,transcriber's ,notes3 ,text between underscores represents italics1 small capitals have been transcribed as ,,all ,,capitals4 ,curly brackets indicate subscripts2 letters between square brackets 7such as ,t and ,u7 represent the shape rahter than the letter itself4 ,more ,transcriber's ,notes may be found at the end of this text4 ,,the ,,anatomy ,,of ,,bridgework ,,the ,,anatomy ,,of ,,bridgework ,,by ,,william ,,henry ,,thorpe ,,assoc4 ,m4 ,,inst4 ,c4 ,e4 ,,with #ajc ,,illustrations ,illustration ,london ,e4 ,f4 ,n4 ,,spon1 ,,limited1 #eg ,,haymarket ,new ,york ,,spon ,,chamberlain1 #abc ,,liberty ,,street #aijf ,,preface ,in offering this little book to the reader interested in ,bridgework1 the author desires to express his acknowledgments to the proprietors of 8,engineering10 in which journal the papers first appeared1 for their courtesy in facilitating the production in book form4 ,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 which1 while familiar to maintenance engineers of experience1 has not been so readily available as is desirable4 ,no theory which fails to stand the test of practical working can maintain its claims to regard2 the study of the behaviour of old work has1 therefore1 a high educational value1 and tends to the occasional correction of views which might otherwise be complacently retained4 #fj ,,winsham ,,street1 ,,clapham ,,common1 ,,london1 ,s4,w4 ,october1 #aijf4 ,,contents ,,chapter ,i4 ,,introduction--,,girder ,,bearings4 ,,page ,pressure distribution--,square and skew bearings--,fixed bearings-- ,knuckles--,rollers--,yield of supports #a ,,chapter ,,ii4 ,,main ,,girders4 ,plate webs3 ,improper loading of flanges--,twisting of girders-- ,remedial measures--,cracks in webs--,stiffening of webs--,t stiffeners #i ,open webs3 ,common faults--,top booms--,buckling of bottom booms-- ,counterbracing--,flat members #ag ,,chapter ,,iii4 ,,bridge ,,floors4 ,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 8skew0 on floor--,water-tightness--,drainage--,tim ber floors--,jack arches-- ,corrugated sheeting--,ballast--,rail joints--,effect of main girders on floors #bj ,,chapter ,,iv4 ,,bracing4 ,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 #cd ,,chapter ,v4 ,,riveted ,,connections4 ,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 #de ,,chapter ,,vi4 ,,high ,,stress4 ,elastic limit--,care in calculation--,impact--,examples of high stress --,early examples of high stress in steel girders--,tabulated examples--,general remarks #fa ,,chapter ,,vii4 ,,deformations4 ,various kinds--,flexing of girder flanges--,examples--,settlement deformations--,creeping--,temperature changes--,local distortions-- ,imperfect workmanship--,deformation of cast-iron arches #gc ,,chapter ,,viii4 ,,deflections4 ,differences as between new work and old--,influence of booms and web structure on deflection--,yield of rivets and stiffness of connections--,working formul--,set--,effect of floor system-- ,deflection diagrams--,loads quickly applied--8,drop0 loads--,flexible girders--,measuring deflections--,new method of observing deflections --,effect of running load #he ,,chapter ,,ix4 ,,decay ,,and ,,painting4 ,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 #if ,,chapter ,x4 ,,examination1 ,,repair1 ,,and ,,strengthening ,,of ,,riveted ,,bridges4 ,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 #ajg ,,chapter ,,xi4 ,,strengthening ,,of ,,riveted ,,bridges ,,by ,,centre ,,girders4 ,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 #abb ,,chapter ,,xii4 ,,cast-,,iron ,,bridges4 ,limitations of cast iron--,stress examples--,advantages and disadvantages--,foundry stresses--,examples--,want of ductility of cast iron--,repairs--,restricted possibilities #ada ,,chapter ,,xiii4 ,,timber ,,bridges4 ,perishable nature--,causes of decay--,sag--,lateral bracing--,piles-- ,uncertainty respecting decay--,examples--,conditions and practice favourable to durability--,bracing--,protection--,repa ir--,piles--,cost #adi ,,chapter ,,xiv4 ,,masonry ,,bridges4 ,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 #aeg ,,chapter ,,xv4 ,,life ,,of ,,bridges--,,relative ,,merits4 ,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 #afe ,,chapter ,,xvi4 ,,reconstruction ,,and ,,widening ,,of ,,bridges4 ,,conclusion4 ,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 #agb ,,index #ahg ,,the ,,anatomy ,,of ,,bridgework4 ,,chapter ,i4 ,,introduction4 ,no book has1 so far as the author is aware1 been written upon that aspect of bridgework to be treated in the following pages4 ,no excuse need1 therefore1 be given for adding to the already large amount of published matter dealing with bridges4 ,indeed1 as it too often happens that the designing of such constructions1 and their after-maintenance1 are in this country entirely separated1 it cannot but be useful to give such results of the behaviour of bridges1 whether new or old1 as have come under observation4 ,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 design1 and he was1 as a result1 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 subject4 ,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 stress1 and the growth of the literature of bridgework during the last forty years4 ,that many mistakes were made is little occasion for surprise2 rather is it a cause for admiration that some very fine bridges1 still in use1 were the product of that time4 ,much may be learned from the study of defects and failures1 even though they be of such a character that no experienced designer would now furnish like examples4 ,modern instances may1 none the less1 be found1 with faults repeated1 which should long since have disappeared from all bridgework1 and are only to be accounted for by the unnatural divorce of design and maintenance already referred to4 ,as the reader proceeds1 it may appear that details are occasionally touched upon of a character altogether too crude and objectionable to need comment2 but the consideration of these cases is none the less interesting1 and1 so far as the author's observation goes1 not altogether unnecessary4 ,most of the instances cited are of bridges1 or parts of bridges1 of quite small dimensions2 but it is these which most commonly give trouble1 both because the effects of impact are in such cases most severely felt1 and possibly because the smaller class of bridges is very generally designed by men of less experience1 than large and imposing structures4 ,the particulars given relate in all cases to bridges of wrought iron1 unless otherwise described4 ,an endeavour has been made to secure some kind of order in dealing with the subject1 but it has been found difficult to avoid a somewhat disjointed treatment1 inseparable1 perhaps1 from the nature of the matter4 ,finally1 the reader may be assured that every case quoted has come under the writer's personal notice4 ,,girder ,,bearings4 ,in girder-work generally1 and more particularly in plate-girders1 considerable latitude obtains in the amount of bearing allowed4 ,clearly1 the surface over which the pressure is distributed should be sufficiently ample to avoid overloading and possible crushing or fracture of bedstones where these exist2 but if no knuckles are introduced1 this is an extremely difficult matter to insure4 ,a long bearing may deliver the load at the extreme end of the surface on which it rests1 or1 more probably1 near the face4 ,if the girder is made with truly level bearings1 and the beds set level1 it will certainly1 when under load1 throw an extreme pressure upon that part of the bearing surface immediately under the forward edge of the bearing-plate4 ,these considerations probably account for bedstones frequently cracking1 in addition to which possibility there is the disadvantage that the designer does not know where the girder will rest1 and cannot truly define the span4 ,the variation of flange-stress due to this cause may1 in a girder of ordinary proportions1 having bearings equal in length to the girder's depth1 be as much as #ae per cent4 above or below that intended4 ,if great care be taken in setting beds1 in the first instance1 to dip toward the centre of the span an amount depending upon the anticipated girder deflection1 it may be possible to insure that when under full load the girder bearing shall rest equally upon its seat2 but this is evidently a difficult condition to obtain practically1 is good only for one degree of loading1 and may at any time be nullified by a disturbance of the supports1 as1 for instance1 the very common occurrence of a slight leaning forward of abutment walls4 ,double or treble thicknesses of hair-felt are sometimes placed beneath girder bearings1 with the object of securing a better distribution of pressure1 no doubt with advantage2 but this practice1 though it may be quite satisfactory as applied to girders carrying an unchangeable load1 hardly meets the case for loads which are variable4 ,notwithstanding the faulty nature of the plain bearing ordinarily used for girders of moderate span1 its extreme simplicity commends it to most engineers4 ,it must be admitted that no serious inconvenience need be anticipated in the majority of cases1 particularly if the bearings are limited in length1 do not approach nearer than #c inches to the face of bedstones1 and are furnished with hair-felt or similar packing4 ,illustration3 ,,fig4 #a4 ,whether with long or short bearings1 the forward edge should be at right angles to the girder's length4 ,in skew bridges it is sometimes seen that this edge follows the angle of skew4 ,the effect on the girder is to twist it1 as will be clear from a little consideration4 ,in evidence of this the case may be quoted of a lattice girder of #ie feet effective span and #g feet deep1 which1 resting on a skew abutment right up to the masonry face at a rather bad angle 7about #ae degrees71 was1 after twenty years1 found canted over at the top to the extent of #d inches1 with the further result of springing a joint in the top flange at about the middle of the girder1 causing some rivets to loosen4 ,the bedstone was also very badly broken at the face1 and had to be replaced in the course of repairs 7,fig4 #a74 ,this girder had1 in addition to the canting from the upright position at its end1 and the distortion of the top flange1 a curvature in the same direction1 though less in amount1 at the bottom--an effect very common in the main girders of skew bridges1 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 hardest1 under frequent applications and removals of the live load1 and accompanying deflections4 ,this tendency to travel may be aggravated in bridges carrying a ballasted road1 in which there may be a considerable thickness of ballast near the bearings1 by the compacting and spreading of this material taking effect upon the girder end1 tending to push it outwards1 being tied only by a few light cross-girders badly placed for useful effect4 ,the movement may be prevented in new work for moderate angles of skew by carrying the end cross-girders well back1 and securing them in some efficient manner2 or by the introduction of a diagonal tie following the skew face1 and attached to cross and main girder flanges 7,fig4 #b7--;a method which may be applied to existing work also4 ,illustration3 ,,fig4 #b4 ,for such a case as that cited it is imperative that ballast pressure at the girder end should be altogether eliminated4 ,the fixing of girder ends by bolts--a practice at one time usual--hardly calls for remark1 as it is now seldom resorted to unless for special reasons2 but it may be well to point out the weakening effect of holes for any purpose in bedstones4 ,bed-plates commonly need no fixing2 the weight carried keeps them in position1 or if1 in the case of very light girders upon separate plates1 it is considered well to secure these from shifting1 it may best be done by letting the plate in bodily a small amount1 or by means of a very shallow feather sunk into a chase4 ,illustration3 ,,fig4 #c4 ,as an improvement upon the plain bearing usually adopted1 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 flange1 distributing the pressure upon the stone1 if there be one1 by means of a simple rectangular plate of sufficient stoutness 7,fig4 #c74 ,an imperfect knuckle will by this means result1 with freedom to slide1 and the girder span be defined within narrow limits4 ,a true knuckle is1 of course1 the best means of securing imposition of the load always in the same place2 but this by itself is not sufficient where the girder is of a length to make temperature and stress variations important1 in which case rollers1 or freedom to slide1 become necessary4 ,bridges exist in which roller-bearings have been adopted without the knuckle1 or its equivalent1 but this is wholly indefensible1 as it is obvious that the forward roller will in all probability take the whole load1 and cannot be expected to keep its shape and roll freely under this mal-treatment4 ,it is sometimes asserted that rollers are never effective after some years' use2 that they become clogged with dirt1 and refuse to perform their office4 ,there is no reason why rollers should not be boxed in to exclude dirt by a casing easily removed1 some attention being given to them1 and any possible accumulation of dirt removed each time the bridge is painted4 ,to test the behaviour of rollers under somewhat unfavourable conditions for their proper action--that of the bearings of main roof trusses of crescent form1 #aij feet span--the author1 some thirty years since1 took occasion to make the necessary observations1 and found evidence of a moderate roller movement1 though there was in this case no direct horizontal member to communicate motion4 ,with girders resting upon columns1 particularly if of cast iron1 a roller and knuckle arrangement is most desirable for any but very small spans1 as1 if not adopted1 the result will be a canting of the columns from side to side--a very small amount1 it is true1 but sufficient to throw the load upon the extreme edges of the base1 though the knuckle alone will relieve the top of this danger4 ,the author at one time took the trouble to examine1 so far as it could be done superficially and without opening out the ground to make a complete inspection possible1 a number of bridges crossing streets1 in which girders rested upon and were secured to cast-iron columns standing in the line of kerb2 and he found cracks1 either at the top or bottom1 in about one of every four columns4 ,when girders passing over columns are not continuous1 it may be difficult to find room for a double roller and knuckle arrangement2 but this inconvenience may be overcome by carrying one girder-end wholly across the column-top1 and securing the next girder-end to it in a manner which a little care and ingenuity will render satisfactory1 one free bearing then serving to carry the load from both girders4 ,though the wisdom of using rollers is apparent in spans exceeding some moderate length1 say #hj feet--as to which engineers do not seem quite decided--and varying with the conditions1 it need not be overlooked that in some cases masonry will be sufficiently accommodating to render them unnecessary2 piers1 if sufficiently tall and slender1 will yield a small amount without injury1 and though shorter1 if resting upon a bottom not absolutely rigid1 will rock and give the necessary relief2 but it is obvious1 if the resistance to movement is sufficiently great1 and the girder cannot slide or roll on its bearings1 bedstones will probably loosen1 as1 indeed1 frequently happens4 ,,chapter ,,ii4 ,,main ,,girders2 ,,plate-,,webs4 ,it is seldom that girders of this description--or1 indeed1 of any other--show signs of failure from mere defect of strength in the principal parts1 even though somewhat highly stressed2 and instances tending to support this statement will be given in a later chapter4 ,for the present1 it is proposed to indicate peculiarities of behaviour only1 generally1 but not always1 harmless4 ,though now less often done1 it was at one time common practice to load plate-girders on the bottom flange by simply resting floor timbers1 rails1 troughs1 or cross-girders upon them4 ,in outside girders one result of this is to cause the top flange to take a curve in plan1 convex towards the road1 every time the live load comes upon the floor of the bridge1 upon the passing of which the flange resumes its figure1 though still affected by that part of the load which is constant4 ,a bridge of #dg feet span1 carrying two lines of way1 having one centre and two outside girders1 with a floor consisting of old ,barlow rails1 resting upon the bottom flanges1 showed the peculiarity named in a marked degree4 ,the outside girders1 under dead load only1 were1 as to the top flanges 7see ,figs4 #d and #e71 #a-a_/d inch and #a-a_/af inch respectively out of straight in their length1 but upon the passing of a goods engine and train curved an additional #a-a_/h inch1 or #b-c_/h inches in all1 for one outside girder1 and #b-c_/af inches for the other4 ,the centre girder1 having a broader and heavier top flange1 curved #e_/h inch towards whichever road might be loaded4 ,the effect of such horizontal flexure is clearly to induce stresses of tension and compression in the flanges1 which1 being 7for the top flange7 compounded with the normal compressive stress due to load carried1 results in a considerable want of uniformity across the section4 ,illustration3 ,,fig4 #d4 ,in the case under notice1 the writer estimates the stresses for an outer girder top flange at #de tons per square inch compression for simple loading1 and #ee tons per square inch of tension and compression1 on the inner and outer edges1 due to flexure1 resulting when compounded in a stress of #a ton per square inch tension on the inside1 and #aj tons per square inch compression on the outside edge4 ,in this rather extreme case the stress on the inner edge1 or that nearest the load1 is reversed in character4 ,the effect described appears to be not wholly due to the twisting moment4 ,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 line4 ,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 cause4 ,consistent with this view of the matter is the fact that the inclination of the girder towards the rails greatly exceeded the calculated slope of the ,barlow rail-ends when under load1 being about five times as great4 ,the inference is that the floor rails bore hard at their extreme ends1 at which point of bearing the calculated twisting moment accounts for less than one-half of the flexure observed in the flanges4 ,illustration3 ,,fig4 #e4 ,the girders upon removal in the course of reconstruction again took the straight form1 showing that the very frequent development of the stresses named had not sensibly injured the metal1 though the bridge carried as many as three hundred trains daily in each direction1 and had done so for very many years4 ,the deformation of the top flange only has been noticed1 yet the same tendency exists in the bottom1 though the actual amount is much less1 both because the lower flanges are in tension1 and are also in great degree confined by the frictional contact of the cross bearers1 even where no proper ties are used4 ,in the case dealt with the bottom flanges of the outer girders curved #a_/h inch outwards only4 ,with the broad flanges commonly adopted in ,english practice1 twisting of the girders1 under conditions similar to the above1 will not generally be a serious matter2 but with narrow flanges possessing little lateral stiffness it might be a source of danger4 ,illustration3 ,,fig4 #f4 ,,fig4 #g4 ,the twisting may be limited in amount by introducing a cross-frame between the girders1 from which they are stiffened2 by strutting the girders immediately from the floor itself1 in which case they cannot cant to a greater extent than that which corresponds to the floor deflection2 or by designing the top flange to be unsymmetrical with reference to the web1 as in ,figs4 #f and #g1 with the object of insuring that under the joint effect of vertical loading and twisting1 the stress in the flange shall at maximum loads be uniform across the section1 and allow it to remain straight4 ,this may be secured by making the eccentricity of the flange section equal to that of the loading4 ,for instance1 if the load be applied #c inches away from the web centre1 the flange should have its centre of gravity #c inches on the other side of the centre line4 ,it can be shown that this is true throughout the length of the girder1 and irrespective of the depth4 ,an instance in which flange eccentricity being in excess1 curvature outwards resulted1 will be found in a later chapter on deformations1 etc4 ,it will not generally be necessary to make the bottom flange eccentric1 as it is commonly tied in some way2 but if done1 the eccentricity should be on the same side as for the top4 ,the flanges remaining straight under these conditions are not subject to the complications of stress referred to in the case first quoted4 ,the author has adopted both the last named details in bridges where he has been obliged to accept unfair loading of the kind discussed4 ,it should be remarked that by the two first methods1 if the stiffening frames are wide apart and attached direct to the web1 there is a liability for this to tear1 under distress1 rather than keep the girder in line4 ,there is one other possible consequence of throwing load upon the flanges of a girder of a much more alarming nature4 ,in girders not very well stiffened1 it may happen that the frequent application of load in this manner finally so injures the web-plate1 just above the top edge of the bottom angle-bars1 as to cause it to rip in a horizontal direction4 ,more likely is this to happen with a centre girder taking load first on one side1 then on the other1 and again on both together4 ,cases may be cited in which cracks right through the webs #c feet or more in length have resulted from this cause4 ,it is very probable1 however1 that in some of these cases the matter was aggravated by the use of a poor iron in the webs1 as at one time engineers1 from mistaken notions of the extreme tenuity permissible in webs near the centre of a girder1 would1 if they could not be made thin enough1 even encourage the use of an indifferent metal as being quite good enough for that part of the work4 ,an instance of web-fracture from somewhat similar causes may be here given4 ,in a bridge of #ca feet #f inches effective span1 and consisting of twin girders carrying rails between1 as shown in ,figs4 #h and #i1 the load resting upon the inner ledges1 formed by the bottom flange1 induced such a bending and tearing action along the web just above the angle-bars1 as to cause a rip in one of the girders1 well open for some distance1 and which could be traced for #ad feet as a continuous crack4 ,illustration3 ,,fig4 #h4 ,illustration3 ,,fig4 #i4 ,it will be noticed in the figure that the ,t stiffeners occur only at the outer face of the web1 and that the inner vertical strips stop short at the top edge of the angles1 the result being that under load the flange would tend to twist around some point1 say ,a1 at each stiffener1 inducing a serious stress in the thin web at that place1 while away from these stiffeners the web would be more free to yield without tearing4 ,the fact that at a number of the stiffeners incipient cracks were observed1 some only a few inches long1 suggests this view of the matter4 ,a case of web-failure from other influences coming under notice showed breaks at the upper part of the web extending downwards4 ,in this bridge1 of #cb feet span1 which had been in existence thirty-two years1 the webs--originally #a_/d inch thick--were1 largely because of cinder ballast in contact with them1 so badly wasted as to be generally little thicker than a crown-piece1 and in places were eaten through2 in addition to which1 the road being on a sharp curve1 the rail-balks had been strutted from the webs to keep them in position1 the effect of which would be to exert a hammering thrust upon the face of the web at the abutting ends1 and assist in starting cracks in webs already much corroded4 ,a feature of this case1 tending to show that the breaks resulted as the joint effect of waste and ill-usage by the strut members1 rather than by excessive stress in the web as reduced1 is to be found in the fact that the girders when removed were observed to be in remarkably good shape--i4e4 the camber1 marked on the original drawings to be #a-a_/b inch1 still showed as a perfectly even curve of that rise1 which would hardly have been the case if the lower flange had been let down by web-rupture1 the result of excessive web-stresses4 ,occasionally webs will crack through the solid unwasted plate1 in a line nearly vertical2 not where shear stress is greatest1 but generally at some other place1 and from no apparent cause1 either of stress or ill-usage4 ,the writer has observed this only in the case of small girders not exceeding #b feet in depth2 and1 for want of any better reason1 attributes these cracks to poor material1 coupled with some latent defect4 ,in a bridge having some thirty cross-girders1 each #bf feet long1 about every other one had a web cracked in this manner after many years' use4 ,web-cracks of the kind first indicated1 are perhaps1 the most probable source of danger in plate-girders1 of any which are likely to occur4 ,the fault is insidious1 difficult to detect when first developed1 and perhaps not seen at all till the bridge1 condemned for some other reason1 has the girders freely exposed and brought into broad light4 ,the manner in which old girders are sometimes partly concealed by timberwork1 or covered by ballast1 makes the detection of these defects an uncertain matter1 unless sufficient trouble is occasionally taken to render inspection complete4 ,the manner in which girders with wasted and fractured webs will still hang together under heavy loading seems to warrant the deduction that1 in designing new work1 it can hardly be necessary to provide such a considerable amount of web-stiffening as is sometimes seen2 experience showing that defects of the web-structure do not commonly occur in the stiffening so frequently as in the plate1 and then in the form of cracks4 ,a case of web-buckling lies1 so far1 without the author's experience4 ,there is no need to introduce1 for web-stresses alone1 more stiffening than that which corresponds to making the stiffeners do duty as vertical struts in an openwork girder2 in which case it is sufficient to insure that the stiffeners occurring in a length equal to the girder's depth shall1 as struts1 be strong enough in the aggregate to take the whole shear force at the section considered1 in no case exceeding this amount on one stiffener4 ,for thin webs in which the free breadth is greater than one hundred and twenty times the thickness1 the diagonal compressive stress may be completely ignored1 and the thickness determined with reference to the diagonal tension stress only4 ,there is one fault which frequently shows itself in stiffeners though not the result of web-stresses1 and when performing an additional function--viz41 the breaking of ,t stiffener knees at the weld1 where brought down on to the tops of cross-girders1 due to the deflection of the floor1 as shown in ,fig4 #aj4 ,when such knees are used1 the angle may properly be filled in with a gusset-plate to relieve the weld of strain and prevent fracture4 ,illustration3 ,,fig4 #aj4 ,there is some little temptation in practice to make use of the solid web as a convenient stop for ballast1 or road material4 ,special means1 perhaps at the cost of some little trouble1 should be adopted1 where necessary1 to avoid this4 ,,main ,,girders2 ,,open ,,webs4 ,with these1 as with plate-girders1 deficiency of strength--i4e4 of section strength--is seldom so marked as to be a reasonable cause of anxiety4 ,in particular instances faults in design may result in stresses of an abnormal amount1 though rarely to an extent occasioning any ill effects4 ,the practice of loading the bottom flanges at a distance from the centre1 the bad effects of which have already been dealt with as applied to plate-girders1 is not commonly resorted to in girders having open webs1 nor are these so liable to be heaped with ballast in immediate proximity to essential members of the structure4 ,some defects are1 however1 occasionally seen which may be remarked4 ,top booms of an inverted ,u section are sometimes made with side webs too thin1 and having the lower edges stiffened insufficiently1 or not at all4 ,where this is the case1 the plates may be seen to have buckled out of truth1 showing that they are unable1 as thin plates1 to sustain the compressive stress to which the rest of the boom is liable4 ,the practice of putting the greater part of the boom section in an outer flange1 characteristic of this defect1 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 members4 ,further1 since all the variation in boom section is thrown into the flange-plates1 the centre of gravity of the section has no constant position along the boom--an additional inconvenience where correct design is aimed at4 ,these considerations indicate the propriety of arranging the bulk1 or all1 of the section at the sides1 thus reducing or getting rid of the objections named4 ,where the bottom boom consists of side plates1 only one point demands attention4 ,it is found that1 though nominally in tension1 the end bays are liable occasionally to buckle1 as though under compressive stress1 and need stiffening1 not excepting girders which at one end are mounted on rollers4 ,this might seem to indicate that the rollers are of no use2 but it is conceivable the resistance arises from other causes1 such as wind forces1 or as in the case of a bridge carrying a railway1 in which the rigidity of the permanent-way may be such that the bridge-structure1 in extending towards the roller end1 cannot move it sufficiently1 causing a reversal of stress on the lighter portions of the bottom boom at the knuckle end2 or by the exposed girder booms becoming very sensibly hotter than the bridge floor1 and by expanding at a greater rate1 cause this effect1 from which rollers cannot protect them4 ,in counterbracing consisting of flat bars it is desirable either to secure these where they cross other members1 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 load4 ,occasionally diagonal ties are made up of two flat bars placed face to face1 to escape the use of one very thick member4 ,where this is done1 the two thicknesses1 if not riveted together along the edges1 will be liable to open1 as the result of rusting between the bars in contact1 when the evil will be aggravated by the greater freedom with which moisture will enter the space4 ,other matters relating to open-web girders will be more conveniently dealt with under their separate headings1 particularly a further consideration of the relationship subsisting between the booms and floor structure4 ,,chapter ,,iii4 ,,bridge ,,floors4 ,the floors of bridges commonly give more trouble in maintenance1 and their defects are more frequently the cause which renders reconstruction necessary1 apart from reasons not concerning strength1 than any other part of such structures4 ,when it is considered that this portion of a bridge is first affected by impact of the load which comes upon it1 