional function—viz., the breaking of<span class="pagenum"><a name="Page_17" id="Page_17">[17]</a></span> +<span class="lettsymb">T</span> stiffener knees at the weld, where brought down on to the +tops of cross-girders, due to the deflection of the floor, as +shown in <a href="#Fig10">Fig. 10</a>. When such knees are used, the angle +may properly be filled in with a gusset-plate to relieve the +weld of strain and prevent fracture.</p> + +<div class="figcenter"><a name="Fig10" id="Fig10"></a> +<img src="images/illo029.png" alt="" width="350" height="343" /> +<p class="caption"><span class="smcap">Fig.</span> 10.</p> +</div> + +<p>There is some little temptation in practice to make use +of the solid web as a convenient stop for ballast, or road +material. Special means, perhaps at the cost of some little +trouble, should be adopted, where necessary, to avoid this.</p> + +<h3><span class="smcap">Main Girders; Open Webs.</span></h3> + +<p>With these, as with plate-girders, deficiency of strength—i.e. +of section strength—is seldom so marked as to be a +reasonable cause of anxiety. In particular instances faults +in design may result in stresses of an abnormal amount, +though rarely to an extent occasioning any ill effects. The +practice of loading the bottom flanges at a distance from<span class="pagenum"><a name="Page_18" id="Page_18">[18]</a></span> +the centre, the bad effects of which have already been dealt +with as applied to plate-girders, is not commonly resorted to +in girders having open webs, nor are these so liable to be +heaped with ballast in immediate proximity to essential +members of the structure.</p> + +<p>Some defects are, however, occasionally seen which may +be remarked. Top booms of an inverted <span class="lettsymb">U</span> section are +sometimes made with side webs too thin, and having the +lower edges stiffened insufficiently, or not at all. Where +this is the case, the plates may be seen to have buckled out +of truth, showing that they are unable, as thin plates, to +sustain the compressive stress to which the rest of the boom +is liable. The practice of putting the greater part of the +boom section in an outer flange, characteristic of this defect, +has the further disadvantage of throwing the centre of gravity +of the section so near its outer edge as to make impracticable +the best arrangement of rivets for connection of the web +members. Further, since all the variation in boom section +is thrown into the flange-plates, the centre of gravity of the +section has no constant position along the boom—an additional +inconvenience where correct design is aimed at.</p> + +<p>These considerations indicate the propriety of arranging +the bulk, or all, of the section at the sides, thus reducing or +getting rid of the objections named.</p> + +<p>Where the bottom boom consists of side plates, only one +point demands attention. It is found that, though nominally +in tension, the end bays are liable occasionally to buckle, as +though under compressive stress, and need stiffening, not +excepting girders which at one end are mounted on rollers. +This might seem to indicate that the rollers are of no use; +but it is conceivable the resistance arises from other causes, +such as wind forces, or as in the case of a bridge carrying a +railway, in which the rigidity of the permanent-way may be +such that the bridge-structure, in extending towards the<span class="pagenum"><a name="Page_19" id="Page_19">[19]</a></span> +roller end, cannot move it sufficiently, causing a reversal of +stress on the lighter portions of the bottom boom at the +knuckle end; or by the exposed girder booms becoming +very sensibly hotter than the bridge floor, and by expanding +at a greater rate, cause this effect, from which rollers cannot +protect them.</p> + +<p>In counterbracing consisting of flat bars it is desirable +either to secure these where they cross other members, or +stiffen them in some manner to avoid the disagreeable +chattering which will otherwise commonly be found to occur +on the passage of the live load.</p> + +<p>Occasionally diagonal ties are made up of two flat bars +placed face to face, to escape the use of one very thick +member. Where this is done, the two thicknesses, if not +riveted together along the edges, will be liable to open, as +the result of rusting between the bars in contact, when the +evil will be aggravated by the greater freedom with which +moisture will enter the space.</p> + +<p>Other matters relating to open-web girders will be more +conveniently dealt with under their separate headings, particularly +a further consideration of the relationship subsisting +between the booms and floor structure.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_20" id="Page_20">[20]</a></span></p> + +<h2>CHAPTER III.<br /> +<span class="chaptitle">BRIDGE FLOORS.</span></h2> + +<p>The floors of bridges commonly give more trouble in maintenance, +and their defects are more frequently the cause +which renders reconstruction necessary, apart from reasons +not concerning strength, than any other part of such structures. +When it is considered that this portion of a bridge +is first affected by impact of the load which comes upon it, +and is usually light in comparison with the main girders +further removed from the load, and to which the latter is +transferred through the more or less elastic floor, the fact +will be readily appreciated by those not already familiar +with it.</p> + +<p>The end attachments of cross and longitudinal girders +are very liable to suffer by loosening of rivets, or, more +rarely, by breaking of the angle-irons which commonly make +such a connection. A not unusual defect of old work, which +may also sometimes be seen in work quite new, where the +cross-girder depth has from any cause been restricted, is the +extremely cramped position of the rivets securing the ends. +There is small chance of these ever being properly tight, if +the act of riveting is rendered difficult by bad design. This +is the more objectionable if it happens that cross-girder ends +abut against opposite sides of the web of an intermediate +main girder, and are secured by the same rivets passing +through. At the best such rivets will not be well placed to +insure good workmanship, and the severe treatment to which +they become subject, as the cross-girders take their load and<span class="pagenum"><a name="Page_21" id="Page_21">[21]</a></span> +deflect under it, will be very apt to loosen them. The author +has seen a case of this kind (see <a href="#Fig11">Figs. 11</a> and <a href="#Fig12">12</a>)—rather +extreme, it is true—in which nearly the whole of the cross-girder +end rivets were loose, some nearly worn through, thus +allowing the cross-girders to be carried, not by their attachments, +but by resting upon the main-girder flanges, which +in turn, by repeated twisting, tore the web for a length of +4 feet; there was also pronounced side flexure of the top +booms. The movements generally on this bridge (of 42-feet +span), whether of main or cross-girders, were very considerable +and disturbing. It was removed after about twenty-three +years’ use.</p> + +<div class="figcenter"><a name="Fig11" id="Fig11"></a> +<img src="images/illo033a.png" alt="" width="400" height="259" /> +<p class="caption"><span class="smcap">Fig.</span> 11.</p> +</div> + +<div class="figcenter"><a name="Fig12" id="Fig12"></a> +<img src="images/illo033b.png" alt="" width="400" height="96" /> +<p class="caption"><span class="smcap">Fig.</span> 12.</p> +</div> + +<p>There is no necessity, as a rule, for the ends of cross-girders +attached to the same main girder at opposite sides +to be placed in line. The author prefers to arrange them to +miss, by which device each connection is entirely separate,<span class="pagenum"><a name="Page_22" id="Page_22">[22]</a></span> +the riveting can be more efficiently executed, erection is +simplified, and the rivets will be more likely to keep tight. +Other special cases of cross-girder ends will be dealt with +under the head “<a href="#Page_45">Riveted Connections</a>.”</p> + +<p>It is sometimes contended that cross-girders attached at +their ends by a riveted connection should be designed as for +fixed ends, in which case they are usually made of the same +flange section throughout, with a view to satisfy the supposed +requirements. But a girder to be rightly considered +as having fixed ends must be secured to something itself +unyielding. With an outer main girder of ordinary construction, +and no overhead bracing, this is so far from being +the case as to leave little occasion for taking the precaution +named. As the cross-girders deflect, the main girders will +commonly yield slightly, inclining bodily towards the cross-girders, +if these are attached to the lower part of the main +girders. The force requisite to cant the main girders in +this manner is usually less than that which corresponds to +fixing the cross-girder ends, and is, generally, slight. It is, +of course, necessary that this measure of resistance at the +connection should be borne in mind for the sake of the joint +itself, quite apart from any question of fixing.</p> + +<p>Possibly, in quite exceptional cases, where very stiff +main girders are braced in such a manner as to prevent +canting, it may be proper to consider the cross-girder ends +as fixed, or for those near the bearings of heavy main +girders; but the author has not met with any example +where cross-girders, apart from attachments, appear to have +suffered from neglect of this consideration.</p> + +<p>With cross-girders placed on either side of a main girder, +and in line, it may also, for new work, be desirable to regard +the ends as fixed, and to detail them with this in view. It +does not, however, appear wise to carry this assumption to +its logical issue, and reduce the flange section to any appreciable<span class="pagenum"><a name="Page_23" id="Page_23">[23]</a></span> +extent on this account. The fixity of the ends will, in +any such case, be imperfect; and when one side only of an +intermediate main girder is loaded, it can have but a +moderate effect in reducing flange stress at the middle of +the loaded floor beam.</p> + +<div class="figc450"><a name="Fig13" id="Fig13"></a><a name="Fig14" id="Fig14"></a><a name="Fig15" id="Fig15"></a> +<img src="images/illo036.png" alt="" width="450" height="315" /> +<p class="caption_b"><span class="left39"><span class="smcap">Fig.</span> 13.</span> +<span class="center34"><span class="smcap">Fig.</span> 14.</span> <span class="right25"><span class="smcap">Fig.</span> 15.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 13., <span class="smcap">Fig.</span> 14. and <span class="smcap">Fig.</span> 15.</p> +</div> + +<p>Similar reasons affect the design of longitudinal girder +attachments to cross-girders, which, if intended to support +rails, cannot of necessity be schemed to come other than in +line. Where the floor is plated as one plane surface, there +will not usually be any trouble resulting if no special precautions +are used, as the plate itself will insure that the +longitudinals act, in a measure, as continuous beams, relieving +the joints of abnormal stress. If the plating is, however, +designed in a manner which does not present this advantage, +or if the floor be of timber, it is better to decide whether +the connections shall be considered as fixed, and made so; +or avowedly flexible, and detailed in such a manner as to +possess a capacity for yielding slightly without injury. +Those connections are most likely to suffer which are neither +of the one character nor the other, offering resistance without +the ability to maintain it. <a href="#Fig13">Figs. 13</a>, <a href="#Fig14">14</a>, and <a href="#Fig15">15</a> give representations +of three “spring joint” methods of insuring yield +in a greater or less degree. For small longitudinals it is, +perhaps, sufficient to use end angles with very broad flanges +against the cross-girder web; these to be riveted in the +manner indicated in <a href="#Fig15">Fig. 15</a>.</p> + +<p>Liberal depth to floor beams is distinctly advantageous +where it can be secured, rendering it easier to design the ends +in a suitable manner, by giving room near mid-depth of the +attachment to get in the necessary number of rivets; or +where the ends are rigidly attached direct to vertical +members of an open-work truss, the greater depth is effective +in reducing the inclination of the end from the vertical, with +a correspondingly reduced cant of the main girders and<span class="pagenum"><a name="Page_24" id="Page_24">[24]</a></span> +flexure of the vertical member, with smaller consequent +secondary stresses. In any case deep girders will contribute +to stiffness of the floor itself, favourable in railway bridges +to the maintenance of permanent-way in good order.</p> + +<div class="figcenter"><a name="Fig16" id="Fig16"></a><a name="Fig17" id="Fig17"></a><a name="Fig18" id="Fig18"></a> +<img src="images/illo037.png" alt="" width="450" height="312" /> +<p class="caption"><span class="smcap">Figs.</span> 16, 17, 18.</p> +</div> + +<p>A point in connection with skew-bridge floors occasionally +overlooked is the combined effect of the skew, and main +girder camber, in throwing the floor structure out of truth, +if no regard has been paid to this. The result is bad cross-girder +or other connections; or, in the case of bearers running +over the tops of main girders, a necessity for special +packings to bring all fair (<a href="#Fig17">Fig. 17</a>). The author has in such +cases, where cross-girders are used, set the main girder beds +at suitable levels, in order that the cross-bearers may all be +horizontal (see <a href="#Fig16">Figs. 16</a> and <a href="#Fig18">18</a>). This may not always be +permissible; but, however the difficulty may be met, it +should be dealt with as part of the design. For small angles +of skew only may it be neglected.</p> + +<p>Rivets attaching cross-girder angles to the web will occasionally<span class="pagenum"><a name="Page_25" id="Page_25">[25]</a></span> +loosen, probably due in most cases to bad work, +together with some circumstance of aggravation, as in the +case of a bridge floor consisting of girders spaced 3 feet 6 +inches apart, with short timber bearers between, carrying +rails. In many girders the top row of rivets, of ordinary +pitch and size, had loosened, allowing the web, about <sup>1</sup>⁄<sub>4</sub> inch +thick, a movement of <sup>1</sup>⁄<sub>8</sub> inch vertically. The rails being +very close down upon the cross-girder tops, though not intended +to touch, had at some time probably done so, and by +“hammering” produced the result described.</p> + +<p>Plated floors are often found which are objectionable on +account of their inability to hold water, arising sometimes +from bad work, as often from wide spacing of rivets. With +rivets arranged to be easily got at, and pitched not more +than 3 inches apart, a tight floor may be expected; but it is +still necessary to drain the floor by a sufficient number of +holes, provided with nozzles projecting below the underside +of the plate, and sufficiently long to deliver direct into +gutters, where these are necessary. Drain-holes should not +be less frequent than one to every 50 square feet of floor, if +flat, and may advantageously be more so. Gutters should<span class="pagenum"><a name="Page_26" id="Page_26">[26]</a></span> +slope well, and care be taken to insure practicable joints and +good methods of attachment—a matter too often left to +take care of itself, with considerable after-annoyance as a +result.</p> + +<p>The use of asphalt, or asphalt concrete, to render a +plated floor water-tight is hardly to be relied upon for railway +bridges, though no doubt effective for those carrying +roads. It is extremely difficult to insure that it shall stand +the jarring and disturbance to which it may be subject, and +under which it will commonly break up, and make matters +worse by holding moisture, and delaying the natural drying +of the floor. In bulk, as in troughs, it may be useful, but +in thin coverings on plates it cannot be depended upon.</p> + +<p>Floors having plated tops are sometimes finished over +abutments or piers in a manner which is not satisfactory, +either as regards the carrying of loads or accessibility for +painting. If the plates are carried on to a dwarf wall with +the intention that the free margin of the plate shall rest +upon it, there will be a difficulty in securing this in an +efficient manner. Commonly such a wall is built up after +the girder work is in place, making it difficult to insure that +the wall really supports the plate, the result being that this +may have to carry itself as best it can. In any case, severe +corrosion will occur on the underside, and the plate rust +through much before the rest of the floor; the masonry also +will usually be disturbed.</p> + +<p>It appears preferable to form the end of the floor with a +vertical skirting-plate having an angle or angles along the +lower edge. This may come down to a dwarf wall, but preferably +not to touch it, the skirting being designed to act +as a carrying girder. A convenient arrangement is shown in +<a href="#Fig19">Fig. 19</a>, which may be used either for a square or skew bridge. +It will be seen that the plate-girders have no end-plates, the +skirting referred to being carried continuously along the<span class="pagenum"><a name="Page_27" id="Page_27">[27]</a></span> +floor edge, and attached to each girder-web, the whole of the +more important parts being open to the painter.</p> + +<div class="figcenter"><a name="Fig19" id="Fig19"></a> +<img src="images/illo039.png" alt="" width="400" height="326" /> +<p class="caption"><span class="smcap">Fig.</span> 19.</p> +</div> + +<p>Trough floors consisting of one or other of the forms of +pressed or rolled section present the objection that it is almost +impracticable to arrange an efficient connection at the ends, +if they abut against main girders, and but little connection +is, as a rule, attempted, and sometimes none. The result is +that the load from these troughs is delivered in an objectionable +manner, and the ends being open or imperfectly closed, +water and dirt escape on to the flange, or other ledge, which +supports them. A description of pressed floor which promises +to overcome this objection, and provide a ready means +of attachment to the webs of plate-girders, or of booms +having vertical plate-webs, has within the last few years been +introduced. This has the ends shaped in such a manner as +to close them and provide a flat surface of sufficient area +for connection by rivets. Each hollow is separately drained +by holes with nozzles. Whether this type of trough will +develop faults of its own, due to over-straining of the metal<span class="pagenum"><a name="Page_28" id="Page_28">[28]</a></span> +in the act of pressing, remains to be seen; but as it appears +possible to produce the desired form without any material +thinning or thickening of the metal, the contention that no +severe usage accompanies the process appears to be reasonable.</p> + +<p>That form of troughing in which the top and bottom +portions are separately formed, and connected by a horizontal +seam of rivets at mid-depth, is found in use upon railway +bridges to be very liable to loosening of those rivets near the +ends; less surprising, perhaps, because the sloping sides are +usually thin.</p> + +<p>It is a distinctly difficult matter to join two or more +lengths of any trough flooring having sloping sides, in a +workmanlike manner; the fit of covers is apt to be imperfect, +and some rivets, being difficult of access, are likely to be but +indifferently tight, so that if the joint occurs where it will +be more than lightly stressed, trouble will probably follow. +A bad place for such joints is immediately over girders +supporting the troughs, as there the stress will be most +severe, any leakage come directly upon the girder, and remedial +measures be more difficult to carry out.</p> + +<p>Timber floors of the best timber, close jointed, are more +durable than might be supposed. The disadvantage is a +difficulty in ascertaining the precise condition of the timber +after many years’ use. The author has seen timbers, 9 inches +by 9 inches, forming in one length a close floor, carried by +three girders, and supporting two lines of way, which, when +taken out, could as to a considerable part be kicked to pieces +with the foot; whilst in another case, with the same arrangement +of girders and close-timbered floor, the wood, after +being in place for thirty-two years, was, when taken out, +found to be perfectly sound, with the exception of a very +few bad places of no great extent. In this instance, however, +it is known that the floor—pitch-pine—was put in by a +contractor who prided himself upon the quality of the timber<span class="pagenum"><a name="Page_29" id="Page_29">[29]</a></span> +that he used; the floor being also covered with tar concrete, +which had in this instance so well performed its office as to +keep the timber quite dry on the top.</p> + +<p>Jack arches between girders make an excellent floor for +road bridges, though heavy; and for small bridges may be +used to carry rails, if the girders are designed to be stiff under +load. The apprehension that brickwork or concrete will +separate from the girder-work, or become broken up under +even moderate vibration, does not seem to be well founded, if +the deflection is small and the brickwork or concrete good.</p> + +<p>The use of corrugated sheeting as a means of rendering +the underside of a bridge drop dry cannot be too strongly +deprecated. If it must be adopted, the arrangement should be +such as to permit ready removal for inspection and painting. +It is evident that by boxing up the floor structure, rust is +favoured, and serious defects may be developed, not to be discovered +till the sheeting is removed, or something happens.</p> + +<div class="figcenter"><a name="Fig20" id="Fig20"></a> +<p class="caption"><span class="smcap">Fig.</span> 20.</p> +<img src="images/illo042a.png" alt="" width="600" height="82" /> +</div> + +<p>A case may be instanced in which it was found, on taking +down sheeting of this description, that the floor girders, previously +hidden, were badly wasted in the webs. One of +these girders had cracked, as shown in <a href="#Fig20">Fig. 20</a>, and others +were in a condition only less bad.</p> + +<p>In any floor carrying ballast or macadam, if means are +not adopted to keep the road material from the structure of +the floor, or from the main girders, corrosion may be serious +in its effects. Cinder ballast is, perhaps, the worst in this +respect, in its action upon steel or ironwork, being distinctly +more damaging than any other kind commonly used.</p> + +<p>Rail-joints upon bridge floors are to be avoided where +practicable by the use of rails as long as can be obtained; if +the bridge is small enough, crossing it in one length. At +each joint there is likely to be hammering and working +extremely detrimental to floor members and connections; +indeed, it may happen that loose rivets will be found in the<span class="pagenum"><a name="Page_30" id="Page_30">[30]</a></span> +neighbourhood of such joints, and nowhere else on the bridge. +Where rail-joints cannot be +avoided, their position should, +if there be any choice, be judiciously +selected, and the plate-layers +taught to close the joints +and jam the fish-bolts.</p> + +<div class="figcenter"><a name="Fig21" id="Fig21"></a> +<img src="images/illo042b.png" alt="" width="600" height="108" /> +<p class="caption"><span class="smcap">Fig.</span> 21.</p> +</div> + +<p>As rail-joints upon a bridge +may injuriously affect the floor, +so also will a weak floor be +very trying to the rails. A +remarkable instance of this has +come under the writer’s notice, +where a bridge (<a href="#Fig21">Fig. 21</a>) of +three 33-feet spans, having +outer and centre main girders, +with cross-girders spaced 3 feet +apart, resting upon the girder +flanges, but not attached, and +carrying two roads, had the permanent-way +in a very bad state. +The rails proper, with supplementary +angle-plates, rested +direct upon the cross-girders, +which were decidedly light, +and the whole floor had much +“life” in it, the ill-effect of +which was shown in thirteen +breaks in the angle-plates, in +each case near their ends, +generally at holes.</p> + +<p>It appears probable that +severe stresses may be thrown +upon the parts of a floor,<span class="pagenum"><a name="Page_31" id="Page_31">[31]</a></span> +whether placed at the level of the bottom booms or of +the top, by changes of length in the booms due to stress. +The author has, unfortunately, no direct evidence to offer +in reference to this, tending either for or against the contention. +If an unplated floor of cross and longitudinal +girders of usual arrangement be at the bottom boom of +a large bridge, as the boom lengthens with the imposition +of load upon the bridge, all the cross-girders from the +centre towards the abutments will be curved horizontally, +the middle portion being restrained by the longitudinals +from moving bodily with the ends. Each cross-girder +except that at the centre, if there be one, will thus present +a figure in plan, concave towards the abutment to which it +is nearest. This will be accompanied by stressing of the +connections, and a transfer to the longitudinals of as much +of the tensile stress properly belonging to the booms as the +stiffness of the cross-girders may communicate.</p> + +<p>This in itself will hardly be considerable, and will be the +less on account of a slight yielding which may be expected +at the end connections of each longitudinal; but the effect +upon the cross-girders by horizontal bending will be much +marked. If the case be supposed of a 200-feet span in steel +at ordinary loads and stresses, carrying one line of way, with +cross-girders 20 feet apart, and having no floor-plates, it may +be ascertained, neglecting for the moment any slight yielding +of the longitudinal girder connections, that upon the bridge +taking its full live load there will be the following approximate +results: Movement at each end of the end cross-girders +of <sup>3</sup>⁄<sub>10</sub> inch, equivalent to a force of 7<sup>1</sup>⁄<sub>2</sub> tons, tending to bend +them horizontally, and a mean stress on the outer edges of the +girders, 12 inches wide, of 8 tons per square inch due to +flexure, which, compounded with the ordinary flange stresses, +will seem to give rather alarming results. There will also be a +longitudinal stress in the rail-girders, at centre part of bridge,<span class="pagenum"><a name="Page_32" id="Page_32">[32]</a></span> +of <sup>3</sup>⁄<sub>4</sub> ton per square inch. Normal elongation of the longitudinal +girder bottom flanges, and compression of the top, modifies +the figures unfavourably as to the cross-girder top flange. +Yielding of the connections named before has been neglected +in arriving at these stresses. If they are sufficiently accommodating +to give freely, to a mean extent, as between the +top and bottom of each joint, of <sup>1</sup>⁄<sub>29</sub> inch, these results will +disappear. It is evident, however, that we cannot rely upon +good work yielding without the existence of considerable forces +to cause it. In the issue it is justifiable to apprehend that the +flexing and stressing of the cross-girders will be considerable.</p> + +<p>The most favourable case has been taken; if now it is +assumed that the floor has continuous plating, the results +would seem to be much more astonishing. It will appear on +this supposition that the boom stresses, instead of being +taken wholly by the booms, are about equally divided between +these and the floor structure, each cross-girder connection +communicating its share of boom stress to the floor, which +for the end cross-girders will approach 40 tons at each +connection—considerably more than the vertical reaction +under normal loads.</p> + +<p>Palpably, these conclusions must be greatly modified by +the yield of longitudinal girder ends, and slip of the floor +rivets in transverse seams. If these rivets be 3<sup>1</sup>⁄<sub>2</sub> inch pitch +and <sup>3</sup>⁄<sub>4</sub> inch in diameter, the stress at each, as estimated, would +be sufficient to induce shear of about 6 tons per square inch—more +than enough to cause “slip.” After making this allowance, +it is still evident there must be very serious forces at +work about the ends of cross-girders under the conditions supposed, +probably not less than one half the amounts named, as +with this reduction the floor rivets should not yield, given +reasonably good work. It is to be observed that the effect of +live load only has been introduced, on the presumption that the +longitudinals and floor-plating have not been riveted up till<span class="pagenum"><a name="Page_33" id="Page_33">[33]</a></span> +the main girders have been allowed to carry the major part +of the dead load; but even this cannot always be conceded. +The deduction appears to be that the floor and cross-girder +connections should be studied with special reference to these +possible effects, either with the object of rendering the communication +of these forces harmless, or making the floor so +that it shall take little or no stress from the main booms, by +arranging joints across the floor specially designed to yield, +the ends of longitudinals being schemed with the same object. +Where there is no plating, the case is, perhaps, sufficiently +provided for by making the cross-girders narrow, and the +longitudinal girder connections flexible, or by putting these +girders upon the top of the cross-girders, when stretching of +the bottom flanges of the rail-bearers under load may be +expected, within a little, to keep pace with the lengthening +of the main booms.</p> + +<p>It would appear that light pressed troughs running across +the longitudinals would, by yielding in every section, also +furnish relief, as compared with the rigidity of flat plates.</p> + +<p>By placing the floor at a level corresponding to the +neutral axis of the main girders, the communication of stress +to the floor may be avoided; but it seldom happens that +there is so free a choice as to floor height relative to the +girders. This solution is, therefore, of limited application.</p> + +<p>It is obvious that somewhat similar effects must obtain to +those considered in detail, when the floor structure lies at the +level of top booms, but with forces of compression from the +booms to deal with, instead of tension.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_34" id="Page_34">[34]</a></span></p> + +<h2>CHAPTER IV.<br /> +<span class="chaptitle">BRACING.</span></h2> + +<p>Bracing, whether to strengthen a structure against wind, to +insure the relative positions of its parts, or for any other +purpose, cannot be arranged with too great care and regard +to its possible effects. Forces may be induced which the +connections will not stand, with loose rivets as a consequence, +and inefficiency of the bracing itself; or, the connections +holding good, stresses in the main structure may, perhaps, +be injuriously altered.</p> + +<p>To take a not uncommon case, let us suppose a bridge +consisting of four main girders placed immediately under +rails of ordinary gauge, and braced in vertical planes only, +right across from one outer girder to the other. If the +roads were loaded always at the same time, nothing objectionable +would result; but, as a fact, this will be the exception. +When one pair of girders only takes live load, and +deflects, the bracing under the six-foot will endeavour to +communicate some part of this load to the other pair of +girders. If the bracing is so designed that some correctly +calculated portion of the load can be transferred in this +manner, without over-stressing the bars and riveted connections, +there will be no harmful consequences; but if not, the +bracings will most probably work at the ends; this, indeed, +is what frequently happens. There is one other effect which +will ensue, if the bracing is wholly efficient; a certain twisting +movement of the bridge will occur, which increases the +live load upon the outer girder on the loaded side of the<span class="pagenum"><a name="Page_35" id="Page_35">[35]</a></span> +bridge to the extent of 10 per cent., with a corresponding +lifting force at the outer girder on the unloaded side. These +amounts are not serious, but wholly dispose of any advantage +it is conceived will be gained by causing the otherwise idle +girders to act through the medium of the bracing. In road +bridges of similar arrangement, over which heavy loads may +pass on any part of the surface, it is clear that the use of +bracing between girders should not be taken as justifying +the assumption that the load is distributed over many girders, +and correspondingly light sections adopted, unless the effect +of twisting on the whole bridge is also considered, and justifies +this view; for, as already stated in the case of the railway +bridge, the net result may be to increase the girder stresses +instead of reducing them. Generally, it may be deduced +that the better plan for railway bridges is to brace the girders +in pairs, leaving, in the case supposed, no bracing between +the two middle girders, though there will be no objection to +connecting these by simple transverse members of no great +stiffness, to assist in checking lateral vibration. For road +bridges of more than five longitudinal girders, equally spaced, +it may be advantageous to brace right across, the twisting +effect with this, or a greater, number of girders not, as a rule, +leading to any increase of load on any girder. <a href="#Fig22">Figs. 22</a> to +<a href="#Fig25">25</a> give the distribution of live load, placed as shown, for 3, +4, 5, and 6 girders.</p> + +<p>It is to be observed that these statements do not apply to +cases where there may be also a complete system of horizontal +bracing, the effect of which, in conjunction with cross +diagonals, may be greatly different, with considerable forces +set up in the bracing, and a modification of girder stresses.</p> + +<p>These effects may be so considerable as to call for special +attention in design where such an arrangement is adopted.</p> + +<div class="figc600"><a name="Fig22" id="Fig22"></a><a name="Fig23" id="Fig23"></a><a name="Fig24" id="Fig24"></a><a name="Fig25" id="Fig25"></a> +<p class="caption_b"><span class="left39"><span class="smcap">Fig.</span> 22.</span> <span class="right60"><span class="smcap">Fig.</span> 24.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 22. and <span class="smcap">Fig.</span> 24.</p> + +<img src="images/illo048.png" alt="" width="600" height="235" /> +<p class="caption_b"><span class="left39"><span class="smcap">Fig.</span> 23.</span> <span class="right60"><span class="smcap">Fig.</span> 25.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 23. and <span class="smcap">Fig.</span> 25.</p> +</div> + +<p>Somewhat similar straining to that first indicated may +occur in bracings placed between the girders of a bridge<span class="pagenum"><a name="Page_36" id="Page_36">[36]</a></span> +much on the skew. If this is, on plan, at right angles to +the girders, as is commonly and properly the case, the ends +will evidently be attached to the girders at points on their +length at different distances from the bearings, which points, +even with both girders loaded, deflect dissimilar amounts, +and the bracing will, if at one end attached near a rigid +bearing, transfer some part of the load from one girder to<span class="pagenum"><a name="Page_37" id="Page_37">[37]</a></span> +the other, notwithstanding that both girders may be of the +same span and equal extraneous loading. It would not be +difficult to ascertain the amount of load so transferred from +a consideration of the relative movements if free, and the +loads on the two girders necessary to render these movements +equal, if the deflections were simply vertical; but as there +will be some twisting and yielding of the girders on their +seats, the calculation becomes involved. If the bracing is +placed at about the middle of the girders, the effects noted +will be greatly reduced; first, because the difference of +movements near the centre will be less; second, any given +difference will correspond to a smaller transference of load; +and, third, because each girder will there be more free to +twist than at the ends. It therefore appears that bracings +between the girders of a skew bridge should not be placed +near the bearings, though they may be put, with much less +risk of injury, near the middle.</p> + +<p>Cross-girders on a skew bridge are subject to forces +somewhat similar to those which may affect bracing, rendering +it desirable to design their attachments in a manner +which shall not aggravate the matter, but rather reduce the +effects of unequal vertical displacement of their ends where +secured to the main girders.</p> + +<p>Crossed flat bars as bracing members are objectionable +on account of their tendency to rattle, after working loose; +but as this effect only ensues in bracing which has first +become loose (it being assumed that the bars in any case are +connected where they cross), this objection is not itself vital, +though greater rigidity is easily obtained by making all such +members of a stiff section.</p> + +<p>Defective bracing between girders, from neglect of the +very considerable forces it may be called upon to communicate, +is very common; the writer has seen many such cases, +of which one is here illustrated in <a href="#Fig26">Fig. 26</a>.</p> + +<p><span class="pagenum"><a name="Page_38" id="Page_38">[38]</a></span></p> + +<div class="figcenter"><a name="Fig26" id="Fig26"></a> +<img src="images/illo050.png" alt="" width="600" height="298" /> +<p class="caption"><span class="smcap">Fig.</span> 26.</p> +</div> + +<p>This bridge, of the section shown, and 85 feet span, had +very light web structure. The bracings, of which there +were two sets, were wholly inefficient, the end rivets being +loose in enlarged holes. Upon the passage of a train there +was a positive lurching of the girder tops from side to side.<span class="pagenum"><a name="Page_39" id="Page_39">[39]</a></span> +The integrity of the bridge was really dependent upon such +stiffness as there was in the girders, and unplated floor.</p> + +<p>A common but indifferent method of keeping the top +members of main girders in line is by the use of overhead +girders alone, frequently curved to give the requisite clearance +over the road. This cannot be considered as wholly +inefficient, as sometimes maintained, since it is evident that +the closed frame formed by the floor beams, the web members +of the main girders, and the overhead girder itself, must +take a greater force to distort it than would be necessary to +cause deformation of a corresponding degree, in an open +frame formed by the omission of the overhead girder; but it +is not a method to be recommended, its precise utility is +difficult to estimate, and, if the cross-girder attachments are +of a rigid character, tends to increase the stresses induced at +those connections. The latter consideration is, however, +not applicable to this arrangement alone. All overhead +bracing favours this by restraining the tendency of the top +booms to cant inwards when the floor beams are loaded; and +though this restraint may be quite harmless, it is desirable +that close attention be given to these effects in designing +bridges which make a complete frame more or less rigid in +its character. “Sway” bracing, sometimes introduced at +right angles to the bridge between opposite verticals, tends +to emphasise these effects by rendering the cross-section of +the bridge still stiffer, besides making it a matter of difficulty +to ascertain how much of the wind forces on the top boom +is carried to the abutment by the top system of bracing, and +how much by the floor. The author does not, however, mean +to suggest that it cannot be used with propriety, but rather +that extreme care is desirable in considering its ultimate +effect on the rest of the structure.</p> + +<p>For girders of moderate depth there may be on these +grounds a distinct advantage in abandoning overhead bracing,<span class="pagenum"><a name="Page_40" id="Page_40">[40]</a></span> +and securing rigidity of the top boom, and adequate +resistance to wind forces, by making the connection between +the cross-girders and the web members sufficiently good to +insure, as a whole, a stiff <span class="lettsymb">U</span>-shaped frame; but this, with +the ordinary type of rocker arrangement under the main +girder bearings, will not be entirely free from objection, as +canting of the girders due to floor loading will throw extreme +pressure on the inner end of each rocker. There appears to +be no reason why the cylindrical knuckle should not in this +case be supplanted by a cup hinge, allowing angular movement +of the girder bearing in any plane.</p> + +<div class="figcenter"><a name="Fig27" id="Fig27"></a> +<img src="images/illo053.png" alt="" width="300" height="357" /> +<p class="caption"><span class="smcap">Fig.</span> 27.</p> +</div> + +<p>The efficient stiffening of light girders, as in the case of +foot-bridges, from the floor, where this is at the bottom +flanges, renders very narrow top booms permissible. This is +a decided advantage where lightness of appearance is aimed +at; but it is not unusual to see an attempt made in this +direction by introducing gusset plates of very ample proportions +between vertical members of the girders, and the projecting +ends of flimsy transoms, carried beyond the width of +the bridge proper, these being of a section wholly out of +proportion to the brackets they are supposed to secure. +Whatever may be the amount of strength necessary at the +point A, in <a href="#Fig27">Fig. 27</a>, there should not be less throughout the +transom from one girder to the other. The degree of +strength and stiffness required in this member, and in the +vertical stiffeners is not, as a rule, great. Information to +enable this question to be dealt with as a matter of calculation +is somewhat scanty; but it would appear to be sufficient +to insure safety that, for an assumed small amount of curvature +in the compression member, the forces outwards corresponding +to this curvature, due to thrust, should be resisted +by verticals and transoms of strength and stiffness sufficient +to restrain it from any further flexure. It will, of course, +be necessary also to take care that the compression member<span class="pagenum"><a name="Page_41" id="Page_41">[41]</a></span> +is good as a strut between the points of restraint. A +simple and sufficiently precise method of dealing with this +question is much needed. In cases where the floor weight +rests on the flange projection, it is also necessary to give +the transom additional strength to an extent enabling it +to resist the twisting effort between any two of these +transverse members; further, resistance to wind on the +girder has to be provided in both transoms and verticals.</p> + +<p>It may be hardly +necessary to insist +that bracing intended +to stiffen a structure +against wind, local +crippling, or vibration, +should be made +complete, not stopping +short at some +point, because it cannot +conveniently be +carried further, as +is sometimes done, +unless the strength +of those parts of +the structure through +which the forces from +the bracing must be communicated to the abutments is +sufficiently great, considered with reference to other stresses +in those parts which have also to be endured.