and is usually light in comparison with the main girders further removed from the load1 and to which the latter is transferred through the more or less elastic floor1 the fact will be readily appreciated by those not already familiar with it4 ,the end attachments of cross and longitudinal girders are very liable to suffer by loosening of rivets1 or1 more rarely1 by breaking of the angle-irons which commonly make such a connection4 ,a not unusual defect of old work1 which may also sometimes be seen in work quite new1 where the cross-girder depth has from any cause been restricted1 is the extremely cramped position of the rivets securing the ends4 ,there is small chance of these ever being properly tight1 if the act of riveting is rendered difficult by bad design4 ,this is the more objectionable if it happens that cross-girder ends abut against opposite sides of the web of an intermediate main girder1 and are secured by the same rivets passing through4 ,at the best such rivets will not be well placed to insure good workmanship1 and the severe treatment to which they become subject1 as the cross-girders take their load and deflect under it1 will be very apt to loosen them4 ,the author has seen a case of this kind 7see ,figs4 #aa and #ab7--rather extreme1 it is true--in which nearly the whole of the cross-girder end rivets were loose1 some nearly worn through1 thus allowing the cross-girders to be carried1 not by their attachments1 but by resting upon the main-girder flanges1 which in turn1 by repeated twisting1 tore the web for a length of #d feet2 there was also pronounced side flexure of the top booms4 ,the movements generally on this bridge 7of #db-;feet span71 whether of main or cross-girders1 were very considerable and disturbing4 ,it was removed after about twenty-three years' use4 ,illustration3 ,,fig4 #aa4 ,illustration3 ,,fig4 #ab4 ,there is no necessity1 as a rule1 for the ends of cross-girders attached to the same main girder at opposite sides to be placed in line4 ,the author prefers to arrange them to miss1 by which device each connection is entirely separate1 the riveting can be more efficiently executed1 erection is simplified1 and the rivets will be more likely to keep tight4 ,other special cases of cross-girder ends will be dealt with under the head 8,riveted ,connections40 ,it is sometimes contended that cross-girders attached at their ends by a riveted connection should be designed as for fixed ends1 in which case they are usually made of the same flange section throughout1 with a view to satisfy the supposed requirements4 ,but a girder to be rightly considered as having fixed ends must be secured to something itself unyielding4 ,with an outer main girder of ordinary construction1 and no overhead bracing1 this is so far from being the case as to leave little occasion for taking the precaution named4 ,as the cross-girders deflect1 the main girders will commonly yield slightly1 inclining bodily towards the cross-girders1 if these are attached to the lower part of the main girders4 ,the force requisite to cant the main girders in this manner is usually less than that which corresponds to fixing the cross-girder ends1 and is1 generally1 slight4 ,it is1 of course1 necessary that this measure of resistance at the connection should be borne in mind for the sake of the joint itself1 quite apart from any question of fixing4 ,possibly1 in quite exceptional cases1 where very stiff main girders are braced in such a manner as to prevent canting1 it may be proper to consider the cross-girder ends as fixed1 or for those near the bearings of heavy main girders2 but the author has not met with any example where cross-girders1 apart from attachments1 appear to have suffered from neglect of this consideration4 ,with cross-girders placed on either side of a main girder1 and in line1 it may also1 for new work1 be desirable to regard the ends as fixed1 and to detail them with this in view4 ,it does not1 however1 appear wise to carry this assumption to its logical issue1 and reduce the flange section to any appreciable extent on this account4 ,the fixity of the ends will1 in any such case1 be imperfect2 and when one side only of an intermediate main girder is loaded1 it can have but a moderate effect in reducing flange stress at the middle of the loaded floor beam4 ,illustration3 ,,fig4 #ac4 ,,fig4 #ad4 ,,fig4 #ae4 ,similar reasons affect the design of longitudinal girder attachments to cross-girders1 which1 if intended to support rails1 cannot of necessity be schemed to come other than in line4 ,where the floor is plated as one plane surface1 there will not usually be any trouble resulting if no special precautions are used1 as the plate itself will insure that the longitudinals act1 in a measure1 as continuous beams1 relieving the joints of abnormal stress4 ,if the plating is1 however1 designed in a manner which does not present this advantage1 or if the floor be of timber1 it is better to decide whether the connections shall be considered as fixed1 and made so2 or avowedly flexible1 and detailed in such a manner as to possess a capacity for yielding slightly without injury4 ,those connections are most likely to suffer which are neither of the one character nor the other1 offering resistance without the ability to maintain it4 ,figs4 #ac1 #ad1 and #ae give representations of three 8spring joint0 methods of insuring yield in a greater or less degree4 ,for small longitudinals it is1 perhaps1 sufficient to use end angles with very broad flanges against the cross-girder web2 these to be riveted in the manner indicated in ,fig4 #ae4 ,liberal depth to floor beams is distinctly advantageous where it can be secured1 rendering it easier to design the ends in a suitable manner1 by giving room near mid-depth of the attachment to get in the necessary number of rivets2 or where the ends are rigidly attached direct to vertical members of an open-work truss1 the greater depth is effective in reducing the inclination of the end from the vertical1 with a correspondingly reduced cant of the main girders and flexure of the vertical member1 with smaller consequent secondary stresses4 ,in any case deep girders will contribute to stiffness of the floor itself1 favourable in railway bridges to the maintenance of permanent-way in good order4 ,illustration3 ,,figs4 #af1 #ag1 #ah4 ,a point in connection with skew-bridge floors occasionally overlooked is the combined effect of the skew1 and main girder camber1 in throwing the floor structure out of truth1 if no regard has been paid to this4 ,the result is bad cross-girder or other connections2 or1 in the case of bearers running over the tops of main girders1 a necessity for special packings to bring all fair 7,fig4 #ag74 ,the author has in such cases1 where cross-girders are used1 set the main girder beds at suitable levels1 in order that the cross-bearers may all be horizontal 7see ,figs4 #af and #ah74 ,this may not always be permissible2 but1 however the difficulty may be met1 it should be dealt with as part of the design4 ,for small angles of skew only may it be neglected4 ,rivets attaching cross-girder angles to the web will occasionally loosen1 probably due in most cases to bad work1 together with some circumstance of aggravation1 as in the case of a bridge floor consisting of girders spaced #c feet #f inches apart1 with short timber bearers between1 carrying rails4 ,in many girders the top row of rivets1 of ordinary pitch and size1 had loosened1 allowing the web1 about #a_/d inch thick1 a movement of #a_/h inch vertically4 ,the rails being very close down upon the cross-girder tops1 though not intended to touch1 had at some time probably done so1 and by 8hammering0 produced the result described4 ,plated floors are often found which are objectionable on account of their inability to hold water1 arising sometimes from bad work1 as often from wide spacing of rivets4 ,with rivets arranged to be easily got at1 and pitched not more than #c inches apart1 a tight floor may be expected2 but it is still necessary to drain the floor by a sufficient number of holes1 provided with nozzles projecting below the underside of the plate1 and sufficiently long to deliver direct into gutters1 where these are necessary4 ,drain-holes should not be less frequent than one to every #ej square feet of floor1 if flat1 and may advantageously be more so4 ,gutters should slope well1 and care be taken to insure practicable joints and good methods of attachment--a matter too often left to take care of itself1 with considerable after-annoyance as a result4 ,the use of asphalt1 or asphalt concrete1 to render a plated floor water-tight is hardly to be relied upon for railway bridges1 though no doubt effective for those carrying roads4 ,it is extremely difficult to insure that it shall stand the jarring and disturbance to which it may be subject1 and under which it will commonly break up1 and make matters worse by holding moisture1 and delaying the natural drying of the floor4 ,in bulk1 as in troughs1 it may be useful1 but in thin coverings on plates it cannot be depended upon4 ,floors having plated tops are sometimes finished over abutments or piers in a manner which is not satisfactory1 either as regards the carrying of loads or accessibility for painting4 ,if the plates are carried on to a dwarf wall with the intention that the free margin of the plate shall rest upon it1 there will be a difficulty in securing this in an efficient manner4 ,commonly such a wall is built up after the girder work is in place1 making it difficult to insure that the wall really supports the plate1 the result being that this may have to carry itself as best it can4 ,in any case1 severe corrosion will occur on the underside1 and the plate rust through much before the rest of the floor2 the masonry also will usually be disturbed4 ,it appears preferable to form the end of the floor with a vertical skirting-plate having an angle or angles along the lower edge4 ,this may come down to a dwarf wall1 but preferably not to touch it1 the skirting being designed to act as a carrying girder4 ,a convenient arrangement is shown in ,fig4 #ai1 which may be used either for a square or skew bridge4 ,it will be seen that the plate-girders have no end-plates1 the skirting referred to being carried continuously along the floor edge1 and attached to each girder-web1 the whole of the more important parts being open to the painter4 ,illustration3 ,,fig4 #ai4 ,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 ends1 if they abut against main girders1 and but little connection is1 as a rule1 attempted1 and sometimes none4 ,the result is that the load from these troughs is delivered in an objectionable manner1 and the ends being open or imperfectly closed1 water and dirt escape on to the flange1 or other ledge1 which supports them4 ,a description of pressed floor which promises to overcome this objection1 and provide a ready means of attachment to the webs of plate-girders1 or of booms having vertical plate-webs1 has within the last few years been introduced4 ,this has the ends shaped in such a manner as to close them and provide a flat surface of sufficient area for connection by rivets4 ,each hollow is separately drained by holes with nozzles4 ,whether this type of trough will develop faults of its own1 due to over-straining of the metal in the act of pressing1 remains to be seen2 but as it appears possible to produce the desired form without any material thinning or thickening of the metal1 the contention that no severe usage accompanies the process appears to be reasonable4 ,that form of troughing in which the top and bottom portions are separately formed1 and connected by a horizontal seam of rivets at mid-depth1 is found in use upon railway bridges to be very liable to loosening of those rivets near the ends2 less surprising1 perhaps1 because the sloping sides are usually thin4 ,it is a distinctly difficult matter to join two or more lengths of any trough flooring having sloping sides1 in a workmanlike manner2 the fit of covers is apt to be imperfect1 and some rivets1 being difficult of access1 are likely to be but indifferently tight1 so that if the joint occurs where it will be more than lightly stressed1 trouble will probably follow4 ,a bad place for such joints is immediately over girders supporting the troughs1 as there the stress will be most severe1 any leakage come directly upon the girder1 and remedial measures be more difficult to carry out4 ,timber floors of the best timber1 close jointed1 are more durable than might be supposed4 ,the disadvantage is a difficulty in ascertaining the precise condition of the timber after many years' use4 ,the author has seen timbers1 #i inches by #i inches1 forming in one length a close floor1 carried by three girders1 and supporting two lines of way1 which1 when taken out1 could as to a considerable part be kicked to pieces with the foot2 whilst in another case1 with the same arrangement of girders and close-timbered floor1 the wood1 after being in place for thirty-two years1 was1 when taken out1 found to be perfectly sound1 with the exception of a very few bad places of no great extent4 ,in this instance1 however1 it is known that the floor--pitch-pine--was put in by a contractor who prided himself upon the quality of the timber that he used2 the floor being also covered with tar concrete1 which had in this instance so well performed its office as to keep the timber quite dry on the top4 ,jack arches between girders make an excellent floor for road bridges1 though heavy2 and for small bridges may be used to carry rails1 if the girders are designed to be stiff under load4 ,the apprehension that brickwork or concrete will separate from the girder-work1 or become broken up under even moderate vibration1 does not seem to be well founded1 if the deflection is small and the brickwork or concrete good4 ,the use of corrugated sheeting as a means of rendering the underside of a bridge drop dry cannot be too strongly deprecated4 ,if it must be adopted1 the arrangement should be such as to permit ready removal for inspection and painting4 ,it is evident that by boxing up the floor structure1 rust is favoured1 and serious defects may be developed1 not to be discovered till the sheeting is removed1 or something happens4 ,illustration3 ,,fig4 #bj4 ,a case may be instanced in which it was found1 on taking down sheeting of this description1 that the floor girders1 previously hidden1 were badly wasted in the webs4 ,one of these girders had cracked1 as shown in ,fig4 #bj1 and others were in a condition only less bad4 ,in any floor carrying ballast or macadam1 if means are not adopted to keep the road material from the structure of the floor1 or from the main girders1 corrosion may be serious in its effects4 ,cinder ballast is1 perhaps1 the worst in this respect1 in its action upon steel or ironwork1 being distinctly more damaging than any other kind commonly used4 ,rail-joints upon bridge floors are to be avoided where practicable by the use of rails as long as can be obtained2 if the bridge is small enough1 crossing it in one length4 ,at each joint there is likely to be hammering and working extremely detrimental to floor members and connections2 indeed1 it may happen that loose rivets will be found in the neighbourhood of such joints1 and nowhere else on the bridge4 ,where rail-joints cannot be avoided1 their position should1 if there be any choice1 be judiciously selected1 and the plate-layers taught to close the joints and jam the fish-bolts4 ,illustration3 ,,fig4 #ba4 ,as rail-joints upon a bridge may injuriously affect the floor1 so also will a weak floor be very trying to the rails4 ,a remarkable instance of this has come under the writer's notice1 where a bridge 7,fig4 #ba7 of three #cc-;feet spans1 having outer and centre main girders1 with cross-girders spaced #c feet apart1 resting upon the girder flanges1 but not attached1 and carrying two roads1 had the permanent-way in a very bad state4 ,the rails proper1 with supplementary angle-plates1 rested direct upon the cross-girders1 which were decidedly light1 and the whole floor had much 8life0 in it1 the ill-effect of which was shown in thirteen breaks in the angle-plates1 in each case near their ends1 generally at holes4 ,it appears probable that severe stresses may be thrown upon the parts of a floor1 whether placed at the level of the bottom booms or of the top1 by changes of length in the booms due to stress4 ,the author has1 unfortunately1 no direct evidence to offer in reference to this1 tending either for or against the contention4 ,if an unplated floor of cross and longitudinal girders of usual arrangement be at the bottom boom of a large bridge1 as the boom lengthens with the imposition of load upon the bridge1 all the cross-girders from the centre towards the abutments will be curved horizontally1 the middle portion being restrained by the longitudinals from moving bodily with the ends4 ,each cross-girder except that at the centre1 if there be one1 will thus present a figure in plan1 concave towards the abutment to which it is nearest4 ,this will be accompanied by stressing of the connections1 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 communicate4 ,this in itself will hardly be considerable1 and will be the less on account of a slight yielding which may be expected at the end connections of each longitudinal2 but the effect upon the cross-girders by horizontal bending will be much marked4 ,if the case be supposed of a #bjj-;feet span in steel at ordinary loads and stresses1 carrying one line of way1 with cross-girders #bj feet apart1 and having no floor-plates1 it may be ascertained1 neglecting for the moment any slight yielding of the longitudinal girder connections1 that upon the bridge taking its full live load there will be the following approximate results3 ,movement at each end of the end cross-girders of #c_/aj inch1 equivalent to a force of #g-a_/b tons1 tending to bend them horizontally1 and a mean stress on the outer edges of the girders1 #ab inches wide1 of #h tons per square inch due to flexure1 which1 compounded with the ordinary flange stresses1 will seem to give rather alarming results4 ,there will also be a longitudinal stress in the rail-girders1 at centre part of bridge1 of #c_/d ton per square inch4 ,normal elongation of the longitudinal girder bottom flanges1 and compression of the top1 modifies the figures unfavourably as to the cross-girder top flange4 ,yielding of the connections named before has been neglected in arriving at these stresses4 ,if they are sufficiently accommodating to give freely1 to a mean extent1 as between the top and bottom of each joint1 of #a_/bi inch1 these results will disappear4 ,it is evident1 however1 that we cannot rely upon good work yielding without the existence of considerable forces to cause it4 ,in the issue it is justifiable to apprehend that the flexing and stressing of the cross-girders will be considerable4 ,the most favourable case has been taken2 if now it is assumed that the floor has continuous plating1 the results would seem to be much more astonishing4 ,it will appear on this supposition that the boom stresses1 instead of being taken wholly by the booms1 are about equally divided between these and the floor structure1 each cross-girder connection communicating its share of boom stress to the floor1 which for the end cross-girders will approach #dj tons at each connection--considerably more than the vertical reaction under normal loads4 ,palpably1 these conclusions must be greatly modified by the yield of longitudinal girder ends1 and slip of the floor rivets in transverse seams4 ,if these rivets be #c-a_/b inch pitch and #c_/d inch in diameter1 the stress at each1 as estimated1 would be sufficient to induce shear of about #f tons per square inch--more than enough to cause 8slip40 ,after making this allowance1 it is still evident there must be very serious forces at work about the ends of cross-girders under the conditions supposed1 probably not less than one half the amounts named1 as with this reduction the floor rivets should not yield1 given reasonably good work4 ,it is to be observed that the effect of live load only has been introduced1 on the presumption that the longitudinals and floor-plating have not been riveted up till the main girders have been allowed to carry the major part of the dead load2 but even this cannot always be conceded4 ,the deduction appears to be that the floor and cross-girder connections should be studied with special reference to these possible effects1 either with the object of rendering the communication of these forces harmless1 or making the floor so that it shall take little or no stress from the main booms1 by arranging joints across the floor specially designed to yield1 the ends of longitudinals being schemed with the same object4 ,where there is no plating1 the case is1 perhaps1 sufficiently provided for by making the cross-girders narrow1 and the longitudinal girder connections flexible1 or by putting these girders upon the top of the cross-girders1 when stretching of the bottom flanges of the rail-bearers under load may be expected1 within a little1 to keep pace with the lengthening of the main booms4 ,it would appear that light pressed troughs running across the longitudinals would1 by yielding in every section1 also furnish relief1 as compared with the rigidity of flat plates4 ,by placing the floor at a level corresponding to the neutral axis of the main girders1 the communication of stress to the floor may be avoided2 but it seldom happens that there is so free a choice as to floor height relative to the girders4 ,this solution is1 therefore1 of limited application4 ,it is obvious that somewhat similar effects must obtain to those considered in detail1 when the floor structure lies at the level of top booms1 but with forces of compression from the booms to deal with1 instead of tension4 ,,chapter ,,iv4 ,,bracing4 ,bracing1 whether to strengthen a structure against wind1 to insure the relative positions of its parts1 or for any other purpose1 cannot be arranged with too great care and regard to its possible effects4 ,forces may be induced which the connections will not stand1 with loose rivets as a consequence1 and inefficiency of the bracing itself2 or1 the connections holding good1 stresses in the main structure may1 perhaps1 be injuriously altered4 ,to take a not uncommon case1 let us suppose a bridge consisting of four main girders placed immediately under rails of ordinary gauge1 and braced in vertical planes only1 right across from one outer girder to the other4 ,if the roads were loaded always at the same time1 nothing objectionable would result2 but1 as a fact1 this will be the exception4 ,when one pair of girders only takes live load1 and deflects1 the bracing under the six-foot will endeavour to communicate some part of this load to the other pair of girders4 ,if the bracing is so designed that some correctly calculated portion of the load can be transferred in this manner1 without over-stressing the bars and riveted connections1 there will be no harmful consequences2 but if not1 the bracings will most probably work at the ends2 this1 indeed1 is what frequently happens4 ,there is one other effect which will ensue1 if the bracing is wholly efficient2 a certain twisting movement of the bridge will occur1 which increases the live load upon the outer girder on the loaded side of the bridge to the extent of #aj per cent41 with a corresponding lifting force at the outer girder on the unloaded side4 ,these amounts are not serious1 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 bracing4 ,in road bridges of similar arrangement1 over which heavy loads may pass on any part of the surface1 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 girders1 and correspondingly light sections adopted1 unless the effect of twisting on the whole bridge is also considered1 and justifies this view2 for1 as already stated in the case of the railway bridge1 the net result may be to increase the girder stresses instead of reducing them4 ,generally1 it may be deduced that the better plan for railway bridges is to brace the girders in pairs1 leaving1 in the case supposed1 no bracing between the two middle girders1 though there will be no objection to connecting these by simple transverse members of no great stiffness1 to assist in checking lateral vibration4 ,for road bridges of more than five longitudinal girders1 equally spaced1 it may be advantageous to brace right across1 the twisting effect with this1 or a greater1 number of girders not1 as a rule1 leading to any increase of load on any girder4 ,figs4 #bb to #be give the distribution of live load1 placed as shown1 for #c1 #d1 #e1 and #f girders4 ,it is to be observed that these statements do not apply to cases where there may be also a complete system of horizontal bracing1 the effect of which1 in conjunction with cross diagonals1 may be greatly different1 with considerable forces set up in the bracing1 and a modification of girder stresses4 ,these effects may be so considerable as to call for special attention in design where such an arrangement is adopted4 ,illustration3 ,,fig4 #bb4 ,illustration3 ,,fig4 #bd4 ,illustration3 ,,fig4 #bc4 ,illustration3 ,,fig4 #be4 ,somewhat similar straining to that first indicated may occur in bracings placed between the girders of a bridge much on the skew4 ,if this is1 on plan1 at right angles to the girders1 as is commonly and properly the case1 the ends will evidently be attached to the girders at points on their length at different distances from the bearings1 which points1 even with both girders loaded1 deflect dissimilar amounts1 and the bracing will1 if at one end attached near a rigid bearing1 transfer some part of the load from one girder to the other1 notwithstanding that both girders may be of the same span and equal extraneous loading4 ,it would not be difficult to ascertain the amount of load so transferred from a consideration of the relative movements if free1 and the loads on the two girders necessary to render these movements equal1 if the deflections were simply vertical2 but as there will be some twisting and yielding of the girders on their seats1 the calculation becomes involved4 ,if the bracing is placed at about the middle of the girders1 the effects noted will be greatly reduced2 first1 because the difference of movements near the centre will be less2 second1 any given difference will correspond to a smaller transference of load2 and1 third1 because each girder will there be more free to twist than at the ends4 ,it therefore appears that bracings between the girders of a skew bridge should not be placed near the bearings1 though they may be put1 with much less risk of injury1 near the middle4 ,cross-girders on a skew bridge are subject to forces somewhat similar to those which may affect bracing1 rendering it desirable to design their attachments in a manner which shall not aggravate the matter1 but rather reduce the effects of unequal vertical displacement of their ends where secured to the main girders4 ,crossed flat bars as bracing members are objectionable on account of their tendency to rattle1 after working loose2 but as this effect only ensues in bracing which has first become loose 7it being assumed that the bars in any case are connected where they cross71 this objection is not itself vital1 though greater rigidity is easily obtained by making all such members of a stiff section4 ,defective bracing between girders1 from neglect of the very considerable forces it may be called upon to communicate1 is very common2 the writer has seen many such cases1 of which one is here illustrated in ,fig4 #bf4 ,illustration3 ,,fig4 #bf4 ,this bridge1 of the section shown1 and #he feet span1 had very light web structure4 ,the bracings1 of which there were two sets1 were wholly inefficient1 the end rivets being loose in enlarged holes4 ,upon the passage of a train there was a positive lurching of the girder tops from side to side4 ,the integrity of the bridge was really dependent upon such stiffness as there was in the girders1 and unplated floor4 ,a common but indifferent method of keeping the top members of main girders in line is by the use of overhead girders alone1 frequently curved to give the requisite clearance over the road4 ,this cannot be considered as wholly inefficient1 as sometimes maintained1 since it is evident that the closed frame formed by the floor beams1 the web members of the main girders1 and the overhead girder itself1 must take a greater force to distort it than would be necessary to cause deformation of a corresponding degree1 in an open frame formed by the omission of the overhead girder2 but it is not a method to be recommended1 its precise utility is difficult to estimate1 and1 if the cross-girder attachments are of a rigid character1 tends to increase the stresses induced at those connections4 ,the latter consideration is1 however1 not applicable to this arrangement alone4 ,all overhead bracing favours this by restraining the tendency of the top booms to cant inwards when the floor beams are loaded2 and though this restraint may be quite harmless1 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 character4 8,sway0 bracing1 sometimes introduced at right angles to the bridge between opposite verticals1 tends to emphasise these effects by rendering the cross-section of the bridge still stiffer1 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 bracing1 and how much by the floor4 ,the author does not1 however1 mean to suggest that it cannot be used with propriety1 but rather that extreme care is desirable in considering its ultimate effect on the rest of the structure4 ,for girders of moderate depth there may be on these grounds a distinct advantage in abandoning overhead bracing1 and securing rigidity of the top boom1 and adequate resistance to wind forces1 by making the connection between the cross-girders and the web members sufficiently good to insure1 as a whole1 a stiff ,u-shaped frame2 but this1 with the ordinary type of rocker arrangement under the main girder bearings1 will not be entirely free from objection1 as canting of the girders due to floor loading will throw extreme pressure on the inner end of each rocker4 ,there appears to be no reason why the cylindrical knuckle should not in this case be supplanted by a cup hinge1 allowing angular movement of the girder bearing in any plane4 ,illustration3 ,,fig4 #bg4 ,the efficient stiffening of light girders1 as in the case of foot-bridges1 from the floor1 where this is at the bottom flanges1 renders very narrow top booms permissible4 ,this is a decided advantage where lightness of appearance is aimed at2 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 girders1 and the projecting ends of flimsy transoms1 carried beyond the width of the bridge proper1 these being of a section wholly out of proportion to the brackets they are supposed to secure4 ,whatever may be the amount of strength necessary at the point ,a1 in ,fig4 #bg1 there should not be less throughout the transom from one girder to the other4 ,the degree of strength and stiffness required in this member1 and in the vertical stiffeners is not1 as a rule1 great4 ,information to enable this question to be dealt with as a matter of calculation is somewhat scanty2 but it would appear to be