</p> + +<p>Bracing stopped short in this way, making only the +central part of a bridge rigid, may have the effect of increasing +the forces to which the unstiffened end members would +otherwise be liable. Such a structure would evidently be +much stiffer against wind-gusts than if no bracing existed—the +resistance to a blow would be increased; but the power to<span class="pagenum"><a name="Page_42" id="Page_42">[42]</a></span> +maintain that greater resistance being confined to the intermediate +bays, the unbraced ends would be subject to greater +maximum forces than if bracing were wholly omitted. The +net effect may still be better than with no bracing, the point +raised being simply that of an increase of stress in particular +end members.</p> + +<p>In the bracing of tall piers, the rising members of which +will be subject to any considerable stress, if the diagonal +members are not finally secured when the piers are under +their full load, or an initial stress of proper amount induced +in those members, the effect of loading will be to render +them slack; so that an appreciable amount of movement at +the top may occur before it can be limited by the efficient +action of the bracings. This effect under blasts of wind or +continual passage of trains may, indeed, be dangerous. +Similar considerations apply to the top wind bracing of deep +girder bridges, influencing also the bottom bracing in a contrary +manner, which calls for attention in fixing the unit +stresses for such members.</p> + +<p>The bracing of sea-piers is very liable to slacken if made +with pin-and-eye ends, as is often done for round rods. The +detail presents advantages in erection, but is not altogether +satisfactory in practice. Such connections are continually +working. In the finest weather, with the sea quite smooth +but for an almost imperceptible wave movement, the lower +parts of such structures will be found, as a rule, to have some +slight motion. This is very trying to bracing; nor is there +room for surprise when it is considered that these oscillations, +occurring at about ten to each minute, never wholly cease, +and amount in the course of one year to over five million in +number.</p> + +<p>Bracing attached in such a manner that there can be no +initial slack, or slack due to wear under endless repetitions +of small amounts of stress, will have a much better chance to<span class="pagenum"><a name="Page_43" id="Page_43">[43]</a></span> +keep tight. The advantage presented by round rods in +offering little surface to the water, is more than negatived +by inefficiency of the usual attachments for such rods.</p> + +<p>The author has observed that bracing of members possessing +some stiffness, and with good end attachments to ample +surfaces, appears to stand best in ordinary sea-pier work. +For such structures the bracing should consist of a few +good members, with a solid form of attachment, rather than +of a multiplicity of lighter adjustable members, which will +commonly give great trouble in maintenance; being very +possibly also, in the case of sea-pier work, in unskilled hands. +If round rods must be used, they will stand much better if +made of large diameter.</p> + +<p>Before leaving the subject of bracing, it may not be out +of place to refer to wind pressure, as this may so much affect +the proportioning of the members.</p> + +<p>Some years since the author had occasion to examine a +number of structures with respect to their stability. Of foot-bridges +from 60 feet to 120 feet long, three or four, when +calculated on the basis recommended by the Board of Trade +as to pressures upon open-work structures, worked out at an +overturning pressure of from 18 lb. to 22 lb. per square foot. +These bridges had been many years in existence; it is, +therefore, fair to assume that no such wind in the direction +required for overturning had expended its force upon them +as to the whole surface.</p> + +<div class="figcenter"><a name="Fig28" id="Fig28"></a> +<img src="images/illo056.png" alt="" width="400" height="333" /> +<p class="caption"><span class="smcap">Fig.</span> 28.</p> +</div> + +<p>Particulars were taken in 1895 of a notice-board, presenting +about 12 square feet of surface, which was blown down +in the great storm of March 24 of that year, at Bilston, in +Staffordshire. It was situated at the foot of a slight slope, +over which the wind came, striking the obstruction at right +angles. The board was mounted on two oak posts of fair +quality and condition, which broke near the ground at bolt +holes (see <a href="#Fig28">Fig. 28</a>). The force required to do this, at 9000 lb.<span class="pagenum"><a name="Page_44" id="Page_44">[44]</a></span> +modulus of rupture—a moderate value—corresponds to 50 lb. +per square foot on the surface exposed above the break.</p> + +<p>In the same neighbourhood, at the same time, considerable +damage was wrought in overturning chimney stacks, to +buildings and roofs; the general impression in the locality +being that the storm was of exceptional, even unprecedented, +violence. Bilston, it should be noted, lies high.</p> + +<p>At Bidston Hill, near Birkenhead, on the same occasion, +a pressure of 27 lb. was registered. In another part of the +country it is said to have been 37 lb. Wind is so capricious +in its effects over small areas as to render it probable that the +maximum pressures have never been recorded; but this is +a matter of little importance where general stability and +strength only are concerned. The instances cited, though by +themselves insufficient to throw much light on the question, +may be of use in connection with other known examples.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_45" id="Page_45">[45]</a></span></p> + +<h2>CHAPTER V.<br /> +<span class="chaptitle">RIVETED CONNECTIONS.</span></h2> + +<p>Considerable latitude is observable in the practice of +engineers in the use of rivets. Numberless experiments to +determine the resistance of riveted connections have from +time to time been made, but these are not to be considered +by themselves as final, when the results of experience in +actual construction, are available for further enlightenment.</p> + +<p>The class of workmanship so largely influences the degree +in which rivets will maintain their integrity that it is only +by the observation of a large number of cases, including all +degrees of workmanship, that any reliable conclusions may +be drawn. In this respect laboratory experiments have an +apparent advantage, as the conditions may be kept sensibly +the same; but, on the other hand, no such investigation +reproduces the circumstances of actual use, which alone must +in the end determine the utility of any inquiry for practical +application.</p> + +<p>The author has studied the particulars of a number of +cases to ascertain under what conditions as to stress, having +due regard to the effects of vibration, rivets will remain tight, +or become loose. Every loose rivet that may be found cannot, +of course, be taken as being due to excessive stress; the more +frequent cause is indifferent work, evidenced by the fact that +neighbouring rivets will frequently be found quite sound, +though the failure of some will cause a greater stress upon +the remainder. When rivets loosen as the direct result of +over-stress, it is usually by compression of the shank and<span class="pagenum"><a name="Page_46" id="Page_46">[46]</a></span> +enlargement of the hole, or by stretching of the rivet and +reduction of its diameter. Instances of failure by partial or +complete shear are extremely rare; indeed, the author has +never yet found one, though when a rivet has first worked +loose, as a result of excessive bearing pressure or bad work, +it is not uncommon to find it cut or bent as an after consequence.</p> + +<p>In estimating stresses at which rivets have remained +tight, or loosened, as the case may be, examples have generally +been chosen in which there could be no reasonable +doubt as to the amount of those stresses by the ordinary +methods of computation. This is clearly most important, +as, if any appreciable uncertainty remained as to the degree +of stress, the results deduced would be of little value. For +this reason those instances in which the loads upon girders, +or parts of girders, may find their way to the supports by +more than one route, are to be regarded with caution, as are +those in which full loading possibly never obtains, but which +may, on the other hand, perhaps have been frequent. The +working diameter of the rivet as it fills the hole has been +used in making the computations; in some cases from +direct measurement from particular rivets, in others with a +suitable allowance for excess diameter of hole, according to +the class of work under consideration.</p> + +<p>Dealing first with main girders, it may be said that rivets +attaching the webs of plate girders to the flange angles rarely +loosen, though subject to considerable stress. In illustration +of this may be named a bridge for two lines of way, 85 feet +effective span, having two main girders with plate webs, and +cross-girders resting on the top flanges, previously referred +to (see <a href="#Fig26">Fig. 26</a>).</p> + +<p>The girders, which were 6 feet 9 inches deep, had a bearing +upon the abutments of 4 feet; the rivets were <sup>7</sup>⁄<sub>8</sub> inch in +diameter and 4 inches pitch. There is in a case of this kind<span class="pagenum"><a name="Page_47" id="Page_47">[47]</a></span> +some little uncertainty as to what is the stress on the flange +angle rivets at, or very near to, the bearings; but, taking +the vertical rows of rivets at the web joints near the ends as +presenting less uncertainty, the stress per rivet works out at +4·8 tons, being 4 tons per square inch on each shear surface, +and 11 tons per square inch bearing pressure upon the shank +in the web plate, which was barely <sup>1</sup>⁄<sub>2</sub> inch thick. This bridge +was frequently loaded upon both roads, but with one road +only carrying live load, the stresses in the more heavily +loaded girder would be fully 90 per cent. of those obtaining +as a maximum. There was on this bridge, which had been +in use 31 years, considerable movement and vibration.</p> + +<p>It is by no means uncommon to find cases of rivets in +main girders taking 11 tons per square inch bearing pressure—occasionally +more—and remaining tight. As furnishing +an instructive, though slightly ambiguous, instance of rivets +in single shear, may be cited a bridge not greatly less than +that just referred to, of about 65 feet span, carrying two +lines of way, there being two outer and one centre main +girder of multiple lattice type, with cross-girders in one +length 4 feet apart, riveted to the bottom booms of the main +girders; these rivets, by the way, were in tension. The +floor was plated, the road consisting of stout timber longitudinals, +chairs, and rails (<a href="#Fig29">Fig. 29</a>).</p> + +<div class="figcenter"><a name="Fig29" id="Fig29"></a> +<img src="images/illo060.png" alt="" width="600" height="186" /> +<p class="caption"><span class="smcap">Fig.</span> 29.</p> +</div> + +<p>It should be noted that there is in this case some difficulty +in ascertaining the precise behaviour of the cross-girders, +affecting the proportion of load carried by the outer +and the inner main girders. Strict continuity of all the +cross-girders could only obtain if the deflection of the main +girders were such as to keep the three points of suspension of +each cross-girder in the same straight line. A close inquiry +showed that this was very far from being the case, and that +while each cross-girder at the centre of the bridge would, +under load, by relative depression of the middle point of<span class="pagenum"><a name="Page_48" id="Page_48">[48]</a></span> +support, be reduced to the condition of two simple beams, +those at the extreme ends of the span would behave as +continuous girders.</p> + +<p>With both roads carrying +engine loads equal to those +coming upon the bridge, the +author estimates that for the +centre main girder the shear +on the rivets of the end diagonals, +secured by one rivet +only, was 14·9 tons per square +inch, and the bearing pressure +16·3 tons; the flange stress +being 7·1 tons per square inch +net. The outer main girders +are most heavily stressed when +but one road, next to the +outer girder considered, carries +live load. For this condition +the stresses work out at +9 tons per square inch shear +on the rivets of the end diagonals, +and 9 tons bearing +pressure, the flange stress being +5·7 tons per square inch +on the net section.</p> + +<p>Without intending to +throw any doubt upon the +substantial truth of these +results, it must be admitted +that instances of greater simplicity +of stress determination +are much to be preferred. For purposes of comparison, but +not as having any other value, the results have also been<span class="pagenum"><a name="Page_49" id="Page_49">[49]</a></span> +worked out on the supposition of all cross-girders acting +each as two simple beams, and also for strict continuity, and +are here tabulated, together with the conclusions given above.</p> + +<p>The cross-girders were moderately stressed, and the tension +on the rivets attaching them to the main girders +probably did not exceed 3 tons per square inch.</p> + +<p>It should be pointed out that the traffic over the bridge +was small. The centre main girder but seldom bore its full +load, though at all times liable to receive it. Much importance +cannot, therefore, be attached to the results for this +girder, other than as showing how a structure may stand for +many years, though liable at any time to the development +of stresses which would commonly be regarded as destructive, +or nearly so.</p> + +<p class="center"><span class="smcap">Examples of Rivet Stresses, etc., in Lattice Girders.</span></p> + +<table class="nowrap" summary="Table page 49"> + +<tr class="bt bb"> +<th rowspan="2" class="br">—</th> +<th class="br">Cross-<br />Girders<br />as Simple<br />Beams.</th> +<th class="br">Cross-<br />Girders<br />as Con-<br />tinuous<br />Beams.</th> +<th>Correct<br />Results.</th> +</tr> + +<tr class="bb"> +<th colspan="3">Stress in Tons per Square Inch.</th> +</tr> + +<tr> +<td class="left padl1 padr1 br">Centre girder, 63 ft. span (both roads loaded):</td> +<td class="br"> </td> +<td class="br"> </td> +<td> </td> +</tr> + +<tr> +<td class="left padl3 padr1 br">Rivets in diagonals—Shear</td> +<td class="right padl1 padr2 br">13·7</td> +<td class="right padl1 padr2 br">17·2</td> +<td class="right padl1 padr2">14·9</td> +</tr> + +<tr> +<td class="left padl3 padr1 br"><span class="noshow">Rivet</span>Do.<span class="noshow">diagonals—</span><span class="padl0">Bearing pressure</span></td> +<td class="right padl1 padr2 br">15·0</td> +<td class="right padl1 padr2 br">18·8</td> +<td class="right padl1 padr2">16·3</td> +</tr> + +<tr> +<td class="left padl3 padr1 br"><span class="noshow">Rivets in diagonals—</span><span class="padl0">Flange stress</span></td> +<td class="right padl1 padr2 br">6·8</td> +<td class="right padl1 padr2 br">8·5</td> +<td class="right padl1 padr2">7·1</td> +</tr> + +<tr> +<td class="left padl1 padr1 br blankabove">Outer girder, 66 ft. span (near road loaded):</td> +<td class="br blankabove"> </td> +<td class="br blankabove"> </td> +<td class=" blankabove"> </td> +</tr> + + +<tr> +<td class="padl3 padr1 br">Rivets in diagonals—Shear</td> +<td class="right padl1 padr2 br">9·6</td> +<td class="right padl1 padr2 br">8·2</td> +<td class="right padl1 padr2">9·0</td> +</tr> + +<tr> +<td class="padl3 padr1 br"><span class="noshow">Rivet</span>Do.<span class="noshow">diagonals—</span><span class="padl0">Bearing pressure</span></td> +<td class="right padl1 padr2 br">9·6</td> +<td class="right padl1 padr2 br">8·2</td> +<td class="right padl1 padr2">9·0</td> +</tr> + +<tr class="bb"> +<td class="left padl3 padr1 br"><span class="noshow">Rivets in diagonals—</span><span class="padl0">Flange stress</span></td> +<td class="right padl1 padr2 br">5·9</td> +<td class="right padl1 padr2 br">5·1</td> +<td class="right padl1 padr2">5·7</td> +</tr> + +</table> + +<p>The material and workmanship of the bridge were good. +The rivets of the centre girder end diagonals, 1 inch in +diameter, were originally <sup>7</sup>⁄<sub>8</sub> inch, but on becoming loose were<span class="pagenum"><a name="Page_50" id="Page_50">[50]</a></span> +cut out, the holes reamered, and replaced by the larger size, +which remained tight, and to which the stress figures apply. +The rivets in the diagonals near the centre, <sup>7</sup>⁄<sub>8</sub> inch in diameter, +which were subject to reversal of stress, occasionally +worked loose, and were more than once replaced. The +riveting in the outer girder diagonals, subject to smaller +stresses, much more frequently developed, also gave trouble, +particularly those liable to counter stresses.</p> + +<p>Apart from looseness of rivets, the general appearance +and behaviour of the bridge, which had been in existence +about twenty years, was not suggestive of any weakness.</p> + +<p>Of smaller girders, an example showing the necessity for +care in discriminating, if it be possible, between looseness +of rivets resulting from over-stress and that due to other +influences may first be quoted. Two trough girders, of +11 feet effective span, each of the section shown in <a href="#Fig30">Fig. 30</a>, +11<sup>1</sup>⁄<sub>2</sub> inches deep at the ends, 14 inches at the middle, with +<sup>1</sup>⁄<sub>4</sub>-inch webs, and rivets <sup>3</sup>⁄<sub>4</sub> inch in diameter, of 4<sup>1</sup>⁄<sub>2</sub>-inch pitch, +showed certain defects, of which one, it may be incidentally +mentioned, was a cracked web (<a href="#Fig31">Fig. 31</a>). From the nature +of the arrangement the lower web rivets, which were loose, +would receive the first shock of the load coming upon the +span, but there were evidences indicative of original bad +work. The angle bars gaped, suggesting that these had +first been riveted to the bottom plate, and left sufficiently +wide to allow the web to be afterwards inserted, the rivets +failing to pull the work close, and then readily working loose. +Here there is considerable uncertainty as to how much of +the loosening is to be attributed to bad work, and how much +to stress. It may, however, be remarked that whatever +bearing stress was the ultimate result of the load hammering +on the lower angle flanges, loosening rivets never perhaps +really tight, the stress of 7 tons per square inch bearing +pressure on the upper rivets, though aggravated by considerable<span class="pagenum"><a name="Page_51" id="Page_51">[51]</a></span> +impactive force, was not sufficient to loosen these. The +girders were taken out after being in place sixteen years.</p> + +<div class="figc600"><a name="Fig30" id="Fig30"></a><a name="Fig31" id="Fig31"></a><a name="Fig32" id="Fig32"></a> +<p class="caption_b"><span class="left53"><span class="smcap">Fig.</span> 30.</span> <span class="right46"><span class="smcap">Fig.</span> 32.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 30. and <span class="smcap">Fig.</span> 32.</p> +<img src="images/illo063.png" alt="" width="600" height="320" /> +<p class="caption"><span class="smcap">Fig.</span> 31.</p> +</div> + +<p>An instance of undoubted excessive bearing pressure +was found in the cross-girders of a bridge, mentioned on +<a href="#Page_15">p. 15</a>, of which so many web plates were cracked. This +bridge, carrying two lines of way, had outer main girders, +and long cross-girders with <sup>1</sup>⁄<sub>4</sub>-inch webs and <sup>3</sup>⁄<sub>4</sub>-inch rivets,<span class="pagenum"><a name="Page_52" id="Page_52">[52]</a></span> +4 inches pitch. The rivet stresses work out at 4·3 tons per +square inch on each shear surface, and 24 tons per square +inch bearing pressure. For +one road only being loaded, the +latter figure falls to 18·5 tons. +The traffic over this bridge, +twenty years old, was considerable, +rapid, and heavy. It is +hardly necessary to add that +a large number of the rivets +were loose, one of which is +shown in <a href="#Fig32">Fig. 32</a>.</p> + +<div class="figcenter"><a name="Fig33" id="Fig33"></a> +<img src="images/illo064.png" alt="" width="600" height="186" /> +<p class="caption"><span class="smcap">Fig.</span> 33.</p> +</div> + +<p>To take another case relating +to a floor system of extremely +bad design (<a href="#Fig33">Fig. 33</a>). +The main girders were 11 feet +apart, 35 feet span, the floor +having two cross-girders only, +spaced at 11 feet 3 inches, and +9 inches deep, supporting hog-backed +trough longitudinals. +The cross-girders were at their +ends but 6<sup>3</sup>⁄<sub>4</sub> inches deep, the +distance from the bearing of +cross-girders to centre of longitudinals +carrying a rail being +2 feet 10 inches, in which +length were eight rivets in the +web and angles at the top, and +six at the bottom, all <sup>3</sup>⁄<sub>4</sub> inch in +diameter.</p> + +<p>The shear stress on the upper rivets works out at 7·3 +tons per square inch on each shear surface, the bearing pressure +20·6 tons per square inch. On the lower rivets the<span class="pagenum"><a name="Page_53" id="Page_53">[53]</a></span> +shear stress becomes 9·7 tons, and the bearing pressure +27·4 tons, per square inch. Care was exercised in computing +these stresses, that part of the bending moment +carried by the web being allowed for, but it must be admitted +that the result is, probably, approximate only. The <a href="#Fig33">sketch</a> +here given shows the cross-girder end and section. The +rivets, though in double shear, were, as might be expected, +loose, notwithstanding that the traffic over the bridge was +moderate, and quite slow. The floor system was remodelled +after twelve years’ use.</p> + +<p>In illustration of the behaviour of rivets in the ends of +long cross-girders, both shallow and weak, and many years +in use under heavy traffic, may be cited connections having +end angle bars to the cross-girders, with six rivets through +the web of main girders. The bearing pressure worked out +at 7·8 tons per square inch. Many rivets were loose, but it +should be remarked that the workmanship was not of the +best class, and the cross girders flexible: a characteristic +very trying to end rivets, and inducing a stretch in some, +already referred to as a possible cause of loosening. This +will be apparent if the probable end slope of weak girders +be considered. The author concludes that this inclination +should not, for ordinary cases, exceed 1 in 250; but the +ratio must largely depend upon the degree of rigidity of the +part to which the connection is made. It is commonly +regarded as bad practice to submit rivets to tension, yet this +is frequently, though unintentionally, permitted in end attachments, +without any attempt to limit the amount of +tension. With suitable restrictions, there appears no serious +objection to rivet tension for many situations.</p> + +<p>Another instance of cross-girder end connections of a +different type is illustrated in <a href="#Fig34">Fig. 34</a>.</p> + +<div class="figcenter"><a name="Fig34" id="Fig34"></a> +<img src="images/illo066a.png" alt="" width="300" height="328" /> +<p class="caption"><span class="smcap">Fig.</span> 34.</p> +</div> + +<p>The main girders of the bridge were 12 feet apart, each +cross-girder end carrying its share of the half of one road.<span class="pagenum"><a name="Page_54" id="Page_54">[54]</a></span> +The mean bearing pressure upon the rivet shanks works out +at 5·8 tons per square inch for the six rivets of the original +joint, but in the particular joint shown some of the rivets +had loosened, making the bearing pressure upon the remainder +about 8·7 tons per square inch. It is apparent +there must have been considerable stress on the top and +bottom rivets which loosened. These two rivets would also, +because of difficult access, be in all likelihood insufficiently +hammered up. The joints worked rather badly; the loose +rivets had “cut” to a considerable extent, a process materially +assisted by the gritty nature of the ballast (limestone), +particles of which, getting into the joint, contributed to the +sawing action; this had clearly been taking effect for some +considerable time. (See <a href="#Fig35">Fig. 35</a>.)</p> + +<div class="figcenter"><a name="Fig35" id="Fig35"></a> +<img src="images/illo066b.png" alt="" width="350" height="219" /> +<p class="caption"><span class="smcap">Fig.</span> 35.</p> +</div> + +<p>The two cases of cross-girder ends given are both rather +exceptional in character, and in each case the defects appear +to be due to general bad design and workmanship rather +than to any serious excess of bearing pressure. This may +be illustrated by taking the common case of cross-girders, +2 feet deep, carrying two roads, and having end angle irons +riveted to the web and stiffeners of the main girders by ten +rivets in single shear at each end. In this example, which<span class="pagenum"><a name="Page_55" id="Page_55">[55]</a></span> +is, for old work, simply typical, and does not relate to any +specific instance, the bearing pressure on the rivets will work +out at from 6 to 8 tons per square inch, and will seldom be +accompanied by looseness of rivets, and then only as a result +of faulty work.</p> + +<p>Some sketches of rivets taken from old bridges have +already been given in connection with the cases to which +they belong; a few others are here shown (<a href="#Fig36">Figs. 36</a> to <a href="#Fig40">40</a>) +to further illustrate what may be the actual condition of +rivets after some years’ use, and how different from the ideal +rivet upon which calculations are based. These are, however, +bad instances.</p> + +<div class="figc350"><a name="Fig36" id="Fig36"></a><a name="Fig37" id="Fig37"></a> +<img src="images/illo067a.png" alt="" width="350" height="88" /> +<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 36.</span> <span class="right49"><span class="smcap">Fig.</span> 37.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 36. and <span class="smcap">Fig.</span> 37.</p> +</div> + +<div class="figc350"><a name="Fig38" id="Fig38"></a><a name="Fig39" id="Fig39"></a> +<img src="images/illo067b.png" alt="" width="350" height="81" /> +<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 38.</span> <span class="right49"><span class="smcap">Fig.</span> 39.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 38. and <span class="smcap">Fig.</span> 39.</p> +</div> + +<div class="figcenter"><a name="Fig40" id="Fig40"></a> +<img src="images/illo067c.png" alt="" width="150" height="84" /> +<p class="caption"><span class="smcap">Fig.</span> 40.</p> +</div> + +<p>It should be noticed that rivets may, if in double shear, +be loose in the middle thickness, due to enlargement of the +hole in the central part and compression of the rivet, and +yet show no sign of this by testing with the hammer. There +is, however, generally marked evidence of another kind in<span class="pagenum"><a name="Page_56" id="Page_56">[56]</a></span> +the “working” of the inner part, as, for instance, the web +of a plate girder, in which case a discoloration due to rust is +to be found along the edges of the angle bars, or a movement +may be detected on the passage of live load. Red rust is, in +fact, frequently an indication of something wrong, when no +other evidence is apparent. In plate girders having <span class="lettsymb">T</span> or <span class="lettsymb">L</span> +bars brought down and cranked on to the top of shallow +cross-girders, it is not uncommon to find the rivets attaching +these bars to the cross-girder tops loose, due to causes already +dealt with. The riveted connection should, as to strength, +bear some relation to the strength and stiffness of the parts +secured, if the rivets are to remain sound.</p> + +<p>It may be well to give here a summarised statement of +the results already named, for purposes of ready reference. +These by themselves are not sufficient to enable working +stresses to be deduced, though they are instructive. The<span class="pagenum"><a name="Page_57" id="Page_57">[57]</a></span> +author has found many instances of shear and bearing +stresses in excess of those usually sanctioned, under which +the rivets behaved well, but is not now able to give precise +particulars of these.</p> + +<p class="center"><span class="smcap">Examples of Rivet Stresses.</span></p> + +<table class="nowrap" summary="Table page 56"> + +<tr class="bt bb"> +<th colspan="4" class="center br">—</th> +<th class="center padl1 padr1 br">Span<br />in<br />Feet.</th> +<th class="center padl1 padr1 br">Where<br />Found.</th> +<th class="center padl1 padr1 br">Shear<br />Stress<br />in Tons<br />per<br />Square<br />Inch.</th> +<th class="center padl1 padr1 br">Single<br />or<br />Double<br />Shear.</th> +<th colspan="3" class="center padl1 padr1 br">Bearing<br />Pressure<br />in Tons<br />per<br />Square<br />Inch.</th> +<th colspan="4" class="center padl1 padr1">Tight<br />or<br />Loose.</th> +</tr> + +<tr> +<td colspan="4" class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td colspan="3" class="thinrow br"> </td> +<td colspan="4" class="thinrow"> </td> +</tr> + +<tr> +<td rowspan="3" class="left padl1 padr1">Main girders</td> +<td rowspan="3" class="right padr0 narrow">-</td> +<td rowspan="3" class="bt bb bl narrow"> </td> +<td rowspan="3" class="narrow br"> </td> +<td class="center padl1 padr1 br">85</td> +<td class="center padl1 padr1 br">Web</td> +<td class="right padl1 padr2 br">4·0</td> +<td class="center padl1 padr1 br">D</td> +<td rowspan="3" colspan="2"> </td> +<td class="right padl1 padr2 br">11·0</td> +<td rowspan="3" colspan="3"> </td> +<td class="left padr1">Tight.</td> +</tr> + +<tr> +<td class="center padl1 padr1 br">66</td> +<td class="center padl1 padr1 br">Diagonals</td> +<td class="right padl1 padr2 br">9·0</td> +<td class="center padl1 padr1 br">S</td> +<td class="right padl1 padr2 br">9·0</td> +<td class="left padr1">Many loose.</td> +</tr> + +<tr> +<td class="center padl1 padr1 br">63</td> +<td class="center padl1 padr1 br">„</td> +<td class="right padl1 padr2 br">14·9</td> +<td class="center padl1 padr1 br">S</td> +<td class="right padl1 padr2 br">16·3</td> +<td class="left padr1">Tight generally.</td> +</tr> + +<tr> +<td colspan="4" class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td colspan="3" class="thinrow br"> </td> +<td colspan="4" class="thinrow"> </td> +</tr> + +<tr> +<td rowspan="4" class="left padl1 padr1">Small girders</td> +<td rowspan="4" class="right padr0 narrow">-</td> +<td rowspan="4" class="bt bb bl narrow"> </td> +<td rowspan="4" class="br narrow"> </td> +<td class="center padl1 padr1 br">11</td> +<td class="center padl1 padr1 br">Web</td> +<td class="right padl1 padr2 br">1·4</td> +<td class="center padl1 padr1 br">D</td> +<td rowspan="4" colspan="2"> </td> +<td class="right padl1 padr2 br">7·0</td> +<td rowspan="4" colspan="3" class="narrow"> </td> +<td class="left padr1">Tight.</td> +</tr> + +<tr> +<td class="center padl1 padr1 br">26</td> +<td class="center br">„</td> +<td class="right padl1 padr2 br">4·3</td> +<td class="center padl1 padr1 br">D</td> +<td class="right padl1 padr2 br">24·0</td> +<td class="left padr1">Many loose.</td> +</tr> + +<tr> +<td class="center padl1 padr1 br">11</td> +<td class="center br">„</td> +<td class="right padl1 padr2 br">7·3</td> +<td class="center padl1 padr1 br">D</td> +<td class="right padl1 padr2 br">20·6</td> +<td class="left padr1">Loose.</td> +</tr> + +<tr> +<td class="center padl1 padr1 br">11</td> +<td class="center br">„</td> +<td class="right padl2 padr1 br">9·7</td> +<td class="center padl1 padr1 br">D</td> +<td class="right padl1 padr2 br">27·4</td> +<td class="left padr1">Loose.</td> +</tr> + +<tr> +<td colspan="4" class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td colspan="3" class="thinrow br"> </td> +<td colspan="4" class="thinrow"> </td> +</tr> + +<tr> +<td rowspan="3" class="left padl1 padr1">End connections</td> +<td rowspan="3" class="right padr0 narrow">-</td> +<td rowspan="3" class="bt bb bl narrow"> </td> +<td rowspan="3" class="br narrow"> </td> +<td class="center padl1 padr1 br">27</td> +<td class="center padl1 padr1 br">Ends</td> +<td class="right padl1 padr2 br">5·4</td> +<td class="center padl1 padr1 br">S</td> +<td colspan="2"> </td> +<td class="right padl1 padr2 br">7·8</td> +<td colspan="3"> </td> +<td class="left padr1">Loose.</td> +</tr> + +<tr> +<td rowspan="2" class="center padl1 padr1 br">12</td> +<td rowspan="2" class="center br">„</td> +<td rowspan="2" class="right padl1 padr2 br">1·8</td> +<td rowspan="2" class="center padl1 padr1 br">D</td> +<td rowspan="2" class="right padr0 narrow">-</td> +<td rowspan="2" class="bt bb bl narrow"> </td> +<td class="right padl1 padr2 br">5·8</td> +<td rowspan="2" class="narrow"> </td> +<td rowspan="2" class="bt br bb narrow"> </td> +<td rowspan="2" class="left padl0 narrow">-</td> +<td rowspan="2" class="left padr1">Many loose.</td> +</tr> + +<tr> +<td class="right padl1 padr2 br">8·7</td> +</tr> + +<tr> +<td colspan="4" class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td class="thinrow br"> </td> +<td colspan="3" class="thinrow br"> </td> +<td colspan="4" class="thinrow"> </td> +</tr> + +<tr class="bb"> +<td class="left padl1 padr1">(Type case)</td> +<td colspan="3" class="br"> </td> +<td class="center padl1 padr1 br">26</td> +<td class="center br">„</td> +<td class="right padl1 padr2 br">4·8</td> +<td class="center padl1 padr1 br">S</td> +<td colspan="2"> </td> +<td class="right padl1 padr2 br">7·0</td> +<td colspan="3"> </td> +<td class="left padr1">Tight.</td> +</tr> + +</table> + +<p>It is probable that the fact of a rivet being in single or +in double shear largely affects its ability to resist the effects +of bearing pressure, as commonly estimated. In the first +case, the rivet-shank must bear heavily on the half-thickness +of the plates or bars through which it passes, rather than on +the whole thickness; and it is to be supposed that under +this condition it will work loose at a lower average stress +than if it were in double shear, and the pressure better distributed.</p> + +<div class="figc400"><a name="Fig41" id="Fig41"></a><a name="Fig42" id="Fig42"></a> +<img src="images/illo069.png" alt="" width="400" height="183" /> +<p class="caption_b"><span class="left43"><span class="smcap">Fig.</span> 41.</span> <span class="right56"><span class="smcap">Fig.</span> 42.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 41. and <span class="smcap">Fig.</span> 42.</p> +</div> + +<p>The author has no very definite information in +support of this contention, but suggests that for double +shear the permissible bearing pressure may probably be as +much as 50 per cent. greater than for rivets in single shear; +the difference being made rather in the direction of increasing +the allowable load on double-shear rivets, than in reducing +that upon rivets in single shear. The propriety of this +is evident when it is considered that the practice has commonly +been to make no distinction, so that whatever bearing +pressures are found to be sufficient for both cases may be +increased for those capable of taking the greater amount. +<a href="#Fig41">Figs. 41</a> and <a href="#Fig42">42</a>, here given, illustrate the behaviour of rivets +under the two conditions.</p> + +<p><span class="pagenum"><a name="Page_58" id="Page_58">[58]</a></span></p> + +<p>With reference to the amounts of the stresses to which +rivets may be subject, the author concludes, as a result of his +experience, coupled with a consideration of known laboratory +tests, that for all dead load these may be quite prudently +higher than is frequently taken. For iron the shear stress +to be 10 per cent. less than the stress of parts joined; and +the bearing pressure—for single-shear rivets, 20 per cent.; +and for double-shear rivets, 80 per cent. greater. For ordinary +mild steel the shear stress to be 20 per cent. less than +the stress in parts connected, and the bearing pressure equal +to it for single-shear rivets; and 50 per cent. more for rivets +in double shear, though the two latter values may probably +approach those for wrought iron in steel of the higher grades +sometimes used in bridge-work. For live load, or part live +and part dead load, the same rules may apply, the reduction +of the nominal working stress, arrived at by any one of the +methods in use which may be adopted, affecting both the +parts connected, and the rivets connecting them. For reverse +stresses it is advisable to keep the shear stress in any +rivet so low, say 3 tons per square inch, that the frictional +resistance of the parts gripped by the rivets shall be sufficient +to prevent any tendency to slip under the influence of the +smaller of the two forces to which the part is liable, to insure +that, if brought to a bearing in one direction by the greater +force, it shall not go back with reversal of stress. This requirement +may be open to some question with respect to +good machine-riveted work, but for hand-riveted connections +it may certainly be adopted with wisdom.</p> + +<p>The following table will show at a glance how the stresses +proposed vary with the unit stresses governing the main +sections.</p> + +<p class="center"><span class="smcap">Proposed Table of Rivet Stresses.</span></p> + +<table class="nowrap" summary="Table page 58"> + +<tr class="bt bb"> +<th class="center padl1 padr1 br">Unit<br />Stress<br />in<br />Member.</th> +<th class="center padl1 padr1 br">Shear<br />Stress.</th> +<th class="center padl1 padr1 br">Bearing<br />Pressure<br />for<br />Single-Shear<br />Rivets.</th> +<th class="center padl1 padr1">Bearing<br />Pressure<br />for<br />Double-Shear<br />Rivets.</th> +</tr> + +<tr> +<td colspan="4" class="center padl1 padr1 highline"><i>Wrought Iron.—Tons per Square Inch.</i></td> +</tr> + +<tr> +<td class="right padl1 padr2 br">3·0</td> +<td class="right padl1 padr2 br">2·7</td> +<td class="right padl1 padr4 br">3·6</td> +<td class="right padl1 padr4">5·4</td> +</tr> + +<tr> +<td class="right padl1 padr2 br">4·0</td> +<td class="right padl1 padr2 br">3·6</td> +<td class="right padl1 padr4 br">4·8</td> +<td class="right padl1 padr4">7·2</td> +</tr> + +<tr> +<td class="right padl1 padr2 br">5·0</td> +<td class="right padl1 padr2 br">4·5</td> +<td class="right padl1 padr4 br">6·0</td> +<td class="right padl1 padr4">9·0</td> +</tr> + +<tr> +<td class="right padl1 padr2 br">6·0</td> +<td class="right padl1 padr2 br">5·4</td> +<td class="right padl1 padr4 br">7·2</td> +<td class="right padl1 padr4">10·8</td> +</tr> + +<tr> +<td class="right padl1 padr2 br">7·0</td> +<td class="right padl1 padr2 br">6·3</td> +<td class="right padl1 padr4 br">8·4</td> +<td class="right padl1 padr4">12·6</td> +</tr> + +<tr> +<td colspan="4" class="center padl1 padr1 highline"><i>Steel.—Tons per Square Inch.</i></td> +</tr> + +<tr> +<td class="right padl1 padr2 br">4·0</td> +<td class="right padl1 padr2 br">3·2</td> +<td class="right padl1 padr4 br">4·0</td> +<td class="right padl1 padr4">6·0</td> +</tr> + +<tr> +<td class="right padl1 padr2 br">5·0</td> +<td class="right padl1 padr2 br">4·0</td> +<td class="right padl1 padr4 br">5·0</td> +<td class="right padl1 padr4">7·5</td> +</tr> + +<tr> +<td class="right padl1 padr2 br">6·0</td> +<td class="right padl1 padr2 br">4·8</td> +<td class="right padl1 padr4 br">6·0</td> +<td class="right padl1 padr4">9·0</td> +</tr> + +<tr> +<td class="right padl1 padr2 br">7·0</td> +<td class="right padl1 padr2 br">5·6</td> +<td class="right padl1 padr4 br">7·0</td> +<td class="right padl1 padr4">10·5</td> +</tr> + +<tr> +<td class="right padl1 padr2 br">8·0</td> +<td class="right padl1 padr2 br">6·4</td> +<td class="right padl1 padr4 br">8·0</td> +<td class="right padl1 padr4">12·0</td> +</tr> + +<tr class="bb"> +<td class="right padl1 padr2 br">9·0</td> +<td class="right padl1 padr2 br">7·2</td> +<td class="right padl1 padr4 br">9·0</td> +<td class="right padl1 padr4">13·5</td> +</tr> + +</table> + +<blockquote> + +<p><span class="smcap">Note.</span>—Tension on rivets to be limited to one-half the permissible +shear stress, the holes being slightly countersunk under snap-head.</p></blockquote> + +<p>It may be objected that the shear stresses in the proposed +table are somewhat high for wrought iron and steel. +This feature is intentional, and is supported by the consideration<span class="pagenum"><a name="Page_59" id="Page_59">[59]</a></span> +that whereas there may be loss of strength in the members +of a structure by waste, there is no such loss in rivets, +if the work is so designed that there shall be no loosening. +Any allowance that may be desirable for loose or defective +field rivets is left to be dealt with as may be considered +advisable for each particular case, the table as it stands being +applicable only to riveting not below the standard of first-rate +hand work.</p> + +<p>Cases of loose rivets in main girders over 50 feet span, +due to any cause but bad work, are extremely rare, unless +resulting from the action of some other part of the structure. +It may be stated broadly that for railway bridges of less than +perfect design, the nearer the rail, the more loose rivets, +generally at connections. This is, no doubt, largely due to +the severe impact of the load, the effects of which are greater +near the rail, both because of the small proportion of dead<span class="pagenum"><a name="Page_60" id="Page_60">[60]</a></span> +load, and because this effect has been but little modified by +the elasticity of any considerable length of intervening girder-work. +In addition to this, it is quite usual to find the rivets +more heavily stressed, even though the load be considered +as “static,” in the floor system than in the main-girders, +though the reverse should be the case. It is unfortunate +that those parts which require the best riveting—viz., the +connections—are commonly dealt with by hand; and for +this reason it is the more necessary to design these with the +greatest care.</p> + +<p>Any arrangement which favours the gradual acceptance +of stress by one part from another will contribute to the +integrity of riveted connections, and lessen the liability of +the material to develop faults. In other branches of design +this is well recognised, but appears in much old bridge work +to have been entirely overlooked.</p> + +<p>Bridges carrying public roads very seldom furnish examples +of loose rivets; the conditions are generally much +more favourable, impact being practically absent, full loading +infrequent, and the proportion of dead load to live, high.</p> + +<p>It is, perhaps, hardly necessary to insist upon rivets +being, apart from mere considerations of strength, sufficiently +near together to insure close work and exclude moisture. +Outside edge seams should never be more widely spaced +than 16 times the thickness of the plates; 12 thicknesses +apart is better. In the case of angle, tee, and channel sections, +the greater stiffness of the section makes wider spacing +allowable up to, say, 20 times the thickness; but this must +be governed largely by the amount of riveting required to +pull the parts close together. Where more than four thicknesses +are to be gripped by the rivets, <sup>3</sup>⁄<sub>4</sub> inch in diameter is +hardly sufficient to insure tight work, and quite unsuitable +if the plates exceed <sup>5</sup>⁄<sub>8</sub> inch thick.