sufficient to insure safety that1 for an assumed small amount of curvature in the compression member1 the forces outwards corresponding to this curvature1 due to thrust1 should be resisted by verticals and transoms of strength and stiffness sufficient to restrain it from any further flexure4 ,it will1 of course1 be necessary also to take care that the compression member is good as a strut between the points of restraint4 ,a simple and sufficiently precise method of dealing with this question is much needed4 ,in cases where the floor weight rests on the flange projection1 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 members2 further1 resistance to wind on the girder has to be provided in both transoms and verticals4 ,it may be hardly necessary to insist that bracing intended to stiffen a structure against wind1 local crippling1 or vibration1 should be made complete1 not stopping short at some point1 because it cannot conveniently be carried further1 as is sometimes done1 unless the strength of those parts of the structure through which the forces from the bracing must be communicated to the abutments is sufficiently great1 considered with reference to other stresses in those parts which have also to be endured4 ,bracing stopped short in this way1 making only the central part of a bridge rigid1 may have the effect of increasing the forces to which the unstiffened end members would otherwise be liable4 ,such a structure would evidently be much stiffer against wind-gusts than if no bracing existed--the resistance to a blow would be increased2 but the power to maintain that greater resistance being confined to the intermediate bays1 the unbraced ends would be subject to greater maximum forces than if bracing were wholly omitted4 ,the net effect may still be better than with no bracing1 the point raised being simply that of an increase of stress in particular end members4 ,in the bracing of tall piers1 the rising members of which will be subject to any considerable stress1 if the diagonal members are not finally secured when the piers are under their full load1 or an initial stress of proper amount induced in those members1 the effect of loading will be to render them slack2 so that an appreciable amount of movement at the top may occur before it can be limited by the efficient action of the bracings4 ,this effect under blasts of wind or continual passage of trains may1 indeed1 be dangerous4 ,similar considerations apply to the top wind bracing of deep girder bridges1 influencing also the bottom bracing in a contrary manner1 which calls for attention in fixing the unit stresses for such members4 ,the bracing of sea-piers is very liable to slacken if made with pin-and-eye ends1 as is often done for round rods4 ,the detail presents advantages in erection1 but is not altogether satisfactory in practice4 ,such connections are continually working4 ,in the finest weather1 with the sea quite smooth but for an almost imperceptible wave movement1 the lower parts of such structures will be found1 as a rule1 to have some slight motion4 ,this is very trying to bracing2 nor is there room for surprise when it is considered that these oscillations1 occurring at about ten to each minute1 never wholly cease1 and amount in the course of one year to over five million in number4 ,bracing attached in such a manner that there can be no initial slack1 or slack due to wear under endless repetitions of small amounts of stress1 will have a much better chance to keep tight4 ,the advantage presented by round rods in offering little surface to the water1 is more than negatived by inefficiency of the usual attachments for such rods4 ,the author has observed that bracing of members possessing some stiffness1 and with good end attachments to ample surfaces1 appears to stand best in ordinary sea-pier work4 ,for such structures the bracing should consist of a few good members1 with a solid form of attachment1 rather than of a multiplicity of lighter adjustable members1 which will commonly give great trouble in maintenance2 being very possibly also1 in the case of sea-pier work1 in unskilled hands4 ,if round rods must be used1 they will stand much better if made of large diameter4 ,before leaving the subject of bracing1 it may not be out of place to refer to wind pressure1 as this may so much affect the proportioning of the members4 ,some years since the author had occasion to examine a number of structures with respect to their stability4 ,of foot-bridges from #fj feet to #abj feet long1 three or four1 when calculated on the basis recommended by the ,board of ,trade as to pressures upon open-work structures1 worked out at an overturning pressure of from #ah lb4 to #bb lb4 per square foot4 ,these bridges had been many years in existence2 it is1 therefore1 fair to assume that no such wind in the direction required for overturning had expended its force upon them as to the whole surface4 ,illustration3 ,,fig4 #bh4 ,particulars were taken in #ahie of a notice-board1 presenting about #ab square feet of surface1 which was blown down in the great storm of ,march #bd of that year1 at ,bilston1 in ,staffordshire4 ,it was situated at the foot of a slight slope1 over which the wind came1 striking the obstruction at right angles4 ,the board was mounted on two oak posts of fair quality and condition1 which broke near the ground at bolt holes 7see ,fig4 #bh74 ,the force required to do this1 at #ijjj lb4 modulus of rupture--a moderate value--corresponds to #ej lb4 per square foot on the surface exposed above the break4 ,in the same neighbourhood1 at the same time1 considerable damage was wrought in overturning chimney stacks1 to buildings and roofs2 the general impression in the locality being that the storm was of exceptional1 even unprecedented1 violence4 ,bilston1 it should be noted1 lies high4 ,at ,bidston ,hill1 near ,birkenhead1 on the same occasion1 a pressure of #bg lb4 was registered4 ,in another part of the country it is said to have been #cg lb4 ,wind is so capricious in its effects over small areas as to render it probable that the maximum pressures have never been recorded2 but this is a matter of little importance where general stability and strength only are concerned4 ,the instances cited1 though by themselves insufficient to throw much light on the question1 may be of use in connection with other known examples4 ,,chapter ,v4 ,,riveted ,,connections4 ,considerable latitude is observable in the practice of engineers in the use of rivets4 ,numberless experiments to determine the resistance of riveted connections have from time to time been made1 but these are not to be considered by themselves as final1 when the results of experience in actual construction1 are available for further enlightenment4 ,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 cases1 including all degrees of workmanship1 that any reliable conclusions may be drawn4 ,in this respect laboratory experiments have an apparent advantage1 as the conditions may be kept sensibly the same2 but1 on the other hand1 no such investigation reproduces the circumstances of actual use1 which alone must in the end determine the utility of any inquiry for practical application4 ,the author has studied the particulars of a number of cases to ascertain under what conditions as to stress1 having due regard to the effects of vibration1 rivets will remain tight1 or become loose4 ,every loose rivet that may be found cannot1 of course1 be taken as being due to excessive stress2 the more frequent cause is indifferent work1 evidenced by the fact that neighbouring rivets will frequently be found quite sound1 though the failure of some will cause a greater stress upon the remainder4 ,when rivets loosen as the direct result of over-stress1 it is usually by compression of the shank and enlargement of the hole1 or by stretching of the rivet and reduction of its diameter4 ,instances of failure by partial or complete shear are extremely rare2 indeed1 the author has never yet found one1 though when a rivet has first worked loose1 as a result of excessive bearing pressure or bad work1 it is not uncommon to find it cut or bent as an after consequence4 ,in estimating stresses at which rivets have remained tight1 or loosened1 as the case may be1 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 computation4 ,this is clearly most important1 as1 if any appreciable uncertainty remained as to the degree of stress1 the results deduced would be of little value4 ,for this reason those instances in which the loads upon girders1 or parts of girders1 may find their way to the supports by more than one route1 are to be regarded with caution1 as are those in which full loading possibly never obtains1 but which may1 on the other hand1 perhaps have been frequent4 ,the working diameter of the rivet as it fills the hole has been used in making the computations2 in some cases from direct measurement from particular rivets1 in others with a suitable allowance for excess diameter of hole1 according to the class of work under consideration4 ,dealing first with main girders1 it may be said that rivets attaching the webs of plate girders to the flange angles rarely loosen1 though subject to considerable stress4 ,in illustration of this may be named a bridge for two lines of way1 #he feet effective span1 having two main girders with plate webs1 and cross-girders resting on the top flanges1 previously referred to 7see ,fig4 #bf74 ,the girders1 which were #f feet #i inches deep1 had a bearing upon the abutments of #d feet2 the rivets were #g_/h inch in diameter and #d inches pitch4 ,there is in a case of this kind some little uncertainty as to what is the stress on the flange angle rivets at1 or very near to1 the bearings2 but1 taking the vertical rows of rivets at the web joints near the ends as presenting less uncertainty1 the stress per rivet works out at #dh tons1 being #d tons per square inch on each shear surface1 and #aa tons per square inch bearing pressure upon the shank in the web plate1 which was barely #a_/b inch thick4 ,this bridge was frequently loaded upon both roads1 but with one road only carrying live load1 the stresses in the more heavily loaded girder would be fully #ij per cent4 of those obtaining as a maximum4 ,there was on this bridge1 which had been in use #ca years1 considerable movement and vibration4 ,it is by no means uncommon to find cases of rivets in main girders taking #aa tons per square inch bearing pressure--occasionally more--and remaining tight4 ,as furnishing an instructive1 though slightly ambiguous1 instance of rivets in single shear1 may be cited a bridge not greatly less than that just referred to1 of about #fe feet span1 carrying two lines of way1 there being two outer and one centre main girder of multiple lattice type1 with cross-girders in one length #d feet apart1 riveted to the bottom booms of the main girders2 these rivets1 by the way1 were in tension4 ,the floor was plated1 the road consisting of stout timber longitudinals1 chairs1 and rails 7,fig4 #bi74 ,illustration3 ,,fig4 #bi4 ,it should be noted that there is in this case some difficulty in ascertaining the precise behaviour of the cross-girders1 affecting the proportion of load carried by the outer and the inner main girders4 ,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 line4 ,a close inquiry showed that this was very far from being the case1 and that while each cross-girder at the centre of the bridge would1 under load1 by relative depression of the middle point of support1 be reduced to the condition of two simple beams1 those at the extreme ends of the span would behave as continuous girders4 ,with both roads carrying engine loads equal to those coming upon the bridge1 the author estimates that for the centre main girder the shear on the rivets of the end diagonals1 secured by one rivet only1 was #adi tons per square inch1 and the bearing pressure #afc tons2 the flange stress being #ga tons per square inch net4 ,the outer main girders are most heavily stressed when but one road1 next to the outer girder considered1 carries live load4 ,for this condition the stresses work out at #i tons per square inch shear on the rivets of the end diagonals1 and #i tons bearing pressure1 the flange stress being #eg tons per square inch on the net section4 ,without intending to throw any doubt upon the substantial truth of these results1 it must be admitted that instances of greater simplicity of stress determination are much to be preferred4 ,for purposes of comparison1 but not as having any other value1 the results have also been worked out on the supposition of all cross-girders acting each as two simple beams1 and also for strict continuity1 and are here tabulated1 together with the conclusions given above4 ,the cross-girders were moderately stressed1 and the tension on the rivets attaching them to the main girders probably did not exceed #c tons per square inch4 ,it should be pointed out that the traffic over the bridge was small4 ,the centre main girder but seldom bore its full load1 though at all times liable to receive it4 ,much importance cannot1 therefore1 be attached to the results for this girder1 other than as showing how a structure may stand for many years1 though liable at any time to the development of stresses which would commonly be regarded as destructive1 or nearly so4 ,,examples ,,of ,,rivet ,,stresses1 ,,etc41 ,,in ,,lattice ,,girders4 ---------------------------------------- ------------------------- ,cross- ,cross- ,girders ,girders as ,correct as ,simple ,continuous ,results4 -- ,beams4 ,beams4 -------------------------------- ,stress in ,tons per ,square ,inch4 ---------------------------------------- ------------------------- ,centre girder1 #fc ft4 span 7both roads loaded73 ,rivets in diagonals--,shear #acg #agb #adi ,do4 ,bearing pressure #aej #ahh #afc ,flange stress #fh #he #ga ,outer girder1 #ff ft4 span 7near road loaded73 ,rivets in diagonals--,shear #if #hb #ij ,do4 ,bearing pressure #if #hb #ij ,flange stress #ei #ea #eg ---------------------------------------- ------------------------- ,the material and workmanship of the bridge were good4 ,the rivets of the centre girder end diagonals1 #a inch in diameter1 were originally #g_/h inch1 but on becoming loose were cut out1 the holes reamered1 and replaced by the larger size1 which remained tight1 and to which the stress figures apply4 ,the rivets in the diagonals near the centre1 #g_/h inch in diameter1 which were subject to reversal of stress1 occasionally worked loose1 and were more than once replaced4 ,the riveting in the outer girder diagonals1 subject to smaller stresses1 much more frequently developed1 also gave trouble1 particularly those liable to counter stresses4 ,apart from looseness of rivets1 the general appearance and behaviour of the bridge1 which had been in existence about twenty years1 was not suggestive of any weakness4 ,of smaller girders1 an example showing the necessity for care in discriminating1 if it be possible1 between looseness of rivets resulting from over-stress and that due to other influences may first be quoted4 ,two trough girders1 of #aa feet effective span1 each of the section shown in ,fig4 #cj1 #aa-a_/b inches deep at the ends1 #ad inches at the middle1 with #a_/d-;inch webs1 and rivets #c_/d inch in diameter1 of #d-a_/b-;inch pitch1 showed certain defects1 of which one1 it may be incidentally mentioned1 was a cracked web 7,fig4 #ca74 ,from the nature of the arrangement the lower web rivets1 which were loose1 would receive the first shock of the load coming upon the span1 but there were evidences indicative of original bad work4 ,the angle bars gaped1 suggesting that these had first been riveted to the bottom plate1 and left sufficiently wide to allow the web to be afterwards inserted1 the rivets failing to pull the work close1 and then readily working loose4 ,here there is considerable uncertainty as to how much of the loosening is to be attributed to bad work1 and how much to stress4 ,it may1 however1 be remarked that whatever bearing stress was the ultimate result of the load hammering on the lower angle flanges1 loosening rivets never perhaps really tight1 the stress of #g tons per square inch bearing pressure on the upper rivets1 though aggravated by considerable impactive force1 was not sufficient to loosen these4 ,the girders were taken out after being in place sixteen years4 ,illustration3 ,,fig4 #cb4 ,illustration3 ,,fig4 #cj4 ,illustration3 ,,fig4 #ca4 ,an instance of undoubted excessive bearing pressure was found in the cross-girders of a bridge1 mentioned on p4 #ae1 of which so many web plates were cracked4 ,this bridge1 carrying two lines of way1 had outer main girders1 and long cross-girders with #a_/d-;inch webs and #c_/d-;inch rivets1 #d inches pitch4 ,the rivet stresses work out at #dc tons per square inch on each shear surface1 and #bd tons per square inch bearing pressure4 ,for one road only being loaded1 the latter figure falls to #ahe tons4 ,the traffic over this bridge1 twenty years old1 was considerable1 rapid1 and heavy4 ,it is hardly necessary to add that a large number of the rivets were loose1 one of which is shown in ,fig4 #cb4 ,illustration3 ,,fig4 #cc4 ,to take another case relating to a floor system of extremely bad design 7,fig4 #cc74 ,the main girders were #aa feet apart1 #ce feet span1 the floor having two cross-girders only1 spaced at #aa feet #c inches1 and #i inches deep1 supporting hog-backed trough longitudinals4 ,the cross-girders were at their ends but #f-c_/d inches deep1 the distance from the bearing of cross-girders to centre of longitudinals carrying a rail being #b feet #aj inches1 in which length were eight rivets in the web and angles at the top1 and six at the bottom1 all #c_/d inch in diameter4 ,the shear stress on the upper rivets works out at #gc tons per square inch on each shear surface1 the bearing pressure #bjf tons per square inch4 ,on the lower rivets the shear stress becomes #ig tons1 and the bearing pressure #bgd tons1 per square inch4 ,care was exercised in computing these stresses1 that part of the bending moment carried by the web being allowed for1 but it must be admitted that the result is1 probably1 approximate only4 ,the sketch here given shows the cross-girder end and section4 ,the rivets1 though in double shear1 were1 as might be expected1 loose1 notwithstanding that the traffic over the bridge was moderate1 and quite slow4 ,the floor system was remodelled after twelve years' use4 ,in illustration of the behaviour of rivets in the ends of long cross-girders1 both shallow and weak1 and many years in use under heavy traffic1 may be cited connections having end angle bars to the cross-girders1 with six rivets through the web of main girders4 ,the bearing pressure worked out at #gh tons per square inch4 ,many rivets were loose1 but it should be remarked that the workmanship was not of the best class1 and the cross girders flexible3 a characteristic very trying to end rivets1 and inducing a stretch in some1 already referred to as a possible cause of loosening4 ,this will be apparent if the probable end slope of weak girders be considered4 ,the author concludes that this inclination should not1 for ordinary cases1 exceed #a in #bej2 but the ratio must largely depend upon the degree of rigidity of the part to which the connection is made4 ,it is commonly regarded as bad practice to submit rivets to tension1 yet this is frequently1 though unintentionally1 permitted in end attachments1 without any attempt to limit the amount of tension4 ,with suitable restrictions1 there appears no serious objection to rivet tension for many situations4 ,another instance of cross-girder end connections of a different type is illustrated in ,fig4 #cd4 ,the main girders of the bridge were #ab feet apart1 each cross-girder end carrying its share of the half of one road4 ,the mean bearing pressure upon the rivet shanks works out at #eh tons per square inch for the six rivets of the original joint1 but in the particular joint shown some of the rivets had loosened1 making the bearing pressure upon the remainder about #hg tons per square inch4 ,it is apparent there must have been considerable stress on the top and bottom rivets which loosened4 ,these two rivets would also1 because of difficult access1 be in all likelihood insufficiently hammered up4 ,the joints worked rather badly2 the loose rivets had 8cut0 to a considerable extent1 a process materially assisted by the gritty nature of the ballast 7limestone71 particles of which1 getting into the joint1 contributed to the sawing action2 this had clearly been taking effect for some considerable time4 7,see ,fig4 #ce47 ,illustration3 ,,fig4 #cd4 ,illustration3 ,,fig4 #ce4 ,the two cases of cross-girder ends given are both rather exceptional in character1 and in each case the defects appear to be due to general bad design and workmanship rather than to any serious excess of bearing pressure4 ,this may be illustrated by taking the common case of cross-girders1 #b feet deep1 carrying two roads1 and having end angle irons riveted to the web and stiffeners of the main girders by ten rivets in single shear at each end4 ,in this example1 which is1 for old work1 simply typical1 and does not relate to any specific instance1 the bearing pressure on the rivets will work out at from #f to #h tons per square inch1 and will seldom be accompanied by looseness of rivets1 and then only as a result of faulty work4 ,some sketches of rivets taken from old bridges have already been given in connection with the cases to which they belong2 a few others are here shown 7,figs4 #cf to #dj7 to further illustrate what may be the actual condition of rivets after some years' use1 and how different from the ideal rivet upon which calculations are based4 ,these are1 however1 bad instances4 ,illustration3 ,,fig4 #cf4 ,illustration3 ,,fig4 #cg4 ,illustration3 ,,fig4 #ch4 ,illustration3 ,,fig4 #ci4 ,illustration3 ,,fig4 #dj4 ,it should be noticed that rivets may1 if in double shear1 be loose in the middle thickness1 due to enlargement of the hole in the central part and compression of the rivet1 and yet show no sign of this by testing with the hammer4 ,there is1 however1 generally marked evidence of another kind in the 8working0 of the inner part1 as1 for instance1 the web of a plate girder1 in which case a discoloration due to rust is to be found along the edges of the angle bars1 or a movement may be detected on the passage of live load4 ,red rust is1 in fact1 frequently an indication of something wrong1 when no other evidence is apparent4 ,in plate girders having ,t or ,l bars brought down and cranked on to the top of shallow cross-girders1 it is not uncommon to find the rivets attaching these bars to the cross-girder tops loose1 due to causes already dealt with4 ,the riveted connection should1 as to strength1 bear some relation to the strength and stiffness of the parts secured1 if the rivets are to remain sound4 ,it may be well to give here a summarised statement of the results already named1 for purposes of ready reference4 ,these by themselves are not sufficient to enable working stresses to be deduced1 though they are instructive4 ,the author has found many instances of shear and bearing stresses in excess of those usually sanctioned1 under which the rivets behaved well1 but is not now able to give precise particulars of these4 ,,examples ,,of ,,rivet ,,stresses4 ---------------------------------------- -------------------- -- ,span ,where ,shear ,single,bearing ,tight or ,loose4 in ,found4 ,stress or ,pressure ,feet4 in ,doublein ,tons ,tons ,shear4 per per ,square ,square ,inch4 ,inch4 ---------------------------------------- -------------------- ,main #he ,web #dj ,d #aaj ,tight4 girders #ff ,diagonals #ij ,s #ij ,many loose4 #fc #adi ,s #afc ,tight generally4 #aa ,web #ad ,d #gj ,tight4 ,small #bf #dc ,d #bdj ,many loose4 girders #aa #gc ,d #bjf ,loose4 #aa #ig ,d #bgd ,loose4 ,end #bg ,ends #ed ,s #gh ,loose4 connec- #ab #ah ,d #eh ,many loose4 tions #hg 7,type case7 #bf #dh ,s #gj ,tight4 ---------------------------------------- -------------------- ,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 pressure1 as commonly estimated4 ,in the first case1 the rivet-shank must bear heavily on the half-thickness of the plates or bars through which it passes1 rather than on the whole thickness2 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 shear1 and the pressure better distributed4 ,illustration3 ,,fig4 #da4 ,illustration3 ,,fig4 #db4 ,the author has no very definite information in support of this contention1 but suggests that for double shear the permissible bearing pressure may probably be as much as #ej per cent4 greater than for rivets in single shear2 the difference being made rather in the direction of increasing the allowable load on double-shear rivets1 than in reducing that upon rivets in single shear4 ,the propriety of this is evident when it is considered that the practice has commonly been to make no distinction1 so that whatever bearing pressures are found to be sufficient for both cases may be increased for those capable of taking the greater amount4 ,figs4 #da and #db1 here given1 illustrate the behaviour of rivets under the two conditions4 ,with reference to the amounts of the stresses to which rivets may be subject1 the author concludes1 as a result of his experience1 coupled with a consideration of known laboratory tests1 that for all dead load these may be quite prudently higher than is frequently taken4 ,for iron the shear stress to be #aj per cent4 less than the stress of parts joined2 and the bearing pressure--for single-shear rivets1 #bj per cent42 and for double-shear rivets1 #hj per cent4 greater4 ,for ordinary mild steel the shear stress to be #bj per cent4 less than the stress in parts connected1 and the bearing pressure equal to it for single-shear rivets2 and #ej per cent4 more for rivets in double shear1 though the two latter values may probably approach those for wrought iron in steel of the higher grades sometimes used in bridge-work4 ,for live load1 or part live and part dead load1 the same rules may apply1 the reduction of the nominal working stress1 arrived at by any one of the methods in use which may be adopted1 affecting both the parts connected1 and the rivets connecting them4 ,for reverse stresses it is advisable to keep the shear stress in any rivet so low1 say #c tons per square inch1 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 liable1 to insure that1 if brought to a bearing in one direction by the greater force1 it shall not go back with reversal of stress4 ,this requirement may be open to some question with respect to good machine-riveted work1 but for hand-riveted connections it may certainly be adopted with wisdom4 ,the following table will show at a glance how the stresses proposed vary with the unit stresses governing the main sections4 ,,proposed ,,table ,,of ,,rivet ,,stresses4 ---------------------------------------- ---------------- ,unit ,stress ,bearing ,pressure,bearing ,pressure in ,shear ,stress4for ,single-,shearfor ,double-,shear ,member4 ,rivets4 ,rivets4 ---------------------------------------- ---------------- ,wrought ,iron4--,tons per ,square ,inch4 #cj #bg #cf #ed #dj #cf #dh #gb #ej #de #fj #ij #fj #ed #gb #ajh #gj #fc #hd #abf ,steel4--,tons per ,square ,inch4 #dj #cb #dj #fj #ej #dj #ej #ge #fj #dh #fj #ij #gj #ef #gj #aje #hj #fd #hj #abj #ij #gb #ij #ace ---------------------------------------- ---------------- ,,note4--,tension on rivets to be limited to one-half the permissible shear stress1 the holes being slightly countersunk under snap-head4 ,it may be objected that the shear stresses in the proposed table are somewhat high for wrought iron and steel4 ,this feature is intentional1 and is supported by the consideration that whereas there may be loss of strength in the members of a structure by waste1 there is no such loss in rivets1 if the work is so designed that there shall be no loosening4 ,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 case1 the table as it stands being applicable only to riveting not below the standard of first-rate hand work4 ,cases of loose rivets in main girders over #ej feet span1 due to any cause but bad work1 are extremely rare1 unless resulting from the action of some other part of the structure4 ,it may be stated broadly that for railway bridges of less than perfect design1 the nearer the rail1 the more loose rivets1 generally at connections4 ,this is1 no doubt1 largely due to the severe impact of the load1 the effects of which are greater near the rail1 both because of the small proportion of dead load1 and because this effect has been but little modified by the elasticity of any considerable length of intervening girder-work4 ,in addition to this1 it is quite usual to find the rivets more heavily stressed1 even though the load be considered as 8static10 in the floor system than in the main-girders1 though the reverse should be the case4 ,it is unfortunate that those parts which require the best riveting--viz41 the connections--are commonly dealt with by hand2 and for this reason it is the more necessary to design these with the greatest care4 ,any arrangement which favours the gradual acceptance of stress by one part from another will contribute to the integrity of riveted connections1 and lessen the liability of the material to develop faults4 ,in other branches of design this is well recognised1 but appears in much old bridge work to have been entirely overlooked4 ,bridges carrying public roads very seldom furnish examples of loose rivets2 the conditions are generally much more favourable1 impact being practically absent1 full loading infrequent1 and the proportion of dead load to live1 high4 ,it is1 perhaps1 hardly necessary to insist upon rivets being1 apart from mere considerations of strength1 sufficiently near together to insure close work and exclude moisture4 ,outside edge seams should never be more widely spaced than #af times the thickness of the plates2 #ab thicknesses apart is better4 ,in the case of angle1 tee1 and channel sections1 the greater stiffness of the section makes wider spacing allowable up to1 say1 #bj times the thickness2 but this must be governed largely by the amount of riveting required to pull the parts close together4 ,where more than four thicknesses are to be gripped by the rivets1 #c_/d inch in diameter is hardly sufficient to insure tight work1 and quite unsuitable if the plates exceed #e_/h inch thick4 ,,chapter ,,vi4 ,,high ,,stress4 ,high stress1 provided it be well below that at which immediate injury results1 or possible failure1 is not uniformly objectionable4 ,it may be first considered relative to the absolute and elastic limits of strength1 next with respect to the range of stress1 and1 finally1 with regard to the frequency of application4 ,for practical purposes--that is1 for the continued efficiency of a structure--the limit of elasticity must be considered to be the limit of strength1 or1 more strictly1 the limit for all those parts of the structure which must1 so long as it lasts1 be liable to the original measure of stress4 ,there may be places in a bridge1 however1 over-stressed only in the earlier period of its existence1 which1 by being over-stressed and suffering deformation1 permit the origin of this distortion to be harmlessly met in some other way4 ,in