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_61" id="Page_61">[61]</a></span></p> + +<h2>CHAPTER VI.<br /> +<span class="chaptitle">HIGH STRESS.</span></h2> + +<p>High stress, provided it be well below that at which immediate +injury results, or possible failure, is not uniformly objectionable. +It may be first considered relative to the absolute +and elastic limits of strength, next with respect to the range +of stress, and, finally, with regard to the frequency of application. +For practical purposes—that is, for the continued +efficiency of a structure—the limit of elasticity must be considered +to be the limit of strength, or, more strictly, the +limit for all those parts of the structure which must, so long +as it lasts, be liable to the original measure of stress. There +may be places in a bridge, however, over-stressed only in the +earlier period of its existence, which, by being over-stressed +and suffering deformation, permit the origin of this distortion +to be harmlessly met in some other way. In such a +case the injury done to that part does not, of necessity, lead +to any culminating disaster; indeed, were it not for this +plasticity it is probable a large number of bridges would fail +after being in use but a short time. As for riveting, so in +dealing with the amount of stress to which a member is +supposed to be liable, it should be clearly understood by what +method this has been arrived at, whether the value assigned +is the actual measure of the stress, or simply the conventional +amount arrived at in the conventional way; perhaps neglecting +web section in plate girders, or without regard to the +various influences which may reduce or increase the nominal +amount of stress, or including only a partial recognition of<span class="pagenum"><a name="Page_62" id="Page_62">[62]</a></span> +those influences. In any case quoted the stress named is +that at which the author arrives by the ordinary methods of +computation carefully applied, where these appear to be +sufficiently precise, unless any qualifying remark be added. +Extreme flange stress is in special cases computed, first on the +gross section by estimating the moment of inertia on that +basis, and deducing the stress at the holes from the ratio of +net to gross section at the extreme fibres; a method more +correct than by reference to the moment of inertia of the net +section. Any exhaustive refinement in the study of stresses +is not attempted, both because it is beyond the author’s +powers of analysis, and for the reason that such results are +not comparable with the results of ordinary methods of calculation +in practice. Effective spans are taken at moderate +values, and all exaggeration is avoided.</p> + +<p>The effects of impact in any part vary so much with +nearness to, or remoteness from, the living load, and the +frequency of development of the maximum stress from all +causes acting together is so much affected by the same consideration, +that it is apparent a nominal stress which may be +harmless in one part of a bridge may be destructive in some +other, a statement borne out by observation. Stress, as +ordinarily stated—i.e., at so much per square inch, uniform +across a section—is seldom a cause of trouble. In nearly all +cases of failure there is an accompanying localised destructive +stress, either in rivets or elsewhere, with crippling or deformation +of some essential part. In the tension flanges of main +girders with uncomplicated stress, this may run up to an +amount very considerably beyond the ordinary limits without +producing signs of distress. The same remark applies to the +compression flanges, if these be in themselves sufficiently +stiff, or properly restrained from side flexure. In support of +the above statement may be quoted the following instances +relating to wrought-iron structures<span class="nowrap">:—</span></p> + +<p><span class="pagenum"><a name="Page_63" id="Page_63">[63]</a></span></p> + +<p>A bridge of 60 feet effective span, having girders +immediately under the rails, had a flange stress of 6·3 tons +per square inch. Another of 64 feet span, carrying two lines +of way, with outside main girders and cross-girders, had the +flanges of the former stressed to 6·8 tons per square inch. +A third, of 76 feet span, of similar construction to the last, +was stressed in the main girder flanges to 7·5 tons per square +inch. The webs were not included in the computation; the +figures, therefore, compare with ordinary practice. In these +three cases the main girders showed no signs of distress, +referable to the results stated, though the top flanges in the +last case were curved inwards. The effect of this flexing of +the flange would be, of course, to increase the amount of +compressive stress along one edge, though to what degree +cannot now be stated.</p> + +<div class="figc600"><a name="Fig43" id="Fig43"></a><a name="Fig45" id="Fig45"></a><a name="Fig44" id="Fig44"></a> +<p class="caption"><span class="smcap">Fig.</span> 43.</p> +<img src="images/illo076.png" alt="" width="600" height="308" /> +<p class="caption_b"><span class="left70"><span class="smcap">Fig.</span> 44.</span> <span class="right29"><span class="smcap">Fig.</span> 45.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 44. and <span class="smcap">Fig.</span> 45.</p> +</div> + +<p>A further instance of considerable flange stress occurred +in a bridge of seven nearly equal continuous spans, 25 feet +generally, the end and greatest span being 29 feet 6 inches, +centre to centre of bearings. Some details of the bridge are +given in <a href="#Fig43">Figs. 43 to 45</a>. The four inner main girders +under rails were 2 feet deep, with webs <sup>1</sup>⁄<sub>2</sub> inch thick over +piers, and <sup>3</sup>⁄<sub>8</sub> inch at abutments, having flanges of two <span class="lettsymb">L</span> bars, +3 inches by 3 inches by <sup>5</sup>⁄<sub>8</sub> inch. There were also two +outer girders of the same depth, with single <span class="lettsymb">L</span> bars. Plate +diaphragms of full girder depth and particularly stiff were +carried right across the bridge at the centre of the spans, +and over the piers. The girders, though evidently designed +to be continuous, had very poor flange joints at each bearing, +of little more than one half the flange strength (see <a href="#Fig45">Fig. 45</a>). +It is doubtful if the girders acted with strict continuity for +long after erection, as the excessive stress in the rivets of the +flange joint would, for that condition, have been nearly +sufficient to shear them. It is probable that this being so, +the joints first yielded, relieving the bending moment over<span class="pagenum"><a name="Page_64" id="Page_64">[64]</a></span> +the piers, and increasing it near mid-span. Whether the end +spans be considered as strictly continuous with the rest, or +as simple beams, the maximum bending moments would not<span class="pagenum"><a name="Page_65" id="Page_65">[65]</a></span> +greatly differ, though occurring for continuity over the pier, +for free beams at the centre. There is, however, an intermediate +condition which makes the moments at these two +places less than either maximum, but equal to each other; +a condition of semi-continuity agreeable to a partial efficiency +of the joints referred to. It is this state which has been +calculated, giving the minimum stress value that can be +accepted. The diaphragm has been assumed to transfer to +the outer girders a due proportion of the load. With this +explanation it may now be stated that, under engine loads +corresponding to those running, the flange stress worked out +at 7·4 tons per square inch tension, web included, or 9·7 +tons per square inch without considering the web; which +stresses, it is more than probable, may have been greater. +The figures include the consideration of anything which may +contribute to lowering the stress, and are hardly to be compared +with those worked to in ordinary design of new work, +in which it would be quite usual to neglect the assistance of +the outer girders and the webs, to work to heaviest engine-loads, +and possibly include an allowance for the effects of +settlement. Dealt with in this way the girders would seem +to be of about one-fourth the strength that would be required +in the design of a new bridge, in which certain elements of +strength would be deliberately ignored.</p> + +<p>The ironwork was in good condition, there was no ordinary +evidence of weakness apart from the calculated results, +the vibration was distinctly moderate, and the deflection, +though not recorded, was certainly small. The bridge did, +indeed, seem somewhat inert under load, and favours a +suspicion, the author entertains, that old girderwork long +overstressed may have a sensibly higher modulus of elasticity +than newer work at more moderate stresses. The traffic was +not very considerable, and both roads, of the same spans, +but seldom loaded at the same time; though with this construction<span class="pagenum"><a name="Page_66" id="Page_66">[66]</a></span> +of bridge there would in either case be very little +difference. The author recalls no reason for supposing that +the piers had yielded in any sensible degree. The bridge +was rebuilt after some thirty-six years’ use.</p> + +<p>Stress of considerable amount in the flanges of a latticed +main girder of 63 feet span has already been noticed in the +chapter on “<a href="#Page_45">Riveted Connections</a>,” which for the tension +boom worked out to 7·1 tons per square inch, the flanges +in this case showing no signs of weakness. An instance has +also been given in dealing with a case of side flexure in +which the extreme fibre stress was calculated to be 10 tons +per square inch, the girder recovering its form when relieved +of load.</p> + +<p>As to stress in cross-girder flanges, an example may be +quoted of a bridge of 109 feet span, carrying two roads, +having outside main girders, with cross-girders between; +these latter were stressed in the flanges to 6·7 tons per +square inch (webs not included), if the partial distribution +among the girders (which were spaced 6 feet apart) by the +rails and longitudinal timbers be neglected. There is some +reason to think in this instance that distribution had the +effect of reducing the stress quoted, as the observed deflection +of the cross-girders was materially less than that calculated +for girders acting independently of each other, though +this may be in part due to a cause already hinted at. +Rigidity of the cross-girder ends, where attached to the +heavy main girders, would also tend to moderate the stress. +No very definite conclusion can therefore be deduced from +this instance.</p> + +<p>To take another case of less uncertainty, the bridge of +35 feet span (see <a href="#Fig33">Fig. 33</a>), referred to in “<a href="#Page_45">Riveted Connections</a>,” +may again be cited. The extreme fibre stress in the +cross-girder flanges worked out at 6·3 tons per square inch, +web included, or 6·5 tons, exclusive of the web. It cannot<span class="pagenum"><a name="Page_67" id="Page_67">[67]</a></span> +be said in this example that the girders showed no signs of +weakness, as the deflection under live load was <sup>1</sup>⁄<sub>2</sub> inch on the +span of 11 feet, in addition to a permanent set of <sup>3</sup>⁄<sub>4</sub> inch, +largely due, however, to “working” rivets.</p> + +<p>A better and altogether conclusive case of the way in +which cross-girders may occasionally suffer considerable +stress, and show no sign, is furnished by two cross-girders, +of which some particulars are here given. These girders +occurred in the floor of a very acute angled skew bridge, +riveted at one end to the main girders in a manner which +was very far from fixing the ends, resting at the other end +on a masonry abutment. The first girder was about 19 feet +effective span, 12 inches deep in the web, with angle bar and +plate flanges. The girders were spaced 6 feet apart, and +were connected under the rails by <span class="lettsymb">T</span>-bars, cranked down to +face the webs, and riveted through. Though these <span class="lettsymb">T</span>’s had +little stiffness, yet the frequent vertical movements of the +girders relative to each other, under passing loads, had broken +the majority of the <span class="lettsymb">T</span>-bars at the bends, so that no notice +need be taken of these as transferring load from any one +cross-girder to its neighbour. The floor covering consisted +of timbers about 4 inches thick, also incompetent to transfer +any sensible proportion of the load on a girder to others 6 +feet distant. Upon the floor was cinder ballast, with sleepers, +chairs, and ordinary bull-headed rails. The stress to which +the girder was liable works out at 8·4 tons per square inch, +on the extreme fibres of the net section, web included; or +9·1 tons, neglecting the web, under engine-loads of a +common amount. The other girder had an effective span +of about 22 feet, as before 12 inches deep in the web, with +angle bar and plate flanges. The stress per square inch was +10·5 tons, web included, or 11·1 tons per square inch, +neglecting the web. This girder carried three rails, one of +which was near to the abutment bearing, so that there was<span class="pagenum"><a name="Page_68" id="Page_68">[68]</a></span> +no great difference in the stress induced whether all three rails +were loaded or the pair only. The traffic over the bridge +was very great, but of moderate speed. It must have been a +common occurrence for the girders to take the full loads. +The heavier engines passed scores of times in a day—lighter +engines probably one hundred times. The bridge was about +twenty years old, yet these cross-girders, when removed, +showed no other sign of age and wear than that due to rust.</p> + +<div class="figcenter"><a name="Fig46" id="Fig46"></a> +<img src="images/illo080.png" alt="" width="500" height="241" /> +<p class="caption"><span class="smcap">Fig.</span> 46.</p> +</div> + +<p>All the foregoing instances relate to wrought-iron bridges. +Two cases of steel construction are here added, the first of +these furnishing an example of high girder stress somewhat +remarkable. This was found in a trough girder of a strange +pattern, of which a section is here given (<a href="#Fig46">Fig. 46</a>). The +bridge to which it belonged carried a siding, over which +engines of less than the heaviest class sometimes passed at a +crawling pace. The larger of the two girders carrying the +rails was 15 feet 8 inches effective span. The sides of the +trough consisted each of two vertical plates, originally <sup>1</sup>⁄<sub>2</sub> inch +thick, but wasted to an aggregate thickness of <sup>5</sup>⁄<sub>8</sub> inch. +These plates 6 inches deep, were connected at their lower +edges to angle bars, 3 inches by 3 inches by <sup>1</sup>⁄<sub>2</sub> inch, which +again were riveted to a bottom plate 16 inches wide, +originally <sup>1</sup>⁄<sub>2</sub> inch thick, wasted to <sup>3</sup>⁄<sub>8</sub> inch. Lying in the bottom<span class="pagenum"><a name="Page_69" id="Page_69">[69]</a></span> +of the trough, and riveted through the inner angle flanges, +was a bridge-rail. Assuming that the metal retained its +elastic properties from top to bottom of the section, at +whatever stress, this works out at 32 tons per square inch +at the extreme top fibre, and 15 tons at the bottom, on the +net section. As puddled steel, of which the girders were +made, may have a tenacity of 45 to 55 tons per square inch, +the assumption is probably correct. The author has no +record of the deflection, but it may be remarked it was +such that to stand under the girder, with a tank engine +passing over, required some determination.</p> + +<p>A point of additional interest in this little bridge is that, +though made of steel, it dates as far back as 1861, having +been in use thirty-two years when removed. The particular +variety of steel used was known as Firth’s puddled. The +evidence of this consists in correspondence showing that permission +had been asked of the controlling authority, by the +only users of the siding, to apply this material, with no evidence +of any refusal. At about the same time this steel was also +used upon the railway concerned in the top flanges of some +girders of considerable span. The appearance of the trough +girders to which the foregoing particulars apply was distinctly +different to that which might be expected in ordinary +wrought iron. The top edges of the vertical plates were +wasted away, smooth, and rounded in a manner strongly +suggestive of a steely character. Finally, the way in which +the girders held up to their work for so long is, by itself, +conclusive on the point. The bridge-rail appeared to be of +wrought iron, the different modulus of elasticity of which +has been included in the calculation upon which the preceding +results are based. That these girders stood so well is, +perhaps, largely due to the fact that the load carried by them +was, though varying within wide limits, practically free from +impact, which, had the load passed over quickly, would, with<span class="pagenum"><a name="Page_70" id="Page_70">[70]</a></span> +girders so small, shallow and flexible, have been very sensible.</p> + +<p>The second instance of steel construction in which somewhat +high stress is manifest is that of some steel troughing of +the Lindsay pattern, used in a bridge built in 1885. The +troughs ran parallel to the rails, having an effective span of +18 feet 8 inches. The depth of the section (which is shown +in <a href="#Fig47">Fig. 47</a>), was 8<sup>1</sup>⁄<sub>2</sub> inches, making a ratio of depth to span +of <sup>1</sup>⁄<sub>28</sub>. The road was of ballast, sleepers, chairs, and 85-lb. +rails.</p> + +<div class="figcenter"><a name="Fig47" id="Fig47"></a> +<img src="images/illo082.png" alt="" width="400" height="208" /> +<p class="caption"><span class="smcap">Fig.</span> 47.</p> +</div> + +<p>Assuming this to be carried on six troughs, which corresponds +to 11 feet 3 inches of width, the extreme fibre stress +works out at 7·5 tons per square inch, under usual engine-loads. +The bridge when examined after fourteen years’ use was +in good condition, and at that time but little rusted; but the +end seam rivets were, as is not uncommon with such troughing, +loose. The traffic over the bridge was considerable, but +not at great speed.</p> + +<p>On the opposite page are set out the results which have +been given, in tabulated form, as was done for rivet stresses, +to enable ready comparison to be made.</p> + +<p class="center"><span class="smcap">Examples of High Stress.</span><span class="pagenum"><a name="Page_71" id="Page_71">[71]</a></span></p> + +<table class="nowrap" summary="Table page 71"> + +<tr class="bt bb"> +<th rowspan="2" colspan="3" class="center padl1 padr1 br">—</th> +<th rowspan="2" colspan="4" class="center padl1 padr1 br">Span<br />in<br />Feet.</th> +<th rowspan="2" class="center padl1 padr1 br">Part<br />Stressed.</th> +<th colspan="2" class="center padl1 padr1 br">Stress per<br />Square Inch.</th> +<th rowspan="2" class="center padl1 padr1 br">Tension<br />or<br />Compression.</th> +<th rowspan="2" colspan="4" class="center padl1 padr1">Condition.</th> +</tr> + +<tr class="bb"> +<th class="center padl1 padr1 br">Webs<br />Included.</th> +<th class="center padl1 padr1 br">Webs not<br />Included.</th> +</tr> + +<tr> +<td class="center padl1 wrappable">Wrought-iron</td> +<td class="center wrappable">main girders,</td> +<td class="left padl1 padr1 br">plate</td> +<td class="right padl1 padr1">60·0</td> +<td rowspan="3" colspan="3" class="br"> </td> +<td class="center padl1 padr1 br">Flange</td> +<td class="center padl1 padr1 br">..</td> +<td class="right padl1 padr3 br">6·3</td> +<td class="center padl1 padr1 br">Tension</td> +<td rowspan="3" colspan="3"> </td> +<td class="left padr1">Good.</td> +</tr> + +<tr> +<td class="center">„</td> +<td class="center">„</td> +<td class="center br">„</td> +<td class="right padl1 padr1">64·0</td> +<td class="center padl1 padr1 br">„</td> +<td class="center padl1 padr1 br">..</td> +<td class="right padl1 padr3 br">6·8</td> +<td class="center padl1 padr1 br">„</td> +<td class="left padr1">Good.</td> +</tr> + +<tr> +<td class="center">„</td> +<td class="center">„</td> +<td class="center br">„</td> +<td class="right padl1 padr1">76·0</td> +<td class="center padl1 padr1 br">„</td> +<td class="center padl1 padr1 br">..</td> +<td class="right padl1 padr3 br">7·5</td> +<td class="center padl1 padr1 br">„</td> +<td class="left padr1">Fair.</td> +</tr> + +<tr> +<td rowspan="2" class="center">„</td> +<td rowspan="2" class="center">„</td> +<td rowspan="2" class="center br">„</td> +<td rowspan="2" class="right padl1 padr1">29·5</td> +<td rowspan="2" class="right padr0 narrow">-</td> +<td rowspan="2" class="bt bb bl narrow"> </td> +<td rowspan="2" class="br narrow"> </td> +<td class="center padl1 padr1 br">„</td> +<td class="right padl1 padr3 br">7·4</td> +<td class="right padl1 padr3 br">9·7</td> +<td class="center padl1 padr1 br">„</td> +<td rowspan="2" class="narrow"> </td> +<td rowspan="2" class="bt br bb narrow"> </td> +<td rowspan="2" class="left padl0 narrow">-</td> +<td rowspan="2" class="left padr1">Good.</td> +</tr> + +<tr> +<td class="center padl1 padr1 br">„</td> +<td class="right padl1 padr3 br">6·3</td> +<td class="right padl1 padr3 br">8·3</td> +<td class="center padl1 padr1 br">Compression</td> +</tr> + +<tr> +<td class="center">„</td> +<td class="center">„</td> +<td class="left padl1 padr1 br">lattice</td> +<td class="right padl1 padr1">63·0</td> +<td rowspan="6" colspan="3" class="br"> </td> +<td class="center padl1 padr1 br">„</td> +<td colspan="2" class="center padl1 padr1 br">7·1</td> +<td class="center padl1 padr1 br">Tension</td> +<td rowspan="6" colspan="3"> </td> +<td class="left padr1">Fair.</td> +</tr> + +<tr> +<td class="center">„</td> +<td class="center">„</td> +<td class="left padl1 padr1 br">plate</td> +<td class="right padl1 padr1">47·0</td> +<td class="center padl1 padr1 br wrappable">Flange edge</td> +<td class="right padl1 padr3 br">10·0</td> +<td class="center padl1 padr1 br">..</td> +<td class="center padl1 padr1 br">Compression</td> +<td class="left padr1">Fair.</td> +</tr> + +<tr> +<td class="center padl1 wrappable">Wrought-iron</td> +<td class="center wrappable">cross-girders,</td> +<td class="left padl1 padr1 br">plate</td> +<td class="right padl1 padr1">26·0</td> +<td class="center padl1 padr1 br">Flange</td> +<td class="center padl1 padr1 br">..</td> +<td class="right padl1 padr3 br">6·7</td> +<td class="center padl1 padr1 br">Tension</td> +<td class="left padr1">Fair.</td> +</tr> + +<tr> +<td class="center">„</td> +<td class="center">„</td> +<td class="center br">„</td> +<td class="right padl1 padr1">11.0</td> +<td class="center br">„</td> +<td class="right padl1 padr3 br">6·3</td> +<td class="right padl1 padr3 br">6·5</td> +<td class="center br">„</td> +<td class="left padr1 wrappable">Bad; loose rivets.</td> +</tr> + +<tr> +<td class="center">„</td> +<td class="center">„</td> +<td class="center br">„</td> +<td class="right padl1 padr1">19·0</td> +<td class="center br">„</td> +<td class="right padl1 padr3 br">8·4</td> +<td class="right padl1 padr3 br">9·1</td> +<td class="center br">„</td> +<td class="left padr1 wrappable">Good, but rusted.</td> +</tr> + +<tr> +<td class="center">„</td> +<td class="center">„</td> +<td class="center br">„</td> +<td class="right padl1 padr1">22·0</td> +<td class="center br">„</td> +<td class="right padl1 padr3 br">10·5</td> +<td class="right padl1 padr3 br">11·1</td> +<td class="center br">„</td> +<td class="left padr1 wrappable">Good, but rusted.</td> +</tr> + +<tr> +<td rowspan="2" colspan="3" class="left padl1 padr1 br">Steel trough girder</td> +<td rowspan="2" class="right padl1 padr1">15.7</td> +<td rowspan="2" class="right padr0 narrow">-</td> +<td rowspan="2" class="bt bb bl narrow"> </td> +<td rowspan="2" class="br narrow"> </td> +<td class="center br">„</td> +<td colspan="2" class="center br">15·0</td> +<td class="center br">„</td> +<td rowspan="2" class="narrow"> </td> +<td rowspan="2" class="bt br bb narrow"> </td> +<td rowspan="2" class="left padl0 narrow">-</td> +<td rowspan="2" class="left padr1 wrappable">Fair, but rusted.</td> +</tr> + +<tr> +<td class="center padl1 padr1 br wrappable">Top edge</td> +<td colspan="2" class="center br">32·0</td> +<td class="center br">Compression</td> +</tr> + +<tr class="bb"> +<td colspan="3" class="left padl1 padr1 br">Steel troughing</td> +<td class="right padl1 padr1">18·7</td> +<td colspan="3" class="br"> </td> +<td class="center padl1 padr1 br">Flanges</td> +<td class="right padl1 padr3 br">7·5</td> +<td class="center padl1 padr1 br">..</td> +<td class="center padl1 padr1 br wrappable">Tension and Compression</td> +<td colspan="3"> </td> +<td class="left padr1">Fair, but rusted.</td> +</tr> + +</table> + +<p>It would be unwise to infer from the instances which<span class="pagenum"><a name="Page_72" id="Page_72">[72]</a></span> +have been quoted that high stress may be regarded with +complaisance. In the most conscientious engineering work +there should still be a liberal margin for material possibly +defective, or even bad, for waste and deterioration, and for +the aggregate effect of minor errors in design, any one of +which considerations, except the first, by itself might not be +of great importance. The conclusion which may, however, +be derived from this and the previous chapters is, that bridge +failures are less likely to occur from high stress of a kind +readily calculated than from failure in detail, obscure and +little suspected, the reason for which is not perhaps apparent, +till the attention is forcibly directed to it by the refusal of +the structure to sustain the forces to which it may be liable.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_73" id="Page_73">[73]</a></span></p> + +<h2>CHAPTER VII.<br /> +<span class="chaptitle">DEFORMATIONS.</span></h2> + +<p>Instructive lessons are to be had from a study of the +various alterations in form to which metallic bridgework is +liable, which alterations may be due simply to the development +of stress of ordinary amount, and are then generally +small; or to abnormal stresses, the result of some distortion +in the bridge structure itself not originally intended, and +possibly extreme. In addition to these there may be deformations +due to settlement, to “creeping” of parts of the +structure relative to the rest, to temperature changes, to rust, +and to original bad workmanship. In any instance quoted +below the methods adopted to ascertain the amounts of such +alterations were quite simple, even crude; but as care was +exercised, and no attempt made to measure any very minute +changes, the results may be accepted as practically correct.</p> + +<p>Dismissing for the present changes of form such as are +to be expected, and touched upon in other places in this +work, with respect to the particular parts of bridge structures +affected by them, a few instances will be adduced of +alterations which, though not very surprising, are such as in +the design of the work are hardly likely, in most instances, +to have been contemplated.</p> + +<p>A case has already been referred to in which, owing to +eccentric loading of main girders, these were, as to the top +flanges, flexed sideways a considerable amount. It is proposed +to supplement this by further remarks relative to +somewhat similar cases. A like effect is frequently to be<span class="pagenum"><a name="Page_74" id="Page_74">[74]</a></span> +observed in trough or twin girders, in which the rails are +supported upon longitudinal timbers resting upon projecting +ledges formed by the bottom angle-bars of such troughs. +In old forms of this arrangement it is common to find the +two girders forming the trough connected only by bolts +passing through the timbers, or just above them and below +the rails; or connected by narrow strips, which serve no +other purpose than to prevent the sides spreading at the +bottom. The top flanges in such cases commonly curve +inwards on the passage of the running load, accompanied of +necessity by an increase of compressive stress upon the outer +edges of the flanges, and perhaps by the working of any +flange-joint which may exist. This, both as to flexing of +the top flange and the working of a joint, was noticed in +the case of a bridge twenty-three years old, very similar to +that illustrated in <a href="#Fig8">Figs. 8</a> and <a href="#Fig9">9</a>, and described on <a href="#Page_13">pages 13</a> +and <a href="#Page_14">14</a>. The top flange consisted, however, of a bridge rail +riveted to the top edge of the web, butting at a joint, and +covered by thick cover strips (see <a href="#Fig48">Fig. 48</a>). The joint itself +was poor, and depended largely upon the character of the +butt, which was not sufficiently good to prevent the top +member kinking at this point, under the joint influence of +transverse effort and compressive stress, with possibly some +help from bolts passing through timber and webs, though +these being loose, the author does not think them at all responsible. +Although not strictly relevant, it may be remarked +in passing that it is very objectionable to use bolts as was +done in this instance; for as the timber settles down on its +seat, taking the bolts with it, these bear hard in the webs, +enlarging or even, as in this case, tearing the holes, accompanied +by injury to the bolts themselves. The practice is +now almost obsolete, but the example is instructive as showing +the impropriety of securing timbers by bolts passing through +them at right angles to the action of the load, unless these +bolts are quite free to move with the timber as it compresses.</p> + +<p><span class="pagenum"><a name="Page_75" id="Page_75">[75]</a></span></p> + +<p>If trough girders must be used, the better plan is to +connect the two sides by a continuous bottom plate, the +trough thus formed being properly drained, if the timber +is not bedded in asphalt concrete; or to introduce stiff +diaphragms at intervals beneath timbers, if the depth +suffices.</p> + +<p>In the case just quoted the curvature of the top members +of the girders was inwards, but in the instance given below, +of twin girders 26 feet effective span, with longitudinal +timbers between, resting, as before, upon the inner ledge +formed by the bottom flanges, the curvature was observed in +three out of four girders to be <sup>1</sup>⁄<sub>2</sub> inch in a contrary direction, +the fourth remaining straight.</p> + +<div class="figc450"><a name="Fig48" id="Fig48"></a><a name="Fig49" id="Fig49"></a> +<img src="images/illo087.png" alt="" width="450" height="201" /> +<p class="caption_b"><span class="left35"><span class="smcap">Fig.</span> 48.</span> <span class="right64"><span class="smcap">Fig.</span> 49.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 48. and <span class="smcap">Fig.</span> 49.</p> +</div> + +<p>An inspection of the accompanying section, <a href="#Fig49">Fig. 49</a>, will, +perhaps, render the reason evident when it is noticed that +the top members are very unsymmetrical in form, the effect +of this being to give these members, under stress, a strong +tendency to flex outwards, apparently more than sufficient +to counteract the tendency of an eccentric application of +load on the bottom flange to bring them inwards. It is to +be observed that the eccentricity of the flange appears to be +not materially in excess, and is actually so, only because the +thinness of the web—<sup>1</sup>⁄<sub>4</sub> inch—renders it incompetent to keep +the bottom flange up to its work, and so secure the full +effect of the eccentric loading in limiting the outward tendency,<span class="pagenum"><a name="Page_76" id="Page_76">[76]</a></span> +due to the section of the top member, the effects of +which are thus more apparent than would have been the +case with a stiffer web. Ties across from one bottom flange +to the other prevent the want of symmetry noticed in these—which, +by the way, is on the wrong side for utility—from +having any particular effect.</p> + +<p>To give one other example of the consequences of eccentric +loading, a bridge of 48 feet effective span may be quoted. +This bridge carried four lines of way supported by five main +girders, trussed by kicking-struts in such a manner as to form +a bastard arch. A part section and plan are given in <a href="#Fig50">Figs. +50</a> and <a href="#Fig51">51</a>.</p> + +<div class="figcenter"><a name="Fig50" id="Fig50"></a> +<img src="images/illo089a.png" alt="" width="450" height="482" /> +<p class="caption"><span class="smcap">Fig.</span> 50.</p> +</div> + +<div class="figcenter"><a name="Fig51" id="Fig51"></a> +<img src="images/illo089b.png" alt="" width="500" height="198" /> +<p class="caption"><span class="smcap">Fig.</span> 51.</p> +</div> + +<p>The floor consisted of Lindsay’s troughing resting upon +the lower flanges of the main girders, the three middle +girders, subject to eccentric loading, sometimes on one side, +sometimes on the other, were, with dead load only, straight; +but the two outer girders, liable to loading only on one side, +had, under repeated applications of such a load, assumed a +permanent curve towards the rails—<sup>13</sup>⁄<sub>16</sub> inch in one case and +1 inch in the other—which curvature, no doubt, increased +when a live load came upon the contiguous roads, though +this was not measured. It should be remarked in passing +that, owing to settlement and the canting of the abutments, +the three middle girders were also “down”—in one case <sup>3</sup>⁄<sub>4</sub> +inch. The girders, with one near road loaded, deflected <sup>1</sup>⁄<sub>8</sub> inch—greatly +less than would have been the case had the main +girder not been trussed. The bridge, at the time these particulars +were obtained, had been in existence six years.</p> + +<p>Deformations due to settlement may be very considerable. +The author recalls two instances affecting continuous girders. +In the first of these, a bridge twenty years old, of two spans +of about 50 feet each, and with girders 4 feet 6 inches deep, +the centre pier had sunk 4 inches, reducing the spans, as +respects the dead load, practically to the condition of simple<span class="pagenum"><a name="Page_77" id="Page_77">[77]</a><br /><a name="Page_78" id="Page_78">[78]</a></span> +beams, just resting, but hardly bearing, upon the piers when +free of live load.</p> + +<p>In the second case, also of two openings of about 55 feet +each, with girders 8 feet deep, one abutment had sunk about +3 inches, more than doubling the stresses over the centre +pier. It is manifest that continuous girders should only be +adopted where settlement of the supporting points is not +likely to occur to any material degree. If this cannot be +relied upon, the theoretical flange sections may hardly be +worked to with any prudence; it being then advisable to +make a liberal allowance for settlement stresses, in which +case any economical advantage that should exist will probably +disappear. It is, however, to be acknowledged that so long +as the girders are in touch, under dead load, with the bearings +intended to support them, the stresses due to a live load +are unaltered, the principal effect in this case being that the +variation in stress due to the live load ranges between limits +that are higher or lower in the scale of stress than is the +case with bearings undisturbed; still, if it is desired that +the maximum stress shall not exceed, say, 6 tons per square +inch, it can hardly be a matter of indifference that settlement +shall induce a maximum of, perhaps, 10 tons, as in that case +the stress must be 4 tons nearer the limit of statical strength.</p> + +<p>Before leaving this matter it may be well to point out +that in the case of continuous girders of uniform section a +moderate settlement of the piers may even be advantageous +by reducing the moments over the piers, and possibly making +them equal to those obtaining near the middle of the spans, +in which case there will be less inequality of stress in the +booms and a reduction of the maximum stress.</p> + +<p>Bridges consisting of simple main girders connected by +cross-girders may be very prejudicially affected by unequal +settlement; for instance, if one girder bearing settles more +than the others, a twist is put upon the structure very trying<span class="pagenum"><a name="Page_79" id="Page_79">[79]</a></span> +to the floor-girder connections, and possibly to the main +girders; to the web if a plate girder, or to the verticals if +an open-webbed truss with rigid cross-girder attachments. +Indeed, settlement of this kind may be much more destructive +to a metallic bridge than to an arch of brick or masonry, +the commonly accepted opinion notwithstanding.</p> + +<p>Instances of deformations due to the creeping of some +part of the structure away from its work, are within the +author’s knowledge, rare; except in the case of the ends of +main girders in skew bridges, already referred to.</p> + +<p>Distortion, the result of temperature changes, is frequently +to be observed in any considerable length of girder +flange or parapet where there is not freedom of movement, +unless due provision is made to check it.</p> + +<p>It is quite common to see parapets out of line, either +because the ends are not free, or because the light work of +the parapet being more exposed to the sun’s rays than the +girder work to which the lower part is attached, expanding +to a greater degree, is subject to considerable compressive +force, and buckles under its influence. The cure for this +condition is obviously to provide such parapets with free or +flexible joints at moderate distances apart, or to make the +parapet sufficiently stiff to take the stresses developed, without +crippling. A parapet may also go out of shape if directly +attached to the top flange of a girder liable to heavy loading, +particularly if the girder be shallower than the parapet, +simply by its inability to maintain truth of line under the +compressive stress, which it shares with the top flange of the +girder proper.</p> + +<p>Rivets spaced too far apart, by allowing the plates or +other parts to spring open slightly, and permitting moisture +to enter, results in the growth of rust, which, as it swells in +forming, forces the parts asunder, and may set up considerable +stress.</p> + +<p><span class="pagenum"><a name="Page_80" id="Page_80">[80]</a></span></p> + +<p>Flat bars riveted together by rivets spaced 12 inches +apart may from this cause be forced asunder, as much as <sup>1</sup>⁄<sub>2</sub> +inch, sufficient to set up a stress, with any practicable thickness +of bar, much exceeding the elastic limit.</p> + +<p>Local distortions may occur as the result of imperfect +workmanship or careless erection, causing quite possibly very +severe local stresses; or girder flanges may be out of straight +as a result of riveting up along one side first, instead of +advancing the riveting simultaneously along the whole +breadth of the flange. The injury done by drifting is well +known, and there is reason to think considerable damage is +sometimes done to girderwork during manufacture by rough +treatment to make the work come together; but the author +has little to offer with respect to these matters that is not +common knowledge. It may, however, be pointed out in +passing that a bridge upon the design of which great care +has been expended, with the idea that theoretical propriety +shall not be violated, may be completely spoiled in this +respect by careless construction. Fortunately, both steel +and wrought iron, if of good quality, are long suffering. +Incompetent erection will sometimes result in the true girder +camber not appearing, or in differences as between girders +supposed to be similar. This is not, of course, a deformation +in the sense in which the word has previously been used, but +it is desirable to bear the fact in mind as a possible cause of +defective camber in dealing with questions of deformation.</p> + +<p>The foregoing has reference chiefly to alterations of form +in bridgework of wrought iron or steel, but a case of considerable +interest is that of a cast-iron arched structure, of +which the author made a very complete examination.</p> + +<div class="figcenter"><a name="Fig52" id="Fig52"></a> +<img src="images/illo093a.png" alt="" width="600" height="119" /> +<p class="caption"><span class="smcap">Fig.</span> 52.</p> +<p class="largeimg"><a href="images/lg093a.png">Large image</a> (41 kB)</p> +</div> + +<div class="figcenter"><a name="Fig53" id="Fig53"></a> +<img src="images/illo093b.png" alt="" width="600" height="157" /> +<p class="caption"><span class="smcap">Fig.</span> 53.</p> +</div> + +<p>This bridge, built in 1839, and carrying two lines of +railway, consisted of three spans, 100 feet each, of 10 feet +rise, made up of four inner and two outer ribs, each rib +being in three nearly equal parts; the floor was of timber,<span class="pagenum"><a name="Page_81" id="Page_81">[81]</a></span> +the abutments and piers of masonry. As originally constructed +there was no bracing between the ribs other than +the frames indicated on the plan here given (<a href="#Fig52">Fig. 52</a>),<span class="pagenum"><a name="Page_82" id="Page_82">[82]</a></span> +stretching from outer rib to outer rib in the neighbourhood +of the rib joints, which were simple butts without bolts or +any equivalent means of connection. The floor was, however, +braced in the horizontal plane, and the structure was +also braced over the masonry piers. After forty-two years’ +use supplementary distance-pieces were introduced between +the ribs, but still no bracing between them, or any efficient +means of checking lateral movement. A crack developing +in one of the outer ribs at the crown, led to an investigation +to trace the cause, the bridge then being fifty-four years old. +Careful plumbing of the abutments revealed the fact that +three out of four abutment pilasters were out of the vertical, +as shown in <a href="#Fig52">Figs. 52</a> and <a href="#Fig53">53</a>, the greatest amount being +<sup>5</sup>⁄<sub>8</sub> inch in 6 feet—at that corner from which the cracked rib +had its springing; there was also other evidence of settlement +in an old crack extending from the top of the abutment +to the ground level, although this movement was very old, +certainly as to the greater part. The ribs of this span were +also out of plumb, that which was cracked being 2<sup>1</sup>⁄<sub>2</sub> inches +out at the centre. The joints of the ribs, which, as already +stated, were simple butts, in some cases opened and shut, as +the load passed over, in such a way as to suggest that the +ribs were acting, in a manner, as four-hinged arches, of +which two hinges were at the springing, and the other two +at the joints, one of which would for most positions of the +load be out of use, reducing the rib to the three-hinged condition; +in other words, as the rolling load passed over the +span, one or other of the two joints of a rib would “gape” +an appreciable amount at the bottom or at the top. Observations +were taken by means of a theodolite placed below, +either upon the bank or upon the tops of the masonry piers, +sighting upon suitable scales attached to the ribs to ascertain +the amounts of vertical and horizontal movement during the<span class="pagenum"><a name="Page_83" id="Page_83">[83]</a></span> +passage of trains over the bridge. The principal results are +set forth in the following table<span class="nowrap">:—</span></p> + +<p class="center"><span class="smcap">Movements of Cast-Iron Ribs under Live Load in a Bridge<br /> +of Three 100-Ft. Spans.</span></p> + +<table class="nowrap" summary="Table page 83"> + +<tr class="bt bb"> +<th colspan="3" class="center padl1 padr1 br">—</th> +<th class="center padl1 padr1 br">Fall<br />in<br />Inches.</th> +<th class="center padl1 padr1 br">Rise<br />in<br />Inches.</th> +<th class="center padl1 padr1">Lateral<br />Movement<br />in Inches.</th> +</tr> + +<tr> +<td colspan="6" class="center highline"><i>Span No. 1.</i></td> +</tr> + +<tr> +<td class="center padl1 padr1">At</td> +<td class="center padl1 padr1">A.</td> +<td class="left padr1 br">Up road loaded</td> +<td class="center padl1 padr1 br">·20</td> +<td class="center padl1 padr1 br">·08</td> +<td class="center padl1 padr1">·04</td> +</tr> + +<tr> +<td class="center padl1 padr1">„</td> +<td class="center padl1 padr1">A.</td> +<td class="left padr1 br">Down road loaded</td> +<td class="center padl1 padr1 br">·08</td> +<td class="center padl1 padr1 br">·03</td> +<td class="center padl1 padr1">·04</td> +</tr> + +<tr> +<td class="center padl1 padr1">„</td> +<td class="center padl1 padr1">B.</td> +<td class="left padr1 br">Down road loaded</td> +<td class="center padl1 padr1 br">·14</td> +<td class="center padl1 padr1 br">No record.</td> +<td class="center padl1 padr1">·02</td> +</tr> + +<tr> +<td colspan="6" class="center highline"><i>Span No. 2.</i></td> +</tr> + +<tr> +<td class="center padl1 padr1">At</td> +<td class="center padl1 padr1">C.</td> +<td class="left padr1 br">Up road loaded</td> +<td class="center padl1 padr1 br">·40</td> +<td class="center padl1 padr1 br">·13</td> +<td class="center padl1 padr1">Slight.</td> +</tr> + +<tr> +<td class="center padl1 padr1">„</td> +<td class="center padl1 padr1">C.</td> +<td class="left padr1 br">Down road loaded</td> +<td class="center padl1 padr1 br">·10</td> +<td class="center padl1 padr1 br">·05</td> +<td class="center padl1 padr1">„</td> +</tr> + +<tr> +<td colspan="6" class="center highline"><i>Span No. 3.</i></td> +</tr> + +<tr> +<td class="center padl1 padr1">At</td> +<td class="center padl1 padr1">D.</td> +<td class="left padr1 br">Up road loaded</td> +<td class="center padl1 padr1 br">·22</td> +<td class="center padl1 padr1 br">No record.</td> +<td class="center padl1 padr1">No record.</td> +</tr> + +<tr class="bb"> +<td class="center padl1 padr1">„</td> +<td class="center padl1 padr1">D.</td> +<td class="left padr1 br">Down road loaded</td> +<td class="center padl1 padr1 br">·15</td> +<td class="center padl1 padr1 br">Slight.</td> +<td class="center padl1 padr1">Slight.</td> +</tr> + +</table> + +<blockquote> + +<p><span class="smcap">Note.</span>—The lateral movements are to either side of the mean +position.</p></blockquote> + +<p>The particulars for spans 2 and 3 were obtained with +the instrument set up on the pier between these spans. The +tremor of this pier was such that no useful readings for +lateral movement could be obtained. Further, as the rolling +load came upon these spans, the effect was to rock the pier +to an extent vitiating the readings for vertical displacement; +but by sighting upon the fixed abutment, and observing the +amount of this rocking, suitable corrections were made in +the apparent rib movements. The figures given in the table +are thus corrected. The pier rocking was equivalent, as an +extreme, to an inclination from the vertical of 1 in 3200. +An attempt to measure the horizontal movement of the pier-top<span class="pagenum"><a name="Page_84" id="Page_84">[84]</a></span> +was unsuccessful, owing to the impracticability of setting +up the instrument in a suitable position, sufficiently near to +the pier to enable readings to be satisfactorily taken. This +horizontal displacement probably amounted to about <sup>1</sup>⁄<sub>16</sub> inch +either way. The rise and fall of the arches, and rocking +either way of the piers, varied, as might be expected, in +accordance with the position of the running load with respect +to the spans. Summarising the results, the greatest vertical +movements downwards were 0·20 inch, 0·40 inch, and 0·22 +inch for spans Nos. 1, 2, and 3, the upward movements being +0·08 inch and 0·13 inch for the first and second spans, +there being no recorded result of this kind for the third +span. With adjacent ribs loaded, the movement of the +ribs unloaded was one from one-third to one-half of the full +amounts. It is to be noted that the lateral displacement in +no case exceeded 0·04 inch either way, nor were the vertical +movements exceptional; yet, as a matter of sensation, when +seated upon the ironwork, it was a little difficult to believe +them really so moderate. Observations were also made to +ascertain the rise of the arches from winter to summer temperatures, +with the result that this was found to be 0·45 +inch, 0·45 inch, and 0·55 inch for the spans in order, the +extreme temperatures being fairly representative of the +English winter and summer. The structure was, as a consequence +of the examination, efficiently braced by diaphragms +between the ribs, and diagonals following the arch ribs round +from springing to springing, with satisfactory results. The +crack already referred to, and its probable causes, will be +dealt with under “<a href="#Page_141">Cast-Iron Bridges</a>.” Eventually this +bridge was reconstructed to meet the requirements of growing +engine-loads.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_85" id="Page_85">[85]</a></span></p> + +<h2>CHAPTER VIII.<br /> +<span class="chaptitle">DEFLECTIONS.</span></h2> + +<p>Deflection, considered only as a fraction of the span, and +without regard to other conditions affecting it, is of very +little use as an indication of a girder’s fitness for its work; +but when taken with reference to the depth of the girder, +the nature and amount of the load producing flexure, and, +further, with regard to the quality of the workmanship and +normal properties of the material of which the beam is constructed, +it may be of some little service in helping to form +a reliable opinion. This consideration applies with less +force, perhaps, to new work than to old, in which there may +be unknown influences at work, or unknown defects which +by excessive deflection may be betrayed. Though too much +importance should not be attached to results of deflection +tests in any one instance, yet the practice of observing such +movements, and considering them with reference to each +case, gives a good general idea of what may be expected in +a fresh instance, any material departure from which should +be a reason for specific inquiry as to the cause. A further +reason with new work is found in the evidence it affords as +to whether the loads carried travel to the supports really as +intended, or by some route not contemplated; or, in the case +of floor beams, in what way the load is distributed amongst +them, if, indeed, there be any such distribution.</p> + +<p>The author has commonly found that new work gives +greater deflections than old—i.e., while calculation gives +the same result for each, it does not apply equally well to +both. The differences may be accidental, but are probably<span class="pagenum"><a name="Page_86" id="Page_86">[86]</a></span> +due to other causes, perhaps to the fact that new work has +not by repeated applications of load lost the resilience of +parts liable to considerable local stress, such as is very liable +to occur at connections, so that the deflection is, whilst new, +greater than after many years’ use, by which time such parts +may develop a definite “set,” and contribute in a less degree, +or not at all, to the total elastic deformation.</p> + +<p>It is also possible, as already suggested, that repeated +high stress may reduce the ratio of strain to stress, the +material gradually becoming more rigid, the modulus of +elasticity being, in fact, increased.</p> + +<p>In girders of ordinary construction, the major part of +the deflection is due to the booms, the remainder to the web; +the latter is for plate girders a small amount only, and is +commonly neglected, but for open web constructions it may +be quite appreciable. For any given type of web arrangement +the deflection due to the web will, for all depths, remain +a constant quantity for the same span and unit stress; and +though a moderate fraction of the whole deflection for a +shallow girder, it may be a very considerable part for a girder +of great depth, in which that part due to the booms is, of +course, smaller, since the deflection due to these varies +inversely as the girders’ depths.</p> + +<p>Deflection, being dependent upon the elasticity of the +material, is of necessity very largely influenced by the value +of its modulus E, itself liable to considerable variation, and +is increased in a small degree by the yield of joints and rivets, +which effect, apart from the initial “set” of the girders, +appears to be negligible. The stiffness of members in resisting +angular distortion at connections must also, for open-web +riveted structures, affect the result, making it somewhat less, +and, finally, section excess at joints and gusset attachments +has an influence in modifying deflection as compared with +that due to the normal gross sections simply.</p> + +<p><span class="pagenum"><a name="Page_87" id="Page_87">[87]</a></span></p> + +<p>From these considerations it is apparent that any simple +deflection formula must be largely empiric in its nature. +For plate girders of uniform depth and flange stress, the +writer has found the following to give good results<span class="nowrap">:—</span></p> + +<p class="formula"><span class="division"><span class="num">S<sup>2</sup></span><span class="denom">D × C</span></span> × <i>f</i> = deflection in inches.</p> + +<p>The span S and depth D are, as a matter of convenience, +taken in feet; the constant C is for wrought iron 3500, and +for mild steel 4000; <i>f</i> is the mean of the extreme tensile +and compressive stresses of the booms, in tons per square +inch, estimated upon the gross sections.</p> + +<p>This, though satisfactory for plate girders, is not so suited +to girders having open webs, in which the deflection will +more nearly be</p> + +<p class="formula"><span class="fsize150">(</span><span class="division"><span class="num">3S</span><span class="denom">C</span></span> + <span class="division"><span class="num">S<sup>2</sup></span><span class="denom">D × C</span></span><span class="fsize150">)</span> × <i>f</i>,</p> + +<p>the constant C being 3900 and 4450 for iron and steel respectively. +The latter values of C correspond to normal +values of the modulus of elasticity of 11,700 and 13,350 tons +for iron and for steel, it being assumed that any slight rivet +yield is off-set by any small section excess—say, 5 per cent.; +it may, however, happen that section excess is greater than +assumed, in which case some allowance may properly be made +for this by increasing C.</p> + +<p>To adapt the formulæ to girders other than those having +parallel booms and uniform stress, the results, as deduced +above, may be multiplied by constants given in column B of +the Table given on <a href="#Page_93">page 93</a>.</p> + +<p>The practice of adopting for E in deflection formulæ a +quantity much smaller than its nominal amount, with the +object of allowing in riveted girder work for the yield of +rivets and of joints, can hardly now be defended, whatever +may have been a case at a time when workmanship was much<span class="pagenum"><a name="Page_88" id="Page_88">[88]</a></span> +inferior, when there was no machine riveting, and joints +were, owing to the small weight of plates and bars, three +times as numerous.</p> + +<p>The initial “set” of a girder consequent upon first loading +is a quantity quite distinct from deflection proper, and may +be so small as to be negligible, or read 10 per cent. of the +true deflection, varying with design and workmanship.</p> + +<p>No estimate of girder deflection can be even approximately +true if there is, at the level of the top or bottom flanges, a +plated or otherwise rigid floor system which is not taken into +account, as this will have the effect of very materially reducing +the boom stress. To neglect this influence, where it +exists, must necessarily lead to disappointing results, and it +is quite practicable in many instances to include it in the +calculation.</p> + +<p>The influence of angular distortion between the various +members has been neglected. It may be pointed out, however, +that the resistance accompanying these movements in +girders having riveted connections, though unimportant as +affecting deflection, is worth some consideration in regard +to secondary stress. For girders of similar type and unit +stress these angular variations will be the same in amount +for any span, but will generally be of less importance in large +girders than in small, because in large girders the ratio of the +breadth of members to their length is commonly less.</p> + +<p>When determining the probable deflection of any girder +of exceptional figure, it will be found convenient to make a +strain diagram—an old device, in which the actual alterations +of length being ascertained for all members, the girder is +carefully set out to a suitable scale, with the lengths of +members increased or reduced by the actual estimated +amounts. The distorted figure resulting will then give the +probable deflection. The value of E for this purpose should +never be taken at less than the normal amount, and may for<span class="pagenum"><a name="Page_89" id="Page_89">[89]</a></span> +a considerable excess of metal in joints and gussets be made +as much as 10 per cent. greater, this being a convenient +means of making the necessary correction.</p> + +<p>The effect of loads quickly applied may here be considered +in connection with elastic deformations of girders +of the same span, but different depths. If these be designed +for similar loads and unit stresses, the deflections due to +webs and booms of the girders compared will bear the same +relation, each to each, as do the weights, whether in both +cases the loads be inert or quickly applied, from which it +follows that the mechanical “work” done by the loads in +falling through the deflection heights is, neglecting inertia, +always in proportion to the girderwork weights, and is a +similar amount per ton, which as the total length of members +remains substantially unaltered, corresponds to a similar +amount of work per unit of section, or similar stress, irrespective +of the depth of the girders.</p> + +<p>But for a “drop” load, as when there is some obstruction +upon a railway bridge, there will be in addition a further +amount of work to be absorbed, which is to be considered +the same whatever the girder’s depth, and will for deep +girders be a larger amount per ton of girderwork than in +those that are shallow; this, taking effect on members of +the same aggregate length, but lighter, will develop a higher +stress than in girders of lesser depth, more particularly in +the booms.</p> + +<p>The influence of the girder’s inertia in modifying drop-load +effects will also be less marked in deep—i.e., light—girders +than in girders shallow and heavy.</p> + +<p>It is, notwithstanding all this, desirable that the depth +of main girders should be liberal for economy’s sake, and +also that of floor beams, for reasons already dealt with; the +probability of the drop load is somewhat remote, and, though +possible, would simply induce, if it occurred, an increment<span class="pagenum"><a name="Page_90" id="Page_90">[90]</a></span> +of stress rather more important in deep girders, making it +specially desirable in these to give particular attention to +the detailing of any connections liable to suffer from impact +effects.</p> + +<p>It should be remarked that for short and very flexible +beams, generally outside the limits of practice, there may +also be, under quickly moving loads, a material increase of +stress due to the centrifugal effort of the load on running +round the deflection curve, and in rising upon the steep part +of the curve beyond the girder’s centre. Where advisable, +these effects may be modified by cambering the rail.</p> + +<p>For pin bridges in which there may be spring in the +pins, excess stress in some eye-bars due to inequalities of +length, and a want of that rigidity peculiar to riveted structures, +the deflection will be greater than above indicated for +girders of the ordinary English type.</p> + +<p>The method in common use for measuring the deflections +of girders but a moderate distance above the ground +by means of sliding-rods, though crude, gives, with care, +results sufficiently accurate for most practical purposes; but +some points necessary to remember may be mentioned with +propriety. The lower rod should rest firmly upon something +solid, say a stone, well bedded and free from any tendency +to rock; the upper end should bear against some part of +the girder above, presenting a hard surface, free from dirt +or scale, and as the running load approaches the bridge it +should be ascertained that there is no slack, that the rods +bear hard at the top and bottom. The upper end having +been depressed, care is to be exercised to make sure of the +reading before the rods alter their relation to each other. +These precautions are so self-evident that an apology is +almost necessary for mentioning them.</p> + +<p>To ascertain deflections with a single pair of rods is only +allowable when the girders rest firmly on their bearings; if<span class="pagenum"><a name="Page_91" id="Page_91">[91]</a></span> +felt has been placed under the girder ends, or if the bedstones +are insecure or rocking, it is necessary to use three +pairs of rods, one pair at the middle and a pair at each end, +in which case the mean of the two end readings must be +deducted from the reading of that at the centre to get the +desired result.</p> + +<p>In the case of a number of spans in series, each resting +upon sill girders common to two sets of bearings, this +method also gives results of indifferent reliability, as the +depression of each end may be greater as the travelling load +comes upon and leaves the span than when it is precisely +over the middle, and it is in general out of the question to +secure by this mode simultaneous readings for a particular +position of the running load, which are what is required.</p> + +<p>The author suggests, as a means of ascertaining deflections +free from these objections, that it should be done by +first measuring the slope at one end, and from this deducing +the deflection at the centre.</p> + +<p>This is to be accomplished by means of a little instrument, +consisting of a telescope with cross-hair sights, and +fitted with a reflecting prism at the eye-piece capable of +being turned round, so that the observer has a wide choice +as to the position he assumes with reference to the instrument, +and may look either directly through it, or at right +angles to the axis of the telescope. This is clamped at one +end of the girder over the bearing, at the other end a scale +is secured, to which the telescope is directed, the cross hair +being made to sight on the zero of the scale, or the reading +noted. For a girder supposed to deflect to uniform curvature +(say, with uniform depth and uniform stress, the +ordinary case) the reading observed will be four times the +deflection; every <sup>1</sup>⁄<sub>10</sub> inch actual reading on the scale will +correspond to <sup>1</sup>⁄<sub>40</sub> inch of girder deflection.</p> + +<p>Apart from the deflection, this method gives a ready<span class="pagenum"><a name="Page_92" id="Page_92">[92]</a></span> +means of observing the end slope, a quantity of equal value +for purposes of comparison. As with girders of similar proportions, +and similarly stressed, the deflection will at all +spans be the same fraction of the span; so should the end +slope be a constant quantity under similar conditions, the +diagram, <a href="#Fig54">Fig. 54</a>, will make the principle quite clear.</p> + +<div class="figcenter"><a name="Fig54" id="Fig54"></a><a name="Fig55" id="Fig55"></a><a name="Fig56" id="Fig56"></a><a name="Fig57" id="Fig57"></a> +<img src="images/illo104.png" alt="" width="350" height="429" /> +<p class="caption"><span class="smcap">Figs.</span> 54 to 57.</p> +</div> + +<p>Strictly the character of the deflection curve is slightly +modified by that part of the deflection due to the web; so +that the depression at the centre would, in the case assumed +above, be somewhat more than one-fourth part of the end +reading, and generally will be a larger fraction of the reading +than that deduced from a consideration of flange stress<span class="pagenum"><a name="Page_93" id="Page_93">[93]</a></span> +simply. In <a href="#Fig55">Figs. 55 to 57</a>, which are intended to explain +this, it will be noticed that deflection due to the web is +shown straight-lined from the bearings to the centre of the +girder; this is strictly true only for a girder correctly designed +for an immovable distributed load; but as there +should be for girders intended for a travelling load, some +excess in web members near the centre under the condition +of uniform loading, the point of the figure should be rounded +off to be in agreement with this case, though it is left as +shown in the diagram for the sake of simplicity.</p> + +<p>Suitable constants, including the corrections necessary, +are given in column A of the table annexed for a few typical +cases, and by these constants the actual readings should be +multiplied to find the deflection. The constants have been +worked out for depths of one-tenth the span; for greater +depths they should be slightly more, and for smaller depths +somewhat less, but they may be used between the limits of +one-sixth and one-fourteenth, with a maximum error hardly +exceeding 5 per cent., and generally much less.</p> + +<p>The figures in column B relate to the formulæ previously +stated, and apply equally well to all depths.</p> + +<p class="center"><span class="smcap">Tables of Multipliers for Deflection.</span></p> + +<table summary="Table page 93"> + +<tr> +<td class="left padr3"><i>Uniform Stress</i>:</td> +<td class="center padl1 padr1">A.</td> +<td class="center padl1 padr1">B.</td> +</tr> + +<tr> +<td class="left top padl3 padr3">Girders of uniform depth, varying flange section</td> +<td class="center bot padl1 padr1">0·27</td> +<td class="center bot padl1 padr1">1·00</td> +</tr> + +<tr> +<td class="left top padl3 padr3">Hog-backed girders, ends half of centre depth, varying flange section</td> +<td class="center bot padl1 padr1">0·24</td> +<td class="center bot padl1 padr1">1·08</td> +</tr> + +<tr> +<td colspan="3" class="left padr3"><i>Varying Stress</i>:</td> +</tr> + +<tr> +<td class="left top padl3 padr3"><a name="FNanchor_1" id="FNanchor_1"></a><a href="#Footnote_1" class="fnanchor">[A]</a>Girders of uniform depth and flange section</td> +<td class="center bot padl1 padr1">0·32</td> +<td class="center bot padl1 padr1">0·87</td> +</tr> + +<tr> +<td class="left top padl3 padr3"><a href="#Footnote_1" class="fnanchor">[A]</a>Hog-backed girders (as above), but uniform flange section</td> +<td class="center bot padl1 padr1">0·29</td> +<td class="center bot padl1 padr1">0·97</td> +</tr> + +<tr> +<td class="left top padl3 padr3"><a href="#Footnote_1" class="fnanchor">[A]</a>Bow-string girders of uniform flange section</td> +<td class="center bot padl1 padr1">0·16</td> +<td class="center bot padl1 padr1">1·30</td> +</tr> + +</table> + +<div class="footnote"> + +<p><a name="Footnote_1" id="Footnote_1"></a><a href="#FNanchor_1"><span class="label">[A]</span></a> For uniform loading.</p></div> + +<p><span class="pagenum"><a name="Page_94" id="Page_94">[94]</a></span></p> + +<p>It is apparent that, if preferred, the scale, instead of +being in inches, divided suitably, may, for each type of +girder, be amplified to the proper degree, so that the amount +of the deflection may be read off at once.</p> + +<p>This method of dealing with deflections is quite independent +of the character of the bearings, and is applicable +to girders at any height above ground or over water; but +its use would hardly be practicable for very small beams, or +those in an awkward position, or near which it would be +impossible to remain with a running load upon the bridge.</p> + +<p>There is a possible source of error in the use of the +instrument, most likely to occur with triangulated girders, +with which, if the instrument is placed at the top of an end +post, the reading observed may be the joint effect of deflection +and of local flexure of the members meeting near the +telescope. This may be tested, and, if necessary, allowed +for, by first sighting upon a scale at the next apex, and +observing the effect of the moving load. Again, as girders +sometimes cant towards the running load, if the instrument +is placed on one edge of a girder, and the cantings of the +two ends are dissimilar, a false reading will result, which +may be amended by ascertaining the amount of cant at each +end, and correcting for the effect of the difference between +the cants upon the observation. Only in exceptional cases +is it likely that either of these considerations would need +attention.</p> + +<p>The author has secured with this instrument very promising +results, notwithstanding that under a running load there +is a slight haziness of the scale as seen through the telescope, +due to “dither,” largely the result of imperfections which +may be remedied.</p> + +<p>Deflections may sometimes be conveniently taken, by a +quick-eyed observer, with a good surveyor’s level and a +specially-divided staff held at the centre of the girder. The +divisions preferred by the author for this purpose are <sup>1</sup>⁄<sub>10</sub> inch,<span class="pagenum"><a name="Page_95" id="Page_95">[95]</a></span> +plainly marked, which may be seen at 50 feet distance with +sufficient clearness to make possible readings by estimation +between the divisions to, say, <sup>1</sup>⁄<sub>50</sub> inch. But it is clearly +desirable not to rely upon a single observation only, where +all the evidence is gone so soon as the sight has been taken.</p> + +<p>In rail-bearers, or other short girders, it may not be +practicable to adopt such methods, either on account of an +inability to find a suitable place for the instrument, or to +read with any telescope with sufficient promptitude as the +load passes rapidly over. The use of rods may also be out +of the question, as the errors attending their manipulation +may be serious where but a small movement has to be noted, +this being complicated in some instances by the bearings +being insecure, and working to an extent which obscures the +measurement sought. In such cases it is preferable to use +a stiff slat lying along the girder, which bears, through +short blocks over the girder bearings, upon the flanges; the +deflection is then read by direct measurement of the girder’s +depression at the centre, relative to the slat.</p> + +<p>The author is, unfortunately, not able to give any precise +information on the effect of running-load as against a +load that is stationary in connection with girder deflections. +It is by no means easy in ordinary work upon a railway to +secure facilities for making such comparative tests. It may, +however, be confidently stated, as a result of such observations +as he has made, that the deflection due to a load coming +rapidly upon a bridge is, as to the main girders of, say, a +50 feet span, but little greater than that due to the same +load stationary; it may be, perhaps, 5 to 10 per cent. more.</p> + +<p>It is evident that to determine the precise difference +where the quantity to be measured is so small needs apparatus +of a more delicate character than that in common use, +and the control of an engine, or engines, for the purpose of +making the special tests, conditions which on a busy line can +only be secured by special arrangements previously made.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_96" id="Page_96">[96]</a></span></p> + +<h2>CHAPTER IX.<br /> +<span class="chaptitle">DECAY AND PAINTING.</span></h2> + +<p>The author has collected particulars as to the amount and +rate of rusting in metallic structures which are of some +interest. In all such instances it is very necessary to note +the conditions which have obtained during the process of +wasting, as without this, misleading conclusions may be +drawn. The information given relates in all cases to wrought +iron, unless otherwise stated.</p> + +<p>A plate-girder bridge, having girders under rails, was +found to be badly rusted. The atmospheric conditions were +unusually trying, the air being damp and impregnated with +acid fumes from adjacent steel works. That the wasting +was largely due to this latter cause was indicated by the fact +that the girders nearest to the steel works suffered more than +those farther removed and partly sheltered from the corrosive +influence.</p> + +<p>The webs were in places eaten right through, having +lost a mean amount of about <sup>1</sup>⁄<sub>8</sub> inch full on each surface in +twenty-eight years. Painting had not been well attended to.</p> + +<p>In a similar bridge, not a great distance from this, but +sufficiently far away to modify the conditions for the better, +considerable wasting was also observed, but more particularly +where the girders had been built into masonry, which, +loosening with the constant movement of the girder-ends, +had allowed moisture to collect, and rust to develop, without +the chance of repainting these surfaces. The amount of +waste at the places indicated was, as in the last case, about<span class="pagenum"><a name="Page_97" id="Page_97">[97]</a></span> +<sup>1</sup>⁄<sub>8</sub> inch on each face, and in the same time, other parts of +the girders having suffered less.</p> + +<div class="figcenter"><a name="Fig58" id="Fig58"></a> +<img src="images/illo109.png" alt="" width="350" height="60" /> +<p class="caption"><span class="smcap">Fig.</span> 58.</p> +</div> + +<p>A third plate-girder bridge, with outer main girders, +cross-girders, and plated floor, carrying a road over a railway +and sidings, and which was known to have been +neglected in the matter of painting, was very badly rusted, +both as to the cross-girders and floor-plates. The atmosphere +was somewhat damp; the chief cause of deterioration +was, however, the smoke and steam from locomotives, which +frequently stood for some time, during shunting operations, +directly under the bridge. The webs of the cross-girders, +which were originally <sup>1</sup>⁄<sub>4</sub> inch thick, had rusted into occasional +holes during fourteen years—i.e. <sup>1</sup>⁄<sub>8</sub> inch from each +surface in that time. When removed a little later the +wasting was so complete that it was possible to knock out +with a light hammer the remains of the web between flanges +and stiffeners, so as to leave an open frame only. One of +the cross-girders was so treated by the men engaged upon +the work, when it presented the appearance shown in <a href="#Fig58">Fig. 58</a>.</p> + +<p>In another case—that of a bridge with lattice girders +under rails—the ends were built into masonry, which had, +of course, loosened, with the usual result. The air of the +locality was certainly pure, but somewhat damp. The general +condition of the ironwork was good, but end-bars of the +diagonal bracing, where they had been closed in, had lost +<sup>1</sup>⁄<sub>8</sub> inch on each surface in thirty-three years. The top flanges +immediately under the timber floor were in a very fair state, +which is of some interest when it is considered that these<span class="pagenum"><a name="Page_98" id="Page_98">[98]</a></span> +were made of steel of the same kind as that already noticed +as being used in the construction of small girders (see <a href="#Fig46">Fig. +46</a>, <i>ante</i>), described in the chapter upon “<a href="#Page_61">High Stress</a>,” both +cases dating from the year 1861. The painting upon the +lattice-girder bridge had been pretty well attended to; but +in the case of the small steel girders it had been greatly—perhaps +altogether—neglected; this, coupled with adverse +atmospheric conditions, had produced the result that the +rate of rusting had for the small girders been much greater +than that of the steel top flange referred to, being fully +<sup>1</sup>⁄<sub>8</sub> inch on each surface, as against a negligible amount +under the more favourable circumstances.</p> + +<p>Girder-work over sea-water, as in piers, seems to rust at +a sensibly greater rate than inland work under average conditions; +but it is hardly practicable to make any strict +comparison, as in either case the rate of oxidation is so +much affected—even controlled—by the care bestowed upon +the structures. This general conclusion is based upon the +results of examination of wrought-iron girder-work over sea-water +of ages varying from fourteen to forty-four years. It +should be remarked, however, that in one case steel girders +but five years old, and which were frequently wetted with +sea-spray, were found to be wasting rather badly—the paint +refusing to keep upon the surface.</p> + +<p>It may be concluded from the above instances, and from +others which have come under notice, that wrought-iron +work, if not properly cared for in respect to painting, or +under conditions otherwise bad, may be expected to rust at +a rate which corresponds to the loss of <sup>1</sup>⁄<sub>8</sub> inch on each surface +in from fifteen to thirty years; but with proper care as +to painting, and exclusive of exceptionally bad conditions, +it does not appear to waste at any measurable rate. In some +instances, upon scraping the paint from girders which had +been in use for thirty years, the author has found, beneath the<span class="pagenum"><a name="Page_99" id="Page_99">[99]</a></span> +original red lead, the metallic surface bright and clean, +showing no trace of rust.</p> + +<p>Of ordinary steelwork the same cannot be said, the common +experience being that mild steel is very liable to be +attacked by rust. With passable care in the bridge-yard +during manufacture, such that with wrought iron no after-trouble +would be noticeable, steel is very liable to show, +within a year of being built up, numerous little blisters on +the painted surface; any one of these being broken away +discloses a small rust-pit. This is more often seen on the +flange surfaces (horizontal) than on web surfaces (vertical), +but it is probable the position has little to do with the +matter, and that it is rather due to the fact that rust has +been earlier started on the flange-plates, upon being put +through the drilling-machines and inundated with slurry, +which occurs only to a more limited extent with webs having +fewer holes. The heads of steel rivets do not show this +tendency to “pit,” or to early development of rust. The +riveting is about the last operation in making a girder, each +rivet being freed of all rust by heating, and quickly coming +under the protection of oil or paint. It may happen in this +way that the heads of rivets on a girder may be exposed +without protection for as many hours only as the rest of the +work for weeks, which fully accounts for the difference in +behaviour.</p> + +<p>The essential point to be observed in all steelwork is to +prevent, if possible, the first development of rust, for once +begun it is much more difficult to arrest than in iron; for +this reason, oiling of all material for a steel bridge, at a very +early stage of its existence, cannot be too strongly insisted +upon. This practice, however, makes the work so objectionable, +and even dangerous when being lifted—because of the +liability to slip—to the men engaged upon it, that it is +commonly very difficult to ensure it being done sufficiently<span class="pagenum"><a name="Page_100" id="Page_100">[100]</a></span> +soon to satisfy a careful inspector. If the work is carried +out under cover, the requirement is less urgent. Strictly, +all material should be oiled so soon as rolled, but the author +does not remember to have seen this done at any of the +mills he has visited, though it is common enough to find it +specified.</p> + +<p>Ironwork does not need the extreme care which should +be bestowed upon steelwork, but it is desirable that it should +be painted as soon as possible, the surfaces being first +thoroughly cleaned.</p> + +<p>There is, probably, for painting girder work nothing to +beat good red lead as a protective coating; but there is considerable +difficulty in getting it reasonably pure, without +which quality its utility will be greatly reduced. The question +of purity will, however, be found to be largely a question +of price. It may be stated broadly that, whether for steel +or for iron, the first protective covering is, perhaps, the most +important of any it will ever receive.</p> + +<p>In repainting old work, care should be taken to remove +all traces of rust previous to laying on the new coat. It is +not an altogether uncommon practice to repaint old structures +by dealing only with the parts readily accessible, which, +being less liable to rust, probably but little need it; leaving +those parts which are difficult of access, and where rust is +developing, untouched; treating the whole business as a +matter of appearance simply. This, it need hardly be said, +is indefensible. It is better rather to neglect the surfaces +freely exposed and ventilated, and devote the whole care +upon those other parts, confined and difficult to get at; +taking the trouble necessary to remove ballast, timber, or +whatever may obstruct the operation, in order that the bad +places may be thoroughly scraped, and then painted. Those +parts which most need attention may cost, perhaps, to reach—and +deal with when exposed—ten times as much per yard<span class="pagenum"><a name="Page_101" id="Page_101">[101]</a></span> +of surface as the rest of the superfices, which needs little, +and is always accessible; but the cost should not deter the +proper carrying out of the work, as it will prove the very +worst sort of economy to deal with painting in a perfunctory +manner.</p> + +<p>It should be noted that girder work, whether of wrought +or cast iron, when embedded in lime or cement concrete, or +mortar, generally proves to be very well preserved, provided +that close contact has obtained. Cast-iron girders, when +carrying jack arches resting upon the bottom flanges, are +found after long use to be in remarkably good order, when +finally taken out, having, indeed, the surface appearance of +new girders. Much the same remarks apply to girders of +wrought iron carrying jack arches, where protected by the +brickwork; provided that the girders are sufficiently stiff to +minimise deflection, and allow the masonry or brickwork to +adhere to the surfaces.</p> + +<p>Such girders are in a very different condition to those +previously referred to, in which the ends of the girders, +carrying a light floor structure, are built into masonry where +the deflection slope is greatest; though, apart from the few +cases where adherence can be relied upon, building-in is an +undesirable practice, and has the disadvantage that after-examination +is only possible by removing portions of the +masonry, which it is evident would very seldom be resorted +to.</p> + +<p>Cast iron has ordinarily—unlike wrought iron or steel—great +capacity for resisting rust, and will, after many years +of absolute neglect, appear but little the worse; an advantage +which is the more pronounced when considered relatively +to the greater thickness of the thinnest parts in +cast-iron girders, the percentage of waste being proportionately +lessened.</p> + +<p>Cast iron does, however, behave somewhat badly in sea-water,<span class="pagenum"><a name="Page_102" id="Page_102">[102]</a></span> +the metal sometimes losing its original character, and +becoming in time quite soft; though, if not worn away, as +by the attrition of shingle, maintaining its original bulk.</p> + +<p>Of some forty-five cast-iron piles belonging to various +structures, examined whilst engaged upon sea-pier work for +Mr. St. George-Moore, though the author found somewhat +diverse results, in no case did there appear to be any general +softening of the whole thickness, but a distinct change for +some definite distance inwards, generally to be decided without +difficulty, beyond which the metal appeared to retain +its original character. In all cases any material depth of +softening was found close to the ground, this depth rapidly +decreasing higher up, till, at a height of 5 feet, but little if +any softening could be detected. At 2 feet above ground +the softening was frequently but one-quarter of that at +ground level. There was, too, often a considerable difference +in the behaviour of different piles in the same structure +under similar conditions; one pile being found to have only +one-fourth part of the softening noticed in others, or possibly +none at all. For six different structures the amount of +softening near ground level, of about twenty-five piles +examined, was as given in the table on the next page.</p> + +<p>The greatest depth of softening found (see No. 2) was +<sup>9</sup>⁄<sub>16</sub> inch, 1 foot above ground, in a pile thirty-six years old. +The decayed material when removed was of a soft, greasy +consistency, perfectly black, which a few hours later was +found to have changed to a dry yellow powder, by the rapid +absorption, it may be supposed, of atmospheric oxygen. It +is apparent, therefore, from this example that deterioration +may proceed to a considerable depth; but it should be +observed that other piles of the set showed softening at +ground level of <sup>1</sup>⁄<sub>8</sub> inch only.</p> + +<p class="center"><span class="smcap">Softening of Cast-Iron Piles in Sea-Water.</span><span class="pagenum"><a name="Page_103" id="Page_103">[103]</a></span></p> + +<table class="nowrap" summary="Table page 103"> + +<tr class="bt bb"> +<th class="center padl1 padr1 br">No.</th> +<th colspan="2" class="center padl1 padr1 br">Age.</th> +<th colspan="2" class="center padl1 padr1 br">Maximum<br />Softening.</th> +<th colspan="6" class="center padl1 padr1 br">Maximum<br />Rate of<br />Softening.</th> +<th colspan="5" class="center padl1 padr1 br">Mean Rate<br />of<br />Softening.</th> +<th class="center padl1 padr1 br">Quality<br />of<br />Metal.</th> +<th class="center padl1 padr1 wrappable">Materials Entered<br />by Piles.</th> +</tr> + +<tr> +<td class="center top br">1</td> +<td class="right top padl1">17</td> +<td class="center top padr1 br">years</td> +<td class="center top"><sup>5</sup>⁄<sub>16</sub></td> +<td class="center top br">in.</td> +<td class="center top padl1"><sup>1</sup>⁄<sub>8</sub></td> +<td class="center top">in.</td> +<td class="center top">in</td> +<td class="right top padr0">7</td> +<td> </td> +<td class="center top padr1 br">years</td> +<td class="center top padl1"><sup>1</sup>⁄<sub>8</sub></td> +<td class="center top">in.</td> +<td class="center top">in</td> +<td class="right top">15</td> +<td class="center top br">years</td> +<td class="center top br">Soft</td> +<td class="left top padl1 padr1 wrappable">Extremely soft sandstone.