such a case the injury done to that part does not1 of necessity1 lead to any culminating disaster2 indeed1 were it not for this plasticity it is probable a large number of bridges would fail after being in use but a short time4 ,as for riveting1 so in dealing with the amount of stress to which a member is supposed to be liable1 it should be clearly understood by what method this has been arrived at1 whether the value assigned is the actual measure of the stress1 or simply the conventional amount arrived at in the conventional way2 perhaps neglecting web section in plate girders1 or without regard to the various influences which may reduce or increase the nominal amount of stress1 or including only a partial recognition of those influences4 ,in any case quoted the stress named is that at which the author arrives by the ordinary methods of computation carefully applied1 where these appear to be sufficiently precise1 unless any qualifying remark be added4 ,extreme flange stress is in special cases computed1 first on the gross section by estimating the moment of inertia on that basis1 and deducing the stress at the holes from the ratio of net to gross section at the extreme fibres2 a method more correct than by reference to the moment of inertia of the net section4 ,any exhaustive refinement in the study of stresses is not attempted1 both because it is beyond the author's powers of analysis1 and for the reason that such results are not comparable with the results of ordinary methods of calculation in practice4 ,effective spans are taken at moderate values1 and all exaggeration is avoided4 ,the effects of impact in any part vary so much with nearness to1 or remoteness from1 the living load1 and the frequency of development of the maximum stress from all causes acting together is so much affected by the same consideration1 that it is apparent a nominal stress which may be harmless in one part of a bridge may be destructive in some other1 a statement borne out by observation4 ,stress1 as ordinarily stated--i4e41 at so much per square inch1 uniform across a section--is seldom a cause of trouble4 ,in nearly all cases of failure there is an accompanying localised destructive stress1 either in rivets or elsewhere1 with crippling or deformation of some essential part4 ,in the tension flanges of main girders with uncomplicated stress1 this may run up to an amount very considerably beyond the ordinary limits without producing signs of distress4 ,the same remark applies to the compression flanges1 if these be in themselves sufficiently stiff1 or properly restrained from side flexure4 ,in support of the above statement may be quoted the following instances relating to wrought-iron structures3-- ,a bridge of #fj feet effective span1 having girders immediately under the rails1 had a flange stress of #fc tons per square inch4 ,another of #fd feet span1 carrying two lines of way1 with outside main girders and cross-girders1 had the flanges of the former stressed to #fh tons per square inch4 ,a third1 of #gf feet span1 of similar construction to the last1 was stressed in the main girder flanges to #ge tons per square inch4 ,the webs were not included in the computation2 the figures1 therefore1 compare with ordinary practice4 ,in these three cases the main girders showed no signs of distress1 referable to the results stated1 though the top flanges in the last case were curved inwards4 ,the effect of this flexing of the flange would be1 of course1 to increase the amount of compressive stress along one edge1 though to what degree cannot now be stated4 ,illustration3 ,,fig4 #dc4 ,illustration3 ,,fig4 #de4 ,illustration3 ,,fig4 #dd4 ,a further instance of considerable flange stress occurred in a bridge of seven nearly equal continuous spans1 #be feet generally1 the end and greatest span being #bi feet #f inches1 centre to centre of bearings4 ,some details of the bridge are given in ,figs4 #dc to #de4 ,the four inner main girders under rails were #b feet deep1 with webs #a_/b inch thick over piers1 and #c_/h inch at abutments1 having flanges of two ,l bars1 #c inches by #c inches by #e_/h inch4 ,there were also two outer girders of the same depth1 with single ,l bars4 ,plate diaphragms of full girder depth and particularly stiff were carried right across the bridge at the centre of the spans1 and over the piers4 ,the girders1 though evidently designed to be continuous1 had very poor flange joints at each bearing1 of little more than one half the flange strength 7see ,fig4 #de74 ,it is doubtful if the girders acted with strict continuity for long after erection1 as the excessive stress in the rivets of the flange joint would1 for that condition1 have been nearly sufficient to shear them4 ,it is probable that this being so1 the joints first yielded1 relieving the bending moment over the piers1 and increasing it near mid-span4 ,whether the end spans be considered as strictly continuous with the rest1 or as simple beams1 the maximum bending moments would not greatly differ1 though occurring for continuity over the pier1 for free beams at the centre4 ,there is1 however1 an intermediate condition which makes the moments at these two places less than either maximum1 but equal to each other2 a condition of semi-continuity agreeable to a partial efficiency of the joints referred to4 ,it is this state which has been calculated1 giving the minimum stress value that can be accepted4 ,the diaphragm has been assumed to transfer to the outer girders a due proportion of the load4 ,with this explanation it may now be stated that1 under engine loads corresponding to those running1 the flange stress worked out at #gd tons per square inch tension1 web included1 or #ig tons per square inch without considering the web2 which stresses1 it is more than probable1 may have been greater4 ,the figures include the consideration of anything which may contribute to lowering the stress1 and are hardly to be compared with those worked to in ordinary design of new work1 in which it would be quite usual to neglect the assistance of the outer girders and the webs1 to work to heaviest engine-loads1 and possibly include an allowance for the effects of settlement4 ,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 bridge1 in which certain elements of strength would be deliberately ignored4 ,the ironwork was in good condition1 there was no ordinary evidence of weakness apart from the calculated results1 the vibration was distinctly moderate1 and the deflection1 though not recorded1 was certainly small4 ,the bridge did1 indeed1 seem somewhat inert under load1 and favours a suspicion1 the author entertains1 that old girderwork long overstressed may have a sensibly higher modulus of elasticity than newer work at more moderate stresses4 ,the traffic was not very considerable1 and both roads1 of the same spans1 but seldom loaded at the same time2 though with this construction of bridge there would in either case be very little difference4 ,the author recalls no reason for supposing that the piers had yielded in any sensible degree4 ,the bridge was rebuilt after some thirty-six years' use4 ,stress of considerable amount in the flanges of a latticed main girder of #fc feet span has already been noticed in the chapter on 8,riveted ,connections10 which for the tension boom worked out to #ga tons per square inch1 the flanges in this case showing no signs of weakness4 ,an instance has also been given in dealing with a case of side flexure in which the extreme fibre stress was calculated to be #aj tons per square inch1 the girder recovering its form when relieved of load4 ,as to stress in cross-girder flanges1 an example may be quoted of a bridge of #aji feet span1 carrying two roads1 having outside main girders1 with cross-girders between2 these latter were stressed in the flanges to #fg tons per square inch 7webs not included71 if the partial distribution among the girders 7which were spaced #f feet apart7 by the rails and longitudinal timbers be neglected4 ,there is some reason to think in this instance that distribution had the effect of reducing the stress quoted1 as the observed deflection of the cross-girders was materially less than that calculated for girders acting independently of each other1 though this may be in part due to a cause already hinted at4 ,rigidity of the cross-girder ends1 where attached to the heavy main girders1 would also tend to moderate the stress4 ,no very definite conclusion can therefore be deduced from this instance4 ,to take another case of less uncertainty1 the bridge of #ce feet span 7see ,fig4 #cc71 referred to in 8,riveted ,connections10 may again be cited4 ,the extreme fibre stress in the cross-girder flanges worked out at #fc tons per square inch1 web included1 or #fe tons1 exclusive of the web4 ,it cannot be said in this example that the girders showed no signs of weakness1 as the deflection under live load was #a_/b inch on the span of #aa feet1 in addition to a permanent set of #c_/d inch1 largely due1 however1 to 8working0 rivets4 ,a better and altogether conclusive case of the way in which cross-girders may occasionally suffer considerable stress1 and show no sign1 is furnished by two cross-girders1 of which some particulars are here given4 ,these girders occurred in the floor of a very acute angled skew bridge1 riveted at one end to the main girders in a manner which was very far from fixing the ends1 resting at the other end on a masonry abutment4 ,the first girder was about #ai feet effective span1 #ab inches deep in the web1 with angle bar and plate flanges4 ,the girders were spaced #f feet apart1 and were connected under the rails by ,t-bars1 cranked down to face the webs1 and riveted through4 ,though these ,t's had little stiffness1 yet the frequent vertical movements of the girders relative to each other1 under passing loads1 had broken the majority of the ,t-bars at the bends1 so that no notice need be taken of these as transferring load from any one cross-girder to its neighbour4 ,the floor covering consisted of timbers about #d inches thick1 also incompetent to transfer any sensible proportion of the load on a girder to others #f feet distant4 ,upon the floor was cinder ballast1 with sleepers1 chairs1 and ordinary bull-headed rails4 ,the stress to which the girder was liable works out at #hd tons per square inch1 on the extreme fibres of the net section1 web included2 or #ia tons1 neglecting the web1 under engine-loads of a common amount4 ,the other girder had an effective span of about #bb feet1 as before #ab inches deep in the web1 with angle bar and plate flanges4 ,the stress per square inch was #aje tons1 web included1 or #aaa tons per square inch1 neglecting the web4 ,this girder carried three rails1 one of which was near to the abutment bearing1 so that there was no great difference in the stress induced whether all three rails were loaded or the pair only4 ,the traffic over the bridge was very great1 but of moderate speed4 ,it must have been a common occurrence for the girders to take the full loads4 ,the heavier engines passed scores of times in a day--lighter engines probably one hundred times4 ,the bridge was about twenty years old1 yet these cross-girders1 when removed1 showed no other sign of age and wear than that due to rust4 ,illustration3 ,,fig4 #df4 ,all the foregoing instances relate to wrought-iron bridges4 ,two cases of steel construction are here added1 the first of these furnishing an example of high girder stress somewhat remarkable4 ,this was found in a trough girder of a strange pattern1 of which a section is here given 7,fig4 #df74 ,the bridge to which it belonged carried a siding1 over which engines of less than the heaviest class sometimes passed at a crawling pace4 ,the larger of the two girders carrying the rails was #ae feet #h inches effective span4 ,the sides of the trough consisted each of two vertical plates1 originally #a_/b inch thick1 but wasted to an aggregate thickness of #e_/h inch4 ,these plates #f inches deep1 were connected at their lower edges to angle bars1 #c inches by #c inches by #a_/b inch1 which again were riveted to a bottom plate #af inches wide1 originally #a_/b inch thick1 wasted to #c_/h inch4 ,lying in the bottom of the trough1 and riveted through the inner angle flanges1 was a bridge-rail4 ,assuming that the metal retained its elastic properties from top to bottom of the section1 at whatever stress1 this works out at #cb tons per square inch at the extreme top fibre1 and #ae tons at the bottom1 on the net section4 ,as puddled steel1 of which the girders were made1 may have a tenacity of #de to #ee tons per square inch1 the assumption is probably correct4 ,the author has no record of the deflection1 but it may be remarked it was such that to stand under the girder1 with a tank engine passing over1 required some determination4 ,a point of additional interest in this little bridge is that1 though made of steel1 it dates as far back as #ahfa1 having been in use thirty-two years when removed4 ,the particular variety of steel used was known as ,firth's puddled4 ,the evidence of this consists in correspondence showing that permission had been asked of the controlling authority1 by the only users of the siding1 to apply this material1 with no evidence of any refusal4 ,at about the same time this steel was also used upon the railway concerned in the top flanges of some girders of considerable span4 ,the appearance of the trough girders to which the foregoing particulars apply was distinctly different to that which might be expected in ordinary wrought iron4 ,the top edges of the vertical plates were wasted away1 smooth1 and rounded in a manner strongly suggestive of a steely character4 ,finally1 the way in which the girders held up to their work for so long is1 by itself1 conclusive on the point4 ,the bridge-rail appeared to be of wrought iron1 the different modulus of elasticity of which has been included in the calculation upon which the preceding results are based4 ,that these girders stood so well is1 perhaps1 largely due to the fact that the load carried by them was1 though varying within wide limits1 practically free from impact1 which1 had the load passed over quickly1 would1 with girders so small1 shallow and flexible1 have been very sensible4 ,the second instance of steel construction in which somewhat high stress is manifest is that of some steel troughing of the ,lindsay pattern1 used in a bridge built in #ahhe4 ,the troughs ran parallel to the rails1 having an effective span of #ah feet #h inches4 ,the depth of the section 7which is shown in ,fig4 #dg71 was #h-a_/b inches1 making a ratio of depth to span of #a_/bh4 ,the road was of ballast1 sleepers1 chairs1 and #he-lb4 rails4 ,illustration3 ,,fig4 #dg4 ,assuming this to be carried on six troughs1 which corresponds to #aa feet #c inches of width1 the extreme fibre stress works out at #ge tons per square inch1 under usual engine-loads4 ,the bridge when examined after fourteen years' use was in good condition1 and at that time but little rusted2 but the end seam rivets were1 as is not uncommon with such troughing1 loose4 ,the traffic over the bridge was considerable1 but not at great speed4 ,on the opposite page are set out the results which have been given1 in tabulated form1 as was done for rivet stresses1 to enable ready comparison to be made4 ,,examples ,,of ,,high ,,stress4 ---------------------------------------- ---------------------- ,span ,part ,stress per ,tension ,condition4 in ,stressed4 ,square ,inch4 or ,feet4 --------------,compres- -- ,webs ,webs sion4 ,in- not cluded4 ,in- cluded4 ---------------------------------------- --------------------- ,wrought-iron main girders1 #fjj ,flange 44 #fc ,tension ,good4 plate ,wrought-iron main girders1 #fdj 44 #fh ,good4 plate ,wrought-iron main girders1 #gfj 44 #ge ,fair4 plate ,wrought-iron #gd #ig main girders1 #bie #fc #hc ,compres-,good4 plate sion ,wrought-iron main girders1 #fcj #ga ,tension ,fair4 lattice ,wrought-iron main girders1 #dgj ,flange #ajj 44 ,compres- ,fair4 plate edge sion ,wrought-iron cross-girders1#bfj ,flange 44 #fg ,tension ,fair4 plate ,wrought-iron cross-girders1#aa4j #fc #fe ,bad2 loose plate rivets4 ,wrought-iron cross-girders1#aij #hd #ia ,good1 but plate rusted4 ,wrought-iron cross-girders1#bbj #aje #aaa ,good1 but plate rusted4 ,steel trough #aej ,fair1 girder #ae4g,top edge #cbj ,compres-but sion rusted4 ,steel #ahg ,flanges #ge 44 ,tension ,fair1 troughing and ,com- but pression rusted4 ---------------------------------------- --------------------- ,it would be unwise to infer from the instances which have been quoted that high stress may be regarded with complaisance4 ,in the most conscientious engineering work there should still be a liberal margin for material possibly defective1 or even bad1 for waste and deterioration1 and for the aggregate effect of minor errors in design1 any one of which considerations1 except the first1 by itself might not be of great importance4 ,the conclusion which may1 however1 be derived from this and the previous chapters is1 that bridge failures are less likely to occur from high stress of a kind readily calculated than from failure in detail1 obscure and little suspected1 the reason for which is not perhaps apparent1 till the attention is forcibly directed to it by the refusal of the structure to sustain the forces to which it may be liable4 ,,chapter ,,vii4 ,,deformations4 ,instructive lessons are to be had from a study of the various alterations in form to which metallic bridgework is liable1 which alterations may be due simply to the development of stress of ordinary amount1 and are then generally small2 or to abnormal stresses1 the result of some distortion in the bridge structure itself not originally intended1 and possibly extreme4 ,in addition to these there may be deformations due to settlement1 to 8creeping0 of parts of the structure relative to the rest1 to temperature changes1 to rust1 and to original bad workmanship4 ,in any instance quoted below the methods adopted to ascertain the amounts of such alterations were quite simple1 even crude2 but as care was exercised1 and no attempt made to measure any very minute changes1 the results may be accepted as practically correct4 ,dismissing for the present changes of form such as are to be expected1 and touched upon in other places in this work1 with respect to the particular parts of bridge structures affected by them1 a few instances will be adduced of alterations which1 though not very surprising1 are such as in the design of the work are hardly likely1 in most instances1 to have been contemplated4 ,a case has already been referred to in which1 owing to eccentric loading of main girders1 these were1 as to the top flanges1 flexed sideways a considerable amount4 ,it is proposed to supplement this by further remarks relative to somewhat similar cases4 ,a like effect is frequently to be observed in trough or twin girders1 in which the rails are supported upon longitudinal timbers resting upon projecting ledges formed by the bottom angle-bars of such troughs4 ,in old forms of this arrangement it is common to find the two girders forming the trough connected only by bolts passing through the timbers1 or just above them and below the rails2 or connected by narrow strips1 which serve no other purpose than to prevent the sides spreading at the bottom4 ,the top flanges in such cases commonly curve inwards on the passage of the running load1 accompanied of necessity by an increase of compressive stress upon the outer edges of the flanges1 and perhaps by the working of any flange-joint which may exist4 ,this1 both as to flexing of the top flange and the working of a joint1 was noticed in the case of a bridge twenty-three years old1 very similar to that illustrated in ,figs4 #h and #i1 and described on pages #ac and #ad4 ,the top flange consisted1 however1 of a bridge rail riveted to the top edge of the web1 butting at a joint1 and covered by thick cover strips 7see ,fig4 #dh74 ,the joint itself was poor1 and depended largely upon the character of the butt1 which was not sufficiently good to prevent the top member kinking at this point1 under the joint influence of transverse effort and compressive stress1 with possibly some help from bolts passing through timber and webs1 though these being loose1 the author does not think them at all responsible4 ,although not strictly relevant1 it may be remarked in passing that it is very objectionable to use bolts as was done in this instance2 for as the timber settles down on its seat1 taking the bolts with it1 these bear hard in the webs1 enlarging or even1 as in this case1 tearing the holes1 accompanied by injury to the bolts themselves4 ,the practice is now almost obsolete1 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 load1 unless these bolts are quite free to move with the timber as it compresses4 ,if trough girders must be used1 the better plan is to connect the two sides by a continuous bottom plate1 the trough thus formed being properly drained1 if the timber is not bedded in asphalt concrete2 or to introduce stiff diaphragms at intervals beneath timbers1 if the depth suffices4 ,in the case just quoted the curvature of the top members of the girders was inwards1 but in the instance given below1 of twin girders #bf feet effective span1 with longitudinal timbers between1 resting1 as before1 upon the inner ledge formed by the bottom flanges1 the curvature was observed in three out of four girders to be #a_/b inch in a contrary direction1 the fourth remaining straight4 ,illustration3 ,,fig4 #dh4 ,illustration3 ,,fig4 #di4 ,an inspection of the accompanying section1 ,fig4 #di1 will1 perhaps1 render the reason evident when it is noticed that the top members are very unsymmetrical in form1 the effect of this being to give these members1 under stress1 a strong tendency to flex outwards1 apparently more than sufficient to counteract the tendency of an eccentric application of load on the bottom flange to bring them inwards4 ,it is to be observed that the eccentricity of the flange appears to be not materially in excess1 and is actually so1 only because the thinness of the web--#a_/d inch--renders it incompetent to keep the bottom flange up to its work1 and so secure the full effect of the eccentric loading in limiting the outward tendency1 due to the section of the top member1 the effects of which are thus more apparent than would have been the case with a stiffer web4 ,ties across from one bottom flange to the other prevent the want of symmetry noticed in these--which1 by the way1 is on the wrong side for utility--from having any particular effect4 ,to give one other example of the consequences of eccentric loading1 a bridge of #dh feet effective span may be quoted4 ,this bridge carried four lines of way supported by five main girders1 trussed by kicking-struts in such a manner as to form a bastard arch4 ,a part section and plan are given in ,figs4 #ej and #ea4 ,illustration3 ,,fig4 #ej4 ,illustration3 ,,fig4 #ea4 ,the floor consisted of ,lindsay's troughing resting upon the lower flanges of the main girders1 the three middle girders1 subject to eccentric loading1 sometimes on one side1 sometimes on the other1 were1 with dead load only1 straight2 but the two outer girders1 liable to loading only on one side1 had1 under repeated applications of such a load1 assumed a permanent curve towards the rails--#ac_/af inch in one case and #a inch in the other--which curvature1 no doubt1 increased when a live load came upon the contiguous roads1 though this was not measured4 ,it should be remarked in passing that1 owing to settlement and the canting of the abutments1 the three middle girders were also 8down0--in one case #c_/d inch4 ,the girders1 with one near road loaded1 deflected #a_/h inch--greatly less than would have been the case had the main girder not been trussed4 ,the bridge1 at the time these particulars were obtained1 had been in existence six years4 ,deformations due to settlement may be very considerable4 ,the author recalls two instances affecting continuous girders4 ,in the first of these1 a bridge twenty years old1 of two spans of about #ej feet each1 and with girders #d feet #f inches deep1 the centre pier had sunk #d inches1 reducing the spans1 as respects the dead load1 practically to the condition of simple beams1 just resting1 but hardly bearing1 upon the piers when free of live load4 ,in the second case1 also of two openings of about #ee feet each1 with girders #h feet deep1 one abutment had sunk about #c inches1 more than doubling the stresses over the centre pier4 ,it is manifest that continuous girders should only be adopted where settlement of the supporting points is not likely to occur to any material degree4 ,if this cannot be relied upon1 the theoretical flange sections may hardly be worked to with any prudence2 it being then advisable to make a liberal allowance for settlement stresses1 in which case any economical advantage that should exist will probably disappear4 ,it is1 however1 to be acknowledged that so long as the girders are in touch1 under dead load1 with the bearings intended to support them1 the stresses due to a live load are unaltered1 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 undisturbed2 still1 if it is desired that the maximum stress shall not exceed1 say1 #f tons per square inch1 it can hardly be a matter of indifference that settlement shall induce a maximum of1 perhaps1 #aj tons1 as in that case the stress must be #d tons nearer the limit of statical strength4 ,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 piers1 and possibly making them equal to those obtaining near the middle of the spans1 in which case there will be less inequality of stress in the booms and a reduction of the maximum stress4 ,bridges consisting of simple main girders connected by cross-girders may be very prejudicially affected by unequal settlement2 for instance1 if one girder bearing settles more than the others1 a twist is put upon the structure very trying to the floor-girder connections1 and possibly to the main girders2 to the web if a plate girder1 or to the verticals if an open-webbed truss with rigid cross-girder attachments4 ,indeed1 settlement of this kind may be much more destructive to a metallic bridge than to an arch of brick or masonry1 the commonly accepted opinion notwithstanding4 ,instances of deformations due to the creeping of some part of the structure away from its work1 are within the author's knowledge1 rare2 except in the case of the ends of main girders in skew bridges1 already referred to4 ,distortion1 the result of temperature changes1 is frequently to be observed in any considerable length of girder flange or parapet where there is not freedom of movement1 unless due provision is made to check it4 ,it is quite common to see parapets out of line1 either because the ends are not free1 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 attached1 expanding to a greater degree1 is subject to considerable compressive force1 and buckles under its influence4 ,the cure for this condition is obviously to provide such parapets with free or flexible joints at moderate distances apart1 or to make the parapet sufficiently stiff to take the stresses developed1 without crippling4 ,a parapet may also go out of shape if directly attached to the top flange of a girder liable to heavy loading1 particularly if the girder be shallower than the parapet1 simply by its inability to maintain truth of line under the compressive stress1 which it shares with the top flange of the girder proper4 ,rivets spaced too far apart1 by allowing the plates or other parts to spring open slightly1 and permitting moisture to enter1 results in the growth of rust1 which1 as it swells in forming1 forces the parts asunder1 and may set up considerable stress4 ,flat bars riveted together by rivets spaced #ab inches apart may from this cause be forced asunder1 as much as #a_/b inch1 sufficient to set up a stress1 with any practicable thickness of bar1 much exceeding the elastic limit4 ,local distortions may occur as the result of imperfect workmanship or careless erection1 causing quite possibly very severe local stresses2 or girder flanges may be out of straight as a result of riveting up along one side first1 instead of advancing the riveting simultaneously along the whole breadth of the flange4 ,the injury done by drifting is well known1 and there is reason to think considerable damage is sometimes done to girderwork during manufacture by rough treatment to make the work come together2 but the author has little to offer with respect to these matters that is not common knowledge4 ,it may1 however1 be pointed out in passing that a bridge upon the design of which great care has been expended1 with the idea that theoretical propriety shall not be violated1 may be completely spoiled in this respect by careless construction4 ,fortunately1 both steel and wrought iron1 if of good quality1 are long suffering4 ,incompetent erection will sometimes result in the true girder camber not appearing1 or in differences as between girders supposed to be similar4 ,this is not1 of course1 a deformation in the sense in which the word has previously been used1 but it is desirable to bear the fact in mind as a possible cause of defective camber in dealing with questions of deformation4 ,the foregoing has reference chiefly to alterations of form in bridgework of wrought iron or steel1 but a case of considerable interest is that of a cast-iron arched structure1 of which the author made a very complete examination4 ,illustration3 ,,fig4 #eb4 ,illustration3 ,,fig4 #ec4 ,this bridge1 built in #ahci1 and carrying two lines of railway1 consisted of three spans1 #ajj feet each1 of #aj feet rise1 made up of four inner and two outer ribs1 each rib being in three nearly equal parts2 the floor was of timber1 the abutments and piers of masonry4 ,as originally constructed there was no bracing between the ribs other than the frames indicated on the plan here given 7,fig4 #eb71 stretching from outer rib to outer rib in the neighbourhood of the rib joints1 which were simple butts without bolts or any equivalent means of connection4 ,the floor was1 however1 braced in the horizontal plane1 and the structure was also braced over the masonry piers4 ,after forty-two years' use supplementary distance-pieces were introduced between the ribs1 but still no bracing between them1 or any efficient means of checking lateral movement4 ,a crack developing in one of the outer ribs at the crown1 led to an investigation to trace the cause1 the bridge then being fifty-four years old4 ,careful plumbing of the abutments revealed the fact that three out of four abutment pilasters were out of the vertical1 as shown in ,figs4 #eb and #ec1 the greatest amount being #e_/h inch in #f feet--at that corner from which the cracked rib had its springing2 there was also other evidence of settlement in an old crack extending from the top of the abutment to the ground level1 although this movement was very old1 certainly as to the greater part4 ,the ribs of this span were also out of plumb1 that which was cracked being #b-a_/b inches out at the centre4 ,the joints of the ribs1 which1 as already stated1 were simple butts1 in some cases opened and shut1 as the load passed over1 in such a way as to suggest that the ribs were acting1 in a manner1 as four-hinged