</td> +</tr> + +<tr> +<td class="center top br">2</td> +<td class="right top">36</td> +<td class="center top br">„</td> +<td class="center top"><sup>9</sup>⁄<sub>16</sub></td> +<td class="center top br">„</td> +<td class="center top padl1"><sup>1</sup>⁄<sub>8</sub></td> +<td class="center top">„</td> +<td class="center top">in</td> +<td class="right top padr0">8</td> +<td class="left top padl0"><sup>1</sup>⁄<sub>2</sub></td> +<td class="center top br">„</td> +<td colspan="5" class="center top br">No result</td> +<td class="center top br">„</td> +<td class="left top padl1 padr1 wrappable">Rubble mound.</td> +</tr> + +<tr> +<td class="center top br">3</td> +<td class="right top">32</td> +<td class="center top br">„</td> +<td class="center top"><sup>3</sup>⁄<sub>8</sub></td> +<td class="center top br">„</td> +<td class="center top padl1"><sup>1</sup>⁄<sub>8</sub></td> +<td class="center top">„</td> +<td class="center top">in</td> +<td class="right top padr0">11</td> +<td> </td> +<td class="center top br">„</td> +<td class="center top padl1"><sup>1</sup>⁄<sub>8</sub></td> +<td class="center top">in.</td> +<td class="center top">in</td> +<td class="right top">15</td> +<td class="center top br">years</td> +<td class="center top padl1 padr1 br wrappable">Moderately hard</td> +<td class="left top padl1 padr1 wrappable">Fine sand.</td> +</tr> + +<tr> +<td class="center top br">4</td> +<td class="right top">38</td> +<td class="center top br">„</td> +<td class="center top"><sup>1</sup>⁄<sub>10</sub></td> +<td class="center top br">„</td> +<td class="center top padl1"><sup>1</sup>⁄<sub>8</sub></td> +<td class="center top">„</td> +<td class="center top">in</td> +<td class="right top padr0">47</td> +<td> </td> +<td class="center top br">„</td> +<td class="center top padl1"><sup>1</sup>⁄<sub>8</sub></td> +<td class="center top">„</td> +<td class="center top">in</td> +<td class="right top">140</td> +<td class="center top br">„</td> +<td class="center top br">Hard</td> +<td class="left top padl1 padr1 wrappable">Extremely hard rock.</td> +</tr> + +<tr> +<td class="center top br">5</td> +<td class="right top">17</td> +<td class="center top br">„</td> +<td colspan="2" class="center top br">Small</td> +<td colspan="6" class="center top padl1 padr1 br">Negligible</td> +<td colspan="5" class="br"> </td> +<td class="center top br">(?)</td> +<td class="left top padl1 padr1 wrappable">Sand and Shingle.</td> +</tr> + +<tr class="bb"> +<td class="center top br">6</td> +<td class="right top">14</td> +<td class="center top br">„</td> +<td colspan="2" class="center top padl1 padr1 br">Negligible</td> +<td colspan="6" class="center top br">Ditto</td> +<td colspan="5" class="br"> </td> +<td class="center top br">(?)</td> +<td class="left top padl1 padr1 wrappable">Sand.</td> +</tr> + +</table> + +<p>The least rate of softening noticed, apart from those +structures of a more recent date, in two of which it was<span class="pagenum"><a name="Page_104" id="Page_104">[104]</a></span> +very slight, occurred in a pier thirty-eight years old (No. 4), +where, of three piles tested, two were quite hard, and the +third softened <sup>1</sup>⁄<sub>10</sub> inch only.</p> + +<p>Whatever may be the precise cause of the change, it +does not appear to be affected by the period or percentage +of immersion during the rise and fall of tides.</p> + +<div class="figcenter"><a name="Fig59" id="Fig59"></a> +<img src="images/illo116.png" alt="" width="500" height="397" /> +<p class="caption"><span class="smcap">Fig.</span> 59.</p> +</div> + +<p>This will be clear from the diagram, <a href="#Fig59">Fig. 59</a>, which +refers to four piles (No. 3 of table), all of the same age, in +the same structure. On each pile the depth of softening is +given at points in strict relation to each other, and to the +tidal range. The percentages of immersion for the various +heights are also given, from a study of which it will be +apparent that these have no relation to the amount of softening; +this, indeed, is always greatest near the ground, at +whatever actual height it may be. For instance, pile A was<span class="pagenum"><a name="Page_105" id="Page_105">[105]</a></span> +at ground-level softened <sup>1</sup>⁄<sub>4</sub> inch, that point being 60 per +cent. of its life under water; but on pile B, at a point 74 +per cent. of the time submerged, and 4 feet above a lower +ground-level, no softening was apparent; further, at ground-level +of this pile, the percentage being there 87, the softening +was no greater than at ground-level at pile A.</p> + +<p>It is probable that while the percentage of submersion +in moving water hardly appears to affect the result, yet prolonged +contact with wet sand, sea-weed, or clinging shell-fish +may do so. This seems to suggest that the process of change, +as between the sea-water and the iron, is slow, and to be +effective must be continuous; so that it is only found to +any considerable extent where the water in contact with the +surface is still. In the two worst cases, Nos. 1 and 2 of the +table, at points 1 foot and 6 inches above ground-level, +the surface was in one pile shrouded in a thick mantle of +heavy sea-weed, and in the other covered by molluscs; in +both instances the surfaces being thus kept moist and undisturbed. +The piles of the fourth case were in hard rock, +were clean, and, where accessible, always either in moving +water or quite dry.</p> + +<p>However this may be, the power to resist softening +certainly appears to vary largely with the quality of the +iron. The piles, referred to above, in which deterioration +proceeded at the most rapid rate were certainly of a soft +metal, the first being markedly so. On the other hand, +certain piles (No. 4) of hard, close-grained iron suffered very +little.</p> + +<p>It may be mentioned with respect to the last named, as +a matter of interest, that the caps of the lower lengths (just +above ground-level) had been cast with short pieces of +wrought iron projecting—possibly for lifting purposes—which +during thirty-eight years had altered in character to +something very like softened cast iron, but laminated, and<span class="pagenum"><a name="Page_106" id="Page_106">[106]</a></span> +harder. Of about 1<sup>1</sup>⁄<sub>4</sub> inch original thickness, only <sup>3</sup>⁄<sub>16</sub> inch +remained having the semblance of wrought iron. The +percentage of submersion was about 60.</p> + +<p>A number of piles, not included in the table, varying +from fifteen to forty-four years old, and of the same structure +to which set No. 2 belonged, were all found to be hard, +with the exception of one showing <sup>3</sup>⁄<sub>16</sub> inch of softening. +These are omitted, because the mud surrounding them was +at the time of examination unusually high, so that the more +normal ground-level could not be reached, at which points +testing might have disclosed different results. It is probable +that for any piles standing in soft material examination +below the surface would reveal more pronounced softening +than where occasionally exposed.</p> + +<p>To meet the effects of sea-water on cast-iron piles, and +for other reasons, it is a common and good practice to make +the lower lengths of greater thickness—say, <sup>3</sup>⁄<sub>8</sub> inch more—than +that sufficient for the upper. Occasionally, also, the +bottom lengths are filled with concrete, which no doubt adds +to the length of time during which they may be relied upon.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_107" id="Page_107">[107]</a></span></p> + +<h2>CHAPTER X.<br /> +<span class="chaptitle">EXAMINATION, REPAIR, AND STRENGTHENING OF +RIVETED BRIDGES.</span></h2> + +<p>In the preceding chapters defects of various kinds to which +riveted bridgework is liable have been more particularly +dealt with; it is now proposed to consider the examination +of such structures, following this by a reference to methods +of repair and strengthening, leaving the treatment of other +classes of bridgework to be developed under their proper +headings, though some of the remarks immediately following +will apply to all.</p> + +<p>The exhaustive survey of a bridge is only to be made +after considerable experience in the work, but it may be +stated that in looking for defects it is well to seek where they +are least expected, till, with practice, one knows better where +to direct attention. When examining with a view to pronouncing +an opinion upon the fitness of the structure to +remain in place, if in any real doubt, it is wise to give a +casting vote against it; and finally it may be said that upon +taking down a bridge condemned for any one or more defects, +it should be examined for worse. This may seem to be +somewhat pessimistic, but is based upon the teachings of +experience.</p> + +<p>Preliminary examination of a bridge may reveal such +faults or weaknesses as at once to ensure its condemnation; +but if this is not the case, and there is a reasonable probability +that the structure may be given a fresh lease of life, +it will, for the purpose of estimating the strength, or for<span class="pagenum"><a name="Page_108" id="Page_108">[108]</a></span> +possible repairs, commonly be desirable to secure precise +particulars of the existing structure independently of any +drawings that may be in existence, and which will very +probably be incorrect, the finished work, if old, seldom +agreeing with the contract drawings. A final decision may in +this case be deferred till after the measuring up has been +completed, the condition of the structure becoming more +familiar in the process.</p> + +<p>It is desirable first to ascertain whether the bridge +remains in good form, whether the camber of girders appears +to be what might be expected, or agreeable with existing +records, though much reliance must not be placed upon +figured cambers, it being quite common for girders to leave +the bridge yards with the camber something other than +that intended. The deflections under live load will also be +observed, and compared with the calculated result, or checked +by judgment. The calculations upon which strength and +deflections are based will, of course, refer to the actual +sections, which are sometimes a little difficult to ascertain if +there has been irregular rusting. In continuous girders also, +levels having been taken, allowance should be made for +effects of settlement, if any; and with arches evidence of +movement of the piers or abutments sought for, with the +like object. It is seldom that the main flanges of girders +show signs of weakness, unless from flexure in the case of +long and narrow top members, insufficiently stiffened; but +there may be want of truth from other causes already dealt +with. In plate girders the webs should be most carefully +scanned for possible cracks, particularly where cross-girders +are connected, and along the upper edges of bottom flange +angles, if the floor rest upon the flange. All riveted connections, +of course, need close attention, both for straining +effects, where there is a liability to wracking, and to detect +loose rivets. Loose rivets and want of tightness in other<span class="pagenum"><a name="Page_109" id="Page_109">[109]</a></span> +parts of the work may frequently be detected at sight by a +reddish bloom which appears on the neighbouring surfaces, +caused by rust working out and spreading under the effects +of weather; it may be seen round rivet-heads or along the +edges of angle-bars, or other parts where there is movement. +Loose rivets, though generally to be detected also by the +hammer, may perhaps in the case of thin-webbed cross-girders +be working in the web-thickness only, possibly to a +considerable extent. This, if not otherwise evident, may +sometimes be detected by simultaneous deflection tests—with +rods—at the top and bottom flanges of a girder, at the same +distance from the bearings. Any difference in the readings +may indicate loose web-rivets, or possibly a tear in the web +running parallel to the flange angles.</p> + +<p>Bracings between girders are very apt to display a rich +harvest of working rivets. Cross-girders and longitudinals +also may have loose rivets at their connections, and be very +badly wasted, with quite possibly cracks in the webs, or +other defects already enlarged upon.</p> + +<p>The condition of the road upon the bridge will frequently +be an indication of the state of the floor which carries it; or +the existence of rail-joints which are working badly may +very properly lead to a critical examination of the girder-work +immediately below, as this is a fruitful source of +damage in light constructions. Floor-plates, where these +exist, should be scanned for leakages, drainage nozzles, and +guttering, to see that they are free, the attachments of the +latter being often loose and unsatisfactory.</p> + +<p>Trough floors may be expected to show loose rivets near +the ends, with a probability of excessive leakage where they +abut against the webs of supporting girders.</p> + +<p>Floor plates resting upon abutments or piers, being very +liable to serious decay, require attention, and girder-work +entering masonry should receive close scrutiny, any obstruction<span class="pagenum"><a name="Page_110" id="Page_110">[110]</a></span> +to a sufficient examination being removed so far as is +judged sufficient for the purpose. The structure should, of +course, be closely watched during the passage of live load +for any signs of abnormal movement, excessive vibration, or +lurching.</p> + +<p>In addition to seeking for these various defects, or others +which have been referred to in these pages at length, it +will be well always to be alive to the possibility of faults +to be seen for the first time, or of which the author has +furnished no instance.</p> + +<p>Having formed a reliable opinion as to the state of the +bridge, this, if satisfactory, may leave to be determined only +the question of strength relative to the loads carried. It is +apparent that stress limits suitable for a new structure, +which has all its life before it, of purpose moderate to cover +possible deteriorations, the growth of loads, and other adverse +influences, may to avoid immediate reconstruction, reasonably +be permitted of a higher value for a further term of +years in the case of a structure which it is known has for a +considerable period behaved well, and remains in good condition. +What this higher value may be will be greatly +influenced by the circumstances of each case, and, being +largely a matter of judgment, may be expected to vary with +different engineers. Experience shows, however, that the +nominal unit stress in an old bridge may be a very considerable +amount in excess of that allowed for new work, +without, of necessity, showing any ill effects; and the author +is of opinion that for old bridges in good condition it is +quite prudent to allow an excess of 33 per cent. beyond that +permissible for a new design. If the structure is too weak +to satisfy this modified condition, it may be possible to +bring it within the stress limit by a reduction of ballast or +other removable dead weight. If this expedient does not +promise to be satisfactory, or the bridge shows actual signs of<span class="pagenum"><a name="Page_111" id="Page_111">[111]</a></span> +weakness, or palpable defects, it will be necessary to deal with +the question of repair, strengthening, or reconstruction.</p> + +<p>The repair of built up bridgework resolves itself largely +into a matter of replacing loose rivets by cutting these out, +rhymering the holes, if desirable, and again riveting. It +will often be sufficient to do this with no particular precautions +as to bolting up temporarily; the rivets having been +loose, may very well be spared for a time. In re-riveting +cross-girder connections it may, however, be imperative to +remove all the rivets, bolting up securely as this is done, in +order to make a tight job, taking out each bolt in turn as +required, and again filling the holes; or it may be well in a +bad case first to remove all loose rivets, substituting good +bolts, in order that work which has gone out of shape owing +to defective rivets may first be brought true.</p> + +<p>Cross-girder webs, cracked vertically or nearly so, are +commonly repaired with splice-plates on either side; but in +doing this it is undesirable to add plates of excessive thickness +relative to the web—probably poor—as by an abrupt +change of web section it appears not unlikely a fresh break +may be favoured.</p> + +<div class="figc450"><a name="Fig60" id="Fig60"></a><a name="Fig61" id="Fig61"></a><a name="Fig62" id="Fig62"></a><a name="Fig63" id="Fig63"></a> +<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 60.</span> <span class="right49"><span class="smcap">Fig.</span> 61.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 60. and <span class="smcap">Fig.</span> 61.</p> +<img src="images/illo124.png" alt="" width="450" height="376" /> +<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 62.</span> <span class="right49"><span class="smcap">Fig.</span> 63.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 62. and <span class="smcap">Fig.</span> 63.</p> +</div> + +<p>Replacing wasted flange-plates, or adding new plates to +those which exist, is occasionally resorted to in the case of +main girders, the flanges of which are sufficiently accessible, +but the operation is difficult, takes some little time, and +should only be attempted under the constant supervision of +a thoroughly capable man. When done, if the girder has +not been relieved of load by staging, the stress under full +load will be unequally distributed between the old and the +new section, the old always taking more by the amount of +the dead-load stress previously carried. The method which +the author has seen applied to lattice girders of about +80 feet span, having good angle-bars in the flanges, with a +shallow vertical web for attachment of diagonals, consisted<span class="pagenum"><a name="Page_112" id="Page_112">[112]</a></span> +in first cutting out the old flange rivets, and substituting +bolts well screwed up, till all the rivets necessary had been +removed. The new plate length having been prepared, was, +on a Sunday, during a few hours’ cessation of traffic, marked +off, the temporary bolts being removed for the purpose, and +then replaced. After the plate had been drilled, on a later +Sunday, it was finally put into position, bolted up, and +riveted at leisure; cover-plates make additional trouble, but +are dealt with on the same principle. The method as shown +in <a href="#Fig60">Fig. 60</a> is, however, barely practicable for so many plates. +It is preferable, if it is proposed to add section, to do this +with as little interference as possible with existing rivets of +importance. This may be accomplished, if the existing +plates are not too wasted at their edges, by riveting on new +strips or angle-bars (see <a href="#Fig61">Figs. 61 to 63</a>). Occasionally the +strength of a girder is increased by the addition to the top<span class="pagenum"><a name="Page_113" id="Page_113">[113]</a></span> +or bottom boom of material in such a form as sensibly to +increase the depth, and thus, while adding increased section +to one boom, to reduce the stress in each, though to dissimilar +amounts. By this device also the relief is effective +only as regards the live-load stress; under dead load only +the new material does no work, provided, of course, that +no relief staging was used during the alterations. For +girders carrying any considerable proportion of dead load the +method is very inefficient, though for others, in which the +live load is relatively large, the result should be more satisfactory.</p> + +<p>As this question of adding new section to old is of much +importance in dealing with repairs and strengthening operations, +a few general remarks upon the subject will be +pertinent. The difficulty in such work commonly is to +cause the new to render any considerable assistance to the +old in those cases which occur in practice. If a bar be +imagined under longitudinal stress varying between 0 and a +maximum, then, if the area of the piece be increased at the +time when it takes no stress, its capacity for resisting the +maximum amount will be increased, and for added material +of similar elasticity the unit stress proportionately reduced. +If, however, the load on the bar does not vary, the mere +addition of metal will not relieve the original section in any +degree. To take a third case, of the maximum being twice +the minimum load, it will be necessary, in order to lower the +maximum unit stress by 25 per cent., to double the original +section of the bar if, as supposed, the extra metal has been +added to the piece when under the smaller load, so that the +new section is only effective in assisting to carry the remainder +of the load at such times as it may be imposed. +The relationship stands thus<span class="nowrap">:—</span></p> + +<p class="formula"><span class="division"><span class="num">Live load</span><span class="denom">Live + dead load</span></span> × <span class="division"><span class="num">New area</span><span class="denom">New + old area</span></span> = relief.</p> + +<p><span class="pagenum"><a name="Page_114" id="Page_114">[114]</a></span></p> + +<p>These statements will be true under the conditions named, +within the elastic limit of the material; but some advantage +would be derived in the second case, and a more marked +benefit in the third, if the load assumed to be a maximum +were exceeded, or if the composite bar were tested to destruction; +as, however, these effects would be outside the +limiting conditions imposed, it must be a matter of judgment +as to how far this reserve of strength may be considered of +value.</p> + +<p>If, instead of simply adding section to the bar, some part +of the constant load is put upon the new section by the +manner of attachment, the combination will, of course, be +more effective.</p> + +<p>To apply these considerations and illustrate the way in +which the two methods of adding flange section work out +when reduced to figures, the case will be supposed of a girder +6 feet deep, carrying a load of which one-third is dead and +two-thirds live. To the flanges of this girder are added +plates equal to 50 per cent. of the original areas, in order to +reduce the stress of 7 tons per square inch to which the +girder before strengthening is liable, the depth remaining +substantially unaltered. With dead load only the original +section would be stressed to 2·3 tons per square inch, the +new section being then unstressed. Under full load the +new and old material take 3·1 tons per square inch additional, +making the modified stress on the original section +5·4 tons per square inch, as against 7 tons; or a reduction +of 22 per cent. This compares with 33 per cent., the relief +due to 50 per cent. increase of flange area under ordinary +conditions of stress distribution.</p> + +<p>Let the second method of strengthening the girder now +be considered, using, for purposes of comparison, the same +total amount of new material to increase the girder depth by +an addition to the top flange. This section will be equal to<span class="pagenum"><a name="Page_115" id="Page_115">[115]</a></span> +the area of one flange, which, though it may be applied in +many different ways, giving a greater or a less increase to the +depth, would probably be used in some +such manner as that shown in <a href="#Fig64">Fig. 64</a>, +increasing the effective depth for live-load +stress by nearly 10 inches.</p> + +<div class="figcenter"><a name="Fig64" id="Fig64"></a> +<img src="images/illo127.png" alt="" width="125" height="494" /> +<p class="caption"><span class="smcap">Fig.</span> 64.</p> +</div> + +<p>The added material will, as in the +previous case, leave the dead-load stress +unaltered, or 2·3 tons per square inch. +The stress in the bottom flange due +to live load will, however, now be 4·1 +tons per square inch, making a total +stress of 6·4 tons per square inch, +against 7 tons—the original stress. +The reduction here is 8 per cent. +only, as compared with 12 per cent., +the relief due, under ordinary conditions, +to an increase of effective depth +from 6 feet to 6 feet 10 inches, and by +the use of additional material, equal, +as before, to one-half of the total +flange areas before the alteration.</p> + +<p>The effect on the top flange need +not be here gone into in detail, but it +may be said that, owing to the increase +of gross section and of depth, +the ultimate stresses of both the new +and old material are greatly less than +as given for the bottom flange.</p> + +<p>Girders strengthened by the first +of these two methods would, it is probable, +if tested to destruction, give +results more nearly in accord with the actual percentage +increase of flange section, plastic deformation of the metal,<span class="pagenum"><a name="Page_116" id="Page_116">[116]</a></span> +before failure, tending to reduce the differences of stress on +the new and old material of the sections.</p> + +<div class="figcenter"><a name="Fig65" id="Fig65"></a><a name="Fig66" id="Fig66"></a> +<img src="images/illo128.png" alt="" width="350" height="470" /> +<p class="caption"><span class="smcap">Figs.</span> 65 and 66.</p> +</div> + +<p>Web members of lattice girders may, if weak, sometimes +be dealt with by the introduction of supplementary bars, +parallel to and between the old members, or by the addition +of strips or angles to the existing diagonals. The treatment +will be largely influenced by the nature of the old detail, +which may lend itself to some one arrangement much better +than to any other.</p> + +<p>End riveting of web members may, if it has become +loose, be dealt with by simply rhymering the holes a size +larger, and re-riveting in the best manner, if the stresses are +not excessive; or it may be necessary to devise some additional +attachments by which new rivets are brought into use +(see <a href="#Fig65">Figs. 65 and 66</a>). The effective relief due to supplementary<span class="pagenum"><a name="Page_117" id="Page_117">[117]</a></span> +rivets will be influenced by similar considerations +to those governing increase of section.</p> + +<div class="figcenter"><a name="Fig67" id="Fig67"></a> +<img src="images/illo129.png" alt="" width="450" height="251" /> +<p class="caption"><span class="smcap">Fig.</span> 67.</p> +</div> + +<div class="figcenter"><a name="Fig68" id="Fig68"></a> +<img src="images/illo130.png" alt="" width="450" height="264" /> +<p class="caption"><span class="smcap">Fig.</span> 68.</p> +</div> + +<p>Old structures are very frequently deficient in bracing, +which may, in such cases, be advantageously introduced; +or girders individually weak may be rendered collectively +efficient by suitable bracing. In considering the advisability +of this, however, the case should be viewed with regard to +the possible effects of such members, as already dealt with +in the chapter relating to these questions. There it has been +pointed out that bracing between a system of parallel girders +may have the effect, under live load, of increasing the stress +on the outer girders due to twisting of the structure as a whole, +though the inner girders will, except for full loading of the +whole bridge, be advantaged as to stress values, and in any +event bettered by being held up to their work. The effect +upon the outer girders may be met by increasing their +strength, if this appears to be necessary. In all such alterations +the detail should be schemed with special care to +ensure simplicity in execution, smith’s work being rigorously +avoided. A good arrangement for supplementary bracing +between plate-girders, which gives little trouble in carrying +out, is shown in <a href="#Fig67">Fig. 67</a>; or where the stiffeners of such girders<span class="pagenum"><a name="Page_118" id="Page_118">[118]</a></span> +are in line across the bridge, the detail given in <a href="#Fig68">Fig. 68</a> may +involve less expenditure. Difficulties may be experienced in +riveting, unless great care is taken in the positioning of rivets. +Fitting-bolts are only to be relied upon as such, if they really +justify the name; they are, though easy to specify, by no +means easy to secure under the conditions of practical work. +Weak cross-girders may make alterations—in some cases +considerable—necessary, to rectify the defect of strength. +The removal of old girders to make room for new is seldom +resorted to, unless the existing detail renders this a simple +operation; but it is not unusual to introduce new girders +between the old in cases where there is no plated floor to +make the work difficult. By this method there is, of course, +an increase of appreciable amount in the dead load carried +by the main girders, which would in many instances be +objectionable. With deep and heavy main girders, having +plate webs, cross-girders may be strengthened by improving +the end connections by suitable gussets, and attachment to +good vertical stiffeners, the fixity of the ends thus aimed at +being assured by overhead struts or girders, from one main +girder to its fellow, at intervals apart well considered with +reference to the horizontal strength of the top flanges, the<span class="pagenum"><a name="Page_119" id="Page_119">[119]</a></span> +whole thus making a closed frame, as shown in <a href="#Fig69">Fig. 69</a>. +The method appears feasible, but it should be stated that +the author has not known it to be applied in its entirety as +a means of strengthening an old floor.</p> + +<div class="figcenter"><a name="Fig69" id="Fig69"></a> +<img src="images/illo131.png" alt="" width="450" height="280" /> +<p class="caption"><span class="smcap">Fig.</span> 69.</p> +</div> + +<p>A simple and very common device consists in substituting +for the ordinary cross-sleeper road, where this exists, stout +timber longitudinals under the rails, which have, where the +cross-girders do not exceed 5 feet centres, a marked distributive +effect, tending to reduce the maximum load upon any +individual girder. With a similar object, trough girders +containing longitudinal timbers are sometimes adopted where +the depth available is not enough to enable sufficiently stiff +timbers to be used alone. In either case the object sought +is the same—to modify the effect of the heavier wheel loads +upon isolated cross-girders. When the spacing is so close +as 4 feet, the beneficial result of this treatment is considerable, +but at 8 feet centres it can have but a moderate effect +where timbers alone are used.</p> + +<p>Occasionally, for long cross-girders, a distributing girder +is placed, with the same intent, in the 6 feet way, its function +being limited to this use only if the depth and strength are<span class="pagenum"><a name="Page_120" id="Page_120">[120]</a></span> +sufficiently small to serve this object alone, as distinct from +the case in which it becomes a carrying girder transferring +load to the abutments. As a distributor simply, the girder +has to equalise the bending moments amongst the cross-girders, +to effect which it will be evident that these moments +having been ascertained for the several cross-girders previous +to alteration, for a position of the wheel loads such that the +heaviest comes upon a centre cross-girder, the mean of these +moments will, when compared with that for each girder, +show the difference to be induced as a result of introducing +the distributor. These differences of moment render necessary +at the centre of the cross-girders reactions upwards +or downwards, as the case may be, of amounts competent +to induce moments below the inner rails equal to these +differences.</p> + +<p>It is these reactions which must be provided by the distributing +girder at a moderate stress, and without flexure of +such an amount as sensibly to modify the reactions. The +greatest section necessary at any one point may then be +adopted for the girder throughout. The result will commonly +work out to a moderate section, but there will be no +harm in a little excess in a case of this kind, the total cost +being but little affected by some small addition to the weight, +where labour upon the site is so considerable an item as in +work of this description. The ends of the distributing girder +should be carried on to the abutments or piers to ensure +adequate relief of the end cross-girders. It will be found +desirable in arranging for distributing girders to ascertain at +an early stage, by boning or by levelling, the condition of +the cross-girders as to uniformity of heights, as this may affect +the length most suitable for separate sections. Between the +underside of the distributor and the cross-girder tops there +will commonly be spaces of varying amounts, which should +be filled by packings to fit, rather than by pulling the work<span class="pagenum"><a name="Page_121" id="Page_121">[121]</a></span> +together by force, introducing undesirable stresses of uncertain +amount.</p> + +<p>In the earlier remarks upon the strengthening of bridgework +by the use of new material, it has been assumed that +the modulus of elasticity of the new metal is similar to that +of the old; it may, however, as in cases where wrought-iron +work is reinforced by additions in steel, be necessary to +take the difference of elastic properties into account, with +which object the new section should be multiplied by a +quantity (greater or less than unity) inversely proportional to +the higher or lower modulus of the new material, that is to +say, by</p> + +<p class="formula"><span class="division"><span class="num">E of old material</span><span class="denom">E of new material</span></span></p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_122" id="Page_122">[122]</a></span></p> + +<h2>CHAPTER XI.<br /> +<span class="chaptitle">STRENGTHENING OF RIVETED BRIDGES BY CENTRE +GIRDERS.</span></h2> + +<p>The addition of distributing girders, described in the last +chapter, as a means of strengthening a bridge floor, while +sufficient in many cases so far as the cross-girders are concerned, +does not in any appreciable way assist the main +girders. When for a two-line bridge, having outer main +girders only, this result also is desired, together with a more +complete relief of the floor structure, centre main girders +may be used, placed either above or below the cross-girders, +on the centre line of the bridge.</p> + +<p>There are two principal ways in which such a girder may +be brought into use; the easier, but generally less economical, +is by making a simple attachment to the cross-girders, +the old girder work still taking the whole dead load. By this +method the new girder does no work but carry itself till the +live load comes upon the bridge, and must be made very +stiff to take any sensible portion of the running load; the +second method is to make the connection adjustable, so that +a part of the floor weights may be imposed upon the new +girder as an initial load. In doing this the old outer girders +will rise slightly, being relieved of stress, and the cross-girders +also lifted at the middle, whilst the new girder is +depressed as the load is brought upon it. With some part +of the live load a very considerable proportion of the total +may in this way be carried by a centre girder of moderate +section. The whole question, by either method, turns upon<span class="pagenum"><a name="Page_123" id="Page_123">[123]</a></span> +deflections; and it is in determining the relative movements +of the girders that the problem chiefly lies.</p> + +<p>It is convenient first to determine the percentage of load +relief to be effected in the main girders, as to which it is to +be observed that as this relief (distributed) is induced by +the upward reaction of the new girder acting at the centre +of the cross-girders, the stress relief of these will, as a rule, +greatly exceed that of the outside girders. For the generality +of cases, it may be taken that the relief suitable for the +outside girders will be satisfactory in its effects upon the +cross-girders, even though it is desired to reduce the stress +in these to a greater degree.</p> + +<p>If, however, it be thought desirable to check this, it may +be done by considering a cross-girder subject to its dead and +live loads acting downwards, and to reactions at the centre +and ends. At the centre the reaction will be the load of +which the two main girders are relieved on a length equal to +the pitch of the cross-girders, or as here given<span class="nowrap">:—</span></p> + +<p class="numform"><a name="Form1" id="Form1"></a><span class="formula"><i>c</i> × <i>t</i> × P = reaction at centre</span> +<span class="number">(1)</span></p> + +<p><i>c</i> being the percentage of relief; <i>t</i> the total load per foot run +of the bridge; and P the pitch of cross-girders. The live +loads carried by the cross-girders are for this purpose taken +at per foot run, as for the main girders. With these data +it will be easy to construct a diagram of moments, making +it evident whether the relief proposed for the main girders +will give a sufficient percentage of relief to the floor beams.</p> + +<p>Granting that this proportion has been decided, and +dealing first with the case in which the centre girder is +simply attached to the cross-girders, and takes no dead load +other than its own weight, then the live load carried by the +outside girders, and previously borne wholly by them, will +be reduced by the amount it is intended to transfer to the +centre girder, and will become</p> + +<p class="numform"><a name="Form2" id="Form2"></a><span class="formula">L<sub class="lg"><i>l</i></sub> - (<i>c</i> × L<sub class="lg"><i>t</i></sub>) = live load on outer girders</span> +<span class="number">(2)</span></p> + +<p><span class="pagenum"><a name="Page_124" id="Page_124">[124]</a></span></p> + +<p>L<sub class="lg"><i>l</i></sub> being the total live load, and L<sub class="lg"><i>t</i></sub> the total dead and live +load carried by the bridge. From this the deflection of the +outer girders corresponding to this modified live load may +be derived.</p> + +<div class="figcenter"><a name="Fig70" id="Fig70"></a> +<img src="images/illo136.png" alt="" width="550" height="251" /> +<p class="caption"><span class="smcap">Fig.</span> 70.</p> +</div> + +<p>It is next necessary to ascertain the vertical movement, +commonly a depression, of the cross-girders at the centre +relative to their ends, when subject to the running load only, +and supported at the middle and ends, the centre reaction +being obtained as before indicated <a href="#Form1">(1)</a>. This movement +will be the difference (if any) between the deflection on the +whole span of the cross-girder due to the live load, and the +upward flexure of the girder due to the centre reaction, +considered as separate effects. Stress values having been +estimated for the two conditions, these results may readily +be deduced by simple flexure formulæ, observing that while +the curve of moments due to live load sufficiently approximates +to that for a distributed load to justify, for this, the +use of a distributed load formula as given in the chapter +“<a href="#Page_85">Deflections</a>,” the flexure due to the centre reaction will be +but 0·80 of that which corresponds to the same stress for +distributed loading. Or, the curve assumed by the girder +under live load may be plotted by a method to be later +explained.</p> + +<p><span class="pagenum"><a name="Page_125" id="Page_125">[125]</a></span></p> + +<p>The sum of the movements now determined—that is, +the live-load deflection of the outer girders, and depression, +as is commonly the case, of the cross-girders—will give the +extreme depression (marked <i>m</i> in <a href="#Fig70">Fig. 70</a>), from the dead-load +condition of the middle cross-girders, when supported +to the extent desired by a centre girder whose proportions are +not yet known, but which, carrying the required percentage +of the total load, must, subject to a reservation presently +stated, deflect only this amount. The unit stress in the +flanges of the new girder, governed by this flexure, will for +a plate girder be</p> + +<p class="numform"><a name="Form3" id="Form3"></a><span class="formula"><span class="division"><span class="num">D × C × <i>m</i></span> +<span class="denom">S<sup>2</sup></span></span> = <i>f</i>, unit stress on gross section</span> +<span class="number_up">(3)</span></p> + +<p>D and S being, as before (see “<a href="#Page_85">Deflections</a>”), the depth and +span respectively in feet, C a constant, <i>m</i> the deflection in +inches, and <i>f</i> the stress per square inch on the gross section +of flange.</p> + +<p>The gross area A, of the flange, is given by</p> + +<p class="numform"><a name="Form4" id="Form4"></a><span class="formula"><span class="division"><span class="num">S × <i>c</i> × L<sub class="lg"><i>t</i></sub></span> +<span class="denom">8 × D × <i>f</i></span></span> = gross area of flange</span><span class="number_up">(4)</span></p> + +<p><i>c</i> × L<sub class="lg"><i>t</i></sub>, being, as in <a href="#Form2">(2)</a>, the load transferred to and carried +by the centre girder.</p> + +<p>The actual stress in the flanges will, of course, be greater +by an amount due to the girder’s own weight; but this does +not affect the question of relief. For any ordinary case the +stress per square inch will be low; but it will manifestly be +useless to assume a greater stress with a view to economy, as +the effect of reducing the section will simply be to make the +girder too flexible, thus causing it to be less effective than +primarily intended. If, as is seldom the case, there is +freedom as to the depth of girder permissible, it is evident +the unit stress may be made a condition, and the depth<span class="pagenum"><a name="Page_126" id="Page_126">[126]</a></span> +deduced by a suitable modification of formula <a href="#Form3">(3)</a>; the +relief desired being in this way equally well assured. Indeed, +in the rare instances in which any depth may be +adopted, this method is—contrary to the general rule—distinctly +economical, particularly if the girder may be placed +below the cross-girders, which simply rest upon it, without +elaborate attachments.</p> + +<div class="figcenter"><a name="Fig71" id="Fig71"></a> +<img src="images/illo138.png" alt="" width="550" height="259" /> +<p class="caption"><span class="smcap">Fig.</span> 71.</p> +</div> + +<p>Considering now the second method of applying centre +girders by which the new girder is made initially to carry +part of the dead load, by adjustment, it will at once be +recognised as a more complex matter. The measure of +relief by which the old girderwork shall benefit need not +be affected by the method of applying the centre girder, +and may be decided on the principles already considered. +The outer girders carrying a reduced load, when the bridge +is fully loaded, and the cross-girders being in part supported +at their centres in the manner already described, will give a +resulting depression <i>m</i> (see <a href="#Fig71">Fig. 71</a>) of the centre cross-girders, +below the original dead-load position, of a similar +amount determined in the same way. This extreme depression +determines also the lowest position of the new centre +girder, which may be designed to carry the required percentage<span class="pagenum"><a name="Page_127" id="Page_127">[127]</a></span> +of the total bridge loads with the maximum stress +and depth, as conditions, leaving the initial dead load and +necessary adjustments to be ascertained. This is the common +case and will be here dealt with, it being assumed to avoid +ambiguity in description that the new girder lies above the +cross-girders.