arches1 of which two hinges were at the springing1 and the other two at the joints1 one of which would for most positions of the load be out of use1 reducing the rib to the three-hinged condition2 in other words1 as the rolling load passed over the span1 one or other of the two joints of a rib would 8gape0 an appreciable amount at the bottom or at the top4 ,observations were taken by means of a theodolite placed below1 either upon the bank or upon the tops of the masonry piers1 sighting upon suitable scales attached to the ribs to ascertain the amounts of vertical and horizontal movement during the passage of trains over the bridge4 ,the principal results are set forth in the following table3-- ,,movements ,,of ,,cast-,,iron ,,ribs ,,under ,,live ,,load ,,in ,a ,,bridge ,,of ,,three #ajj-;,,ft4 ,,spans4 ---------------------------------------- ---------- ,fall in ,rise in ,lateral -- ,inches4 ,inches4 ,movement in ,inches4 ---------------------------------------- ---------- ,span ,no4 #a4 ,at ,a4 ,up road loaded #bj #jh #jd ,a4 ,down road loaded #jh #jc #jd ,b4 ,down road loaded #ad ,no record4 #jb ,span ,no4 #b4 ,at ,c4 ,up road loaded #dj #ac ,slight4 ,c4 ,down road loaded #aj #je ,span ,no4 #c4 ,at ,d4 ,up road loaded #bb ,no record4 ,no record4 ,d4 ,down road loaded #ae ,slight4 ,slight4 ---------------------------------------- ---------- ,,note4--,the lateral movements are to either side of the mean position4 ,the particulars for spans #b and #c were obtained with the instrument set up on the pier between these spans4 ,the tremor of this pier was such that no useful readings for lateral movement could be obtained4 ,further1 as the rolling load came upon these spans1 the effect was to rock the pier to an extent vitiating the readings for vertical displacement2 but by sighting upon the fixed abutment1 and observing the amount of this rocking1 suitable corrections were made in the apparent rib movements4 ,the figures given in the table are thus corrected4 ,the pier rocking was equivalent1 as an extreme1 to an inclination from the vertical of #a in #cbjj4 ,an attempt to measure the horizontal movement of the pier-top was unsuccessful1 owing to the impracticability of setting up the instrument in a suitable position1 sufficiently near to the pier to enable readings to be satisfactorily taken4 ,this horizontal displacement probably amounted to about #a_/af inch either way4 ,the rise and fall of the arches1 and rocking either way of the piers1 varied1 as might be expected1 in accordance with the position of the running load with respect to the spans4 ,summarising the results1 the greatest vertical movements downwards were #jbj inch1 #jdj inch1 and #jbb inch for spans ,nos4 #a1 #b1 and #c1 the upward movements being #jjh inch and #jac inch for the first and second spans1 there being no recorded result of this kind for the third span4 ,with adjacent ribs loaded1 the movement of the ribs unloaded was one from one-third to one-half of the full amounts4 ,it is to be noted that the lateral displacement in no case exceeded #jjd inch either way1 nor were the vertical movements exceptional2 yet1 as a matter of sensation1 when seated upon the ironwork1 it was a little difficult to believe them really so moderate4 ,observations were also made to ascertain the rise of the arches from winter to summer temperatures1 with the result that this was found to be #jde inch1 #jde inch1 and #jee inch for the spans in order1 the extreme temperatures being fairly representative of the ,english winter and summer4 ,the structure was1 as a consequence of the examination1 efficiently braced by diaphragms between the ribs1 and diagonals following the arch ribs round from springing to springing1 with satisfactory results4 ,the crack already referred to1 and its probable causes1 will be dealt with under 8,cast-,iron ,bridges40 ,eventually this bridge was reconstructed to meet the requirements of growing engine-loads4 ,,chapter ,,viii4 ,,deflections4 ,deflection1 considered only as a fraction of the span1 and without regard to other conditions affecting it1 is of very little use as an indication of a girder's fitness for its work2 but when taken with reference to the depth of the girder1 the nature and amount of the load producing flexure1 and1 further1 with regard to the quality of the workmanship and normal properties of the material of which the beam is constructed1 it may be of some little service in helping to form a reliable opinion4 ,this consideration applies with less force1 perhaps1 to new work than to old1 in which there may be unknown influences at work1 or unknown defects which by excessive deflection may be betrayed4 ,though too much importance should not be attached to results of deflection tests in any one instance1 yet the practice of observing such movements1 and considering them with reference to each case1 gives a good general idea of what may be expected in a fresh instance1 any material departure from which should be a reason for specific inquiry as to the cause4 ,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 intended1 or by some route not contemplated2 or1 in the case of floor beams1 in what way the load is distributed amongst them1 if1 indeed1 there be any such distribution4 ,the author has commonly found that new work gives greater deflections than old--i4e41 while calculation gives the same result for each1 it does not apply equally well to both4 ,the differences may be accidental1 but are probably due to other causes1 perhaps to the fact that new work has not by repeated applications of load lost the resilience of parts liable to considerable local stress1 such as is very liable to occur at connections1 so that the deflection is1 whilst new1 greater than after many years' use1 by which time such parts may develop a definite 8set10 and contribute in a less degree1 or not at all1 to the total elastic deformation4 ,it is also possible1 as already suggested1 that repeated high stress may reduce the ratio of strain to stress1 the material gradually becoming more rigid1 the modulus of elasticity being1 in fact1 increased4 ,in girders of ordinary construction1 the major part of the deflection is due to the booms1 the remainder to the web2 the latter is for plate girders a small amount only1 and is commonly neglected1 but for open web constructions it may be quite appreciable4 ,for any given type of web arrangement the deflection due to the web will1 for all depths1 remain a constant quantity for the same span and unit stress2 and though a moderate fraction of the whole deflection for a shallow girder1 it may be a very considerable part for a girder of great depth1 in which that part due to the booms is1 of course1 smaller1 since the deflection due to these varies inversely as the girders' depths4 ,deflection1 being dependent upon the elasticity of the material1 is of necessity very largely influenced by the value of its modulus ,e1 itself liable to considerable variation1 and is increased in a small degree by the yield of joints and rivets1 which effect1 apart from the initial 8set0 of the girders1 appears to be negligible4 ,the stiffness of members in resisting angular distortion at connections must also1 for open-web riveted structures1 affect the result1 making it somewhat less1 and1 finally1 section excess at joints and gusset attachments has an influence in modifying deflection as compared with that due to the normal gross sections simply4 ,from these considerations it is apparent that any simple deflection formula must be largely empiric in its nature4 ,for plate girders of uniform depth and flange stress1 the writer has found the following to give good results3-- ,s#b ----- f deflection in inches4 ,d ,c ,the span ,s and depth ,d are1 as a matter of convenience1 taken in feet2 the constant ,c is for wrought iron #cejj1 and for mild steel #djjj2 f is the mean of the extreme tensile and compressive stresses of the booms1 in tons per square inch1 estimated upon the gross sections4 ,this1 though satisfactory for plate girders1 is not so suited to girders having open webs1 in which the deflection will more nearly be 7#c,s ,s#b 7 7-- -----7 f1 7,c ,d ,c7 the constant ,c being #cijj and #ddej for iron and steel respectively4 ,the latter values of ,c correspond to normal values of the modulus of elasticity of #aa1gjj and #ac1cej tons for iron and for steel1 it being assumed that any slight rivet yield is off-set by any small section excess--say1 #e per cent42 it may1 however1 happen that section excess is greater than assumed1 in which case some allowance may properly be made for this by increasing ,c4 ,to adapt the formul to girders other than those having parallel booms and uniform stress1 the results1 as deduced above1 may be multiplied by constants given in column ,b of the ,table given on page #ic4 ,the practice of adopting for ,e in deflection formul a quantity much smaller than its nominal amount1 with the object of allowing in riveted girder work for the yield of rivets and of joints1 can hardly now be defended1 whatever may have been a case at a time when workmanship was much inferior1 when there was no machine riveting1 and joints were1 owing to the small weight of plates and bars1 three times as numerous4 ,the initial 8set0 of a girder consequent upon first loading is a quantity quite distinct from deflection proper1 and may be so small as to be negligible1 or read #aj per cent4 of the true deflection1 varying with design and workmanship4 ,no estimate of girder deflection can be even approximately true if there is1 at the level of the top or bottom flanges1 a plated or otherwise rigid floor system which is not taken into account1 as this will have the effect of very materially reducing the boom stress4 ,to neglect this influence1 where it exists1 must necessarily lead to disappointing results1 and it is quite practicable in many instances to include it in the calculation4 ,the influence of angular distortion between the various members has been neglected4 ,it may be pointed out1 however1 that the resistance accompanying these movements in girders having riveted connections1 though unimportant as affecting deflection1 is worth some consideration in regard to secondary stress4 ,for girders of similar type and unit stress these angular variations will be the same in amount for any span1 but will generally be of less importance in large girders than in small1 because in large girders the ratio of the breadth of members to their length is commonly less4 ,when determining the probable deflection of any girder of exceptional figure1 it will be found convenient to make a strain diagram--an old device1 in which the actual alterations of length being ascertained for all members1 the girder is carefully set out to a suitable scale1 with the lengths of members increased or reduced by the actual estimated amounts4 ,the distorted figure resulting will then give the probable deflection4 ,the value of ,e for this purpose should never be taken at less than the normal amount1 and may for a considerable excess of metal in joints and gussets be made as much as #aj per cent4 greater1 this being a convenient means of making the necessary correction4 ,the effect of loads quickly applied may here be considered in connection with elastic deformations of girders of the same span1 but different depths4 ,if these be designed for similar loads and unit stresses1 the deflections due to webs and booms of the girders compared will bear the same relation1 each to each1 as do the weights1 whether in both cases the loads be inert or quickly applied1 from which it follows that the mechanical 8work0 done by the loads in falling through the deflection heights is1 neglecting inertia1 always in proportion to the girderwork weights1 and is a similar amount per ton1 which as the total length of members remains substantially unaltered1 corresponds to a similar amount of work per unit of section1 or similar stress1 irrespective of the depth of the girders4 ,but for a 8drop0 load1 as when there is some obstruction upon a railway bridge1 there will be in addition a further amount of work to be absorbed1 which is to be considered the same whatever the girder's depth1 and will for deep girders be a larger amount per ton of girderwork than in those that are shallow2 this1 taking effect on members of the same aggregate length1 but lighter1 will develop a higher stress than in girders of lesser depth1 more particularly in the booms4 ,the influence of the girder's inertia in modifying drop-load effects will also be less marked in deep--i4e41 light--girders than in girders shallow and heavy4 ,it is1 notwithstanding all this1 desirable that the depth of main girders should be liberal for economy's sake1 and also that of floor beams1 for reasons already dealt with2 the probability of the drop load is somewhat remote1 and1 though possible1 would simply induce1 if it occurred1 an increment of stress rather more important in deep girders1 making it specially desirable in these to give particular attention to the detailing of any connections liable to suffer from impact effects4 ,it should be remarked that for short and very flexible beams1 generally outside the limits of practice1 there may also be1 under quickly moving loads1 a material increase of stress due to the centrifugal effort of the load on running round the deflection curve1 and in rising upon the steep part of the curve beyond the girder's centre4 ,where advisable1 these effects may be modified by cambering the rail4 ,for pin bridges in which there may be spring in the pins1 excess stress in some eye-bars due to inequalities of length1 and a want of that rigidity peculiar to riveted structures1 the deflection will be greater than above indicated for girders of the ordinary ,english type4 ,the method in common use for measuring the deflections of girders but a moderate distance above the ground by means of sliding-rods1 though crude1 gives1 with care1 results sufficiently accurate for most practical purposes2 but some points necessary to remember may be mentioned with propriety4 ,the lower rod should rest firmly upon something solid1 say a stone1 well bedded and free from any tendency to rock2 the upper end should bear against some part of the girder above1 presenting a hard surface1 free from dirt or scale1 and as the running load approaches the bridge it should be ascertained that there is no slack1 that the rods bear hard at the top and bottom4 ,the upper end having been depressed1 care is to be exercised to make sure of the reading before the rods alter their relation to each other4 ,these precautions are so self-evident that an apology is almost necessary for mentioning them4 ,to ascertain deflections with a single pair of rods is only allowable when the girders rest firmly on their bearings2 if felt has been placed under the girder ends1 or if the bedstones are insecure or rocking1 it is necessary to use three pairs of rods1 one pair at the middle and a pair at each end1 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 result4 ,in the case of a number of spans in series1 each resting upon sill girders common to two sets of bearings1 this method also gives results of indifferent reliability1 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 middle1 and it is in general out of the question to secure by this mode simultaneous readings for a particular position of the running load1 which are what is required4 ,the author suggests1 as a means of ascertaining deflections free from these objections1 that it should be done by first measuring the slope at one end1 and from this deducing the deflection at the centre4 ,this is to be accomplished by means of a little instrument1 consisting of a telescope with cross-hair sights1 and fitted with a reflecting prism at the eye-piece capable of being turned round1 so that the observer has a wide choice as to the position he assumes with reference to the instrument1 and may look either directly through it1 or at right angles to the axis of the telescope4 ,this is clamped at one end of the girder over the bearing1 at the other end a scale is secured1 to which the telescope is directed1 the cross hair being made to sight on the zero of the scale1 or the reading noted4 ,for a girder supposed to deflect to uniform curvature 7say1 with uniform depth and uniform stress1 the ordinary case7 the reading observed will be four times the deflection2 every #a_/aj inch actual reading on the scale will correspond to #a_/dj inch of girder deflection4 ,apart from the deflection1 this method gives a ready means of observing the end slope1 a quantity of equal value for purposes of comparison4 ,as with girders of similar proportions1 and similarly stressed1 the deflection will at all spans be the same fraction of the span2 so should the end slope be a constant quantity under similar conditions1 the diagram1 ,fig4 #ed1 will make the principle quite clear4 ,illustration3 ,,figs4 #ed to #eg4 ,strictly the character of the deflection curve is slightly modified by that part of the deflection due to the web2 so that the depression at the centre would1 in the case assumed above1 be somewhat more than one-fourth part of the end reading1 and generally will be a larger fraction of the reading than that deduced from a consideration of flange stress simply4 ,in ,figs4 #ee to #eg1 which are intended to explain this1 it will be noticed that deflection due to the web is shown straight-lined from the bearings to the centre of the girder2 this is strictly true only for a girder correctly designed for an immovable distributed load2 but as there should be for girders intended for a travelling load1 some excess in web members near the centre under the condition of uniform loading1 the point of the figure should be rounded off to be in agreement with this case1 though it is left as shown in the diagram for the sake of simplicity4 ,suitable constants1 including the corrections necessary1 are given in column ,a of the table annexed for a few typical cases1 and by these constants the actual readings should be multiplied to find the deflection4 ,the constants have been worked out for depths of one-tenth the span2 for greater depths they should be slightly more1 and for smaller depths somewhat less1 but they may be used between the limits of one-sixth and one-fourteenth1 with a maximum error hardly exceeding #e per cent41 and generally much less4 ,the figures in column ,b relate to the formul previously stated1 and apply equally well to all depths4 ,,tables ,,of ,,multipliers ,,for ,,deflection4 ,uniform ,stress3 ,a4 ,b4 ,girders of uniform depth1 varying flange section #jbg #ajj ,hog-backed girders1 ends half of centre depth1 varying flange section #jbd #ajh ,varying ,stress3 #a;,girders of uniform depth and flange section #jcb #jhg #a;,hog-backed girders 7as above71 but uniform flange section #jbi #jig #a;,bow-string girders of uniform flange section #jaf #acj ,footnote #a3 ,for uniform loading4 ,it is apparent that1 if preferred1 the scale1 instead of being in inches1 divided suitably1 may1 for each type of girder1 be amplified to the proper degree1 so that the amount of the deflection may be read off at once4 ,this method of dealing with deflections is quite independent of the character of the bearings1 and is applicable to girders at any height above ground or over water2 but its use would hardly be practicable for very small beams1 or those in an awkward position1 or near which it would be impossible to remain with a running load upon the bridge4 ,there is a possible source of error in the use of the instrument1 most likely to occur with triangulated girders1 with which1 if the instrument is placed at the top of an end post1 the reading observed may be the joint effect of deflection and of local flexure of the members meeting near the telescope4 ,this may be tested1 and1 if necessary1 allowed for1 by first sighting upon a scale at the next apex1 and observing the effect of the moving load4 ,again1 as girders sometimes cant towards the running load1 if the instrument is placed on one edge of a girder1 and the cantings of the two ends are dissimilar1 a false reading will result1 which may be amended by ascertaining the amount of cant at each end1 and correcting for the effect of the difference between the cants upon the observation4 ,only in exceptional cases is it likely that either of these considerations would need attention4 ,the author has secured with this instrument very promising results1 notwithstanding that under a running load there is a slight haziness of the scale as seen through the telescope1 due to 8dither10 largely the result of imperfections which may be remedied4 ,deflections may sometimes be conveniently taken1 by a quick-eyed observer1 with a good surveyor's level and a specially-divided staff held at the centre of the girder4 ,the divisions preferred by the author for this purpose are #a_/aj inch1 plainly marked1 which may be seen at #ej feet distance with sufficient clearness to make possible readings by estimation between the divisions to1 say1 #a_/ej inch4 ,but it is clearly desirable not to rely upon a single observation only1 where all the evidence is gone so soon as the sight has been taken4 ,in rail-bearers1 or other short girders1 it may not be practicable to adopt such methods1 either on account of an inability to find a suitable place for the instrument1 or to read with any telescope with sufficient promptitude as the load passes rapidly over4 ,the use of rods may also be out of the question1 as the errors attending their manipulation may be serious where but a small movement has to be noted1 this being complicated in some instances by the bearings being insecure1 and working to an extent which obscures the measurement sought4 ,in such cases it is preferable to use a stiff slat lying along the girder1 which bears1 through short blocks over the girder bearings1 upon the flanges2 the deflection is then read by direct measurement of the girder's depression at the centre1 relative to the slat4 ,the author is1 unfortunately1 not able to give any precise information on the effect of running-load as against a load that is stationary in connection with girder deflections4 ,it is by no means easy in ordinary work upon a railway to secure facilities for making such comparative tests4 ,it may1 however1 be confidently stated1 as a result of such observations as he has made1 that the deflection due to a load coming rapidly upon a bridge is1 as to the main girders of1 say1 a #ej feet span1 but little greater than that due to the same load stationary2 it may be1 perhaps1 #e to #aj per cent4 more4 ,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 use1 and the control of an engine1 or engines1 for the purpose of making the special tests1 conditions which on a busy line can only be secured by special arrangements previously made4 ,,chapter ,,ix4 ,,decay ,,and ,,painting4 ,the author has collected particulars as to the amount and rate of rusting in metallic structures which are of some interest4 ,in all such instances it is very necessary to note the conditions which have obtained during the process of wasting1 as without this1 misleading conclusions may be drawn4 ,the information given relates in all cases to wrought iron1 unless otherwise stated4 ,a plate-girder bridge1 having girders under rails1 was found to be badly rusted4 ,the atmospheric conditions were unusually trying1 the air being damp and impregnated with acid fumes from adjacent steel works4 ,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 influence4 ,the webs were in places eaten right through1 having lost a mean amount of about #a_/h inch full on each surface in twenty-eight years4 ,painting had not been well attended to4 ,in a similar bridge1 not a great distance from this1 but sufficiently far away to modify the conditions for the better1 considerable wasting was also observed1 but more particularly where the girders had been built into masonry1 which1 loosening with the constant movement of the girder-ends1 had allowed moisture to collect1 and rust to develop1 without the chance of repainting these surfaces4 ,the amount of waste at the places indicated was1 as in the last case1 about #a_/h inch on each face1 and in the same time1 other parts of the girders having suffered less4 ,illustration3 ,,fig4 #eh4 ,a third plate-girder bridge1 with outer main girders1 cross-girders1 and plated floor1 carrying a road over a railway and sidings1 and which was known to have been neglected in the matter of painting1 was very badly rusted1 both as to the cross-girders and floor-plates4 ,the atmosphere was somewhat damp2 the chief cause of deterioration was1 however1 the smoke and steam from locomotives1 which frequently stood for some time1 during shunting operations1 directly under the bridge4 ,the webs of the cross-girders1 which were originally #a_/d inch thick1 had rusted into occasional holes during fourteen years--i4e4 #a_/h inch from each surface in that time4 ,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 stiffeners1 so as to leave an open frame only4 ,one of the cross-girders was so treated by the men engaged upon the work1 when it presented the appearance shown in ,fig4 #eh4 ,in another case--that of a bridge with lattice girders under rails--the ends were built into masonry1 which had1 of course1 loosened1 with the usual result4 ,the air of the locality was certainly pure1 but somewhat damp4 ,the general condition of the ironwork was good1 but end-bars of the diagonal bracing1 where they had been closed in1 had lost #a_/h inch on each surface in thirty-three years4 ,the top flanges immediately under the timber floor were in a very fair state1 which is of some interest when it is considered that these were made of steel of the same kind as that already noticed as being used in the construction of small girders 7see ,fig4 #df1 ante71 described in the chapter upon 8,high ,stress10 both cases dating from the year #ahfa4 ,the painting upon the lattice-girder bridge had been pretty well attended to2 but in the case of the small steel girders it had been greatly--perhaps altogether--neglected2 this1 coupled with adverse atmospheric conditions1 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 to1 being fully #a_/h inch on each surface1 as against a negligible amount under the more favourable circumstances4 ,girder-work over sea-water1 as in piers1 seems to rust at a sensibly greater rate than inland work under average conditions2 but it is hardly practicable to make any strict comparison1 as in either case the rate of oxidation is so much affected--even controlled--by the care bestowed upon the structures4 ,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 years4 ,it should be remarked1 however1 that in one case steel girders but five years old1 and which were frequently wetted with sea-spray1 were found to be wasting rather badly--the paint refusing to keep upon the surface4 ,it may be concluded from the above instances1 and from others which have come under notice1 that wrought-iron work1 if not properly cared for in respect to painting1 or under conditions otherwise bad1 may be expected to rust at a rate which corresponds to the loss of #a_/h inch on each surface in from fifteen to thirty years2 but with proper care as to painting1 and exclusive of exceptionally bad conditions1 it does not appear to waste at any measurable rate4 ,in some instances1 upon scraping the paint from girders which had been in use for thirty years1 the author has found1 beneath the original red lead1 the metallic surface bright and clean1 showing no trace of rust4 ,of ordinary steelwork the same cannot be said1 the common experience being that mild steel is very liable to be attacked by rust4 ,with passable care in the bridge-yard during manufacture1 such that with wrought iron no after-trouble would be noticeable1 steel is very liable to show1 within a year of being built up1 numerous little blisters on the painted surface2 any one of these being broken away discloses a small rust-pit4 ,this is more often seen on the flange surfaces 7horizontal7 than on web surfaces 7vertical71 but it is probable the position has little to do with the matter1 and that it is rather due to the fact that rust has been earlier started on the flange-plates1 upon being put through the drilling-machines and inundated with slurry1 which occurs only to a more limited extent with webs having fewer holes4 ,the heads of steel rivets do not show this tendency to 8pit10 or to early development of rust4 ,the riveting is about the last operation in making a girder1 each rivet being freed of all rust by heating1 and quickly coming under the protection of oil or paint4 ,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 weeks1 which fully accounts for the difference in behaviour4 ,the essential point to be observed in all steelwork is to prevent1 if possible1 the first development of rust1 for once begun it is much more difficult to arrest than in iron2 for this reason1 oiling of all material for a steel bridge1 at a very early stage of its existence1 cannot be too strongly insisted upon4 ,this practice1 however1 makes the work so objectionable1 and even dangerous when being lifted--because of the liability to slip--to the men engaged upon it1 that it is commonly very difficult to ensure it being done sufficiently soon to satisfy a careful inspector4 ,if the work is carried out under cover1 the requirement is less urgent4 ,strictly1 all material should be oiled so soon as rolled1 but the author does not remember to have seen this done at any of the mills he has visited1 though it is common enough to find it specified4 ,ironwork does not need the extreme care which should be bestowed upon steelwork1 but it is desirable that it should be painted as soon as possible1 the surfaces being first thoroughly cleaned4 ,there is1 probably1 for painting girder work nothing to beat good red lead as a protective coating2 but there is considerable difficulty in getting it reasonably pure1 without which quality its utility will be greatly reduced4 ,the question of purity will1 however1 be found to be largely a question of price4 ,it may be stated broadly that1 whether for steel or for iron1 the first protective covering is1 perhaps1 the most important of any it will ever receive4 ,in repainting old work1 care should be taken to remove all traces of rust previous to laying on the new coat4 ,it is not an altogether uncommon practice to repaint old structures by dealing only with the parts readily accessible1 which1 being less liable to rust1 probably but little need it2 leaving those parts which are difficult of access1 and where rust is developing1 untouched2 treating the whole business as a matter of appearance simply4 ,this1 it need hardly be said1 is indefensible4 ,it is better rather to neglect the surfaces freely exposed and ventilated1 and devote the whole care upon those other parts1 confined and difficult to get at2 taking the trouble necessary to remove ballast1 timber1 or whatever may obstruct the operation1 in order that the bad places may be thoroughly scraped1 and then painted4 ,those parts which most need attention may cost1 perhaps1 to reach--and deal with when exposed--ten times as much per yard of surface as the rest of the superfices1 which needs little1 and is always accessible2 but the cost should not deter the proper carrying out of the work1 