</p> + +<p>The centre girder of fixed depth being then required to +carry a definite load at a definite flange stress, will deflect a +definite amount at this stress. If this deflection equalled +the extreme depression <i>m</i> of the old girder work, no adjustment +would be necessary, the centre girder then carrying no +initial dead load, as by the first method; but for centre +girders designed for economical flange stress the deflection will +in ordinary cases greatly exceed this, the depth generally +being small, and in order to ensure that the new girder shall +do its full work, some dead load must be put upon it. In the +act of adjustment the cross-girders must be lifted and the +centre girder depressed, till the joint movement equals the +excess <i>s</i> of the centre girder deflection over <i>m</i>, when the +new girder will carry the proper amount of initial load, and +upon further deflection under live load give the full measure +of relief. The amount of “lift” or upward flexure of the +old girder work, and the depression or “drop” of the new +girder, during adjustment, will depend upon relative stiffness, +and may be ascertained as follows<span class="nowrap">:—</span></p> + +<p>For unit reactions at the centre of the cross-girders the +upward flexure of these may be ascertained, as also the +upward flexure of the two outer girders when subject to +forces of the same total amount (one-half to each) applied +at the cross-girder ends. The sum of these movements will +give the total lift of the centre cross-girders, when all are +subject to unit lifting forces; similarly, the depression of +the centre girder for unit loads applied at the cross-girders +may be determined. There will then be known the movements<span class="pagenum"><a name="Page_128" id="Page_128">[128]</a></span> +upwards and downwards of the old and new work +when being drawn together by unit forces applied as stated.</p> + +<p>If</p> + +<table class="formula nowrap" summary="Table page 128"> + +<tr> +<td class="left"><i>l</i></td> +<td class="center padl1 padr1">=</td> +<td class="left">lift due to unit loads,</td> +</tr> + +<tr> +<td class="left"><i>l<sub class="lg">t</sub></i></td> +<td class="center padl1 padr1">=</td> +<td class="left">total lift due to adjustment,</td> +</tr> + +<tr> +<td class="left"><i>d</i></td> +<td class="center padl1 padr1">=</td> +<td class="left">drop due to unit loads,</td> +</tr> + +<tr> +<td class="left"><i>d<sub class="lg">t</sub></i></td> +<td class="center padl1 padr1">=</td> +<td class="left">total drop due to adjustment,</td> +</tr> + +<tr> +<td class="left"><i>s</i></td> +<td class="center padl1 padr1">=</td> +<td class="left">deflection excess = gross adjustment,</td> +</tr> + +</table> + +<p>there will then be</p> + +<p class="formula"><span class="division"><span class="num"><i>d</i></span> +<span class="denom"><i>l</i> + <i>d</i></span></span> × <i>s</i> = <i>d</i><sub class="lg"><i>t</i></sub>,</p> + +<p>total drop of centre girder under adjustment,</p> + +<p class="formula"><span class="division"><span class="num"><i>l</i></span> +<span class="denom"><i>l</i> + <i>d</i></span></span> × <i>s</i> = <i>l</i><sub class="lg"><i>t</i></sub>,</p> + +<p>total lift of centre cross girders under adjustment,</p> + +<p class="formula"><span class="division"><span class="num"><i>d</i><sub class="lg"><i>t</i></sub></span><span class="denom"><i>d</i></span></span> × unit load =</p> + +<p>initial load put upon centre girder at each cross-girder.</p> + +<p>The rise of the two outer girders for upward forces +together equal to those depressing the centre girder may +readily be deduced.</p> + +<div class="figcenter"><a name="Fig72" id="Fig72"></a> +<img src="images/illo141.png" alt="" width="350" height="321" /> +<p class="caption"><span class="smcap">Fig.</span> 72.</p> +</div> + +<div class="figcenter"><a name="Fig73" id="Fig73"></a> +<img src="images/illo142.png" alt="" width="500" height="258" /> +<p class="caption"><span class="smcap">Fig.</span> 73.</p> +</div> + +<p>The act of adjustment may conveniently be effected by +the arrangement shown in <a href="#Fig72">Fig. 72</a>, in which each cross-girder +is hung up at its centre by four bolts. At the middle of +the centre girder the total amount to be screwed up will be +that corresponding to the deflection excess <i>s</i>, but towards +the ends this amount decreases, and may advantageously be +represented by a diagram as <a href="#Fig73">Fig. 73</a>, in which, if <i>s</i> represents +to scale the amount to be screwed up at a centre cross-girder, +the corresponding amounts for other girders may be read off +direct. It will be apparent that it must be necessary to<span class="pagenum"><a name="Page_129" id="Page_129">[129]</a></span> +place the centre girder at such a height as to leave a space +between the old and the new work greater than the amount +to be screwed up, this excess clearance being ultimately filled +by a packing.</p> + +<p>The precautions to be observed in carrying out this +kind of work, and the practical methods of adjustment +adopted by the author after some little experience, may here +be given.</p> + +<p>Great care is necessary at the outset to ascertain the true +spacing of the cross-girders, to ensure that the bolt-holes in +the bottom flange of the centre girder shall come where +desired. The fixing of the cross-girder brackets also needs +close attention to avoid after trouble, the bolt-holes in the +brackets being preferably drilled on the site after fixing. +It will, for masonry abutments, be necessary to fix bedstones +to receive the new centre girder, which, being carried out +quite possibly under adverse traffic conditions, will perhaps<span class="pagenum"><a name="Page_130" id="Page_130">[130]</a></span> +leave the stones liable to settle slightly when the full load +is carried. To eliminate the bad effect of this upon the +ultimate adjustment, and to take up any initial set of the +new girder work, which would be prejudicial in the same +way, it is desirable, the centre girder being in place, to screw +up the bolts temporarily and leave the work for a week +or two. To ensure regularity in the screwing up process, it +is convenient to prepare, for use at the bridge, a diagram +somewhat similar to <a href="#Fig73">Fig. 73</a>, giving the amount by which +the new and old work are to be brought together at each +cross-girder, with the number of turns for each nut to effect +this. With a man at each side of the girder, the whole +length is traversed, giving a half-turn to each nut; this is +repeated as often as necessary, and so managed as to bring +all up proportionately to the final requirement, keeping tally +with chalk marks over each cross-girder as a check. The +preliminary screwing up should be conducted with little less +care than that adopted for the later adjustment, to avoid +damage to the old work. This later adjustment having in +due course been effected, it is then necessary to measure for +packings to fill the spaces remaining between the old cross-girders<span class="pagenum"><a name="Page_131" id="Page_131">[131]</a></span> +and the new centre girder. These spaces should be +callipered at each of the four corners, care being taken to +avoid after-confusion. The measurements ascertained will, +however, be too great for the finished packings, as an allowance +of not less than <sup>1</sup>⁄<sub>10</sub> inch (total), will commonly be +wanted to cover irregularities in the surfaces. The packings, +having been prepared and checked, may be slipped into +place after slacking all the bolts a small amount to permit +this to be done, finally screwing up tight and securing +the nuts by split-pins, through holes drilled as the last +operation.</p> + +<p>As a check upon the calculations and adjustment, the +“lift” of the outer girders and cross-girders, and the “drop” +of the centre girder may be observed by levelling. For this +purpose the author has used a staff of inches divided into +tenths, with which, and a good level, very accurate readings +may be taken for short distances.</p> + +<p>No reference has been made to the effect of skew in a +bridge on the above methods, the explanation given applying +rather to bridges square on plan. The influence of skew on +the load distribution will largely be a matter of detailed +calculation. The flexure of the girders may also be sensibly +affected, but may be arrived at with sufficient accuracy +without any great trouble. The chief effect of skew is to +modify the amount of screwing up during adjustment, which +may be better understood by reference to <a href="#Fig74">Fig. 74</a>, and comparing +it with <a href="#Fig73">Fig. 73</a>, the adjustment diagram for a square +bridge.</p> + +<p>To illustrate how these methods of strengthening work +out, and compare as to weights of centre girders required, +the case has been assumed of a wrought iron bridge of 60-feet +span, having outer girders 5 feet deep, of 39 square inches +gross flange area; and cross-girders, at 8-feet centres, 27-feet +span, 1 foot 9 inches deep, with a gross flange area of twenty<span class="pagenum"><a name="Page_132" id="Page_132">[132]</a></span> +square inches. The dead load and live load on either road +are each 1·75 tons per foot run.</p> + +<p>The stress in the outer girders previous to the alteration +being 6 tons per square inch gross, it is desired to relieve +this to the extent of 33 per cent. by a steel centre girder. +In the table here given the quantities given in italics are +fixed as primary conditions<span class="nowrap">:—</span></p> + +<p class="center"><span class="smcap">Centre Strengthening Girders for 60-ft. Span.</span></p> + +<table class="nowrap" summary="Table page 132"> + +<tr class="bt bb"> +<th class="center br">—</th> +<th colspan="2" class="center padl1 padr1 br">Centre<br />Girder,<br />Stress<br />Unknown.</th> +<th colspan="2" class="center padl1 padr1 br">Centre<br />Girder,<br />Depth<br />Unknown.</th> +<th colspan="2" class="center padl1 padr1">Adjust-<br />ments<br />Unknown.</th> +</tr> + +<tr> +<td class="center padl1 padr1 br highline"><i>Outer Girder.</i></td> +<td colspan="2" class="br highline"> </td> +<td colspan="2" class="br highline"> </td> +<td colspan="2" class="highline"> </td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Deflection under modified live load</td> +<td class="left bot padl3 padr0">·42</td> +<td class="center bot padl0 padr1 br">in.</td> +<td class="left bot padl3 padr0">·42</td> +<td class="center bot padl0 padr1 br">in.</td> +<td class="left bot padl3 padr0">·42</td> +<td class="center bot padl0 padr1">in.</td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Lift of adjustment</td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td class="left bot padl3 padr0">·153</td> +<td class="center bot padl0 padr1">„</td> +</tr> + +<tr> +<td class="center padl1 padr1 br highline"><i>Cross Girders.</i></td> +<td colspan="2" class="br highline"> </td> +<td colspan="2" class="br highline"> </td> +<td colspan="2" class="highline"> </td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Depression under live load—modified conditions of support</td> +<td class="left bot padl3 padr0">·13</td> +<td class="center bot padl0 padr1 br">in.</td> +<td class="left bot padl3 padr0">·13</td> +<td class="center bot padl0 padr1 br">in.</td> +<td class="left bot padl3 padr0">·13</td> +<td class="center bot padl0 padr1">„</td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Extreme depression (<i>m</i>)</td> +<td class="left bot padl3 padr0">·55</td> +<td class="center bot padl0 padr1 br">„</td> +<td class="left bot padl3 padr0">·55</td> +<td class="center bot padl0 padr1 br">„</td> +<td class="left bot padl3 padr0">·55</td> +<td class="center bot padl0 padr1">„</td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Lift of adjustment (cross-girder only)</td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td class="left bot padl3 padr0">·095</td> +<td class="center bot padl0 padr1">„</td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Total lift of adjustment (<i>l<sub class="lg">t</sub></i>)</td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td class="left bot padl3 padr0">·248</td> +<td class="center bot padl0 padr1">„</td> +</tr> + +<tr> +<td class="center padl1 padr1 br highline"><i>Centre Girder.</i></td> +<td colspan="2" class="br highline"> </td> +<td colspan="2" class="br highline"> </td> +<td colspan="2" class="highline"> </td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Depth</td> +<td colspan="2" class="center bot padl1 padr1 br"><i>3·5 ft.</i></td> +<td colspan="2" class="center bot padl1 padr1 br">8·2 ft.</td> +<td colspan="2" class="center bot padl1 padr1"><i>3·5 ft.</i></td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Unit stress on gross section (ex girder’s weight)</td> +<td colspan="2" class="center bot padl1 padr1 br">2·14 tons</td> +<td colspan="2" class="center bot padl1 padr1 br"><i>5·0 tons</i></td> +<td colspan="2" class="center bot padl1 padr1"><i>5·0 tons</i></td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Total deflection (ex girder’s weight)</td> +<td colspan="2" class="center bot padl1 padr1 br">·55 in.</td> +<td colspan="2" class="center bot padl1 padr1 br">·55 in.</td> +<td class="left bot padl2 padr0">1·28</td> +<td class="center bot padl0 padr1">in.</td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Deflection excess (<i>s</i>)</td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td class="left bot padl3 padr0">·73</td> +<td class="center bot padl0 padr1">„</td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Depression, or “drop” of adjustment (<i>d<sub class="lg">t</sub></i>)</td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td> +<td class="left bot padl3 padr0">·482</td> +<td class="center bot padl0 padr1">„</td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Gross area of flange</td> +<td colspan="2" class="center bot padl1 padr1 br">105 sq. in.</td> +<td colspan="2" class="center bot padl1 padr1 br">19·2 sq. in.</td> +<td colspan="2" class="center bot padl1 padr1">44·5 sq. in.</td> +</tr> + +<tr> +<td class="left top padl1 padr1 br wrappable">Weight</td> +<td colspan="2" class="center bot padl1 padr1 br">20 tons</td> +<td colspan="2" class="center bot padl1 padr1 br">10·4 tons</td> +<td colspan="2" class="center bot padl1 padr1">11·4 tons</td> +</tr> + +<tr class="bb"> +<td class="left top padl1 padr1 br wrappable">Net flange stress (including girder’s weight)</td> +<td colspan="2" class="center bot padl1 padr1 br">3·19 tons</td> +<td colspan="2" class="center bot padl1 padr1 br">6·87 tons</td> +<td colspan="2" class="center bot padl1 padr1">6·94 tons</td> +</tr> + +</table> + +<p>Girders subject to distributed load are treated as having<span class="pagenum"><a name="Page_133" id="Page_133">[133]</a></span> +uniform stress, but where this is not strictly the case, as in +some light girders, it will be necessary to take the fact into +account. For centre girders of wrought iron, and a unit +stress on the gross section of 4 instead of 5 tons, the girder +weights are between 9 and 10 per cent. greater.</p> + +<div class="figcenter"><a name="Fig74" id="Fig74"></a> +<img src="images/illo145.png" alt="" width="500" height="237" /> +<p class="caption"><span class="smcap">Fig.</span> 74.</p> +</div> + +<p>In the above treatment of the application of centre +strengthening girders there is a source of error which should +be touched upon. If, under live load, the centre girder +deflects more than the outer girders, as it commonly will, +there must be a want of uniformity in the behaviour of the +cross-girders, those near the abutments being more relieved +than the estimated amount of relief of those at the centre, +which will have less than that intended; but the reduction +of stress in the cross-girders will generally be so considerable +that any such ambiguity of excess or defect is commonly +unimportant; the effect of this also upon the main girders +is much less than might be supposed, being, for the third of +the cases just given, about 2<sup>1</sup>⁄<sub>2</sub> per cent. excess for the centre +girder, and generally a much smaller error. With this +qualification, the method can, however, be regarded as +approximate only. It is possible to eliminate some part of<span class="pagenum"><a name="Page_134" id="Page_134">[134]</a></span> +the error by lifting the end cross-girders during adjustment, +a less amount than that given by the diagrams, <a href="#Fig73">Figs. 73</a> and +<a href="#Fig74">74</a>, taking care that the centre girder is depressed its full +amount by lifting the centre cross-girders a little more; this +refinement is hardly necessary, and unless controlled by +calculation cannot be depended upon for precise results.</p> + +<p>Particulars are here given of five ordinary cases, comparing +the calculated and observed results of adjustment. The +operation of levelling was conducted by a quick-eyed and +capable assistant, who was not made acquainted with the +results expected, in order to avoid any sub-conscious tendency +to match the calculated figures<span class="nowrap">:—</span></p> + +<p class="center"><span class="smcap">Examples of Centre Girder Adjustments.</span></p> + +<table class="nowrap" summary="Table page 134-135"> + +<tr class="bt bb"> +<th class="center br">—</th> +<th colspan="2" class="center padl1 padr1 br">Calculated.</th> +<th colspan="2" class="center padl1 padr1">Observed.</th> +</tr> + +<tr> +<th class="br"> </th> +<th colspan="2" class="center padl1 padr1 br">in.</th> +<th colspan="2" class="center padl1 padr1">in.</th> +</tr> + +<tr> +<td colspan="5" class="center highline">No. 1.—56-<i>Ft. Span.</i></td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Depression of centre girder</td> +<td colspan="2" class="center padl1 padr1 br">·82</td> +<td colspan="2" class="center padl1 padr1">·84</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of cross-girders at centre</td> +<td colspan="2" class="center padl1 padr1 br">·23</td> +<td colspan="2" class="center padl1 padr1">·22</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of outer girders</td> +<td colspan="2" class="center padl1 padr1 br">·20</td> +<td colspan="2" class="center padl1 padr1">·10 and ·13</td> +</tr> + +<tr> +<td colspan="5" class="center highline">No. 2.—57-<i>Ft. Span.</i></td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Depression of centre girder</td> +<td colspan="2" class="center padl1 padr1 br">·50</td> +<td colspan="2" class="center padl1 padr1">·50</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of cross-girders at centre</td> +<td colspan="2" class="center padl1 padr1 br">·18</td> +<td colspan="2" class="center padl1 padr1">·20</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of outer girders</td> +<td colspan="2" class="center padl1 padr1 br">·11</td> +<td colspan="2" class="center padl1 padr1">·08 and ·10</td> +</tr> + +<tr> +<td colspan="5" class="center highline">No. 3.—67-<i>Ft. Span.</i></td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Depression of centre girder</td> +<td colspan="2" class="center padl1 padr1 br">·70</td> +<td colspan="2" class="center padl1 padr1">·75</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of cross-girders at centre</td> +<td colspan="2" class="center padl1 padr1 br">·15</td> +<td colspan="2" class="center padl1 padr1">·17</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of outer girders</td> +<td colspan="2" class="center padl1 padr1 br">·10</td> +<td colspan="2" class="center padl1 padr1">·09</td> +</tr> + +<tr> +<td colspan="5" class="center highline">No. 4.—68-<i>Ft. Span.</i></td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Depression of centre girder</td> +<td colspan="2" class="center padl1 padr1 br">·70</td> +<td colspan="2" class="center padl1 padr1">·65</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of cross-girders at centre</td> +<td colspan="2" class="center padl1 padr1 br">·20</td> +<td colspan="2" class="center padl1 padr1">·18</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of outer girders</td> +<td colspan="2" class="center padl1 padr1 br">·13</td> +<td colspan="2" class="center padl1 padr1">·14</td> +</tr> + +<tr> +<td colspan="5" class="center highline">No. 5.—52-<i>Ft. and</i> 28-<i>Ft. Spans continuous.<span class="pagenum"><a name="Page_135" id="Page_135">[135]</a></span></i></td> +</tr> + +<tr class="bb"> +<th class="br"> </th> +<th class="center padl1 padr1 br">Long<br />Span.</th> +<th class="center padl1 padr1 br">Short<br />Span.</th> +<th class="center padl1 padr1 br">Long<br />Span.</th> +<th class="center padl1 padr1">Short<br />Span.</th> +</tr> + +<tr> +<th class="br"> </th> +<th class="center padl1 padr1 br">in.</th> +<th class="center padl1 padr1 br">in.</th> +<th class="center padl1 padr1 br">in.</th> +<th class="center padl1 padr1">in.</th> +</tr> + +<tr> +<td class="left padl1 padr1 br">Depression of centre girder</td> +<td class="center padl1 padr1 br">·28</td> +<td class="center padl1 padr1 br">..</td> +<td class="center padl1 padr1 br">·29</td> +<td class="center padl1 padr1">..</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of centre girder</td> +<td class="center padl1 padr1 br">..</td> +<td class="center padl1 padr1 br">·04</td> +<td class="center padl1 padr1 br">..</td> +<td class="center padl1 padr1">·03</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of cross-girders (centre of spans)</td> +<td class="center padl1 padr1 br">·17</td> +<td class="center padl1 padr1 br">·09</td> +<td class="center padl1 padr1 br">·15</td> +<td class="center padl1 padr1">·13</td> +</tr> + +<tr> +<td class="left padl1 padr1 br">Lift of outer girders</td> +<td class="center padl1 padr1 br">·08</td> +<td class="center padl1 padr1 br">..</td> +<td class="center padl1 padr1 br">·08</td> +<td class="center padl1 padr1">..</td> +</tr> + +<tr class="bb"> +<td class="left padl1 padr1 br">Depression of outer girder</td> +<td class="center padl1 padr1 br">..</td> +<td class="center padl1 padr1 br">·01</td> +<td class="center padl1 padr1 br">..</td> +<td class="center padl1 padr1">negli-<br />gible.</td> +</tr> + +</table> + +<p>The method of calculation adopted for these cases was +not precisely that given, though depending upon the same +broad principles. The first cannot be considered a good +example. The last, having continuous girders, of course +needed special treatment.</p> + +<p>Of about seventeen bridges strengthened in the manner +described, the effect generally was satisfactory, in reducing +deflection and vibration; but in two cases of small span, +owing probably to settlement of bedstones, the results were +not so good.</p> + +<p>From first to last the work of putting in a centre girder +takes some little time, owing to the slow progress generally +made in fixing the brackets, preparing packings, etc. The +cost of a typical case was about 23 per cent. of the cost of a +new superstructure, with a 30 per cent. relief of stress.</p> + +<div class="figcenter"><a name="Fig75" id="Fig75"></a> +<img src="images/illo148.png" alt="" width="500" height="303" /> +<p class="caption"><span class="smcap">Fig.</span> 75.</p> +</div> + +<div class="figcenter"><a name="Fig76" id="Fig76"></a> +<img src="images/illo149.png" alt="" width="500" height="283" /> +<p class="caption"><span class="smcap">Fig.</span> 76.</p> +</div> + +<p>A special case of strengthening by a centre girder, having +considerable interest, may be here referred to. The primary +idea involved was not the author’s. The bridge dealt with +has already been noticed under “<a href="#Page_34">Bracing</a>” and a section, +before alteration, shown in <a href="#Fig26">Fig. 26</a>. The span being 85 +feet, there was no room for a centre girder of sufficient depth +above the cross-girders and between the roads, nor was it +considered economical to place the girder wholly below the<span class="pagenum"><a name="Page_136" id="Page_136">[136]</a></span> +floor, because of the costly staging this would have necessitated +for erection purposes, the height above ground level +being very great. A girder was therefore designed, having +open latticing at an angle of 60 degrees, with a bottom boom +to be below the cross-girders, the top being as high above +the rails as could be permitted (see <a href="#Fig75">Figs. 75</a> and <a href="#Fig76">76</a>). A +temporary boom was arranged at the intersection of diagonals, +the lower boom proper not being fixed till the girder +having been lifted into place, with the diagonal members +passing between the cross-girders, allowed this to be done. +The girder for some time carried itself from bearing to bearing, +with the temporary boom in tension, the deflection being +then 2 inches. The permanent boom was then put in place, +and the girder restored as nearly as was practicable to the +camber it was intended to have when complete, but without +throwing, during the process, any improper loads upon the +old work.</p> + +<p>The lower boom being finally riveted up, the cross-girders +were made to bear upon it by suitable packings. There +were, in addition to the new girder, two stiff frames between +the old main girders, to which the new was secured.</p> + +<p><span class="pagenum"><a name="Page_137" id="Page_137">[137]</a></span></p> + +<p>The girder was designed with the intention that under +dead load only the cross-girders should just rest, but throw +no weight, upon the new work, the latter assisting to carry +live load only. The floor beams being of small span, and +securely riveted to the old girder tops, the centre girder was +required to deflect, under its share of live load, the same +amount as the old main girders under the remaining portion, +the three points of support of the cross-girders thus not +altering their relative levels. That this resulted was evident +from the fact that, previous to connecting the cross-frames +to the centre-girder, the work being otherwise complete, a +space between the two of about <sup>1</sup>⁄<sub>2</sub> inch, afterwards filled by +a packing, showed no alteration, the closest measurement +failing to disclose any relative movement upon the passage +of live load. The reduction of vibration was, as might be +expected, very marked.</p> + +<p>In the conduct of that class of strengthening work which +has been dealt with in this chapter, it is essential, in the +author’s judgment, that the man responsible for the detailed +calculations and design should himself see the operations of<span class="pagenum"><a name="Page_138" id="Page_138">[138]</a></span> +adjustment carried out, or delegate it only to one equally +familiar with the requirements.</p> + +<p>Before dismissing the subject, it will be well to refer to +a method of approximately determining flexure curves, of +occasional use in dealing with centre girder or similar questions. +The figure assumed is plotted to an exaggerated scale, +with which object the actual radius of curvature at points +along the girder’s length are first ascertained by the formula</p> + +<p class="formula"><span class="division"><span class="num">E × D</span><span class="denom"><i>f</i> × 2</span></span> = R, radius of curvature in feet,<br /> +</p> + +<p>and the radius of curvature for the diagram by</p> + +<p class="numform"><a name="Form5" id="Form5"></a><span class="formula">12 × R × F<sup>2</sup> = <i>r</i>, radius for plotting, in inches</span> +<span class="number">(5)</span></p> + +<p>E being the modulus of elasticity, D the girder’s depth in +feet, <i>f</i> the mean of the extreme flange stresses per square +inch of gross area, and F the fraction indicating scale as <sup>1</sup>⁄<sub>48</sub>, +where <sup>1</sup>⁄<sub>4</sub> inch = 1 foot. The curve, being plotted, shows by +direct scaling the movement of any point relative to its +original position. Near the ends of the curve where the +radii may be of considerable length, the arcs may be drawn +with the help of template curves, or even set out as pieces of +“straight.”</p> + +<p>When the curve is laid down so that its chord equals the +span to scale, the method involves an error of excess in the +resulting deflection or droop which is as much as 7 per cent. +when the mean radius for plotting equals the span as drawn, +or when the droop of curve approaches one-eighth of the +span. As the exaggeration of curvature is made less pronounced, +this error rapidly diminishes, till for a droop of +about one-sixteenth the percentage is one-fourth part of that +above given. This excess in the droop of curve may be +amended by the following expression<span class="nowrap">:—</span></p> + +<p class="formula">droop - <span class="fsize150">(</span><span class="division"><span class="num">droop<sup>3</sup></span><span class="denom">chord<sup>2</sup></span></span> +× 3·73<span class="fsize150">)</span> = corrected droop, or deflection.</p> + +<p><span class="pagenum"><a name="Page_139" id="Page_139">[139]</a></span></p> + +<p>For some purposes it may be preferable to amend the +radii for plotting, so that the curve, as laid down, shall be<span class="pagenum"><a name="Page_140" id="Page_140">[140]</a></span> +correct, which may be effected by the formula here given, to +be applied to each value of r, as first ascertained<span class="nowrap">:—</span></p> + +<p class="formula"><i>r</i> + <span class="fsize150">(</span><span class="division"><span class="num">chord<sup>2</sup></span> +<span class="denom"><i>r</i></span></span> × ·0625<span class="fsize150">)</span> = corrected plotting radius.</p> + +<p>If, however, the length of curve is made equal to the +span (the chord then being less), and the radii for plotting +as given by <a href="#Form5">(5)</a> are used, the result will for most purposes +be sufficiently precise, though there will now be an error of +a contrary kind, which, for a curve having a droop of one-eighth, +will be about 2 per cent. too little. A somewhat +similar method of setting out deflection curves is described +by Professor Fleeming Jenkin in the article “Bridges” of +the “Encyclopædia Britannica,” but without corrections.</p> + +<p>A careful comparison of results by the above means, with +those calculated, shows that with good draughtsmanship they +may be relied upon for considerable accuracy. Equally +applicable to girders of varying depth and flange stress, +they have also a limited use in cases of continuity.</p> + +<div class="figcenter"><a name="Fig77" id="Fig77"></a><a name="Fig78" id="Fig78"></a> +<img src="images/illo151.png" alt="" width="264" height="550" /> +<p class="caption"><span class="smcap">Figs.</span> 77 and 78.</p> +</div> + +<p><a href="#Fig77">Figs. 77 and 78</a> illustrate the deflection and stress diagrams +for the cross-girders of the bridge supposed to have +been strengthened by a centre-girder, when under the +influence of live load and a centre reaction of a definite +amount. As a matter of convenience, each radius length +has been halved, before correction, so that the resulting +droop of the curve is twice the true amount.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_141" id="Page_141">[141]</a></span></p> + +<h2>CHAPTER XII.<br /> +<span class="chaptitle">CAST-IRON BRIDGES.</span></h2> + +<p>Cast Iron as a material for bridges has of late years fallen +into disrepute. It is now entirely tabooed by the Board of +Trade for railway under-bridges, unless of arched construction. +This condemnation of cast iron followed, and was +apparently the result of, an accident which occurred to an +under-bridge on one of the southern lines, which bridge had +already earned for itself an ill repute by breaking down on a +previous occasion. The ultimate issue was, however, good, +inasmuch as it led to a thorough overhaul of all railway +under-bridges in this country, and the renewal of a great +number no longer in a condition suited to the carriage of +heavy or of passenger traffic; yet there is little doubt +that, in the author’s judgment, many excellent cast-iron +bridges were then removed at considerable cost, to be replaced +by others of wrought iron or steel, which will not last +so long as many of those displaced had done, or would still +have lasted had they not been dismantled.</p> + +<p>The earlier cast-iron bridges were commonly made of +cold-blast iron, a material of such strength and toughness as +to give an extraordinary amount of trouble in breaking up +the heavier parts, when the time arrived to do this, and with +which material ordinary hot-blast iron is not to be compared +for reliability.</p> + +<div class="figcenter"><a name="Fig79" id="Fig79"></a> +<img src="images/illo154.png" alt="" width="500" height="186" /> +<p class="caption"><span class="smcap">Fig.</span> 79.</p> +</div> + +<p>As illustrating the very considerable stress to which cast +iron may be subjected, without of necessity leading to any +mishap, two cases may be cited. The first, a bridge of 32<span class="pagenum"><a name="Page_142" id="Page_142">[142]</a></span> +feet effective span, carrying two lines of way, each pair of +rails being supported upon Barlow rails, forming the bridge +floor, the ends resting upon the bottom flanges of inverted +<span class="lettsymb">T</span>-shaped girders, 2 feet 3 inches deep, as shown in <a href="#Fig79">Fig. 79</a>.</p> + +<p>The extreme fibre stress works out at 2·9 tons per square +inch in tension, and 5·9 tons per square inch compression, +calculated as it would be in ordinary office work; but for +the actual loads, at a span as above, exceeding the clear span +by 6 inches only, and without regard to the effects of eccentric +application of the load. The girders when taken out showed +upon examination no sign of overstrain. The practice of +loading cast-iron girders in this manner cannot, however, be +too strongly condemned, notwithstanding that in this case no +ill resulted. It is evident that a piece of the lower flange +being broken out from this cause, as occasionally happens, +might so reduce the section as to result in complete failure.</p> + +<div class="figcenter"><a name="Fig80" id="Fig80"></a><a name="Fig81" id="Fig81"></a> +<img src="images/illo155.png" alt="" width="500" height="382" /> +<p class="caption"><span class="smcap">Figs.</span> 80 and 81.</p> +</div> + +<p>The second example is that of a small railway under-bridge +of two spans, continuous over the central pier, each +span being 16 feet 6 inches. The rails were supported upon +longitudinal timbers lying within trough-shaped girders, as +shown in <a href="#Fig80">Figs 80 and 81</a>.</p> + +<p>The stress over the pier, in the extreme fibres of the top +flange, is estimated at 4·7 tons per square inch in tension, +but it should be noted that the effect of the timber longitudinal +and rail has been neglected in arriving at this result,<span class="pagenum"><a name="Page_143" id="Page_143">[143]</a></span> +which might possibly on this account be reduced to near +3 tons per square inch.</p> + +<p>The case is noticeable because no evidence of high stress +was apparent. The author saw nothing to suggest sinking +of the central pier, the effect of which, within limits, would +be to further reduce the stress as calculated; but it is quite +possible some slight settlement had occurred; this, as the +spans were so small, would have a sensible effect. While too +much reliance should not, it is clear, be placed upon any +estimated result about which there is a lingering doubt, it +should be remarked that, as it would be necessary the pier +should sink <sup>3</sup>⁄<sub>16</sub> of an inch, for each ton of reduced stress, it +is not probable that the results quoted are in excess to any +material degree; they are, indeed, more probably low, as no +notice has been taken of impact.</p> + +<p>Though cast-iron girders for railway under-bridges are +now prohibited in this country for new works, there are still +uses to which they may be applied, and it may be well to +insist that girders of this material should be fairly loaded, the<span class="pagenum"><a name="Page_144" id="Page_144">[144]</a></span> +weight being brought upon them in such a way that there +shall be no serious secondary stress, such as arises when wide +flanges are made to carry concentrated loads; the author has, +indeed, met with no instance of a cast-iron girder breaking +down under a load fairly applied. Preference is now given +to steel or wrought iron for columns; while this is often +quite justifiable, there remain many cases in which nothing +better need be desired for this purpose than good cast iron, +provided only that the column be loaded in a suitable +manner—i.e., axially, and that the arrangement and details +of the super-structure are such that there shall be no cross-breaking +efforts, or rocking of the column due to temperature +or other causes; unless, indeed, such cross-breaking or +rocking is definitely taken into account in designing the work. +The same care observed in the detailing of cast-iron work +that is not infrequently taken in the design of structures +made of rolled sections would, in suitable cases, the author +has no doubt, yield results just as reliable in practice, with +the advantage of greater resistance to rust, and a reduced +cost in maintenance.</p> + +<p>Good cast iron is, in fact, when used with discretion, a +most excellent material, popular predjudice notwithstanding. +The oldest metallic bridge in this country at the present +moment is of that metal.</p> + +<p>The one chief respect in which cast iron is at a disadvantage +compared with wrought iron or steel is that it does not +give premonitory warning of failure—it remains intact, or it +breaks. The indications of weakness, which may be read by +an experienced inspector of other metallic bridges, are in +a great measure absent. There is also an objection which +may exist, but is to be avoided by good design and care in +the foundry—viz., internal stress due to unequal cooling. +In extreme cases this may lead to fracture before the work<span class="pagenum"><a name="Page_145" id="Page_145">[145]</a></span> +has left the maker’s hands, but it can only occur by neglect +of ordinary precautions.</p> + +<div class="figcenter"><a name="Fig82" id="Fig82"></a><a name="Fig83" id="Fig83"></a> +<img src="images/illo158a.png" alt="" width="550" height="265" /> +<p class="caption"><span class="smcap">Figs.</span> 82 and 83.</p> +</div> + +<p>In a case which has already been referred to in the +chapter on “<a href="#Page_73">Deformations</a>,” <a href="#Page_80">page 80</a>, an outer rib of a +cast-iron arch fractured near the crown after fifty-four years’ +use. Owing to the nature of the design, and the fact that +the near abutment had closed in slightly, bringing the linear +arch of necessity near the lower edges of the arch segment +in question, it was possible to estimate, with a probability of +truth, the extreme fibre stress (tensile) due to the load forces, +at the upper edge where fracture commenced. The result +was very far from explaining the occurrence of the break, +but an examination of the details shown in <a href="#Fig82">Figs. 82 and 83</a> +will make it apparent that, in addition to the tensile stress, as +calculated, there was probably a severe initial stress of the +same character due to irregular cooling in the foundry half a +century before. The sum of these stresses, it is suggested, +placed this particular casting in a critical condition, such +that operations in the construction of a new bridge adjacent +either by producing a small further settlement of the foundations, +of which the author saw no evidence, or, as is more +probable, the attachment of a rope to this rib for the purpose +of keeping a barge in position, which certainly did occur, +gave the arch rib just such an additional strain as to result +in the break shown, though no one of these causes acting +singly would have been sufficient to induce fracture. The +inner ribs were of a much less objectionable section.</p> + +<div class="figcenter"><a name="Fig84" id="Fig84"></a> +<img src="images/illo158b.png" alt="" width="550" height="182" /> +<p class="caption"><span class="smcap">Fig.</span> 84.</p> +</div> + +<p>Cast-iron arches, though still allowed by the Board of +Trade rules, are, indeed, liable to be seriously affected by +settlement, or yielding of the abutments, unless hinges at the +crown are introduced. As an instance of this may be quoted +a bridge of some 45 feet span, in which the arches were cast +in two pieces abutting, and very efficiently bolted together at +the crown, the springing and vertical abutment member of<span class="pagenum"><a name="Page_146" id="Page_146">[146]</a></span> +the spandrel being bolted and built solidly into heavy +masonry. The arch sank at the crown, caused by, or itself +the cause of, a movement of the abutment, with the result +that the lower bolts at the crown joint broke away, rupturing +the casting, as shown in <a href="#Fig84">Fig. 84</a>. The arch must then have +acted as though hinged at the crown, as effectiveness of the +connection was destroyed. It had been better, evidently, if +a proper hinge had originally been provided. The break +happened to occur so as to leave a sufficiently good bearing<span class="pagenum"><a name="Page_147" id="Page_147">[147]</a></span> +face at the crown; there was, indeed, no tendency for one +surface to slide upon another; but in the accidental fracture +of cast iron this cannot be assured, and the liability to it is +a risk which should be eliminated if possible.</p> + +<p>A second case of very much the same character has also +been under the author’s observation, though in this the ends +of the spandrels were not built into the brickwork of which +the abutments were composed. Other instances of fracture +either in the arch proper or in the spandrel work, have come +under notice, though particulars cannot now be adduced; +but the examples cited are by themselves sufficient to justify +the conclusion that it is imprudent to construct a cast-iron +arch without a central pin or its equivalent, unless the abutments, +being exceptionally well founded, may be relied upon +as free from any liability to move. It is, however, to be +borne in mind that movement in the abutments of a small +arch of any given absolute amount is more injurious than the +same amount of movement in the abutments of large arches +of similar design, so that what may be negligible in the latter +case would perhaps be destructive in the former.</p> + +<p>To the absence of ductility and liability to initial stress +must be added yet another disadvantage to which cast-iron +work is prone—viz., the possibility of concealed defects, +blow-holes or cold-shuts; these in good foundry practice are +not very likely to occur, but, as they are possible, cannot +be overlooked in considering the suitability of cast iron for +bridgework, or, indeed, any structural work liable to serious +stress, and particularly tensile stress. With these remarks +by way of qualification, the author reiterates his opinion that +there is still a use for cast iron in bridgework.</p> + +<p>With respect to the repair of cast-iron bridges, but little +is to be said; the possibilities in this direction are very +limited. Occasionally it may be desired to deal with the +fracture of some member in the spandrel bracing of an arch,<span class="pagenum"><a name="Page_148" id="Page_148">[148]</a></span> +when it is commonly sufficient, and even preferable, to limit +the repair work to confining the fractured parts in such a +way as to prevent displacement.