as it will prove the very worst sort of economy to deal with painting in a perfunctory manner4 ,it should be noted that girder work1 whether of wrought or cast iron1 when embedded in lime or cement concrete1 or mortar1 generally proves to be very well preserved1 provided that close contact has obtained4 ,cast-iron girders1 when carrying jack arches resting upon the bottom flanges1 are found after long use to be in remarkably good order1 when finally taken out1 having1 indeed1 the surface appearance of new girders4 ,much the same remarks apply to girders of wrought iron carrying jack arches1 where protected by the brickwork2 provided that the girders are sufficiently stiff to minimise deflection1 and allow the masonry or brickwork to adhere to the surfaces4 ,such girders are in a very different condition to those previously referred to1 in which the ends of the girders1 carrying a light floor structure1 are built into masonry where the deflection slope is greatest2 though1 apart from the few cases where adherence can be relied upon1 building-in is an undesirable practice1 and has the disadvantage that after-examination is only possible by removing portions of the masonry1 which it is evident would very seldom be resorted to4 ,cast iron has ordinarily--unlike wrought iron or steel--great capacity for resisting rust1 and will1 after many years of absolute neglect1 appear but little the worse2 an advantage which is the more pronounced when considered relatively to the greater thickness of the thinnest parts in cast-iron girders1 the percentage of waste being proportionately lessened4 ,cast iron does1 however1 behave somewhat badly in sea-water1 the metal sometimes losing its original character1 and becoming in time quite soft2 though1 if not worn away1 as by the attrition of shingle1 maintaining its original bulk4 ,of some forty-five cast-iron piles belonging to various structures1 examined whilst engaged upon sea-pier work for ,mr4 ,st4 ,george-,moore1 though the author found somewhat diverse results1 in no case did there appear to be any general softening of the whole thickness1 but a distinct change for some definite distance inwards1 generally to be decided without difficulty1 beyond which the metal appeared to retain its original character4 ,in all cases any material depth of softening was found close to the ground1 this depth rapidly decreasing higher up1 till1 at a height of #e feet1 but little if any softening could be detected4 ,at #b feet above ground the softening was frequently but one-quarter of that at ground level4 ,there was1 too1 often a considerable difference in the behaviour of different piles in the same structure under similar conditions2 one pile being found to have only one-fourth part of the softening noticed in others1 or possibly none at all4 ,for six different structures the amount of softening near ground level1 of about twenty-five piles examined1 was as given in the table on the next page4 ,the greatest depth of softening found 7see ,no4 #b7 was #i_/af inch1 #a foot above ground1 in a pile thirty-six years old4 ,the decayed material when removed was of a soft1 greasy consistency1 perfectly black1 which a few hours later was found to have changed to a dry yellow powder1 by the rapid absorption1 it may be supposed1 of atmospheric oxygen4 ,it is apparent1 therefore1 from this example that deterioration may proceed to a considerable depth2 but it should be observed that other piles of the set showed softening at ground level of #a_/h inch only4 ,,softening ,,of ,,cast-,,iron ,,piles ,,in ,,sea-,,water4 ---------------------------------------- -------------------- ,no4 ,age4 ,maximum ,maximum ,mean ,rate ,quality ,materials ,softening4 ,rate of of of ,metal4,entered ,softening4 ,softening4 by ,piles4 ---------------------------------------- -------------------- #a #ag years#e_/af in4 #a_/h in4 in #a_/h in4 in,soft ,extremely #g years #ae years soft sandstone4 #b #cf years#i_/af #a_/h in4 in ,no result ,rubble #h-a_/b years mound4 #c #cb years#c_/h #a_/h in4 in #a_/h in4 in,moderate-,fine #aa years #ae years ly hard sand4 #d #ch years#a_/aj #a_/h in4 in #a_/h in4 in,hard ,extremely #dg years #adj years hard rock4 #e #ag years,small ,negligible 787 ,sand and ,shingle4 #f #ad years,negligible,ditto 787 ,sand4 ---------------------------------------- --------------------- ,the least rate of softening noticed1 apart from those structures of a more recent date1 in two of which it was very slight1 occurred in a pier thirty-eight years old 7,no4 #d71 where1 of three piles tested1 two were quite hard1 and the third softened #a_/aj inch only4 ,whatever may be the precise cause of the change1 it does not appear to be affected by the period or percentage of immersion during the rise and fall of tides4 ,illustration3 ,,fig4 #ei4 ,this will be clear from the diagram1 ,fig4 #ei1 which refers to four piles 7,no4 #c of table71 all of the same age1 in the same structure4 ,on each pile the depth of softening is given at points in strict relation to each other1 and to the tidal range4 ,the percentages of immersion for the various heights are also given1 from a study of which it will be apparent that these have no relation to the amount of softening2 this1 indeed1 is always greatest near the ground1 at whatever actual height it may be4 ,for instance1 pile ,a was at ground-level softened #a_/d inch1 that point being #fj per cent4 of its life under water2 but on pile ,b1 at a point #gd per cent4 of the time submerged1 and #d feet above a lower ground-level1 no softening was apparent2 further1 at ground-level of this pile1 the percentage being there #hg1 the softening was no greater than at ground-level at pile ,a4 ,it is probable that while the percentage of submersion in moving water hardly appears to affect the result1 yet prolonged contact with wet sand1 sea-weed1 or clinging shell-fish may do so4 ,this seems to suggest that the process of change1 as between the sea-water and the iron1 is slow1 and to be effective must be continuous2 so that it is only found to any considerable extent where the water in contact with the surface is still4 ,in the two worst cases1 ,nos4 #a and #b of the table1 at points #a foot and #f inches above ground-level1 the surface was in one pile shrouded in a thick mantle of heavy sea-weed1 and in the other covered by molluscs2 in both instances the surfaces being thus kept moist and undisturbed4 ,the piles of the fourth case were in hard rock1 were clean1 and1 where accessible1 always either in moving water or quite dry4 ,however this may be1 the power to resist softening certainly appears to vary largely with the quality of the iron4 ,the piles1 referred to above1 in which deterioration proceeded at the most rapid rate were certainly of a soft metal1 the first being markedly so4 ,on the other hand1 certain piles 7,no4 #d7 of hard1 close-grained iron suffered very little4 ,it may be mentioned with respect to the last named1 as a matter of interest1 that the caps of the lower lengths 7just above ground-level7 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 iron1 but laminated1 and harder4 ,of about #a-a_/d inch original thickness1 only #c_/af inch remained having the semblance of wrought iron4 ,the percentage of submersion was about #fj4 ,a number of piles1 not included in the table1 varying from fifteen to forty-four years old1 and of the same structure to which set ,no4 #b belonged1 were all found to be hard1 with the exception of one showing #c_/af inch of softening4 ,these are omitted1 because the mud surrounding them was at the time of examination unusually high1 so that the more normal ground-level could not be reached1 at which points testing might have disclosed different results4 ,it is probable that for any piles standing in soft material examination below the surface would reveal more pronounced softening than where occasionally exposed4 ,to meet the effects of sea-water on cast-iron piles1 and for other reasons1 it is a common and good practice to make the lower lengths of greater thickness--say1 #c_/h inch more--than that sufficient for the upper4 ,occasionally1 also1 the bottom lengths are filled with concrete1 which no doubt adds to the length of time during which they may be relied upon4 ,,chapter ,x4 ,,examination1 ,,repair1 ,,and ,,strengthening ,,of ,,riveted ,,bridges4 ,in the preceding chapters defects of various kinds to which riveted bridgework is liable have been more particularly dealt with2 it is now proposed to consider the examination of such structures1 following this by a reference to methods of repair and strengthening1 leaving the treatment of other classes of bridgework to be developed under their proper headings1 though some of the remarks immediately following will apply to all4 ,the exhaustive survey of a bridge is only to be made after considerable experience in the work1 but it may be stated that in looking for defects it is well to seek where they are least expected1 till1 with practice1 one knows better where to direct attention4 ,when examining with a view to pronouncing an opinion upon the fitness of the structure to remain in place1 if in any real doubt1 it is wise to give a casting vote against it2 and finally it may be said that upon taking down a bridge condemned for any one or more defects1 it should be examined for worse4 ,this may seem to be somewhat pessimistic1 but is based upon the teachings of experience4 ,preliminary examination of a bridge may reveal such faults or weaknesses as at once to ensure its condemnation2 but if this is not the case1 and there is a reasonable probability that the structure may be given a fresh lease of life1 it will1 for the purpose of estimating the strength1 or for possible repairs1 commonly be desirable to secure precise particulars of the existing structure independently of any drawings that may be in existence1 and which will very probably be incorrect1 the finished work1 if old1 seldom agreeing with the contract drawings4 ,a final decision may in this case be deferred till after the measuring up has been completed1 the condition of the structure becoming more familiar in the process4 ,it is desirable first to ascertain whether the bridge remains in good form1 whether the camber of girders appears to be what might be expected1 or agreeable with existing records1 though much reliance must not be placed upon figured cambers1 it being quite common for girders to leave the bridge yards with the camber something other than that intended4 ,the deflections under live load will also be observed1 and compared with the calculated result1 or checked by judgment4 ,the calculations upon which strength and deflections are based will1 of course1 refer to the actual sections1 which are sometimes a little difficult to ascertain if there has been irregular rusting4 ,in continuous girders also1 levels having been taken1 allowance should be made for effects of settlement1 if any2 and with arches evidence of movement of the piers or abutments sought for1 with the like object4 ,it is seldom that the main flanges of girders show signs of weakness1 unless from flexure in the case of long and narrow top members1 insufficiently stiffened2 but there may be want of truth from other causes already dealt with4 ,in plate girders the webs should be most carefully scanned for possible cracks1 particularly where cross-girders are connected1 and along the upper edges of bottom flange angles1 if the floor rest upon the flange4 ,all riveted connections1 of course1 need close attention1 both for straining effects1 where there is a liability to wracking1 and to detect loose rivets4 ,loose rivets and want of tightness in other parts of the work may frequently be detected at sight by a reddish bloom which appears on the neighbouring surfaces1 caused by rust working out and spreading under the effects of weather2 it may be seen round rivet-heads or along the edges of angle-bars1 or other parts where there is movement4 ,loose rivets1 though generally to be detected also by the hammer1 may perhaps in the case of thin-webbed cross-girders be working in the web-thickness only1 possibly to a considerable extent4 ,this1 if not otherwise evident1 may sometimes be detected by simultaneous deflection tests--with rods--at the top and bottom flanges of a girder1 at the same distance from the bearings4 ,any difference in the readings may indicate loose web-rivets1 or possibly a tear in the web running parallel to the flange angles4 ,bracings between girders are very apt to display a rich harvest of working rivets4 ,cross-girders and longitudinals also may have loose rivets at their connections1 and be very badly wasted1 with quite possibly cracks in the webs1 or other defects already enlarged upon4 ,the condition of the road upon the bridge will frequently be an indication of the state of the floor which carries it2 or the existence of rail-joints which are working badly may very properly lead to a critical examination of the girder-work immediately below1 as this is a fruitful source of damage in light constructions4 ,floor-plates1 where these exist1 should be scanned for leakages1 drainage nozzles1 and guttering1 to see that they are free1 the attachments of the latter being often loose and unsatisfactory4 ,trough floors may be expected to show loose rivets near the ends1 with a probability of excessive leakage where they abut against the webs of supporting girders4 ,floor plates resting upon abutments or piers1 being very liable to serious decay1 require attention1 and girder-work entering masonry should receive close scrutiny1 any obstruction to a sufficient examination being removed so far as is judged sufficient for the purpose4 ,the structure should1 of course1 be closely watched during the passage of live load for any signs of abnormal movement1 excessive vibration1 or lurching4 ,in addition to seeking for these various defects1 or others which have been referred to in these pages at length1 it will be well always to be alive to the possibility of faults to be seen for the first time1 or of which the author has furnished no instance4 ,having formed a reliable opinion as to the state of the bridge1 this1 if satisfactory1 may leave to be determined only the question of strength relative to the loads carried4 ,it is apparent that stress limits suitable for a new structure1 which has all its life before it1 of purpose moderate to cover possible deteriorations1 the growth of loads1 and other adverse influences1 may to avoid immediate reconstruction1 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 well1 and remains in good condition4 ,what this higher value may be will be greatly influenced by the circumstances of each case1 and1 being largely a matter of judgment1 may be expected to vary with different engineers4 ,experience shows1 however1 that the nominal unit stress in an old bridge may be a very considerable amount in excess of that allowed for new work1 without1 of necessity1 showing any ill effects2 and the author is of opinion that for old bridges in good condition it is quite prudent to allow an excess of #cc per cent4 beyond that permissible for a new design4 ,if the structure is too weak to satisfy this modified condition1 it may be possible to bring it within the stress limit by a reduction of ballast or other removable dead weight4 ,if this expedient does not promise to be satisfactory1 or the bridge shows actual signs of weakness1 or palpable defects1 it will be necessary to deal with the question of repair1 strengthening1 or reconstruction4 ,the repair of built up bridgework resolves itself largely into a matter of replacing loose rivets by cutting these out1 rhymering the holes1 if desirable1 and again riveting4 ,it will often be sufficient to do this with no particular precautions as to bolting up temporarily2 the rivets having been loose1 may very well be spared for a time4 ,in re-riveting cross-girder connections it may1 however1 be imperative to remove all the rivets1 bolting up securely as this is done1 in order to make a tight job1 taking out each bolt in turn as required1 and again filling the holes2 or it may be well in a bad case first to remove all loose rivets1 substituting good bolts1 in order that work which has gone out of shape owing to defective rivets may first be brought true4 ,cross-girder webs1 cracked vertically or nearly so1 are commonly repaired with splice-plates on either side2 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 favoured4 ,illustration3 ,,fig4 #fj4 ,illustration3 ,,fig4 #fa4 ,illustration3 ,,fig4 #fb4 ,illustration3 ,,fig4 #fc4 ,replacing wasted flange-plates1 or adding new plates to those which exist1 is occasionally resorted to in the case of main girders1 the flanges of which are sufficiently accessible1 but the operation is difficult1 takes some little time1 and should only be attempted under the constant supervision of a thoroughly capable man4 ,when done1 if the girder has not been relieved of load by staging1 the stress under full load will be unequally distributed between the old and the new section1 the old always taking more by the amount of the dead-load stress previously carried4 ,the method which the author has seen applied to lattice girders of about #hj feet span1 having good angle-bars in the flanges1 with a shallow vertical web for attachment of diagonals1 consisted in first cutting out the old flange rivets1 and substituting bolts well screwed up1 till all the rivets necessary had been removed4 ,the new plate length having been prepared1 was1 on a ,sunday1 during a few hours' cessation of traffic1 marked off1 the temporary bolts being removed for the purpose1 and then replaced4 ,after the plate had been drilled1 on a later ,sunday1 it was finally put into position1 bolted up1 and riveted at leisure2 cover-plates make additional trouble1 but are dealt with on the same principle4 ,the method as shown in ,fig4 #fj is1 however1 barely practicable for so many plates4 ,it is preferable1 if it is proposed to add section1 to do this with as little interference as possible with existing rivets of importance4 ,this may be accomplished1 if the existing plates are not too wasted at their edges1 by riveting on new strips or angle-bars 7see ,figs4 #fa to #fc74 ,occasionally the strength of a girder is increased by the addition to the top or bottom boom of material in such a form as sensibly to increase the depth1 and thus1 while adding increased section to one boom1 to reduce the stress in each1 though to dissimilar amounts4 ,by this device also the relief is effective only as regards the live-load stress2 under dead load only the new material does no work1 provided1 of course1 that no relief staging was used during the alterations4 ,for girders carrying any considerable proportion of dead load the method is very inefficient1 though for others1 in which the live load is relatively large1 the result should be more satisfactory4 ,as this question of adding new section to old is of much importance in dealing with repairs and strengthening operations1 a few general remarks upon the subject will be pertinent4 ,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 practice4 ,if a bar be imagined under longitudinal stress varying between #j and a maximum1 then1 if the area of the piece be increased at the time when it takes no stress1 its capacity for resisting the maximum amount will be increased1 and for added material of similar elasticity the unit stress proportionately reduced4 ,if1 however1 the load on the bar does not vary1 the mere addition of metal will not relieve the original section in any degree4 ,to take a third case1 of the maximum being twice the minimum load1 it will be necessary1 in order to lower the maximum unit stress by #be per cent41 to double the original section of the bar if1 as supposed1 the extra metal has been added to the piece when under the smaller load1 so that the new section is only effective in assisting to carry the remainder of the load at such times as it may be imposed4 ,the relationship stands thus3-- ,live load ,new area ---------------- -------------- relief4 ,live dead load ,new old area ,these statements will be true under the conditions named1 within the elastic limit of the material2 but some advantage would be derived in the second case1 and a more marked benefit in the third1 if the load assumed to be a maximum were exceeded1 or if the composite bar were tested to destruction2 as1 however1 these effects would be outside the limiting conditions imposed1 it must be a matter of judgment as to how far this reserve of strength may be considered of value4 ,if1 instead of simply adding section to the bar1 some part of the constant load is put upon the new section by the manner of attachment1 the combination will1 of course1 be more effective4 ,to apply these considerations and illustrate the way in which the two methods of adding flange section work out when reduced to figures1 the case will be supposed of a girder #f feet deep1 carrying a load of which one-third is dead and two-thirds live4 ,to the flanges of this girder are added plates equal to #ej per cent4 of the original areas1 in order to reduce the stress of #g tons per square inch to which the girder before strengthening is liable1 the depth remaining substantially unaltered4 ,with dead load only the original section would be stressed to #bc tons per square inch1 the new section being then unstressed4 ,under full load the new and old material take #ca tons per square inch additional1 making the modified stress on the original section #ed tons per square inch1 as against #g tons2 or a reduction of #bb per cent4 ,this compares with #cc per cent41 the relief due to #ej per cent4 increase of flange area under ordinary conditions of stress distribution4 ,let the second method of strengthening the girder now be considered1 using1 for purposes of comparison1 the same total amount of new material to increase the girder depth by an addition to the top flange4 ,this section will be equal to the area of one flange1 which1 though it may be applied in many different ways1 giving a greater or a less increase to the depth1 would probably be used in some such manner as that shown in ,fig4 #fd1 increasing the effective depth for live-load stress by nearly #aj inches4 ,illustration3 ,,fig4 #fd4 ,the added material will1 as in the previous case1 leave the dead-load stress unaltered1 or #bc tons per square inch4 ,the stress in the bottom flange due to live load will1 however1 now be #da tons per square inch1 making a total stress of #fd tons per square inch1 against #g tons--the original stress4 ,the reduction here is #h per cent4 only1 as compared with #ab per cent41 the relief due1 under ordinary conditions1 to an increase of effective depth from #f feet to #f feet #aj inches1 and by the use of additional material1 equal1 as before1 to one-half of the total flange areas before the alteration4 ,the effect on the top flange need not be here gone into in detail1 but it may be said that1 owing to the increase of gross section and of depth1 the ultimate stresses of both the new and old material are greatly less than as given for the bottom flange4 ,girders strengthened by the first of these two methods would1 it is probable1 if tested to destruction1 give results more nearly in accord with the actual percentage increase of flange section1 plastic deformation of the metal1 before failure1 tending to reduce the differences of stress on the new and old material of the sections4 ,illustration3 ,,figs4 #fe and #ff4 ,web members of lattice girders may1 if weak1 sometimes be dealt with by the introduction of supplementary bars1 parallel to and between the old members1 or by the addition of strips or angles to the existing diagonals4 ,the treatment will be largely influenced by the nature of the old detail1 which may lend itself to some one arrangement much better than to any other4 ,end riveting of web members may1 if it has become loose1 be dealt with by simply rhymering the holes a size larger1 and re-riveting in the best manner1 if the stresses are not excessive2 or it may be necessary to devise some additional attachments by which new rivets are brought into use 7see ,figs4 #fe and #ff74 ,the effective relief due to supplementary rivets will be influenced by similar considerations to those governing increase of section4 ,illustration3 ,,fig4 #fg4 ,illustration3 ,,fig4 #fh4 ,old structures are very frequently deficient in bracing1 which may1 in such cases1 be advantageously introduced2 or girders individually weak may be rendered collectively efficient by suitable bracing4 ,in considering the advisability of this1 however1 the case should be viewed with regard to the possible effects of such members1 as already dealt with in the chapter relating to these questions4 ,there it has been pointed out that bracing between a system of parallel girders may have the effect1 under live load1 of increasing the stress on the outer girders due to twisting of the structure as a whole1 though the inner girders will1 except for full loading of the whole bridge1 be advantaged as to stress values1 and in any event bettered by being held up to their work4 ,the effect upon the outer girders may be met by increasing their strength1 if this appears to be necessary4 ,in all such alterations the detail should be schemed with special care to ensure simplicity in execution1 smith's work being rigorously avoided4 ,a good arrangement for supplementary bracing between plate-girders1 which gives little trouble in carrying out1 is shown in ,fig4 #fg2 or where the stiffeners of such girders are in line across the bridge1 the detail given in ,fig4 #fh may involve less expenditure4 ,difficulties may be experienced in riveting1 unless great care is taken in the positioning of rivets4 ,fitting-bolts are only to be relied upon as such1 if they really justify the name2 they are1 though easy to specify1 by no means easy to secure under the conditions of practical work4 ,weak cross-girders may make alterations--in some cases considerable--necessary1 to rectify the defect of strength4 ,the removal of old girders to make room for new is seldom resorted to1 unless the existing detail renders this a simple operation2 but it is not unusual to introduce new girders between the old in cases where there is no plated floor to make the work difficult4 ,by this method there is1 of course1 an increase of appreciable amount in the dead load carried by the main girders1 which would in many instances be objectionable4 ,with deep and heavy main girders1 having plate webs1 cross-girders may be strengthened by improving the end connections by suitable gussets1 and attachment to good vertical stiffeners1 the fixity of the ends thus aimed at being assured by overhead struts or girders1 from one main girder to its fellow1 at intervals apart well considered with reference to the horizontal strength of the top flanges1 the whole thus making a closed frame1 as shown in ,fig4 #fi4 ,the method appears feasible1 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 floor4 ,illustration3 ,,fig4 #fi4 ,a simple and very common device consists in substituting for the ordinary cross-sleeper road1 where this exists1 stout timber longitudinals under the rails1 which have1 where the cross-girders do not exceed #e feet centres1 a marked distributive effect1 tending to reduce the maximum load upon any individual girder4 ,with a similar object1 trough girders containing longitudinal timbers are sometimes adopted where the depth available is not enough to enable sufficiently stiff timbers to be used alone4 ,in either case the object sought is the same--to modify the effect of the heavier wheel loads upon isolated cross-girders4 ,when the spacing is so close as #d feet1 the beneficial result of this treatment is considerable1 but at #h feet centres it can have but a moderate effect where timbers alone are used4 ,occasionally1 for long cross-girders1 a distributing girder is placed1 with the same intent1 in the #f feet way1 its function being limited to this use only if the depth and strength are sufficiently small to serve this object alone1 as distinct from the case in which it becomes a carrying girder transferring load to the abutments4 ,as a distributor simply1 the girder has to equalise the bending moments amongst the cross-girders1 to effect which it will be evident that these moments having been ascertained for the several cross-girders previous to alteration1 for a position of the wheel loads such that the heaviest comes upon a centre cross-girder1 the mean of these moments will1 when compared with that for each girder1 show the difference to be induced as a result of introducing the distributor4 ,these differences of moment render necessary at the centre of the cross-girders reactions upwards or downwards1 as the case may be1 of amounts competent to induce moments below the inner rails equal to these differences4 ,it is these reactions which must be provided by the distributing girder at a moderate stress1 and without flexure of such an amount as sensibly to modify the reactions4 ,the greatest section necessary at any one point may then be adopted for the girder throughout4 ,the result will commonly work out to a moderate section1 but there will be no harm in a little excess in a case of this kind1 the total cost being but little affected by some small addition to the weight1 where labour upon the site is so considerable an item as in work of this description4 ,the ends of the distributing girder should be carried on to the abutments or piers to ensure adequate relief of the end cross-girders4 ,it will be found desirable in arranging for distributing girders to ascertain at an early stage1 by boning or by levelling1 the condition of the cross-girders as to uniformity of heights1 as this may affect the length most suitable for separate sections4 ,between the underside of the distributor and the cross-girder tops there will commonly be spaces of varying amounts1 which should be filled by packings to fit1 rather than by pulling the work together by force1 introducing undesirable stresses of uncertain amount4 ,in the earlier remarks upon the strengthening of bridgework by the use of new material1 it has been assumed that the modulus of elasticity of the new metal is similar to that of the old2 it may1 however1 as in cases where wrought-iron work is reinforced by additions in steel1 be necessary to take the difference of elastic properties into account1 with which object the new section should be multiplied by a quantity 7greater or less than unity7 inversely proportional to the higher or lower modulus of the new material1 that is to say1 by ,e of old material ----------------- ,e of new material ,,chapter ,,xi4 ,,strengthening ,,of ,,riveted ,,bridges ,,by ,,centre ,,girders4 ,the addition of distributing girders1 described in the last chapter1 as a means of strengthening a bridge floor1 while sufficient in many cases so far as the cross-girders are concerned1 does not in any appreciable way assist the main girders4 ,when for a two-line bridge1 having outer main girders only1 this result also is desired1 together with a more complete relief of the floor structure1 centre main girders may be used1 placed either above or below the cross-girders1 on the centre line of the bridge4 ,there are two principal ways in which such a girder may be brought into use2 the easier1 but generally