</p> + +<p>Rarely it may happen that an arch fractures as a result +of settlement, or other movement, when, if it is decided that +safety of the structure is not imperilled, it will in this case +also be preferable to confine the parts simply by flitch-plates +or other contrivance, with no attempt rigidly to make good +the break, the consequences of which treatment would +probably be to induce fracture in some other place. Effective +strengthening of a cast-iron structure is seldom practicable, +though something may occasionally be done by the +negative process of lightening the dead load, or by remodelling +the permanent way. Arches may, however, be +rendered much more reliable by the introduction of suitable +bracing where this is either wanting or inefficient.</p> + +<p>In scheming such additions it is desirable to arrange for +as little drilling of the old work as is possible; where this +cannot be altogether avoided, the position of the holes should +be carefully chosen with regard to the effect they may have +upon the strength of the old work.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_149" id="Page_149">[149]</a></span></p> + +<h2>CHAPTER XIII.<br /> +<span class="chaptitle">TIMBER BRIDGES.</span></h2> + +<p>Timber bridges, though probably the most ancient in +type, are yet the least durable in any particular instance. +The perishable nature of the material when used for exposed +construction renders it peculiarly liable to develop defects +which quickly put a limit to the life of the structure. In +addition to decay in the body of the main members—which +may perhaps be long delayed, so that a simple beam bridge +may last for many years—there is in more complex designs +decay at connections and joints, which proves very detrimental +to the integrity of the whole. Water running upon +the surface of a member gravitates to its lower end, and, if +there be a joint or other connection, settles there, to be productive +of lasting mischief. From this cause, together with +a very common deficiency of bearing surface relative to the +forces to be met, the joints soon develop some movement; +working of the structure commences under passing loads, its +final destruction being then a question of time only. Each +joint is, in fact, in timber bridge construction a source of +serious weakness to a degree which has no parallel in well-designed +metallic bridges.</p> + +<p>Wrought-iron straps to confine the ends of raking +members, or for other uses, are liable to crush into the wood, +and bolts are apt to enlarge the hole through which they +pass. Wood keys, where these are introduced to prevent one +timber from sliding upon another, are also prone to develop +cracks in the main members, and fibre crippling from excess<span class="pagenum"><a name="Page_150" id="Page_150">[150]</a></span> +of stress. All these defects are, however, in timber-work +more easily defined than efficiently remedied, as it is barely +practicable for any but the harder woods to ensure, for heavy +loads, a sufficiency of bearing surfaces.</p> + +<p>The most readily detected evidence of deterioration in +timber bridges is the sag of its bearing members, or trusses, +for the simple reason that if there is no local trouble at the +joints, there will probably be no appreciable drop at the +centre of the span. The existence of such a depression +may, however, be caused in rare instances by the spread +of the supporting piers or abutments, particularly in +the case of beams trussed by end diagonal rakers and +having no tie.</p> + +<p>Bridges formed of deep trusses, with the road upon the +top, are sometimes found to be wanting in lateral bracing, +the result of which is that the main trusses go out of line, +leaning considerably one way or the other, being checked +only by such rigidity as the joints and floor-beam attachments +may have, with possibly some assistance from the end connections +of the span.</p> + +<p>The decay of piles where entering the ground or water +is, of course, a fruitful source of trouble, as also is the sinking +of piles, where these are insufficient in number, or have +not been well driven in the first place.</p> + +<p>A vital difficulty with timber structures generally is the +uncertainty that will commonly exist as to how far decay +extends in those cases where it has started. Timber does +not necessarily show upon its surface the evidences of internal +rotting. Memel timber may, indeed, be sometimes found +to have become thoroughly unreliable, yet showing no sign +of this upon its painted surface. By sounding the wood +with a hammer, or by probing, its condition may commonly +be ascertained. In cases of doubt, an auger-hole will make +it clear as to whether the interior be good or otherwise, as<span class="pagenum"><a name="Page_151" id="Page_151">[151]</a></span> +to the particular parts tested; but only as to those parts, +leaving it a matter of guesswork as to the remainder.</p> + +<div class="figcenter"><a name="Fig85" id="Fig85"></a> +<img src="images/illo164a.png" alt="" width="550" height="186" /> +<p class="caption"><span class="smcap">Fig.</span> 85.</p> +</div> + +<p>A railway bridge having many of the defects which have +been indicated may be quoted as an example. This structure +crossed a canal, supported upon piles, some of which were in +water, others carrying land spans. The canal span consisted +of four trusses, one under each rail, or nearly so, framed in +the manner shown in <a href="#Fig85">Fig. 85</a>, precise details not, however, +being now available. The trusses, apart from deflection +under live load, sagged considerably—in one instance, +4<sup>1</sup>⁄<sub>2</sub> inches; one inside truss was also leaning towards the +centre line of the bridge as much as 3 inches. One raker, +or diagonal strut, was rotted half through its thickness, and +many other timbers were badly decayed. The end connections +and joints were also in a bad condition. The vertical +tie-bolts of the main trusses were all slack. The piles +generally, many of which were badly decayed, had sunk and +inclined towards one end of the bridge about 4 inches in +7 feet of height, the ground being soft and unreliable.</p> + +<p>Movement under a passenger train crawling over the +bridge was very appreciable, but not startling. There had +been introduced, from time to time, additional timbers and +iron ties, with the object of rendering the spans more reliable, +but leaving it somewhat difficult to determine the function +of the several members. The bridge was, of course, reconstructed.</p> + +<div class="figcenter"><a name="Fig86" id="Fig86"></a> +<img src="images/illo164b.png" alt="" width="550" height="182" /> +<p class="caption"><span class="smcap">Fig.</span> 86.</p> +</div> + +<div class="figc550"><a name="Fig87" id="Fig87"></a><a name="Fig88" id="Fig88"></a> +<img src="images/illo165.png" alt="" width="550" height="209" /> +<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 87.</span> <span class="right49"><span class="smcap">Fig.</span> 88.</span></p> +<p class="caption_e"><span class="smcap">Fig.</span> 87. and <span class="smcap">Fig.</span> 88.</p> +</div> + +<p>An instance may here be cited showing how badly distorted +a timber structure may become without actually +falling. The bridge referred to consisted of three spans of +29 feet, each span having two trusses, between which ran +a colliery tramroad, 1-foot 6-inch gauge; the corves running +upon this, at 4 feet 6 inch centres, weighed, when full, +about 10 cwt. each. The trusses were badly out of shape, +the centre span having sagged 5<sup>1</sup>⁄<sub>2</sub> inches, with one truss of<span class="pagenum"><a name="Page_152" id="Page_152">[152]</a></span> +the same span nearly 10 inches out of line at the centre. +This little bridge, of which some details are shown in <a href="#Fig86">Figs. +86</a>, <a href="#Fig87">87, and 88</a>, had been in use about twenty years.</p> + +<div class="figcenter"><a name="Fig89" id="Fig89"></a> +<img src="images/illo166.png" alt="" width="600" height="212" /> +<p class="caption"><span class="smcap">Fig.</span> 89.</p> +</div> + +<p>A third case which may be named is that of a road bridge, +about 12 feet wide, crossing by thirteen spans a shallow river +liable to floods. The construction was of a simple character, +as indicated in <a href="#Fig89">Fig. 89</a>, and consisted of piles supporting +trussed beams, which had sagged in some instances over<span class="pagenum"><a name="Page_153" id="Page_153">[153]</a></span> +2<sup>1</sup>⁄<sub>2</sub> inches. The bridge had, some years previous to the +author’s inspection, been heavily repaired, many new strut +and stretching pieces having been introduced, the piles also +being reinforced or renewed. Five years before, a traction +engine, said to weigh 5 tons, had passed across the bridge in +safety; but the author noticed that a coal wagon, which, +with the horse, weighed about 50 cwt., when walked slowly +over set up much movement. This bridge had been in use +nearly thirty years, and was very much out of line from end +to end.</p> + +<p>Though timber bridges cannot at the best be considered +durable, yet, by attention to certain points in design and +construction, their length of life may be materially enhanced.<span class="pagenum"><a name="Page_154" id="Page_154">[154]</a></span> +Every cut across the grain may be considered an element of +weakness by exposing the material to quicker decay, for which +reason the number of ends, or of joints, should be reduced +to a minimum. An additional reason for reducing the +number of joints or other +connections is the liability +of these to develop movement, +as already stated, the +yield of any one joint, being +the cause of movement in +others, which might, but for +this, have remained close. +These considerations lead +to the conclusion that fewness +of parts is, in timber +construction, as in structural +work generally, an excellent +principle to observe. Mortising, +elaborate scarf joints, +recessing, or any cutting into +the timber which is not essential, +should be avoided, the +simplest forms of connection +being preferable, if at +all suitable. If a step or +butt surface is wanted for +any member, it is commonly +better to provide this by a +cleat or other added piece, +rather than by cutting into the timber butted against.</p> + +<p>A complicated joint formed in the body of main timbers +can only be renewed by renewal of the timber itself, whereas +by the method indicated the joint is readily tightened, or +re-made, without involving the main member. Bearing<span class="pagenum"><a name="Page_155" id="Page_155">[155]</a></span> +surfaces should be ample, straps of liberal dimensions, +and bolts large (with good washers), both for the sake +of bearing surface in the holes, and reduction of any +liability to bend under cross-stress. In trusses of the +form shown in <a href="#Fig85">Figs. 85</a> and <a href="#Fig86">86</a>, it is desirable to introduce +diagonal members in the middle bay, even though it +may appear that the stiffness of the main beams is sufficient +to render this unnecessary as a matter of strength, as without +these there is apt to be, under rolling load, a slight +distortion, leading to working of the joints and free entry +of moisture. Lateral bracings should also, for much the +same reasons, be introduced, even though they may not +appear necessary in the new structure, with joints all close +and effective.</p> + +<p>Projecting ends of timbers should be carried out well +beyond the requirement of strength or bearing, in order to +ensure a liberal margin for that decay in the end fibres which +commonly develops. Timbers resting upon abutments, or +running into confined spaces, should be arranged for free +ventilation and ready drying. Occasionally joints at the +lower ends of timbers are protected by lead or zinc flashings +to prevent water running into them, a method which should +have some protective value. Whatever measures may be +adopted, whether in the design or execution of timber bridge-work, +will, however, be but little effective, if the timber itself +is not good of its kind, and well seasoned.</p> + +<p>Creosoting to be useful should be thorough and something +more than skin deep. The timber itself should be well dried +before treatment.</p> + +<p>The repair of timber bridges very largely consists in the +renewal of decaying timbers, where this is practicable, or in +adding supplementary pieces where the old cannot conveniently +be displaced. Joints may be tightened up by +hard-wood wedges, properly secured to prevent slacking back,<span class="pagenum"><a name="Page_156" id="Page_156">[156]</a></span> +all bolts being also screwed up tight, perhaps some additional +being introduced.</p> + +<p>Piles standing in water, which have decayed, may be +strengthened by driving other piles between the old, or on +either side, but not of necessity opposite to them, and by +means of waling timbers bolted to the old piles, put in a +position to take load, either by the walings resting upon +their tops, or being bolted to them. Piles decayed where +entering solid ground may generally be strengthened by +bolting on supplementary timbers to reach well above and +below the decayed part, or by cutting out the bad length, +introducing a new piece, and fishing the butt-joints in a +proper manner. But all remedial measures have generally +to be considered with reference to cost, as compared with +the probable increase of life of the structure. With a bridge +in an advanced state of decrepitude, such repairs may prove +anything but economical, and at the best defer reconstruction +but a very moderate length of time.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_157" id="Page_157">[157]</a></span></p> + +<h2>CHAPTER XIV.<br /> +<span class="chaptitle">MASONRY BRIDGES.</span></h2> + +<p>Masonry bridges, in which description it is intended to +include structures both in stone and brick, are, when well +built, amongst the most durable and long-suffering of any +which come under the care of a maintenance engineer; yet +when developing the faults peculiar to their kind, they may +be the occasion of much anxiety, and render necessary frequent +inspection, or even continuous watching.</p> + +<p>Apart from decay of mortar or material, defects may very +commonly be traced to the foundations, or to earth-slips. +Sinking, when uniform, may be quite harmless, though +possibly inconvenient; irregular sinking of piers or abutments +is quite a different matter. It is, however, remarkable +to what a degree sinking may be evident, without of necessity +rendering a structure unsafe. Movement of an amount and +kind which would be fatal to the connections of metallic +bridgework is endured by bridges of stone or brick; not, it +may be, without damage, yet with no occasion for alarm. +The superstructure of metallic bridges may often, however, +be restored to the true level before the mischief has become +serious, whereas in the case of masonry arches this is not +practicable.</p> + +<p>Spreading of the abutments is very seldom the cause of +any great injury to an arch, though it is common enough to +find old and flat arches slightly down at the crown; but the +contrary case of abutments closing in is not very unusual +when these are high, or terminate a viaduct over a deep<span class="pagenum"><a name="Page_158" id="Page_158">[158]</a></span> +valley. Such an abutment may move during or soon after +construction, throwing up the crown of the end span affected; +or, if the arches are very solid and heavy, the abutment may +slide forward at the base, with no sensible reduction of the +opening.</p> + +<p>When a viaduct connects the two ends of a high embankment, +it may happen that the end piers are not clear of the +embankment slope, in which event a pier may, should the +bank slip, move with it, as to that part not in solid ground; +with the result, in a bad case, that it is broken across and the +superstructure imperilled.</p> + +<div class="figcenter"><a name="Fig90" id="Fig90"></a> +<img src="images/illo170.png" alt="" width="450" height="248" /> +<p class="caption"><span class="smcap">Fig.</span> 90.</p> +</div> + +<p>A case of abutment movement is illustrated in <a href="#Fig90">Fig. 90</a>, +which represents the end arch of a masonry viaduct, one +abutment of which had moved forward in the manner +already referred to. From the springing upwards the arch +retained its form to within a short distance of the crown, +where it was forced up in the way indicated. When the +movement became pronounced, heavy timber centering was +introduced, with the object of preventing any mishap, the +damaged portions being ultimately cut out and made good. +The structure was thirty-five years old.</p> + +<p>The practical utility of stop piers in long arched viaducts +is, perhaps, rather in checking movement of the tops of piers<span class="pagenum"><a name="Page_159" id="Page_159">[159]</a></span> +under moving load than in arresting actual failure of a series +of arches. That the tops of piers do move very sensibly +need not be doubted. The author has attempted to measure +this in the case of piers about 60 feet to the springing, by +means of a theodolite placed below, but has reached no more +definite result than that a movement existed, of which he +was not able to determine the amount. If in a viaduct some +arches are more heavily loaded than others, each spreading +slightly, the end piers of the group will move amounts which +together equal the sum of the individual span spreads, with +a tendency in the arches beyond those of the group overloaded +to rise.</p> + +<p>This rocking may be detrimental both to the piers and +arches, and helps to account for the disintegration of mortar +in arches and piers, which not infrequently happens. The +soffits will sometimes be seen with a thick incrustation of +lime, which has washed out of the joints, or from limestone +ballast above, where this has been in use. Arches of tall +viaducts may, indeed, become in so bad a condition that +pieces of stone or brick will drop out, necessitating repair at +heavy expense, of which scaffolding is commonly a large +part.</p> + +<p>Tall piers may be found badly out of the upright due to +sinking of foundations. A marked case of this kind came +under the author’s notice—a viaduct of fifteen semicircular +arches, in which, though many piers were wanting in truth, +one in particular was about 1 foot 4 inches out of vertical, +making one side of the shaft plumb, and doubling the normal +batter of the other. Inquiry showed that in this instance +the pier had never been upright from its earliest history +dating back thirty-six years. This makes clear the desirability, +to avoid hasty conclusions, of ascertaining, when it is +possible to do so, the complete record of any structure.</p> + +<p>A bridge fifty-eight years old, of three skew spans, carrying<span class="pagenum"><a name="Page_160" id="Page_160">[160]</a></span> +a railway over a canal, and having somewhat flat brick +arches with stone quoins upon low piers, developed the somewhat +unusual defect, as to the centre arch, of splitting along +its length for about 10 feet, parallel to and some 7 feet from +one face. In this case there was reason to believe that there +had been considerable local settlement of the piers on that +side of the bridge. The arches were otherwise in bad condition, +the brickwork poor, and the mortar decayed. Each +arch was down at the centre, and displayed a fault not +unusual where bad brickwork joins up to good cut stonework, +the quoins showing a tendency to separate from the +brick rings. Below the bridge were coal-workings.</p> + +<p>Brick arches built in parallel rings sometimes separate +one ring from the other, demonstrating the known propriety +of bonding the rings together properly, and of carrying the +arch round, when building, at its full thickness.</p> + +<div class="figcenter"><a name="Fig91" id="Fig91"></a> +<img src="images/illo172.png" alt="" width="550" height="245" /> +<p class="caption"><span class="smcap">Fig.</span> 91.</p> +</div> + +<p>An instance of bridge failure from a somewhat peculiar +cause may be quoted as of some interest, largely because the +structure was very ancient, having been in existence some +400 years. This bridge, carrying a road, was of the type +usual in old masonry bridges over a river, having small +arches, thick piers, and solid backings to the arches. Two<span class="pagenum"><a name="Page_161" id="Page_161">[161]</a></span> +flood-openings at one end had, by sinking and want of care, +become partly closed. The centre arch had, however, been +widened about 140 years previously. During a severe flood, +the swollen river, overflowing its banks, trespassed upon a +timber yard a little above bridge, and washed down into the +stream a large quantity of sawn timber; this, unable to get +through the main arch with freedom, compacted into a serious +obstruction. The flood water, thus checked in its passage, +seems to have scoured below the timber, and robbed the piers +of such support as they formerly had (see <a href="#Fig91">Fig. 91</a>). The +bridge stood in this condition till the water lowered, when +the middle part of the structure broke up, and subsided into +the hole which had been washed out. But for the monolithic +character of the old work it is probable the bridge would +have failed long before, as the gravel bed on which the piers +stood had been partly undermined +for very many years. +The case is instructive, as +showing how a slight accident—powerless +by itself +to work mischief—may be +very damaging when allied +with so powerful an agent +as running water.</p> + +<div class="figcenter"><a name="Fig92" id="Fig92"></a> +<img src="images/illo173.png" alt="" width="300" height="351" /> +<p class="caption"><span class="smcap">Fig.</span> 92.</p> +</div> + +<p>The enduring character +of even the roughest class +of masonry arch, if only +the material be good and +abutments stable, is shown +when it becomes necessary to destroy old work of this +character. <a href="#Fig92">Fig. 92</a> represents a short length of “cut and +cover” arching in process of demolition, just before it +fell in. The masonry was of hard sandstone rubble and +had been cut away, as shown, till at the point A only a very<span class="pagenum"><a name="Page_162" id="Page_162">[162]</a></span> +small piece of the arch remained, when the length finally +broke up and dropped. Arches have commonly a great +reserve of strength; tunnel linings are, indeed, often badly +out of shape, closed in, and sunken; yet continue, with close +watching, and occasional repairs where the work has decayed +or bulged, to serve the purpose intended.</p> + +<p>Though the equilibrium of masonry arches has been the +occasion of much profound study, and the nicest calculation +has sometimes been applied to the design of such work, yet +it appears that when an arch is well backed up, the theoretical +linear arch need have but little connection with the figure of +the intrados; a statement consonant both with common-sense +and the teachings of experience. With solid backing, this +would indeed seem to be more important than any part of +the arch ring below the top of the backing, the lower part +of the ring serving chiefly to preserve the face of the solid +work. Arches are frequently to be met with so out of their +true shape that but for the consideration named, failure +would seem to be inevitable. The masonry or brickwork +does not always show evidence of damage, if the distortion +has been slow; suggesting that structures of this kind have +a power of accommodation with which they are not generally +credited.</p> + +<p>A noticeable cause of deterioration of masonry structures, +which may be quite independent of settlement, is serious +vibration. This is well known in connection with church +belfries, and is also locally apparent when telegraph or other +poles are attached to masonry parapets. Vibration, when +caused by heavy railway traffic, acting upon arches light or +originally bad, may demoralise the structure to such an extent +that repair becomes exceedingly difficult, because of the extensive +character of the mischief; but masonry bridges substantially +built, and particularly those carrying ordinary roads, +and not subject to much vibration, have great lasting powers,<span class="pagenum"><a name="Page_163" id="Page_163">[163]</a></span> +if repaired with skill, or even let alone. Distortion of the +arch may be quite consistent with practical stability, if the +movement or decay with which it originated is not progressive, +or has been arrested. In this connection a distinction +is to be made between arches well backed, to which the foregoing +remarks apply, and in which the two halves of each +arch may act as separate monoliths meeting at the crown, and +the case of a true arch ring independent of any outside resistance, +such as backing or spandrels may give, and depending +almost wholly upon the proper balance of its component +voussoirs for its stability. With the latter class of structure +no liberties may be taken; whilst with the former there is +seldom cause for fear, if the foundations do not give way, +and the work is dealt with judiciously, if at all. It must, +however, be understood that there are limits as to what +may be done effectively, short of rebuilding, in dealing with +structures in which, perhaps, brickwork is rotten and mortar +decayed and crumbling, the whole being little better than a +broken mass of rubbish.</p> + +<p>In cases where it may be prudent to introduce safety +centring, as in an instance already referred to, it is commonly +expedient to refrain from causing this to take any sensible +part of the load till all movement has ceased, the centres +being at the outset largely precautionary. The requirement +with an arch in bad condition is to avoid disturbing it for +the worse. If the centres are wedged up whilst movement +is still going on, the effect may be to cause the arch to break +up upon the centring, and precipitate repair work which +might otherwise have been left to a more convenient time, +when all movement had stopped or been checked by suitable +measures. Viaduct arches in a bad condition, but not +necessitating the use of relief centres, are commonly dealt +with piecemeal by cutting out the bad places, a small part<span class="pagenum"><a name="Page_164" id="Page_164">[164]</a></span> +at a time, and making good. The work requires the greatest +care of experienced men.</p> + +<p>Pointing masonry or brickwork is effective for little +other than protective purposes, and to check further weathering; +it has obviously no effect upon the interior work, and +if made to cover up the evidences of internal decay, is even +misleading and objectionable. In extreme cases it may be +desirable to open out the road and deal with the filling, to +relieve or to strengthen the outer spandrel walls, which sometimes +bulge, or for other purposes, as, for example, for rebuilding +inner spandrel walls, grouting up or otherwise +repairing solid backing, in which operations some regard +must be had to the effect of the work upon the balance of +the opposing halves of the arch.</p> + +<p>Of the different classes of masonry commonly used in +bridgework, it may be well to remark that good coursed +rubble, or preferably that variety bonding both vertically +and horizontally, of a durable stone, perhaps quite unfit for +any but rough dressing, may make a most lasting structure, +the mortar, of course, being good. Each rough-dressed stone +presents a durable piece, fragments removed separate from +the block, probably along some line of relative weakness—there +is no “nursing” of weak corners; whereas with stones +reduced to a perfectly regular shape by chisel work, the +plane surfaces and geometrical angles are made with partial +regard only to the natural grain of the stone.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_165" id="Page_165">[165]</a></span></p> + +<h2>CHAPTER XV.<br /> +<span class="chaptitle">LIFE OF BRIDGES—RELATIVE MERITS.</span></h2> + +<p>The life of bridges of differing materials has been incidentally +touched upon by the examples quoted, in dealing with +each class of structure. It will be useful to recapitulate +some of the facts adduced, and to compare the terms of life +so far as they appear to be indicated; but in doing this it is +necessary to remember that the life of a bridge of any one +material is inseparably connected with its own private history. +The duration of any such structure may be limited by adverse +conditions, peculiar to the case considered, by defects +of design, material, or workmanship—present from the first—or +by neglect, overloading, or accident, making up its later +record.</p> + +<p>With the exception of timber structures, it is difficult to +find any class of bridges furnishing examples which have +reached the limit of life, independently of the evils named, +and as a result of unavoidable decrepitude. There are none +the less influences at work tending to this condition, and +which it is too much to expect can in all cases be foreseen or +completely guarded against, such as the shifting or scouring +of river-beds, settlement of foundations, natural decay, and +minor faults in design, which even in the most capable hands +may be expected ever to fall short of perfection. At the +best, then, the life of any structure, though long, must have +a limit. With bridges of more average or inferior qualities +the life may be positively short, even without the destructive +influence of overloading.</p> + +<p><span class="pagenum"><a name="Page_166" id="Page_166">[166]</a></span></p> + +<p>Dealing with instances of metallic bridges, the adjacent +table gives the time each had been in existence when removed, +and some indication of the reason for its condemnation. +Those marked with an asterisk were cases of pronounced high +stress. From a study of the table it appears that in actual +practice, making no excuses of any sort, the length of life of +the wrought-iron bridges specified varied between twelve and +thirty-six years; but these figures applied to this collection +of cases only. It is to be remarked that many other bridges +outlasted these, and are likely to continue reliable. These +results show, then, no more than that some wrought-iron +bridges are short-lived, having, in fact, been selected as +examples of this. Longer-lived exceptions are useful, as +indicating that the durability of such structures is by no +means so limited as the table would suggest. It is to be +observed that, as design and maintenance are now better and +more generally understood than when experience was largely +wanting, it is to be expected that later examples will show +no such poor results.</p> + +<p>Of steel bridges little can be said, because of the limited +time this material has been in use; but the generally acknowledged +belief, quite in agreement with the author’s observation, +that steel rusts more freely than wrought iron, suggests +that such bridges will have a shorter lease of life, the more +so that the surface-to-section ratio is also greater for higher +unit stresses, though other adverse influences are much the +same for one material as for the other.</p> + +<p>Of cast-iron structures but few cases have been given; of +these, cast-iron arches have been noticed as developing defects +which led to reconstruction, or to limiting the loads to be +carried. Plain cast-iron girders, on the other hand, have +never, under the author’s direct observation, been removed +for any other reason than because they were cast iron, or +from over-stress, due to the growth of loads; never from<span class="pagenum"><a name="Page_167" id="Page_167">[167]</a></span> +defects or wasting, though it is not suggested no such cases +exist. The author has no evidence which points to what +may be the limit of life of a good cast-iron girder fairly +treated.</p> + +<p class="center"><i>Examples of Life of Metallic Bridges.</i></p> + +<table class="nowrap" summary="Table page 167"> + +<tr class="bt bb"> +<th class="center padl1 padr1 br">Description.</th> +<th colspan="2" class="center padl1 padr1 br">Span.</th> +<th class="center padl1 padr1 br">Age.</th> +<th class="center padl1 padr1 br">Defect.</th> +<th class="center padl1 padr1">Reference.</th> +</tr> + +<tr> +<th class="br"> </th> +<th class="center padl1 padr1">ft.</th> +<th class="center padl1 padr1 br">in.</th> +<th class="center padl1 padr1 br">Years.</th> +<th class="br"> </th> +<th> </th> +</tr> + +<tr> +<td colspan="6" class="center highline"><i>Wrought Iron.</i></td> +</tr> + +<tr> +<td class="left padl1 padr1 br"><span class="noshow">*</span>Plate girders</td> +<td colspan="2" class="center padl1 br">(?)</td> +<td class="center padl1 padr1 br">12</td> +<td class="center padl1 padr1 br">Loose rivets</td> +<td> </td> +</tr> + +<tr> +<td class="left padl3 padr1 br">*Ditto</td> +<td class="right padl1 padr1">35</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">12</td> +<td class="center padl1 padr1 br">Ditto</td> +<td class="left padl1 padr1"><a href="#Page_52">p. 52</a></td> +</tr> + +<tr> +<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td> +<td class="right padl1 padr1">55</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">14</td> +<td class="center padl1 padr1 br">Rust. Distortion</td> +<td class="left padl1 padr1"><a href="#Page_78">pp. 78</a> & <a href="#Page_97">97</a></td> +</tr> + +<tr> +<td class="left padl1 padr1 br"><span class="noshow">*</span>Trough girders</td> +<td class="right padl1 padr1">11</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">16</td> +<td class="center padl1 padr1 br">Loose rivets. Cracked webs</td> +<td class="left padl1 padr1"><a href="#Page_50">p. 50</a></td> +</tr> + +<tr> +<td class="left padl1 padr1 br"><span class="noshow">*</span>Plate girders</td> +<td colspan="2" class="center padl1 br">(?)</td> +<td class="center padl1 padr1 br">22</td> +<td class="center padl1 padr1 br">Loose rivets</td> +<td> </td> +</tr> + +<tr> +<td class="left padl1 padr1 br"><span class="noshow">*</span>Twin girders</td> +<td class="right padl1 padr1">31</td> +<td class="right padl1 padr1 br">6</td> +<td class="center padl1 padr1 br">23</td> +<td class="center padl1 padr1 br">Weak. Cracked webs</td> +<td class="left padl1 padr1"><a href="#Page_13">p. 13</a></td> +</tr> + +<tr> +<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td> +<td class="right padl1 padr1">35</td> +<td class="right padl1 padr1 br">6</td> +<td class="center padl1 padr1 br">23</td> +<td class="center padl1 padr1 br">Weak. Distorted.</td> +<td class="left padl1 padr1"><a href="#Page_74">p. 74</a></td> +</tr> + +<tr> +<td class="left padl1 padr1 br"><span class="noshow">*</span>Plate girders</td> +<td class="right padl1 padr1">42</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">23</td> +<td class="center padl1 padr1 br">Loose rivets. Cracked webs</td> +<td class="left padl1 padr1"><a href="#Page_21">p. 21</a></td> +</tr> + +<tr> +<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td> +<td class="right padl1 padr1">72</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">29</td> +<td class="center padl1 padr1 br">Weak. Loose rivets</td> +<td class="left padl1 padr1"><a href="#Page_53">p. 53</a></td> +</tr> + +<tr> +<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td> +<td class="right padl1 padr1">47</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">24</td> +<td class="center padl1 padr1 br">Distortion</td> +<td class="left padl1 padr1"><a href="#Page_9">p. 9</a></td> +</tr> + +<tr> +<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td> +<td class="right padl1 padr1">32</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">32</td> +<td class="center padl1 padr1 br">Rust. Cracked webs</td> +<td class="left padl1 padr1"><a href="#Page_14">p. 14</a></td> +</tr> + +<tr> +<td class="left padl3 padr1 br">*Ditto</td> +<td class="right padl1 padr1">25</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">36</td> +<td class="center padl1 padr1 br">Weak</td> +<td class="left padl1 padr1"><a href="#Page_63">p. 63</a></td> +</tr> + +<tr> +<td colspan="6" class="center highline"><i>Steel.</i></td> +</tr> + +<tr> +<td class="left padl1 padr1 br">*Trough girders</td> +<td class="right padl1 padr1">15</td> +<td class="right padl1 padr1 br">8</td> +<td class="center padl1 padr1 br">32</td> +<td class="center padl1 padr1 br">Weak. Rusted</td> +<td class="left padl1 padr1"><a href="#Page_68">pp. 68</a> & <a href="#Page_98">98</a></td> +</tr> + +<tr> +<td colspan="6" class="center highline"><i>Cast Iron.</i></td> +</tr> + +<tr> +<td class="left padl1 padr1 br">*Girders</td> +<td class="right padl1 padr1">32</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">36</td> +<td class="center padl1 padr1 br">Weak</td> +<td class="left padl1 padr1"><a href="#Page_141">p. 141</a></td> +</tr> + +<tr> +<td class="left padl1 padr1 br"><span class="noshow">*</span>Girders, cast-iron piles</td> +<td colspan="2" class="center padl1 br">(?)</td> +<td class="center padl1 padr1 br">44</td> +<td class="center padl1 padr1 br">Ditto</td> +<td> </td> +</tr> + +<tr> +<td class="left padl1 padr1 br"><span class="noshow">*</span>Arches</td> +<td class="right padl1 padr1">45</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">55</td> +<td class="center padl1 padr1 br">Crack. Settlement</td> +<td class="left padl1 padr1"><a href="#Page_145">p. 145</a></td> +</tr> + +<tr class="bb"> +<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td> +<td class="right padl1 padr1">100</td> +<td class="right padl1 padr1 br">0</td> +<td class="center padl1 padr1 br">62</td> +<td class="center padl1 padr1 br">Crack. Deformation</td> +<td class="left padl1 padr1"><a href="#Page_80">pp. 80</a> & <a href="#Page_145">145</a></td> +</tr> + +</table> + +<p>With timber bridges the length of life appears to be about +twenty-five years, but this is very largely dependent upon +the question of maintenance, and may range from fifteen to +thirty-five years. It is manifest that repairs, when extensive +and consisting of the renewal of the more essential parts of<span class="pagenum"><a name="Page_168" id="Page_168">[168]</a></span> +the structure, border upon reconstruction, and may be continued +indefinitely. The length of life in ordinary cases, +and for the timbers commonly used in this country, may, for +railway bridges, be taken as stated, though for highway +bridges possibly longer.</p> + +<p>Of masonry bridges little is to be said but that it is only +in cases of bad work or material—with, perhaps, vibration +or settlement—that these have a shortness of life comparable +with that of defective metallic bridges. Where these adverse +conditions obtain, heavy repairs may be necessary before the +structure is many years old; but, under reasonably fair conditions, +bridges of masonry may be expected to outlast structures +in any other material. Apart from road-bridges which +are admittedly long-lived, there are a large number of railway +bridges and viaducts of masonry which, despite heavy loads +and vibration, have been in use for the past seventy years.</p> + +<p>Dealing with the cost of maintenance, this with bridges +of wrought iron or steel should result simply from scraping +and painting, with such other incidental work as may be +necessary on the subsidiary materials used in the structure. +The cost of painting will vary with the height and character +of the bridge, and the amount of scaffolding, if any, and +may be from 5<i>d</i>. to 1<i>s</i>. or more per square yard; this if +distributed over five years, a not unusual interval between +each painting, works out at an appreciable figure, which may +vary from one-third to one per cent. of the first cost, per +annum. The yearly cost of painting steel-work will, for +shorter intervals, come to a somewhat higher figure. Serious +occasional items of expense are those which should not be +necessary, repairs and possibly strengthening, which may +raise the total cost of maintenance very considerably.</p> + +<p>Cast-iron bridges, being less liable to rust, cost less for +painting than other metallic bridges; and if the cast iron is +closed in by masonry, practically nothing; they do, indeed,<span class="pagenum"><a name="Page_169" id="Page_169">[169]</a></span> +involve very little expenditure in the maintenance. Not +being very amenable to repair or strengthening, cast-iron +bridges commonly remain very much as built, or are reconstructed.</p> + +<p>The proper care of timber bridges may become costly as +the structure gains in age, and soon grow to a very wasteful +expenditure. This is evident when it is considered that +repairs may be necessary after ten years, and that whatever +may have been the cost of any part when new, it cannot be +replaced for the same amount, having regard to the labour +expended in removing the old member, and the special precautions +to be observed in dealing with an old structure +carrying its load. In addition to ordinary repairs, there will +be paint or other protective coating to be applied, though +this is not always done.</p> + +<p>The upkeep charges of masonry bridges will be practically +nothing in favourable cases; but, on the other hand, where +extensive repairs become necessary, may reach a considerable +amount. Exceptional outlays are, however, infrequent, and +may be spread over a large number of years, in those rare +instances in which they become imperative.</p> + +<table class="nowrap" summary="Table page 169"> + +<tr> +<th class="center"><i>Durability.</i></th> +<th class="center padl3 padr3"><i>Maintenance<br />Charges.</i></th> +<th class="center"><i>First Cost.</i></th> +</tr> + +<tr> +<td class="left">Masonry</td> +<td class="left padl3 padr3">Masonry</td> +<td class="left">Timber</td> +</tr> + +<tr> +<td class="left">Cast Iron</td> +<td class="left padl3 padr3">Cast iron</td> +<td class="left">Masonry</td> +</tr> + +<tr> +<td class="left">Wrought iron</td> +<td class="left padl3 padr3">Wrought iron</td> +<td class="left">Steel</td> +</tr> + +<tr> +<td class="left">Steel</td> +<td class="left padl3 padr3">Steel</td> +<td class="left">Cast iron</td> +</tr> + +<tr> +<td class="left">Timber</td> +<td class="left padl3 padr3">Timber</td> +<td class="left">Wrought iron</td> +</tr> + +</table> + +<p>For purposes of ready comparison, placing bridges of the +materials under review in order of durability, they would +appear as in column 1 of the table above; in order of low +maintenance charges, generally as in column 2; and in order +of low first cost, as in column 3. With respect to the question +of first cost, the arrangement of the third column applies +only to small bridges, say, up to 70-foot span; and, being<span class="pagenum"><a name="Page_170" id="Page_170">[170]</a></span> +liable to variation with the conditions, is but approximately +correct. The less costly descriptions of masonry are alone +considered in this connection.</p> + +<p>It may be added that the total yearly charge of interest +on first cost, redemption, and maintenance, appears to be for +masonry bridges, about one-half only of the corresponding +totals for bridges of wrought iron, steel, or timber; those of +cast iron taking an intermediate place.</p> + +<p>Summarising the above considerations, and dealing with +the relative merits of bridges in the different materials, it +may be broadly stated that for conditions at all suitable +nothing seems to be superior to masonry—including in +this description first-class brickwork—whether for road or +railway bridges. One pronounced advantage of such bridges +with respect to length of life, is that they are but little +affected by increase of loads. The mass of a masonry arched +structure is so great, and the margin of strength commonly +so liberal, that considerable increments of load may have but +little effect upon the reliability of the structure.</p> + +<p>Cast iron has, for bridges of simple design, a strong claim +to the second place, though its want of ductility is a demerit. +It can, however, have but a limited use in bridge construction, +being applicable only to small girder spans and skilfully-designed +arched structures.</p> + +<p>For bridges of moderate span in which the question of +cost does not control the matter, wrought iron should probably +come next, steel being best reserved for those of a larger +size, in which weight of the structure greatly affects economy.</p> + +<p>Timber may be regarded as a material rarely to be used +in this country for structures to occupy a permanent place, +unless for urgent economic reasons of the moment.</p> + +<p>While expressing this general view of the matter, it is to +be admitted that the propriety of these conclusions is somewhat +discounted by the difficulty there now is in obtaining<span class="pagenum"><a name="Page_171" id="Page_171">[171]</a></span> +cast iron of the desired toughness, or wrought iron with +promptitude and sufficient variety of section at a reasonable +price.</p> + +<p>It is apparent, also, that the choice of material may be +largely influenced—even determined—by considerations of +headway, construction depth, or character of foundations; so +that no very definite rules can be usefully laid down, though +the adoption of unsuitable materials has not been so unusual +as to make these suggestions altogether purposeless.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_172" id="Page_172">[172]</a></span></p> + +<h2>CHAPTER XVI.<br /> +<span class="chaptitle">RECONSTRUCTION AND WIDENING—CONCLUSION.</span></h2> + +<p>The need for the reconstruction of bridges, arising from +various causes which have been treated in the preceding +chapters, original weakness or faults in design, decay or defects, +may also be caused by such extraneous considerations as the +growth of loads, widening of the openings spanned, or improvement +of the headway.</p> + +<p>In any case, a precise survey or measuring up of the +structure and its immediate surroundings is required, in the +execution of which the greatest care is desirable, and with +respect to which it may be well to give a few hints.</p> + +<p>The surveying chain, when used, should be tested, the +measure of accuracy required rendering this imperative in a +degree peculiar to work of this class. Linen tapes should +also be compared with a reliable steel tape, and used only +where sufficiently accurate for the particular purpose. A +careful and observant man may do very good work with a +linen tape, making just that allowance in the sag of the tape +which corrects for the inevitable stretch; but there is still +some uncertainty involved in its use, and the author prefers +to rely upon a steel tape, notwithstanding the inconvenience +commonly experienced from its intractable nature and liability +to damage.</p> + +<p>Instruments used must also be in the best adjustment; +as errors, which in ordinary field work may not be of great +importance, are inadmissible in bridge work.</p> + +<p>It is not necessary here to enter upon the methods of<span class="pagenum"><a name="Page_173" id="Page_173">[173]</a></span> +small survey work, but it may be desirable to point out that +abutment walls should be plumbed for verticality; girders, +which are liable to be leaning, defined in position by reference +to their bearings; and generally that it should never be taken +for granted that there is truth in old work, or that this may +be assumed as to line or level.</p> + +<p>In cases where disputes with any local authority as to +headway are likely to arise, it is prudent to supplement the +information as to level of soffits by rods cut to length in strict +agreement with the clear height, before removing the old +superstructure.</p> + +<p>It is apparent that in cases where the superstructure is +already condemned, the detail measurements may be confined +to that part of the structure which is to remain, securing +only such information as to the work superseded which may +be required in arranging for the new work.</p> + +<p>In taking particulars of skew bridges, needless as the +warning may seem, it is yet necessary to remark that there +may be right or left-hand skews which will not reverse. +The author has known a disregard of this to make serious +trouble in two instances.</p> + +<p>Dealing first with reconstruction of the superstructure of +railway under-bridges, these, if small, may not give much +trouble, though the demand for greater strength will, perhaps, +involve some difficulty in working to the limiting construction +depth—i.e., the distance from the top of rail to soffit of +bridge—particularly as many old bridges have a very niggardly +allowance in this respect. It may be, and quite +commonly is, necessary to raise the rails a small amount, or, +if headway is not restricted, to lower the soffit. Clearances +between the running gauge and girder-work may also be +difficult to secure, more liberal allowances being now required +than formerly. Complications in the character of the permanent +way, so frequently found upon old bridges, should,<span class="pagenum"><a name="Page_174" id="Page_174">[174]</a></span> +of course, be got rid of, if possible; but the endeavour may +introduce further difficulties. Regard must throughout be +had to the methods to be adopted in removing old work and +in erecting the new. Perhaps the simplest case to deal with +is that where girders lie parallel to, and under the rails, with +a timber floor upon which the permanent way is carried, as +sections of the road involving pairs of girders may be readily +removed, and replaced by the new girder-work (see <a href="#Fig93">Fig. 93</a>). +If the deck be of trough flooring or old rails, the matter may +not be so simple, as regard must then be had to the position +of joints in the existing floor, and the new work be schemed +with respect to the number and office of girders which may +be got in at any one breaking of the road. A slight slewing +of rails may sometimes be resorted to on occasion, where this +has the effect of releasing some part of the work not otherwise +to be dealt with.</p> + +<div class="figcenter"><a name="Fig93" id="Fig93"></a><a name="Fig94" id="Fig94"></a> +<img src="images/illo186.png" alt="" width="450" height="325" /> +<p class="caption"><span class="smcap">Figs.</span> 93 and 94.</p> +</div> + +<p>Bridges having main girders, with timber or trough flooring +resting upon the bottom flanges, or suspended by bolts, +will, if carrying many roads, cause some little difficulty, as +the dismantling of any one span involves the disturbance of<span class="pagenum"><a name="Page_175" id="Page_175">[175]</a></span> +others; where, however, many lines are concerned, it may +be feasible to put one or more temporarily out of use, preserving +the continuity of traffic over those which remain, +but refraining from any diversion of the more important +roads.</p> + +<p>Somewhat similar troubles occur where main girders with +cross-girders at the lower flanges are found, particularly if +the cross-girders are arranged in line, the ends abutting on +each side of the same main girder webs. It is seldom, however, +that this construction is used in bridges of small span +carrying many roads; but where it does occur, it may necessitate +the use of timbering below, to carry the ends of cross-girders +when freed from their supporting main girders. +(See <a href="#Fig94">Fig. 94</a>.)</p> + +<div class="figcenter"><a name="Fig95" id="Fig95"></a> +<img src="images/illo187.png" alt="" width="500" height="109" /> +<p class="caption"><span class="smcap">Fig.</span> 95.</p> +</div> + +<p>If it is proposed to use new main and cross-girders, it is +desirable to arrange these in the manner already recommended, +the cross-girders not in line; this has peculiar advantages in +reconstruction work, as the bolting up and riveting of the +cross-girder ends is not hampered by other cross-girder +attachments, leaving each piece of floor complete in itself. +Twin main girders are occasionally used with the same object, +and present the advantage of simplicity in erection and independence +of one span from those adjoining (see <a href="#Fig95">Fig. 95</a>); +but the method is wasteful of space, and involves a somewhat +greater total weight in the main girders.</p> + +<p>The foregoing observations apply more generally to small<span class="pagenum"><a name="Page_176" id="Page_176">[176]</a></span> +single-span bridges, the operations on which may be effected +without any material disturbance of traffic arrangements; +though this can seldom be wholly avoided, it should be confined, +where practicable, to a few hours on a Sunday.</p> + +<p>The reconstruction of bridges over 70-feet span may have +to be dealt with under more elaborate arrangements, if carrying +two lines only, possibly with single-line working for a +period more or less protracted; or it may be necessary, having +regard to the weight of main girders to be removed, to carry +the whole structure upon temporary staging, supporting the +road independently, cutting up and removing the old work, +and later putting the new work in place, either by detailed +erection in its ultimate position, or by erection at one side +and drawing across. The latter method is, however, commonly +reserved for cases in which no special staging is used +under the old structure.</p> + +<p>Bridges of a number of openings are usually dealt with +by securing full possession of one road at a time, which for +double-line bridges necessitates single-line working. It is +commonly out of the question, even with moderate spans, +to deal with some of these only at a time, and so avoid continuous +possession of one road, for a lengthened period; and +it can only, as a rule, be managed where the ends of the new +main girders do not in any way interfere with those of the +old, and where it is not necessary to reset bed-stones, or make +other alterations in the bearings which necessitate the complete +clearance of the pier-tops. In exceptional cases it may +be found possible to arrange for the complete removal of a +small number of moderate spans on a Sunday, and the putting +in place of the new work, as in the case of small single spans.</p> + +<p>Spans erected to one side of the final position, to be later +travelled across, are commonly mounted upon gantry staging, +and up to 50 tons weight may rest directly upon rails well +greased. The power adopted to move the span is usually<span class="pagenum"><a name="Page_177" id="Page_177">[177]</a></span> +that of screw or hydraulic jacks, or occasionally engine haulage, +special tackle being in that case necessary to apply the +engine power in the right direction. If the time is limited, +or weight considerable, a more elaborate arrangement by +which the load is supported upon wheels, may be necessary, +with a view to reducing the resistance to a manageable +amount. All work which it is possible to do before shifting +into place, including the permanent way, where this is of a +special character, should be executed in advance, leaving only +the rail connections to be made good when the span is in +position.</p> + +<p>Where timber staging is used to carry the permanent +way before dismantling an old structure, it is convenient to +begin by placing stout balks of timber under the sleepers +from end to end of the bridge, or directly under the rails if +space is limited; the staging is then arranged to give support +to the running timbers.</p> + +<p>Metallic under-bridges of ample headway, perhaps over +coal-workings (since settled down), or for some less sufficient +reason made of metal, may be cheaply replaced by brick +arches built below the old superstructure, the springings of +the arch being checked into the face of the existing abutments. +With stout walls, careful work and good material will make +this an efficient and durable job.</p> + +<p>It being a primary condition of reconstruction work to +interfere but little with ordinary traffic arrangements, single-line +working is avoided wherever practicable; as this, always +objectionable, may necessitate the erection of special signals +and signal apparatus, besides the temporary remodelling of +the roads, and in this country may involve also a Board of +Trade inspection—altogether a troublesome and expensive +business.</p> + +<p>Any bridgework which is accompanied by breaking or +blocking the road can only be undertaken by arrangement<span class="pagenum"><a name="Page_178" id="Page_178">[178]</a></span> +with the traffic department, after notice duly given and +published in the periodical record of such matters; it is +generally fixed for a Sunday. Preparatory to this, it is +necessary to make all ready by getting as much done beforehand +as is possible. Wherever practicable and prudent, the +whole work is released from its surroundings, masonry cut +away, rivets cut out and replaced by good bolts, nuts removed +from holding down bolts, or the bolts cut through, etc. +Particular care should be exercised to ascertain what remains +to be done immediately prior to removal. It is necessary +further to arrange for trucks to be in readiness to receive old +material, and others containing new girder work to be conveniently +stationed, having been loaded up to come right end +foremost; engine power, cranes, empty and loaded trucks, +being all marshalled and so placed as to be available in proper +order, and as wanted. There must be no mistake as to what +roads will be fouled by swinging the crane with its load, or +as to the reach of the crane in effecting its work.</p> + +<p>The whole operation to be conducted on any Sunday +should be well within the resources of the men and plant +engaged in it, or so managed that it is a matter of no serious +importance if the whole cannot be completed as originally +desired.</p> + +<p>Possession of the roads to be blocked having been secured +between certain hours, if some part only of the work to be +carried out has been completed as the time grows short, any +attempt to execute the remainder may result in checking +trains until such time as the line may be reported clear—a +contingency to be avoided—though the temptation to save +another Sunday’s work by delay of a few minutes to some +one train may be considerable.</p> + +<p>In scheming any reconstruction, it may be insisted that +at least one feasible method of carrying out the work must +be secured, though it is the author’s experience that frequently<span class="pagenum"><a name="Page_179" id="Page_179">[179]</a></span> +some other method than that contemplated is in the end +adopted, when, some months later, the final arrangements +for fixing are made. The tendency of a zealous erector is +commonly to take full advantage of any facilities offered, +with a view to a moderate amount of work being done at any +one time, and to achieve as much more as he can himself +secure by scheming, or a liberal use of labour; all Sunday +work, with attendance of engines and cranes, being of necessity +expensive.</p> + +<p>Railway over-bridges do not commonly present any +particular difficulties. The spans to be dealt with are +usually small, and the weights to be lifted moderate. The +height above rails may, however, be above the lift of any +crane; and, for the purpose of raising main girders, a derrick +may become necessary, the rearing and guying of which may +block many roads during the time it is in use. The girders +of larger spans, too unmanageable to be lifted whole, may +be erected upon staging; to secure the requisite headway +it may be necessary to build the girders at a level above +that at which they will finally be, lowering them into +position when self-supporting, and after the removal of the +staging.</p> + +<p>The widening of railway under-bridges is, as a rule, a +matter of no special difficulty, but some remarks may be of +use. Widenings should be planned with a regard to later +reconstruction of the original bridge, if that is at all likely +to be necessary, and with the object that, when complete, +the whole should be a consistent piece of work.</p> + +<p>It may, indeed, happen that widening of a bridge may +involve the remodelling or reconstruction of the old work, +to enable the new roads to be laid down as desired; this is +more likely to be necessary where there exist main girders +not competent to take any additional load, and to duplicate +which would sacrifice space between the new and old roads;<span class="pagenum"><a name="Page_180" id="Page_180">[180]</a></span> +or it may be unavoidable because of slewing of the old rails, +as part of a general rearrangement.</p> + +<div class="figcenter"><a name="Fig96" id="Fig96"></a> +<img src="images/illo192.png" alt="" width="450" height="195" /> +<p class="caption"><span class="smcap">Fig.</span> 96.</p> +</div> + +<p>Dealing with widenings simply, there is often some little +trouble in contriving a connection between the new and the +old work, as this may have to be made under, or close to, the +sleeper ends of the existing roads. It is desirable to arrange +this part so that no drilling of old work for rivets or bolts +shall be necessary, there being, in fact, no strict connection. +By judicious scheming, this may be effected, whilst securing +freedom from leakage of water at the joint. (See <a href="#Fig96">Figs. 96</a> +and <a href="#Fig97">97</a>.) If tying of the new and old structure is desired, +this can usually be done quite simply, well below the floor at +some more accessible level.</p> + +<div class="figcenter"><a name="Fig97" id="Fig97"></a><a name="Fig98" id="Fig98"></a> +<img src="images/illo193.png" alt="" width="350" height="453" /> +<p class="caption"><span class="smcap">Figs.</span> 97 and 98.</p> +</div> + +<p>The strict jointing-up of trough flooring, new to old, at +right angles to the troughs, cannot be contemplated, but may +be dealt with by treating each part independently, the ends +being near together, separated by the space of an inch or so. +Each trough end being closed up by a diaphragm or oak +block to prevent ballast dropping through, the top of the +space may be covered by a loose strip, secured to prevent it +shifting, the bottom provided with a gutter of liberal dimensions +to take away leakage, as it is practically impossible to +make this arrangement “drop dry” under the conditions +common in executing work of this kind (see <a href="#Fig98">Fig. 98</a>).</p> + +<p><span class="pagenum"><a name="Page_181" id="Page_181">[181]</a></span></p> + +<div class="figcenter"><a name="Fig99" id="Fig99"></a><a name="Fig100" id="Fig100"></a> +<img src="images/illo194.png" alt="" width="350" height="375" /> +<p class="caption"><span class="smcap">Figs.</span> 99 and 100.</p> +</div> + +<p>Where trough flooring, new and old, has to be made good +parallel to the troughs, the difficulty of making a direct connection +is less marked, and it is not unusual to introduce a +strip cover simply; but if accessible, the work is still troublesome, +as there is commonly a want of strict alignment and +truth as to level, between the new and the old troughs. It +is preferable to arrange for junctions of a more convenient +type, as in <a href="#Fig99">Figs. 99 and 100</a>.</p> + +<p>When widening masonry arch bridges by girder-work, it +is desirable to insure that any girders parallel to the masonry +face shall be sufficiently far removed from it to enable painting +to be executed. The space remaining between the girder +and the arch may then be bridged by floor-plates, or an extension +of the timber floor if that is adopted.</p> + +<p><span class="pagenum"><a name="Page_182" id="Page_182">[182]</a></span></p> + +<div class="figcenter"><a name="Fig101" id="Fig101"></a><a name="Fig102" id="Fig102"></a> +<img src="images/illo195.png" alt="" width="350" height="529" /> +<p class="caption"><span class="smcap">Figs.</span> 101 and 102.</p> +</div> + +<div class="figcenter"><a name="Fig103" id="Fig103"></a> +<img src="images/illo196.png" alt="" width="300" height="289" /> +<p class="caption"><span class="smcap">Fig.</span> 103.</p> +</div> + +<p>In effecting a junction such as this, the author has used +the arrangement shown in <a href="#Fig101">Fig. 101</a>, the advantage being +that the piece of connecting-floor is sufficiently wide, and +also sufficiently flexible, to allow the girder-work freedom to +deflect without doing harm. The load carried by the width +of floor is, as to one part, delivered well on to the old +masonry, in preference to being imposed near to the face. +If it should for any reason be imperative to place the girder +close to the arch face, it is preferable to scheme the floor so +that there shall be no actual contact, the new floor in that +case slightly overhanging the masonry, as in <a href="#Fig102">Fig. 102</a>, or +dealt with as in <a href="#Fig103">Fig. 103</a>, if depth is restricted.</p> + +<p>The widening of masonry arch bridges by masonry, calls +for no other remark than that the new work should be free +from the old; though it may be advisable, when the widening<span class="pagenum"><a name="Page_183" id="Page_183">[183]</a></span> +is narrow, to tie the new work to the old in such a way as +to permit independent settlement.</p> + +<p>If the widening is exceptionally narrow, there may be +no choice but to bond the new and old work together, and +in the best manner, with the object of minimising the risk +of separation.</p> + +<p>The above matters relative to widenings, though apparently +trifling, may by neglect cause much trouble and expense +in maintenance. They principally concern small bridges, +the extension of larger structures coming rather in the category +of independent works.</p> + +<p><span class="pagenum"><a name="Page_184" id="Page_184">[184]</a></span></p> + +<h3><span class="smcap">Conclusion.</span></h3> + +<p>In bringing these chapters, dealing largely with questions +affecting maintenance, to a close, it may be well to draw +attention to the fact that economy in design (apart from +improper reduction of sections) goes hand-in-hand with +economy of upkeep. Given good material, that which favours +low first cost, simplicity of detail, fewness of parts, absence +of smithing, the use of rolled sections, and good depth to +girders, favours also small expenditure in maintenance. +The less complex the design, the easier will it be to keep the +structure in order; the less the number of parts, the fewer +will be the connections. Freedom from smithing eliminates +liability to failure at cranks, or other work which has been +subject to fire. It is apparent also that the free use of rolled +instead of built-up sections, reduces the liability to trouble +from bad riveting, or from good riveting overstressed. A +liberal depth to all girders, by reducing deflections, limits the +inclination of the ends and gives the connections a better +chance of remaining intact. Lastly, with work of this +character, the labour of scraping and painting is simplified +and cheapened.</p> + +<p><span class="pagenum"><a name="Page_185" id="Page_185">[185]</a></span></p> + +<p>The author wishes to reiterate the statement made in +the opening paragraphs of this book, that all instances of +decrepitude, failure, or peculiar behaviour cited, have been +under his direct observation. The fact is insisted upon +simply that the reader may appreciate that the information +is at first hand.</p> + +<p>It has not been thought necessary, nor was it considered +desirable, to indicate the locality of each case referred to; +but it may be said that the matter of these chapters has been +accumulating during many years, and relates to structures +under the control of many different bodies.</p> + +<p>The study of old bridges is strongly recommended, +particularly with respect to stress and strain, which in structures +new or old, occur possibly as may be expected—certainly +as they must. Consideration of existing work may thus be a +useful check upon the fanciful requirements of some methods +of design. There is a recent tendency, for instance, in English +practice to over-stiffen the webs of plate-girders, such that if +the theory upon which the results are based were true, many +old bridges carrying their loads with no sign of distress, should +have failed long ago. Excess in riveting is a common extravagance, +to which the same criticism may in a less degree +apply. Considerable impact allowances for girders of large +span may also be referred to as an application of empiric +theory not justified by experience, which, as in all cases +where such considerations fight with facts, should be modified +or rejected.</p> + +<hr class="chap" /> + +<p><span class="pagenum"><a name="Page_186" id="Page_186"></a><br /><a name="Page_187" id="Page_187">[187]</a></span></p> + +<h2>INDEX</h2> + +<ul class="index"> +<li class="first">Abutments, leaning, <a href="#Page_82">82</a>, <a href="#Page_173">173</a></li> +<li>— movements of, <a href="#Page_158">158</a></li> +<li>— settlement of, <a href="#Page_78">78</a></li> +<li>Adjustment of centre girders, <a href="#Page_128">128</a></li> +<li>— of distributing girders, <a href="#Page_120">120</a></li> +<li>Angular distortions, <a href="#Page_88">88</a></li> +<li>Arches, equilibrium of, <a href="#Page_162">162</a></li> +<li>— repair of, <a href="#Page_163">163</a></li> +<li>Arrangement of cross girders, <a href="#Page_21">21</a>, <a href="#Page_175">175</a></li> +<li>Asphalt, <a href="#Page_26">26</a></li> +<li class="first">Ballast, <a href="#Page_29">29</a></li> +<li>Bearing pressure on rivets, <a href="#Page_47">47</a>, <a href="#Page_51">51</a>, <a href="#Page_57">57</a></li> +<li>Bearings, skew, <a href="#Page_4">4</a></li> +<li>Bottom booms, end bays, <a href="#Page_18">18</a></li> +<li>Bracing, additional, <a href="#Page_117">117</a></li> +<li>— effects of, <a href="#Page_34">34</a></li> +<li>— flat bars, <a href="#Page_37">37</a></li> +<li>— incomplete, <a href="#Page_41">41</a></li> +<li>— sea piers, <a href="#Page_42">42</a></li> +<li>Bridge floors, <a href="#Page_20">20</a></li> +<li>— repairs, <a href="#Page_107">107</a></li> +<li>— surveys, <a href="#Page_107">107</a></li> +<li>Bridges, life of, <a href="#Page_165">165</a></li> +<li>Breaks in <span class="lettsymb">T</span> bars, <a href="#Page_16">16</a></li> +<li>Buckling of webs, <a href="#Page_16">16</a></li> +<li class="first">Camber, <a href="#Page_24">24</a>, <a href="#Page_80">80</a></li> +<li>Cast-iron arches, <a href="#Page_80">80</a>, <a href="#Page_145">145</a></li> +<li>— — bridges, <a href="#Page_141">141</a></li> +<li>— — columns, <a href="#Page_7">7</a>,144</li> +<li>— — girders, <a href="#Page_141">141</a></li> +<li>— — in sea water, <a href="#Page_101">101</a></li> +<li>Centre girders, <a href="#Page_122">122</a></li> +<li>Cinder ballast, <a href="#Page_29">29</a></li> +<li>Cold-blast iron, <a href="#Page_141">141</a></li> +<li>Cooling stresses in cast iron, <a href="#Page_145">145</a></li> +<li>Construction depth, <a href="#Page_173">173</a></li> +<li>Corrugated sheeting, <a href="#Page_29">29</a></li> +<li>Cost of centre girders, <a href="#Page_135">135</a></li> +<li>— of maintenance, <a href="#Page_168">168</a></li> +<li>Counterbracing, <a href="#Page_19">19</a></li> +<li>Cracked bedstones, <a href="#Page_3">3</a></li> +<li>— columns, <a href="#Page_7">7</a></li> +<li>— web plates, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_50">50</a></li> +<li>Cross girder arrangement, <a href="#Page_21">21</a></li> +<li>— girders, fixed ends, <a href="#Page_22">22</a>, <a href="#Page_118">118</a></li> +<li>— — rusted, <a href="#Page_29">29</a>, <a href="#Page_97">97</a></li> +<li>— — weak, <a href="#Page_30">30</a>, <a href="#Page_66">66</a></li> +<li class="first">Decay and painting, <a href="#Page_96">96</a></li> +<li>— of floor plates, <a href="#Page_109">109</a></li> +<li>— of timber, <a href="#Page_28">28</a>, <a href="#Page_150">150</a></li> +<li>Deflection, <a href="#Page_85">85</a></li> +<li>— due to booms and web, <a href="#Page_86">86</a></li> +<li>— exceptional cases, <a href="#Page_88">88</a></li> +<li>— in new and old work, <a href="#Page_85">85</a></li> +<li>— working formulæ, <a href="#Page_87">87</a></li> +<li>Deformations, <a href="#Page_73">73</a></li> +<li>Depth of girders,<span class="pagenum"><a name="Page_188" id="Page_188">[188]</a></span> <a href="#Page_23">23</a>, <a href="#Page_89">89</a>, <a href="#Page_184">184</a></li> +<li>Diagonal ties, <a href="#Page_19">19</a>, <a href="#Page_42">42</a></li> +<li>Distortion due to temperature changes, <a href="#Page_79">79</a>, <a href="#Page_84">84</a></li> +<li>Distributing girders, <a href="#Page_120">120</a></li> +<li>Drainage holes, <a href="#Page_25">25</a></li> +<li>“Drop” loads, <a href="#Page_89">89</a></li> +<li>Dwarf walls under floors, <a href="#Page_26">26</a></li> +<li class="first">Early steel girders, <a href="#Page_68">68</a></li> +<li>Economy, <a href="#Page_184">184</a></li> +<li>Effect of earth slips, <a href="#Page_157">157</a></li> +<li>— of floor on deflection, <a href="#Page_88">88</a></li> +<li>— — — on stresses, <a href="#Page_23">23</a>, <a href="#Page_30">30</a></li> +<li>— of high stress, <a href="#Page_86">86</a></li> +<li>— of permanent way on stresses, <a href="#Page_18">18</a></li> +<li>—of skew on bridge floors, <a href="#Page_25">25</a></li> +<li>— — — on centre girders, <a href="#Page_131">131</a></li> +<li>— of transverse bracings, <a href="#Page_34">34</a></li> +<li>— of vibration on masonry, <a href="#Page_162">162</a></li> +<li>— of wave action on sea piers, <a href="#Page_42">42</a></li> +<li>End bays, bottom booms, <a href="#Page_18">18</a></li> +<li>Equilibrium of masonry arches, <a href="#Page_162">162</a></li> +<li>Examination of bridges, <a href="#Page_107">107</a></li> +<li>Examples of cast-iron bridges overstressed, <a href="#Page_141">141</a></li> +<li>— of high stress, <a href="#Page_70">70</a></li> +<li>— of life of bridges, <a href="#Page_167">167</a></li> +<li>— of rivet stress, <a href="#Page_56">56</a></li> +<li>— of strengthening, <a href="#Page_114">114</a></li> +<li>— — — by centre girders, <a href="#Page_131">131</a>, <a href="#Page_134">134</a></li> +<li>Excessive bearing pressure, <a href="#Page_51">51</a></li> +<li class="first">Faulty workmanship, <a href="#Page_80">80</a></li> +<li>Fixed ends to cross girders, <a href="#Page_22">22</a>, <a href="#Page_118">118</a></li> +<li>Flange stresses, <a href="#Page_63">63</a>, <a href="#Page_66">66</a>, <a href="#Page_67">67</a></li> +<li>Flanges, side loaded, <a href="#Page_9">9</a>, <a href="#Page_73">73</a></li> +<li>Flat bar bracing, <a href="#Page_37">37</a></li> +<li>Flexing of girders, <a href="#Page_9">9</a>, <a href="#Page_74">74</a>, <a href="#Page_76">76</a></li> +<li>Flexure curves, <a href="#Page_138">138</a></li> +<li>Fractured bedstones, <a href="#Page_3">3</a></li> +<li>— rails, <a href="#Page_30">30</a></li> +<li>— webs, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_50">50</a></li> +<li>Fractures in cast iron, <a href="#Page_7">7</a>, <a href="#Page_145">145</a></li> +<li class="first">Girder bearings, <a href="#Page_2">2</a></li> +<li>Girders on columns, <a href="#Page_7">7</a></li> +<li>— on masonry, <a href="#Page_8">8</a></li> +<li>Girderwork in masonry, <a href="#Page_101">101</a></li> +<li class="first">Headway, <a href="#Page_173">173</a></li> +<li>High stress, <a href="#Page_61">61</a></li> +<li>— in cast iron, <a href="#Page_141">141</a></li> +<li>— in rivets, <a href="#Page_47">47</a>, <a href="#Page_52">52</a></li> +<li>Holes for drainage, <a href="#Page_25">25</a></li> +<li class="first">Impact, <a href="#Page_20">20</a>, <a href="#Page_62">62</a></li> +<li>Inclination of girder ends, <a href="#Page_23">23</a>, <a href="#Page_53">53</a></li> +<li>Incomplete bracing, <a href="#Page_41">41</a></li> +<li>Initial set, <a href="#Page_88">88</a></li> +<li>Interference with traffic, <a href="#Page_177">177</a></li> +<li class="first">Jack arches, <a href="#Page_29">29</a>, <a href="#Page_101">101</a></li> +<li>Joints in rails, <a href="#Page_29">29</a>, <a href="#Page_109">109</a></li> +<li>— in trough floors, <a href="#Page_28">28</a>, <a href="#Page_180">180</a></li> +<li>Junction between metallic and masonry bridges, <a href="#Page_183">183</a></li> +<li>— — new and old masonry bridges, <a href="#Page_182">182</a></li> +<li>— — new and old metallic bridges, <a href="#Page_180">180</a></li> +<li class="first">Lattice girder stresses, <a href="#Page_47">47</a>-<a href="#Page_66">66</a></li> +<li>Liberal depth to girders, <a href="#Page_23">23</a>, <a href="#Page_89">89</a>, <a href="#Page_184">184</a></li> +<li>Life of bridges,<span class="pagenum"><a name="Page_189" id="Page_189">[189]</a></span> <a href="#Page_165">165</a></li> +<li>Limit of elasticity, <a href="#Page_61">61</a></li> +<li>Linen tapes, <a href="#Page_172">172</a></li> +<li>Longitudinal floor girders, <a href="#Page_23">23</a></li> +<li>Loose rivets, <a href="#Page_21">21</a>, <a href="#Page_25">25</a>, <a href="#Page_51">51</a>, <a href="#Page_53">53</a>, <a href="#Page_56">56</a>, <a href="#Page_109">109</a></li> +<li class="first">Main girders, <a href="#Page_9">9</a>-<a href="#Page_17">17</a></li> +<li>Masonry bridges, <a href="#Page_157">157</a></li> +<li>— enduring character of, <a href="#Page_161">161</a></li> +<li>Memel timber, <a href="#Page_150">150</a></li> +<li>Methods of calculation, <a href="#Page_46">46</a>, <a href="#Page_61">61</a></li> +<li>— of observing deflection, <a href="#Page_90">90</a></li> +<li>— of setting out deflection curves, <a href="#Page_138">138</a></li> +<li>Movements of abutments, <a href="#Page_158">158</a></li> +<li>— of cast-iron bridge, <a href="#Page_82">82</a></li> +<li>— of piers, <a href="#Page_42">42</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li> +<li>— of rollers, <a href="#Page_7">7</a></li> +<li>— of wrought-iron bridges, <a href="#Page_4">4</a>, <a href="#Page_21">21</a>, <a href="#Page_38">38</a>, <a href="#Page_73">73</a></li> +<li class="first">New members to old work, <a href="#Page_116">116</a></li> +<li class="first">Oiling steelwork, <a href="#Page_99">99</a></li> +<li>Old drawings unreliable, <a href="#Page_108">108</a></li> +<li>— rivets, <a href="#Page_21">21</a>, <a href="#Page_51">51</a>, <a href="#Page_54">54</a>, <a href="#Page_55">55</a></li> +<li>Open webs, <a href="#Page_17">17</a></li> +<li>Overhead bracing, <a href="#Page_39">39</a></li> +<li>— girders, <a href="#Page_118">118</a></li> +<li class="first">Painting, <a href="#Page_98">98</a></li> +<li>Parapets, <a href="#Page_79">79</a></li> +<li>Permissible stress in old work, <a href="#Page_110">110</a></li> +<li>Piers, movements of, <a href="#Page_42">42</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li> +<li>— out of plumb, <a href="#Page_159">159</a></li> +<li>Piles, decay of, <a href="#Page_102">102</a>, <a href="#Page_150">150</a></li> +<li>Pitch pine, <a href="#Page_28">28</a></li> +<li>Plasticity, <a href="#Page_61">61</a></li> +<li>Plate webs, <a href="#Page_9">9</a></li> +<li>Plated floors, <a href="#Page_23">23</a>, <a href="#Page_25">25</a>, <a href="#Page_30">30</a></li> +<li>Pointing masonry, <a href="#Page_164">164</a></li> +<li>Proposed rivet stresses, <a href="#Page_58">58</a></li> +<li class="first">Quickly applied loads, <a href="#Page_89">89</a></li> +<li class="first">Rail joints, <a href="#Page_29">29</a>, <a href="#Page_109">109</a></li> +<li>Rails, breaks in, <a href="#Page_30">30</a></li> +<li>Reaction of cross girder with centre support, <a href="#Page_127">127</a></li> +<li>Red-lead, <a href="#Page_98">98</a>, <a href="#Page_100">100</a></li> +<li>Relative merits of bridges, <a href="#Page_169">169</a></li> +<li>Relief by centre girders, <a href="#Page_122">122</a></li> +<li>Repainting, <a href="#Page_100">100</a></li> +<li>Repair of bridges, <a href="#Page_107">107</a>, <a href="#Page_147">147</a>, <a href="#Page_155">155</a>, <a href="#Page_163">163</a></li> +<li>— of timber piles, <a href="#Page_156">156</a></li> +<li>Replacing flange plates, <a href="#Page_110">110</a></li> +<li>— rivets, <a href="#Page_111">111</a></li> +<li>Resistance of cast iron to rust, <a href="#Page_101">101</a></li> +<li>Riveted connections, <a href="#Page_45">45</a>, <a href="#Page_86">86</a></li> +<li>Rivets in cramped positions, <a href="#Page_20">20</a></li> +<li>— in cross girder ends, <a href="#Page_21">21</a>, <a href="#Page_49">49</a>, <a href="#Page_53">53</a>, <a href="#Page_54">54</a></li> +<li>— in road bridges, <a href="#Page_60">60</a></li> +<li>— in webs of main girders, <a href="#Page_46">46</a></li> +<li>— spacing of, <a href="#Page_60">60</a>, <a href="#Page_80">80</a></li> +<li>— stresses in, <a href="#Page_56">56</a></li> +<li>Rocking of piers, <a href="#Page_8">8</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li> +<li>Roller bearings, <a href="#Page_7">7</a></li> +<li>Rubble masonry, <a href="#Page_161">161</a>-<a href="#Page_164">164</a></li> +<li>Running load and deflection, <a href="#Page_95">95</a></li> +<li>Rusting, instances of, <a href="#Page_29">29</a>, <a href="#Page_96">96</a></li> +<li>— of steelwork, <a href="#Page_99">99</a></li> +<li>— over sea-water, <a href="#Page_98">98</a></li> +<li class="first">Sag in timber bridges, <a href="#Page_150">150</a></li> +<li>— of tapes, <a href="#Page_172">172</a></li> +<li>Scour under piers,<span class="pagenum"><a name="Page_190" id="Page_190">[190]</a></span> <a href="#Page_161">161</a></li> +<li>Sea piers, <a href="#Page_42">42</a>, <a href="#Page_102">102</a></li> +<li>Setting bedstones, <a href="#Page_3">3</a>, <a href="#Page_129">129</a>, <a href="#Page_176">176</a></li> +<li>Settlements, <a href="#Page_76">76</a>, <a href="#Page_157">157</a></li> +<li>Skew bearings, <a href="#Page_4">4</a></li> +<li>— bridges, right and left, <a href="#Page_173">173</a></li> +<li>— — floors, <a href="#Page_25">25</a></li> +<li>Skirting plate, <a href="#Page_26">26</a></li> +<li>Slope of girder ends, <a href="#Page_92">92</a></li> +<li>Softening of cast-iron in sea-water, <a href="#Page_101">101</a></li> +<li>Spacing of rivets, <a href="#Page_60">60</a>, <a href="#Page_79">79</a></li> +<li>Spread of abutments, <a href="#Page_157">157</a></li> +<li>Spring joints, <a href="#Page_23">23</a></li> +<li>Steel trough girders, <a href="#Page_68">68</a></li> +<li>— troughing, <a href="#Page_70">70</a></li> +<li>Stiffening girders from floor, <a href="#Page_12">12</a>, <a href="#Page_40">40</a></li> +<li>— to webs, <a href="#Page_16">16</a>, <a href="#Page_38">38</a>, <a href="#Page_185">185</a></li> +<li>Stop piers, <a href="#Page_158">158</a></li> +<li>Strength of light top booms, <a href="#Page_40">40</a></li> +<li>Strengthening of bridges, <a href="#Page_107">107</a>, <a href="#Page_122">122</a></li> +<li>— bridge floors, <a href="#Page_118">118</a></li> +<li>— cross girders, <a href="#Page_123">123</a></li> +<li>Stress in plated floors, <a href="#Page_31">31</a></li> +<li>Study of old bridges, <a href="#Page_185">185</a></li> +<li class="first">Tall piers, <a href="#Page_42">42</a>, <a href="#Page_159">159</a></li> +<li>Timber bridges, <a href="#Page_149">149</a></li> +<li>— floors, <a href="#Page_27">27</a></li> +<li>— staging, <a href="#Page_177">177</a></li> +<li>Top booms, <a href="#Page_18">18</a></li> +<li>Traffic during reconstruction, <a href="#Page_177">177</a></li> +<li>Transverse bracing, <a href="#Page_34">34</a>, <a href="#Page_117">117</a></li> +<li>Trough floors, <a href="#Page_27">27</a>, <a href="#Page_180">180</a></li> +<li>— girders, <a href="#Page_50">50</a>, <a href="#Page_74">74</a></li> +<li><span class="lettsymb">T</span> stiffeners, breaks in, <a href="#Page_16">16</a></li> +<li>Twin girders, <a href="#Page_15">15</a>, <a href="#Page_75">75</a></li> +<li>Twisting of girders, <a href="#Page_11">11</a>, <a href="#Page_68">68</a>, <a href="#Page_73">73</a></li> +<li>— — — corrected, <a href="#Page_12">12</a></li> +<li>Types of reconstruction, <a href="#Page_174">174</a></li> +<li class="first"><span class="lettsymb">U</span>-shaped booms, <a href="#Page_18">18</a></li> +<li>Uncomplicated stress, <a href="#Page_62">62</a></li> +<li>Uniform pressure on bearings, <a href="#Page_6">6</a></li> +<li class="first">Value of E in deflection formulæ, <a href="#Page_87">87</a></li> +<li>Vibration, <a href="#Page_162">162</a></li> +<li class="first">Wasted webs, <a href="#Page_14">14</a>, <a href="#Page_29">29</a>, <a href="#Page_96">96</a></li> +<li>Water, scour of, <a href="#Page_161">161</a></li> +<li>Web buckling, <a href="#Page_16">16</a></li> +<li>— plates, cracked, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_50">50</a></li> +<li>— rivets, <a href="#Page_46">46</a>, <a href="#Page_50">50</a></li> +<li>— stiffening, <a href="#Page_16">16</a>, <a href="#Page_38">38</a>, <a href="#Page_185">185</a></li> +<li>Widening masonry bridges, <a href="#Page_182">182</a></li> +<li>— metallic bridges, <a href="#Page_179">179</a></li> +<li>Wide spaced rivets, <a href="#Page_79">79</a></li> +<li>Wind pressure, <a href="#Page_41">41</a>, <a href="#Page_43">43</a></li> +<li class="first">Yielding of piers, <a href="#Page_8">8</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li> +</ul> + +<hr class="chap" /> + +<p class="center fsize80">LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,<br /> +GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.</p> + +<hr class="chap" /> + +<div class="tnbox"><a name="TN" id="TN"></a> +<h2>Transcriber’s Notes</h2> + +<p>The text of the original work (including inconsistent spelling, hyphenation, formatting etc.) has been retained, except as mentioned below.<br /> +The slight differences between the Table of Contents and the text have not been changed</p> + +<p><b>Changes made to the text:</b><br /> +Some punctuation errors and obvious typographical errors have been corrected silently.<br /> +Several illustrations have been moved to where they are described in the text.<br /> +Page 123, formula (2): the original shows an unclear superscript after the first L. As described in the following line of the text, this has been changed to L<sub class="lg"><i>l</i></sub>.</p> + +</div> + +<div>*** END OF THE PROJECT GUTENBERG EBOOK 44371 ***</div> +</body> +</html> diff --git a/44371-h/images/cover-b.jpg b/44371-h/images/cover-b.jpg Binary files differnew file mode 100644 index 0000000..25be0fb --- /dev/null +++ b/44371-h/images/cover-b.jpg diff --git a/44371-h/images/cover.jpg b/44371-h/images/cover.jpg Binary files differnew file mode 100644 index 0000000..c8ff298 --- /dev/null +++ b/44371-h/images/cover.jpg diff --git a/44371-h/images/illo003.png b/44371-h/images/illo003.png Binary files differnew file mode 100644 index 0000000..2b29efa --- /dev/null +++ b/44371-h/images/illo003.png diff --git a/44371-h/images/illo016.png b/44371-h/images/illo016.png Binary files differnew file mode 100644 index 0000000..bd0f58c --- /dev/null +++ b/44371-h/images/illo016.png diff --git a/44371-h/images/illo017.png b/44371-h/images/illo017.png Binary files 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