less economical1 is by making a simple attachment to the cross-girders1 the old girder work still taking the whole dead load4 ,by this method the new girder does no work but carry itself till the live load comes upon the bridge1 and must be made very stiff to take any sensible portion of the running load2 the second method is to make the connection adjustable1 so that a part of the floor weights may be imposed upon the new girder as an initial load4 ,in doing this the old outer girders will rise slightly1 being relieved of stress1 and the cross-girders also lifted at the middle1 whilst the new girder is depressed as the load is brought upon it4 ,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 section4 ,the whole question1 by either method1 turns upon deflections2 and it is in determining the relative movements of the girders that the problem chiefly lies4 ,it is convenient first to determine the percentage of load relief to be effected in the main girders1 as to which it is to be observed that as this relief 7distributed7 is induced by the upward reaction of the new girder acting at the centre of the cross-girders1 the stress relief of these will1 as a rule1 greatly exceed that of the outside girders4 ,for the generality of cases1 it may be taken that the relief suitable for the outside girders will be satisfactory in its effects upon the cross-girders1 even though it is desired to reduce the stress in these to a greater degree4 ,if1 however1 it be thought desirable to check this1 it may be done by considering a cross-girder subject to its dead and live loads acting downwards1 and to reactions at the centre and ends4 ,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-girders1 or as here given3-- c t ,p reaction at centre 7#a7 c being the percentage of relief2 t the total load per foot run of the bridge2 and ,p the pitch of cross-girders4 ,the live loads carried by the cross-girders are for this purpose taken at per foot run1 as for the main girders4 ,with these data it will be easy to construct a diagram of moments1 making it evident whether the relief proposed for the main girders will give a sufficient percentage of relief to the floor beams4 ,granting that this proportion has been decided1 and dealing first with the case in which the centre girder is simply attached to the cross-girders1 and takes no dead load other than its own weight1 then the live load carried by the outside girders1 and previously borne wholly by them1 will be reduced by the amount it is intended to transfer to the centre girder1 and will become ,ll - 7c ,lt7 live load on outer girders 7#b7 ,ll being the total live load1 and ,lt the total dead and live load carried by the bridge4 ,from this the deflection of the outer girders corresponding to this modified live load may be derived4 ,illustration3 ,,fig4 #gj4 ,it is next necessary to ascertain the vertical movement1 commonly a depression1 of the cross-girders at the centre relative to their ends1 when subject to the running load only1 and supported at the middle and ends1 the centre reaction being obtained as before indicated 7#a74 ,this movement will be the difference 7if any7 between the deflection on the whole span of the cross-girder due to the live load1 and the upward flexure of the girder due to the centre reaction1 considered as separate effects4 ,stress values having been estimated for the two conditions1 these results may readily be deduced by simple flexure formul1 observing that while the curve of moments due to live load sufficiently approximates to that for a distributed load to justify1 for this1 the use of a distributed load formula as given in the chapter 8,deflections10 the flexure due to the centre reaction will be but #jhj of that which corresponds to the same stress for distributed loading4 ,or1 the curve assumed by the girder under live load may be plotted by a method to be later explained4 ,the sum of the movements now determined--that is1 the live-load deflection of the outer girders1 and depression1 as is commonly the case1 of the cross-girders--will give the extreme depression 7marked m in ,fig4 #gj71 from the dead-load condition of the middle cross-girders1 when supported to the extent desired by a centre girder whose proportions are not yet known1 but which1 carrying the required percentage of the total load1 must1 subject to a reservation presently stated1 deflect only this amount4 ,the unit stress in the flanges of the new girder1 governed by this flexure1 will for a plate girder be ,d ,c m ----------- f1 unit stress on gross section 7#c7 ,s#b ,d and ,s being1 as before 7see 8,deflections071 the depth and span respectively in feet1 ,c a constant1 m the deflection in inches1 and f the stress per square inch on the gross section of flange4 ,the gross area ,a1 of the flange1 is given by ,s c ,lt ---------------- gross area of flange 7#d7 #h ,d f c ,lt1 being1 as in 7#b71 the load transferred to and carried by the centre girder4 ,the actual stress in the flanges will1 of course1 be greater by an amount due to the girder's own weight2 but this does not affect the question of relief4 ,for any ordinary case the stress per square inch will be low2 but it will manifestly be useless to assume a greater stress with a view to economy1 as the effect of reducing the section will simply be to make the girder too flexible1 thus causing it to be less effective than primarily intended4 ,if1 as is seldom the case1 there is freedom as to the depth of girder permissible1 it is evident the unit stress may be made a condition1 and the depth deduced by a suitable modification of formula 7#c72 the relief desired being in this way equally well assured4 ,indeed1 in the rare instances in which any depth may be adopted1 this method is--contrary to the general rule--distinctly economical1 particularly if the girder may be placed below the cross-girders1 which simply rest upon it1 without elaborate attachments4 ,illustration3 ,,fig4 #ga4 ,considering now the second method of applying centre girders by which the new girder is made initially to carry part of the dead load1 by adjustment1 it will at once be recognised as a more complex matter4 ,the measure of relief by which the old girderwork shall benefit need not be affected by the method of applying the centre girder1 and may be decided on the principles already considered4 ,the outer girders carrying a reduced load1 when the bridge is fully loaded1 and the cross-girders being in part supported at their centres in the manner already described1 will give a resulting depression m 7see ,fig4 #ga7 of the centre cross-girders1 below the original dead-load position1 of a similar amount determined in the same way4 ,this extreme depression determines also the lowest position of the new centre girder1 which may be designed to carry the required percentage of the total bridge loads with the maximum stress and depth1 as conditions1 leaving the initial dead load and necessary adjustments to be ascertained4 ,this is the common case and will be here dealt with1 it being assumed to avoid ambiguity in description that the new girder lies above the cross-girders4 ,the centre girder of fixed depth being then required to carry a definite load at a definite flange stress1 will deflect a definite amount at this stress4 ,if this deflection equalled the extreme depression m of the old girder work1 no adjustment would be necessary1 the centre girder then carrying no initial dead load1 as by the first method2 but for centre girders designed for economical flange stress the deflection will in ordinary cases greatly exceed this1 the depth generally being small1 and in order to ensure that the new girder shall do its full work1 some dead load must be put upon it4 ,in the act of adjustment the cross-girders must be lifted and the centre girder depressed1 till the joint movement equals the excess s of the centre girder deflection over m1 when the new girder will carry the proper amount of initial load1 and upon further deflection under live load give the full measure of relief4 ,the amount of 8lift0 or upward flexure of the old girder work1 and the depression or 8drop0 of the new girder1 during adjustment1 will depend upon relative stiffness1 and may be ascertained as follows3-- ,for unit reactions at the centre of the cross-girders the upward flexure of these may be ascertained1 as also the upward flexure of the two outer girders when subject to forces of the same total amount 7one-half to each7 applied at the cross-girder ends4 ,the sum of these movements will give the total lift of the centre cross-girders1 when all are subject to unit lifting forces2 similarly1 the depression of the centre girder for unit loads applied at the cross-girders may be determined4 ,there will then be known the movements upwards and downwards of the old and new work when being drawn together by unit forces applied as stated4 ,if l lift due to unit loads1 lt total lift due to adjustment1 d drop due to unit loads1 dt total drop due to adjustment1 s deflection excess gross adjustment1 there will then be d --------- s dt1 l d total drop of centre girder under adjustment1 l --------- s lt1 l d total lift of centre cross girders under adjustment1 dt ------ unit load d initial load put upon centre girder at each cross-girder4 ,the rise of the two outer girders for upward forces together equal to those depressing the centre girder may readily be deduced4 ,illustration3 ,,fig4 #gb4 ,illustration3 ,,fig4 #gc4 ,the act of adjustment may conveniently be effected by the arrangement shown in ,fig4 #gb1 in which each cross-girder is hung up at its centre by four bolts4 ,at the middle of the centre girder the total amount to be screwed up will be that corresponding to the deflection excess s1 but towards the ends this amount decreases1 and may advantageously be represented by a diagram as ,fig4 #gc1 in which1 if s represents to scale the amount to be screwed up at a centre cross-girder1 the corresponding amounts for other girders may be read off direct4 ,it will be apparent that it must be necessary to 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 up1 this excess clearance being ultimately filled by a packing4 ,the precautions to be observed in carrying out this kind of work1 and the practical methods of adjustment adopted by the author after some little experience1 may here be given4 ,great care is necessary at the outset to ascertain the true spacing of the cross-girders1 to ensure that the bolt-holes in the bottom flange of the centre girder shall come where desired4 ,the fixing of the cross-girder brackets also needs close attention to avoid after trouble1 the bolt-holes in the brackets being preferably drilled on the site after fixing4 ,it will1 for masonry abutments1 be necessary to fix bedstones to receive the new centre girder1 which1 being carried out quite possibly under adverse traffic conditions1 will perhaps leave the stones liable to settle slightly when the full load is carried4 ,to eliminate the bad effect of this upon the ultimate adjustment1 and to take up any initial set of the new girder work1 which would be prejudicial in the same way1 it is desirable1 the centre girder being in place1 to screw up the bolts temporarily and leave the work for a week or two4 ,to ensure regularity in the screwing up process1 it is convenient to prepare1 for use at the bridge1 a diagram somewhat similar to ,fig4 #gc1 giving the amount by which the new and old work are to be brought together at each cross-girder1 with the number of turns for each nut to effect this4 ,with a man at each side of the girder1 the whole length is traversed1 giving a half-turn to each nut2 this is repeated as often as necessary1 and so managed as to bring all up proportionately to the final requirement1 keeping tally with chalk marks over each cross-girder as a check4 ,the preliminary screwing up should be conducted with little less care than that adopted for the later adjustment1 to avoid damage to the old work4 ,this later adjustment having in due course been effected1 it is then necessary to measure for packings to fill the spaces remaining between the old cross-girders and the new centre girder4 ,these spaces should be callipered at each of the four corners1 care being taken to avoid after-confusion4 ,the measurements ascertained will1 however1 be too great for the finished packings1 as an allowance of not less than #a_/aj inch 7total71 will commonly be wanted to cover irregularities in the surfaces4 ,the packings1 having been prepared and checked1 may be slipped into place after slacking all the bolts a small amount to permit this to be done1 finally screwing up tight and securing the nuts by split-pins1 through holes drilled as the last operation4 ,as a check upon the calculations and adjustment1 the 8lift0 of the outer girders and cross-girders1 and the 8drop0 of the centre girder may be observed by levelling4 ,for this purpose the author has used a staff of inches divided into tenths1 with which1 and a good level1 very accurate readings may be taken for short distances4 ,no reference has been made to the effect of skew in a bridge on the above methods1 the explanation given applying rather to bridges square on plan4 ,the influence of skew on the load distribution will largely be a matter of detailed calculation4 ,the flexure of the girders may also be sensibly affected1 but may be arrived at with sufficient accuracy without any great trouble4 ,the chief effect of skew is to modify the amount of screwing up during adjustment1 which may be better understood by reference to ,fig4 #gd1 and comparing it with ,fig4 #gc1 the adjustment diagram for a square bridge4 ,to illustrate how these methods of strengthening work out1 and compare as to weights of centre girders required1 the case has been assumed of a wrought iron bridge of #fj-;feet span1 having outer girders #e feet deep1 of #ci square inches gross flange area2 and cross-girders1 at #h-;feet centres1 #bg-;feet span1 #a foot #i inches deep1 with a gross flange area of twenty square inches4 ,the dead load and live load on either road are each #age tons per foot run4 ,the stress in the outer girders previous to the alteration being #f tons per square inch gross1 it is desired to relieve this to the extent of #cc per cent4 by a steel centre girder4 ,in the table here given the quantities given in italics are fixed as primary conditions3-- ,,centre ,,strengthening ,,girders ,,for #fj-;,,ft4 ,,span4 ---------------------------------------- ----------------------- ,centre ,centre ,girder1 ,girder1 ,adjustments ---- ,stress ,depth ,unknown4 ,unknown4 ,unknown4 ---------------------------------------- ----------------------- ,outer ,girder4 ,deflection under modified live load #db in4 #db in4 #db in4 ,lift of adjustment nil nil #aec ,cross ,girders4 ,depression under live load --modified conditions of support #ac in4 #ac in4 #ac ,extreme depression 7m7 #ee #ee #ee ,lift of adjustment 7cross- girder only7 nil nil #jie ,total lift of adjustment 7lt7 nil nil #bdh ,centre ,girder4 ,depth #ce ft4 #hb ft4 #ce ft4 ,unit stress on gross section 7ex girder's weight7 #bad tons #ej tons #ej tons ,total deflection 7ex girder's weight7 #ee in4 #ee in4 #abh in4 ,deflection excess 7s7 nil nil #gc ,depression1 or 8drop0 of adjustment 7dt7 nil nil #dhb ,gross area of flange #aje sq4 in4#aib sq4 in4#dde sq4 in4 ,weight #bj tons #ajd tons #aad tons ,net flange stress 7including girder's weight7 #cai tons #fhg tons #fid tons ---------------------------------------- ----------------------- ,girders subject to distributed load are treated as having uniform stress1 but where this is not strictly the case1 as in some light girders1 it will be necessary to take the fact into account4 ,for centre girders of wrought iron1 and a unit stress on the gross section of #d instead of #e tons1 the girder weights are between #i and #aj per cent4 greater4 ,illustration3 ,,fig4 #gd4 ,in the above treatment of the application of centre strengthening girders there is a source of error which should be touched upon4 ,if1 under live load1 the centre girder deflects more than the outer girders1 as it commonly will1 there must be a want of uniformity in the behaviour of the cross-girders1 those near the abutments being more relieved than the estimated amount of relief of those at the centre1 which will have less than that intended2 but the reduction of stress in the cross-girders will generally be so considerable that any such ambiguity of excess or defect is commonly unimportant2 the effect of this also upon the main girders is much less than might be supposed1 being1 for the third of the cases just given1 about #b-a_/b per cent4 excess for the centre girder1 and generally a much smaller error4 ,with this qualification1 the method can1 however1 be regarded as approximate only4 ,it is possible to eliminate some part of the error by lifting the end cross-girders during adjustment1 a less amount than that given by the diagrams1 ,figs4 #gc and #gd1 taking care that the centre girder is depressed its full amount by lifting the centre cross-girders a little more2 this refinement is hardly necessary1 and unless controlled by calculation cannot be depended upon for precise results4 ,particulars are here given of five ordinary cases1 comparing the calculated and observed results of adjustment4 ,the operation of levelling was conducted by a quick-eyed and capable assistant1 who was not made acquainted with the results expected1 in order to avoid any sub-conscious tendency to match the calculated figures3-- ,,examples ,,of ,,centre ,,girder ,,adjustments4 ---------------------------------------- --------------------------- -- ,calculated4 ,observed4 ---------------------------------------- --------------------------- in4 in4 ,no4 #a4--ef-;,ft4 ,span4 ,depression of centre girder #hb #hd ,lift of cross-girders at centre #bc #bb ,lift of outer girders #bj #aj and #ac ,no4 #b4--eg-;,ft4 ,span4 ,depression of centre girder #ej #ej ,lift of cross-girders at centre #ah #bj ,lift of outer girders #aa #jh and #aj ,no4 #c4--fg-;,ft4 ,span4 ,depression of centre girder #gj #ge ,lift of cross-girders at centre #ae #ag ,lift of outer girders #aj #ji ,no4 #d4--fh-;,ft4 ,span4 ,depression of centre girder #gj #fe ,lift of cross-girders at centre #bj #ah ,lift of outer girders #ac #ad ,no4 #e4--eb-;,ft4 and #bh-;,ft4 ,spans continuous4 ,long ,short,long ,short ,span4,span4,span4,span4 ---------------------------------------- ------------------------- in4 in4 in4 in4 ,depression of centre girder #bh 44 #bi 44 ,lift of centre girder 44 #jd 44 #jc ,lift of cross-girders 7centre of spans7 #ag #ji #ae #ac ,lift of outer girders #jh 44 #jh 44 ,depression of outer girder 44 #ja 44 negligible4 ---------------------------------------- ------------------------- ,the method of calculation adopted for these cases was not precisely that given1 though depending upon the same broad principles4 ,the first cannot be considered a good example4 ,the last1 having continuous girders1 of course needed special treatment4 ,of about seventeen bridges strengthened in the manner described1 the effect generally was satisfactory1 in reducing deflection and vibration2 but in two cases of small span1 owing probably to settlement of bedstones1 the results were not so good4 ,from first to last the work of putting in a centre girder takes some little time1 owing to the slow progress generally made in fixing the brackets1 preparing packings1 etc4 ,the cost of a typical case was about #bc per cent4 of the cost of a new superstructure1 with a #cj per cent4 relief of stress4 ,illustration3 ,,fig4 #ge4 ,illustration3 ,,fig4 #gf4 ,a special case of strengthening by a centre girder1 having considerable interest1 may be here referred to4 ,the primary idea involved was not the author's4 ,the bridge dealt with has already been noticed under 8,bracing0 and a section1 before alteration1 shown in ,fig4 #bf4 ,the span being #he feet1 there was no room for a centre girder of sufficient depth above the cross-girders and between the roads1 nor was it considered economical to place the girder wholly below the floor1 because of the costly staging this would have necessitated for erection purposes1 the height above ground level being very great4 ,a girder was therefore designed1 having open latticing at an angle of #fj degrees1 with a bottom boom to be below the cross-girders1 the top being as high above the rails as could be permitted 7see ,figs4 #ge and #gf74 ,a temporary boom was arranged at the intersection of diagonals1 the lower boom proper not being fixed till the girder having been lifted into place1 with the diagonal members passing between the cross-girders1 allowed this to be done4 ,the girder for some time carried itself from bearing to bearing1 with the temporary boom in tension1 the deflection being then #b inches4 ,the permanent boom was then put in place1 and the girder restored as nearly as was practicable to the camber it was intended to have when complete1 but without throwing1 during the process1 any improper loads upon the old work4 ,the lower boom being finally riveted up1 the cross-girders were made to bear upon it by suitable packings4 ,there were1 in addition to the new girder1 two stiff frames between the old main girders1 to which the new was secured4 ,the girder was designed with the intention that under dead load only the cross-girders should just rest1 but throw no weight1 upon the new work1 the latter assisting to carry live load only4 ,the floor beams being of small span1 and securely riveted to the old girder tops1 the centre girder was required to deflect1 under its share of live load1 the same amount as the old main girders under the remaining portion1 the three points of support of the cross-girders thus not altering their relative levels4 ,that this resulted was evident from the fact that1 previous to connecting the cross-frames to the centre-girder1 the work being otherwise complete1 a space between the two of about #a_/b inch1 afterwards filled by a packing1 showed no alteration1 the closest measurement failing to disclose any relative movement upon the passage of live load4 ,the reduction of vibration was1 as might be expected1 very marked4 ,in the conduct of that class of strengthening work which has been dealt with in this chapter1 it is essential1 in the author's judgment1 that the man responsible for the detailed calculations and design should himself see the operations of adjustment carried out1 or delegate it only to one equally familiar with the requirements4 ,before dismissing the subject1 it will be well to refer to a method of approximately determining flexure curves1 of occasional use in dealing with centre girder or similar questions4 ,the figure assumed is plotted to an exaggerated scale1 with which object the actual radius of curvature at points along the girder's length are first ascertained by the formula ,e ,d ------- ,r1 radius of curvature in feet1 f #b and the radius of curvature for the diagram by #ab ,r ,f#b r1 radius for plotting1 in inches 7#e7 ,e being the modulus of elasticity1 ,d the girder's depth in feet1 f the mean of the extreme flange stresses per square inch of gross area1 and ,f the fraction indicating scale as #a_/dh1 where #a_/d inch #a foot4 ,the curve1 being plotted1 shows by direct scaling the movement of any point relative to its original position4 ,near the ends of the curve where the radii may be of considerable length1 the arcs may be drawn with the help of template curves1 or even set out as pieces of 8straight40 ,when the curve is laid down so that its chord equals the span to scale1 the method involves an error of excess in the resulting deflection or droop which is as much as #g per cent4 when the mean radius for plotting equals the span as drawn1 or when the droop of curve approaches one-eighth of the span4 ,as the exaggeration of curvature is made less pronounced1 this error rapidly diminishes1 till for a droop of about one-sixteenth the percentage is one-fourth part of that above given4 ,this excess in the droop of curve may be amended by the following expression3-- 7droop#c 7 droop - 7------- #cgc7 corrected droop1 or deflection4 7chord#b 7 ,for some purposes it may be preferable to amend the radii for plotting1 so that the curve1 as laid down1 shall be correct1 which may be effected by the formula here given1 to be applied to each value of r1 as first ascertained3-- 7chord#b 7 r 7------- #jfbe7 corrected plotting radius4 7 r 7 ,if1 however1 the length of curve is made equal to the span 7the chord then being less71 and the radii for plotting as given by 7#e7 are used1 the result will for most purposes be sufficiently precise1 though there will now be an error of a contrary kind1 which1 for a curve having a droop of one-eighth1 will be about #b per cent4 too little4 ,a somewhat similar method of setting out deflection curves is described by ,professor ,fleeming ,jenkin in the article 8,bridges0 of the 8,encyclopdia ,britannica10 but without corrections4 ,a careful comparison of results by the above means1 with those calculated1 shows that with good draughtsmanship they may be relied upon for considerable accuracy4 ,equally applicable to girders of varying depth and flange stress1 they have also a limited use in cases of continuity4 ,illustration3 ,,figs4 #gg and #gh4 ,figs4 #gg and #gh illustrate the deflection and stress diagrams for the cross-girders of the bridge supposed to have been strengthened by a centre-girder1 when under the influence of live load and a centre reaction of a definite amount4 ,as a matter of convenience1 each radius length has been halved1 before correction1 so that the resulting droop of the curve is twice the true amount4 ,,chapter ,,xii4 ,,cast-,,iron ,,bridges4 ,cast ,iron as a material for bridges has of late years fallen into disrepute4 ,it is now entirely tabooed by the ,board of ,trade for railway under-bridges1 unless of arched construction4 ,this condemnation of cast iron followed1 and was apparently the result of1 an accident which occurred to an under-bridge on one of the southern lines1 which bridge had already earned for itself an ill repute by breaking down on a previous occasion4 ,the ultimate issue was1 however1 good1 inasmuch as it led to a thorough overhaul of all railway under-bridges in this country1 and the renewal of a great number no longer in a condition suited to the carriage of heavy or of passenger traffic2 yet there is little doubt that1 in the author's judgment1 many excellent cast-iron bridges were then removed at considerable cost1 to be replaced by others of wrought iron or steel1 which will not last so long as many of those displaced had done1 or would still have lasted had they not been dismantled4 ,the earlier cast-iron bridges were commonly made of cold-blast iron1 a material of such strength and toughness as to give an extraordinary amount of trouble in breaking up the heavier parts1 when the time arrived to do this1 and with which material ordinary hot-blast iron is not to be compared for reliability4 ,illustration3 ,,fig4 #gi4 ,as illustrating the very considerable stress to which cast iron may be subjected1 without of necessity leading to any mishap1 two cases may be cited4 ,the first1 a bridge of #cb feet effective span1 carrying two lines of way1 each pair of rails being supported upon ,barlow rails1 forming the bridge floor1 the ends resting upon the bottom flanges of inverted ,t-shaped girders1 #b feet #c inches deep1 as shown in ,fig4 #gi4 ,the extreme fibre stress works out at #bi tons per square inch in tension1 and #ei tons per square inch compression1 calculated as it would be in ordinary office work2 but for the actual loads1 at a span as above1 exceeding the clear span by #f inches only1 and without regard to the effects of eccentric application of the load4 ,the girders when taken out showed upon examination no sign of overstrain4 ,the practice of loading cast-iron girders in this manner cannot1 however1 be too strongly condemned1 notwithstanding that in this case no ill resulted4 ,it is evident that a piece of the lower flange being broken out from this cause1 as occasionally happens1 might so reduce the section as to result in complete failure4 ,illustration3 ,,figs4 #hj and #ha4 ,the second example is that of a small railway under-bridge of two spans1 continuous over the central pier1 each span being #af feet #f inches4 ,the rails were supported upon longitudinal timbers lying within trough-shaped girders1 as shown in ,figs #hj and #ha4 ,the stress over the pier1 in the extreme fibres of the top flange1 is estimated at #dg tons per square inch in tension1 but it should be noted that the effect of the timber longitudinal and rail has been neglected in arriving at this result1 which might possibly on this account be reduced to near #c tons per square inch4 ,the case is noticeable because no evidence of high stress was apparent4 ,the author saw nothing to suggest sinking of the central pier1 the effect of which1 within limits1 would be to further reduce the stress as calculated2 but it is quite possible some slight settlement had occurred2 this1 as the spans were so small1 would have a sensible effect4 ,while too much reliance should not1 it is clear1 be placed upon any estimated result about which there is a lingering doubt1 it should be remarked that1 as it would be necessary the pier should sink #c_/af of an inch1 for each ton of reduced stress1 it is not probable that the results quoted are in excess to any material degree2 they are1 indeed1 more probably low1 as no notice has been taken of impact4 ,though cast-iron girders for railway under-bridges are now prohibited in this country for new works1 there are still uses to which they may be applied1 and it may be well to insist that girders of this material should be fairly loaded1 the weight being brought upon them in such a way that there shall be no serious secondary stress1 such as arises when wide flanges are made to carry concentrated loads2 the author has1 indeed1 met with no instance of a cast-iron girder breaking down under a load fairly applied4 ,preference is now given to steel or wrought iron for columns2 while this is often quite justifiable1 there remain many cases in which nothing better need be desired for this purpose than good cast iron1 provided only that the column be loaded in a suitable manner--i4e41 axially1 and that the arrangement and details of the super-structure are such that there shall be no cross-breaking efforts1 or rocking of the column due to temperature or other causes2 unless1 indeed1 such cross-breaking or rocking is definitely taken into account in designing the work4 ,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 would1 in suitable cases1 the author has no doubt1 yield results just as reliable in practice1 with the advantage of greater resistance to rust1 and a reduced cost in maintenance4 ,good cast iron is1 in fact1 when used with discretion1 a most excellent material1 popular predjudice notwithstanding4 ,the oldest metallic bridge in this country at the present moment is of that metal4 ,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 intact1 or it breaks4 ,the indications of weakness1 which may be read by an experienced inspector of other metallic bridges1 are in a great measure absent4 ,there is also an objection which may exist1 but is to be avoided by good design and care in the foundry--viz41 internal stress due to unequal cooling4 ,in extreme cases this may lead to fracture before the work has left the maker's hands1 but it can only occur by neglect of ordinary precautions4 ,illustration3 ,,figs4 #hb and #hc4 ,in a case which has already been referred to in the chapter on 8,deformations10 page #hj1 an outer rib of a cast-iron arch fractured near the crown after fifty-four years' use4 ,owing to the nature of the design1 and the fact that the near abutment had closed in slightly1 bringing the linear arch of necessity near the lower edges of the arch segment in question1 it was possible to estimate1 with a probability of truth1 the extreme fibre stress 7tensile7 due to the load forces1 at the upper edge where fracture commenced4 ,the result was very far from explaining the occurrence of the break1 but an examination of the details shown in ,figs4 #hb and #hc will make it apparent that1 in addition to the tensile stress1 as calculated1 there was probably a severe initial stress of the same character due to irregular cooling in the foundry half a century before4 ,the sum of these stresses1 it is suggested1 placed this particular casting in a critical condition1 such that operations in the construction of a new bridge adjacent either by producing a small further settlement of the foundations1 of which the author saw no evidence1 or1 as is more probable1 the attachment of a rope to this rib for the purpose of keeping a barge in position1 which certainly did occur1 gave the arch rib just such an additional strain as to result in the break shown1 though no one of these causes acting singly would have been sufficient to induce fracture4 ,the inner ribs were of a much less objectionable section4 ,illustration3 ,,fig4 #hd4 ,cast-iron arches1 though still allowed by the ,board of ,trade rules1 are1 indeed1 liable to be seriously affected by settlement1 or yielding of the abutments1 unless hinges at the crown are introduced4 ,as an instance of this may be quoted a bridge of some #de feet span1 in which the arches were cast in two pieces abutting1 and very efficiently bolted together at the crown1 the springing and vertical abutment member of the spandrel being bolted and built solidly into heavy masonry4 ,the arch sank at the crown1 caused by1 or itself the cause of1 a movement of the abutment1 with the result that the lower bolts at the crown joint broke away1 rupturing the casting1 as shown in ,fig4 #hd4 ,the arch must then have acted as though hinged at the crown1 as effectiveness of the connection was destroyed4 ,it had been better1 evidently1 if a proper hinge had originally been provided4 ,the break happened to occur so as to leave a sufficiently good bearing face at the crown2 there was1 indeed1 no tendency for one surface to slide upon another2 but in the accidental fracture of cast iron this cannot be assured1 and the liability to it is a risk which should be eliminated if possible4 ,a second case of very much the same character has also been under the author's observation1 though in this the ends of the spandrels were not built into the brickwork of which the abutments were composed4 ,other instances of fracture either in the arch proper or in the spandrel work1 have come under notice1 though particulars cannot now be adduced2 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 equivalent1 unless the abutments1 being exceptionally well founded1 may be relied upon as free from any liability to move4 ,it is1 however1 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 design1 so that what may be negligible in the latter case would perhaps be destructive in the former4 ,to the absence of ductility and liability to initial stress must be added yet another disadvantage to which cast-iron work is prone--viz41 the possibility of concealed defects1 blow-holes or cold-shuts2 these in good foundry practice are not very likely to occur1 but1 as they are possible1 cannot be overlooked in considering the suitability of cast iron for bridgework1 or1 indeed1 any structural work liable to serious stress1 and particularly tensile stress4 ,with these remarks by way of qualification1 the author reiterates his opinion that there is still a use for cast iron in bridgework4 ,with respect to the repair of cast-iron bridges1 but little is to be said2 the possibilities in this direction are very limited4 ,occasionally it may be desired to deal with the fracture of some member in the spandrel bracing of an arch1 when it is commonly sufficient1 and even preferable1 to limit the repair work to confining the fractured parts in such a way as to prevent displacement4 ,rarely it may happen that an arch fractures as a result of settlement1 or other movement1 when1 if it is decided that safety of the structure is not imperilled1 it will in this case also be preferable to confine the parts simply by flitch-plates or other contrivance1 with no attempt rigidly to make good the break1 the consequences of which treatment would probably be to induce fracture in some other place4 ,effective strengthening of a cast-iron structure is seldom practicable1 though something may occasionally be done by the negative process of lightening the dead load1 or by remodelling the permanent way4 ,arches may1 however1 be rendered much more reliable by the introduction of suitable bracing where this is either wanting or inefficient4 ,in scheming such additions it is desirable to arrange for as little drilling of the old work as is possible2 where this cannot be altogether avoided1 the position of the holes should be carefully chosen with regard to the effect they may have upon the strength of the old work4 ,,chapter ,,xiii4 ,,timber ,,bridges4 ,timber bridges1 though probably the most ancient in type1 are yet the least durable in any particular instance4 ,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 structure4 ,in addition to decay in the body of the main members--which may perhaps be long delayed1 so that a simple beam bridge may last for many years--there is in more complex designs decay at connections and joints1 which proves very detrimental to the integrity of the whole4 ,water running upon the surface of a member gravitates to its lower end1 and1 if there be a joint or other connection1 settles there1 to be productive of lasting mischief4 ,from this cause1 together with a very common deficiency of bearing surface relative to the forces to be met1 the joints soon develop some movement2 working of the structure commences under passing loads1 its final destruction being then a question of time only4 ,each joint is1 in fact1 in timber bridge construction a source of serious weakness to a degree which has no parallel in well-designed metallic bridges4 ,wrought-iron straps to confine the ends of raking members1 or for other uses1 are liable to crush into the wood1 and bolts are apt to enlarge the hole through which they pass4 ,wood keys1 where these are introduced to prevent one timber from sliding upon another1 are also prone to develop cracks in the main members1 and fibre crippling from excess of stress4 ,all these defects are1 however1 in timber-work more easily defined than efficiently remedied1 as it is barely practicable for any but the harder woods to ensure1 for heavy loads1 a sufficiency of bearing surfaces4 ,the most readily detected evidence of deterioration in timber bridges is the sag of its bearing members1 or trusses1 for the simple reason that if there is no local trouble at the joints1 there will probably be no appreciable drop at the centre of the span4 ,the existence of such a depression may1 however1 be caused in rare instances by the spread of the supporting piers or abutments1 particularly in the case of beams trussed by end diagonal rakers and having no tie4 ,bridges formed of deep trusses1 with the road upon the top1 are sometimes found to be wanting in lateral bracing1 the result of which is that the main trusses go out of line1 leaning considerably one way or the other1 being checked only by such rigidity as the joints and floor-beam attachments may have1 with possibly some assistance from the end connections of the span4 ,the decay of piles where entering the ground or water is1 of course1 a fruitful source of trouble1 as also is the sinking of piles1 where these are insufficient in number1 or have not been well driven in the first place4 ,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 started4 ,timber does not necessarily show upon its surface the evidences of internal rotting4 ,memel timber may1 indeed1 be sometimes found to have become thoroughly unreliable1 yet showing no sign of this upon its painted surface4 ,by sounding the wood with a hammer1 or by probing1 its condition may commonly be ascertained4 ,in cases of doubt1 an auger-hole will make it clear as to whether the interior be good or otherwise1 as to the particular parts tested2 but only as to those parts1 leaving it a matter of guesswork as to the remainder4 ,illustration3 ,,fig4 #he4 ,a railway bridge having many of the defects which have been indicated may be quoted as an example4 ,this structure crossed a canal1 supported upon piles1 some of which were in water1 others carrying land spans4 ,the canal span consisted of four trusses1 one under each rail1 or nearly so1 framed in the manner shown in ,fig4 #he1 precise details not1 however1 being now available4 ,the trusses1 apart from deflection under live load1 sagged considerably--in one instance1 #d-a_/b inches2 one inside truss was also leaning towards the centre line of the bridge as much as #c inches4 ,one raker1 or diagonal strut1 was rotted half through its thickness1 and many other timbers were badly decayed4 ,the end connections and joints were also in a bad condition4 ,the vertical tie-bolts of the main trusses were all slack4 ,the piles generally1 many of which were badly decayed1 had sunk and inclined towards one end of the bridge about #d inches in #g feet of height1 the ground being soft and unreliable4 ,movement under a passenger train crawling over the bridge was very appreciable1 but not startling4 ,there had been introduced1 from time to time1 additional timbers and iron ties1 with the object of rendering the spans more reliable1 but leaving it somewhat difficult to determine the function of the several members4 ,the bridge was1 of course1 reconstructed4 ,illustration3 ,,fig4 #hf4 ,illustration3 ,,fig4 #hg4 ,illustration3 ,,fig4 #hh4 ,an instance may here be cited showing how badly distorted a timber structure may become without actually falling4 ,the bridge referred to consisted of three spans of #bi feet1 each span having two trusses1 between which ran a colliery tramroad1 #a-;foot #f-;inch gauge2 the corves running upon this1 at #d feet #f inch centres1 weighed1 when full1 about #aj cwt4 each4 ,the trusses were badly out of shape1 the centre span having sagged #e-a_/b inches1 with one truss of the same span nearly #aj inches out of line at the centre4 ,this little bridge1 of which some details are shown in ,figs4 #hf1 #hg1 and #hh1 had been in use about twenty years4 ,illustration3 ,,fig4 #hi4 ,a third case which may be named is that of a road bridge1 about #ab feet wide1 crossing by thirteen spans a shallow river liable to floods4 ,the construction was of a simple character1 as indicated in ,fig4 #hi1 and consisted of piles supporting trussed beams1 which had sagged in some instances over #b-a_/b inches4 ,the bridge had1 some years previous to the author's inspection1 been heavily repaired1 many new strut and stretching pieces having been introduced1 the piles also being reinforced or renewed4 ,five years before1 a traction engine1 said to weigh #e tons1 had passed across the bridge in safety2 but the author noticed that a coal wagon1 which1 with the horse1 weighed about #ej cwt41 when walked slowly over set up much movement4 ,this bridge had been in use nearly thirty years1 and was very much out of line from end to end4 ,though timber bridges cannot at the best be considered durable1 yet1 by attention to certain points in design and construction1 their length of life may be materially enhanced4 ,every cut across the grain may be considered an element of weakness by exposing the material to quicker decay1 for which reason the number of ends1 or of joints1 should be reduced to a minimum4 ,an additional reason for reducing the number of joints or other connections is the liability of these to develop movement1 as already stated1 the yield of any one joint1 being the cause of movement in others1 which might1 but for this1 have remained close4 ,these considerations lead to the conclusion that fewness of parts is1 in timber construction1 as in structural work generally1 an excellent principle to observe4 ,mortising1 elaborate scarf joints1 recessing1 or any cutting into the timber which is not essential1 should be avoided1 the simplest forms of connection being preferable1 if at all suitable4 ,if a step or butt surface is wanted for any member1 it is commonly better to provide this by a cleat or other added piece1 rather than by cutting into the timber butted against4 ,a complicated joint formed in the body of main timbers can only be renewed by renewal of the timber itself1 whereas by the method indicated the joint is readily tightened1 or re-made1 without involving the main member4 ,bearing surfaces should be ample1 straps of liberal dimensions1 and bolts large 7with good washers71 both for the sake of bearing surface in the holes1 and reduction of any liability to bend under cross-stress4 ,in trusses of the form shown in ,figs4 #he and #hf1 it is desirable to introduce diagonal members in the middle bay1 even though it may appear that the stiffness of the main beams is sufficient to render this unnecessary as a matter of strength1 as without these there is apt to be1 under rolling load1 a slight distortion1 leading to working of the joints and free entry of moisture4 ,lateral bracings should also1 for much the same reasons1 be introduced1 even though they may not appear necessary in the new structure1 with joints all close and effective4 ,projecting ends of timbers should be carried out well beyond the requirement of strength or bearing1 in order to ensure a liberal margin for that decay in the end fibres which commonly develops4 ,timbers resting upon abutments1 or running into confined spaces1 should be arranged for free ventilation and ready drying4 ,occasionally joints at the lower ends of timbers are protected by lead or zinc flashings to prevent water running into them1 a method which should have some protective value4 ,whatever measures may be adopted1 whether in the design or execution of timber bridge-work1 will1 however1 be but little effective1 if the timber itself is not good of its kind1 and well seasoned4 ,creosoting to be useful should be thorough and something more than skin deep4 ,the timber itself should be well dried before treatment4 ,the repair of timber bridges very largely consists in the renewal of decaying timbers1 where this is practicable1 or in adding supplementary pieces where the old cannot conveniently be displaced4 ,joints may be tightened up by hard-wood wedges1 properly secured to prevent slacking back1 all bolts being also screwed up tight1 perhaps some additional being introduced4 ,piles standing in water1 which have decayed1 may be strengthened by driving other piles between the old1 or on either side1 but not of necessity opposite to them1 and by means of waling timbers bolted to the old piles1 put in a position to take load1 either by the walings resting upon their tops1 or being bolted to them4 ,piles decayed where entering solid ground may generally be strengthened by bolting on supplementary timbers to reach well above and below the decayed part1 or by cutting out the bad length1 introducing a new piece1 and fishing the butt-joints in a proper manner4 ,but all remedial measures have generally to be considered with reference to cost1 as compared with the probable increase of life of the structure4 ,with a bridge in an advanced state of decrepitude1 such repairs may prove anything but economical1 and at the best defer reconstruction but a very moderate length of time4 ,,chapter ,,xiv4 ,,masonry ,,bridges4 ,masonry bridges1 in which description it is intended to include structures both in stone and brick1 are1 when well built1 amongst the most durable and long-suffering of any which come under the care of a maintenance engineer2 yet when developing the faults peculiar to their kind1 they may be the occasion of much anxiety1 and render necessary frequent inspection1 or even continuous watching4 ,apart from decay of mortar or material1 defects may very commonly be traced to the foundations1 or to earth-slips4 ,sinking1 when uniform1 may be quite harmless1 though possibly inconvenient2 irregular sinking of piers or abutments is quite a different matter4 ,it is1 however1 remarkable to what a degree sinking may be evident1 without of necessity rendering a structure unsafe4 ,movement of an amount and kind which would be fatal to the connections of metallic bridgework is endured by bridges of stone or brick2 not1 it may be1 without damage1 yet with no occasion for alarm4 ,the superstructure of metallic bridges may often1 however1 be restored to the true level before the mischief has become serious1 whereas in the case of masonry arches this is not practicable4 ,spreading of the abutments is very seldom the cause of any great injury to an arch1 though it is common enough to find old and flat arches slightly down at the crown2 but the contrary case of abutments closing in is not very unusual when these are high1 or terminate a viaduct over a deep valley4 ,such an abutment may move during or soon after construction1 throwing up the crown of the end span affected2 or1 if the arches are very solid and heavy1 the abutment may slide forward at the base1 with no sensible reduction of the opening4 ,when a viaduct connects the two ends of a high embankment1 it may happen that the end piers are not clear of the embankment slope1 in which event a pier may1 should the bank slip1 move with it1 as to that part not in solid ground2 with the result1 in a bad case1 that it is broken across and the superstructure imperilled4 ,illustration3 ,,fig4 #ij4 ,a case of abutment movement is illustrated in ,fig4 #ij1 which represents the end arch of a masonry viaduct1 one abutment of which had moved forward in the manner already referred to4 ,from the springing upwards the arch retained its form to within a short distance of the crown1 where it was forced up in the way indicated4 ,when the movement became pronounced1 heavy timber centering was introduced1 with the object of preventing any mishap1 the damaged portions being ultimately cut out and made good4 ,the structure was thirty-five years old4 ,the practical utility of stop piers in long arched viaducts is1 perhaps1 rather in checking movement of the tops of piers under moving load than in arresting actual failure of a series of arches4 ,that the tops of piers do move very sensibly need not be doubted4 ,the author has attempted to measure this in the case of piers about #fj feet to the springing1 by means of a theodolite placed below1 but has reached no more definite result than that a movement existed1 of which he was not able to determine the amount4 ,if in a viaduct some arches are more heavily loaded than others1 each spreading slightly1 the end piers of the group will move amounts which together equal the sum of the individual span spreads1 with a tendency in the arches beyond those of the group overloaded to rise4 ,this rocking may be detrimental both to the piers and arches1 and helps to account for the disintegration of mortar in arches and piers1 which not infrequently happens4 ,the soffits will sometimes be seen with a thick incrustation of lime1 which has washed out of the joints1 or from limestone ballast above1 where this has been in use4 ,arches of tall viaducts may1 indeed1 become in so bad a condition that pieces of stone or brick will drop out1 necessitating repair at heavy expense1 of which scaffolding is commonly a large part4 ,tall piers may be found badly out of the upright due to sinking of foundations4 ,a marked case of this kind came under the author's notice--a viaduct of fifteen semicircular arches1 in which1 though many piers were wanting in truth1 one in particular was about #a foot #d inches out of vertical1 making one side of the shaft plumb1 and doubling the normal batter of the other4 ,inquiry showed that in this instance the pier had never been upright from its earliest history dating back thirty-six years4 ,this makes clear the desirability1 to avoid hasty conclusions1 of ascertaining1 when it is possible to do so1 the complete record of any structure4 ,a bridge fifty-eight years old1 of three skew spans1 carrying a railway over a canal1 and having somewhat flat brick arches with stone quoins upon low piers1 developed the somewhat unusual defect1 as to the centre arch1 of splitting along its length for about #aj feet1 parallel to and some #g feet from one face4 ,in this case there was reason to believe that there had been considerable local settlement of the piers on that side of the bridge4 ,the arches were otherwise in bad condition1 the brickwork poor1 and the mortar decayed4 ,each arch was down at the centre1 and displayed a fault not unusual where bad brickwork joins up to good cut stonework1 the quoins showing a tendency to separate from the brick rings4 ,below the bridge were coal-workings4 ,brick arches built in parallel rings sometimes separate one ring from the other1 demonstrating the known propriety of bonding the rings together properly1 and of carrying the arch round1 when building1 at its full thickness4 ,illustration3 ,,fig4 #ia4 ,an instance of bridge failure from a somewhat peculiar cause may be quoted as of some interest1 largely because the structure was very ancient1 having been in existence some #djj years4 ,this bridge1 carrying a road1 was of the type usual in old masonry bridges over a river1 having small arches1 thick piers1 and solid backings to the arches4 ,two flood-openings at one end had1 by sinking and want of care1 become partly closed4 ,the centre arch had1 however1 been widened about #adj years previously4 ,during a severe flood1 the swollen river1 overflowing its banks1 trespassed upon a timber yard a little above bridge1 and washed down into the stream a large quantity of sawn timber2 this1 unable to get through the main arch with freedom1 compacted into a serious obstruction4 ,the flood water1 thus checked in its passage1 seems to have scoured below the timber1 and robbed the piers of such support as they formerly had 7see ,fig4 #ia74 ,the bridge stood in this condition till the water lowered1 when the middle part of the structure broke up1 and subsided into the hole which had been washed out4 ,but for the monolithic character of the old work it is probable the bridge would have failed long before1 as the gravel bed on which the piers stood had been partly undermined for very many years4 ,the case is instructive1 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 water4 ,illustration3 ,,fig4 #ib4 ,the enduring character of even the roughest class of masonry arch1 if only the material be good and abutments stable1 is shown when it becomes necessary to destroy old work of this character4 ,fig4 #ib represents a short length of 8cut and cover0 arching in process of demolition1 just before it fell in4 ,the masonry was of hard sandstone rubble and had been cut away1 as shown1 till at the point ,a only a very small piece of the arch remained1 when the length finally broke up and dropped4 ,arches have commonly a great reserve of strength2 tunnel linings are1 indeed1 often badly out of shape1 closed in1 and sunken2 yet continue1 with close watching1 and occasional repairs where the work has decayed or bulged1 to serve the purpose intended4 ,though the equilibrium of masonry arches has been the occasion of much profound study1 and the nicest calculation has sometimes been applied to the design of such work1 yet it appears that when an arch is well backed up1 the theoretical linear arch need have but little connection with the figure of the intrados2 a statement consonant both with common-sense and the teachings of experience4 ,with solid backing1 this would indeed seem to be more important than any part of the arch ring below the top of the backing1 the lower part of the ring serving chiefly to preserve the face of the solid work4 ,arches are frequently to be met with so out of their true shape that but for the consideration named1 failure would seem to be inevitable4 ,the masonry or brickwork does not always show evidence of damage1 if the distortion has been slow2 suggesting that structures of this kind have a power of accommodation with which they are not generally credited4 ,a noticeable cause of deterioration of masonry structures1 which may be quite independent of settlement1 is serious vibration4 ,this is well known in connection with church belfries1 and is also locally apparent when telegraph or other poles are attached to masonry parapets4 ,vibration1 when caused by heavy railway traffic1 acting upon arches light or originally bad1 may demoralise the structure to such an extent that repair becomes exceedingly difficult1 because of the extensive character of the mischief2 but masonry bridges substantially built1 and particularly those carrying ordinary roads1 and not subject to much vibration1 have great lasting powers1 if repaired with skill1 or even let alone4 ,distortion of the arch may be quite consistent with practical stability1 if the movement or decay with which it originated is not progressive1 or has been arrested4 ,in this connection a distinction is to be made between arches well backed1 to which the foregoing remarks apply1 and in which the two halves of each arch may act as separate monoliths meeting at the crown1 and the case of a true arch ring independent of any outside resistance1 such as backing or spandrels may give1 and depending almost wholly upon the proper balance of its component voussoirs for its stability4 ,with the latter class of structure no liberties may be taken2 whilst with the former there is seldom cause for fear1 if the foundations do not give way1 and the work is dealt with judiciously1 if at all4 ,it must1 however1 be understood that there are limits as to what may be done effectively1 short of rebuilding1 in dealing with structures in which1 perhaps1 brickwork is rotten and mortar decayed and crumbling1 the whole being little better than a broken mass of rubbish4 ,in cases where it may be prudent to introduce safety centring1 as in an instance already referred to1 it is commonly expedient to refrain from causing this to take any sensible part of the load till all movement has ceased1 the centres being at the outset largely precautionary4 ,the requirement with an arch in bad condition is to avoid disturbing it for the worse4 ,if the centres are wedged up whilst movement is still going on1 the effect may be to cause the arch to break up upon the centring1 and precipitate repair work which might otherwise have been left to a more convenient time1 when all movement had stopped or been checked by suitable measures4 ,viaduct arches in a bad condition1 but not necessitating the use of relief centres1 are commonly dealt with piecemeal by cutting out the bad places1 a small part at a time1 and making good4 ,the work requires the greatest care of experienced men4 ,pointing masonry or brickwork is effective for little other than protective purposes1 and to check further weathering2 it has obviously no effect upon the interior work1 and if made to cover up the evidences of internal decay1 is even misleading and objectionable4 ,in extreme cases it may be desirable to open out the road and deal with the filling1 to relieve or to strengthen the outer spandrel walls1 which sometimes bulge1 or for other purposes1 as1 for example1 for rebuilding inner spandrel walls1 grouting up or otherwise repairing solid backing1 in which operations some regard must be had to the effect of the work upon the balance of the opposing halves of the arch4 ,of the different classes of masonry commonly used in bridgework1 it may be well to remark that good coursed rubble1 or preferably that variety bonding both vertically and horizontally1 of a durable stone1 perhaps quite unfit for any but rough dressing1 may make a most lasting structure1 the mortar1 of course1 being good4 ,each rough-dressed stone presents a durable piece1 fragments removed separate from the block1 probably along some line of relative weakness--there is no 8nursing0 of weak corners2 whereas with stones reduced to a perfectly regular shape by chisel work1 the plane surfaces and geometrical angles are made with partial regard only to the natural grain of the stone4 ,,chapter ,,xv4 ,,life ,,of ,,bridges--,,relative ,,merits4 ,the life of bridges of differing materials has been incidentally touched upon by the examples quoted1 in dealing with each class of structure4 ,it will be useful to recapitulate some of the facts adduced1 and to compare the terms of life so far as they appear to be indicated2 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 history4 ,the duration of any such structure may be limited by adverse conditions1 peculiar to the case considered1 by defects of design1 material1 or workmanship--present from the first--or by neglect1 overloading1 or accident1 making up its later record4 ,with the exception of timber structures1 it is difficult to find any class of bridges furnishing examples which have reached the limit of life1 independently of the evils named1 and as a result of unavoidable decrepitude4 ,there are none the less influences at work tending to this condition1 and which it is too much to expect can in all cases be foreseen or completely guarded against1 such as the shifting or scouring of river-beds1 settlement of foundations1 natural decay1 and minor faults in design1 which even in the most capable hands may be expected ever to fall short of perfection4 ,at the best1 then1 the life of any structure1 though long1 must have a limit4 ,with bridges of more average or inferior qualities the life may be positively short1 even without the destructive influence of overloading4 ,dealing with instances of metallic bridges1 the adjacent table gives the time each had been in existence when removed1 and some indication of the reason for its condemnation4 ,those marked with an asterisk were cases of pronounced high stress4 ,from a study of the table it appears that in actual practice1 making no excuses of any sort1 the length of life of the wrought-iron bridges specified varied between twelve and thirty-six years2 but these figures applied to this collection of cases only4 ,it is to be remarked that many other bridges outlasted these1 and are likely to continue reliable4 ,these results show1 then1 no more than that some wrought-iron bridges are short-lived1 having1 in fact1 been selected as examples of this4 ,longer-lived exceptions are useful1 as indicating that the durability of such structures is by no means so limited as the table would suggest4 ,it is to be observed that1 as design and maintenance are now better and more generally understood than when experience was largely wanting1 it is to be expected that later examples will show no such poor results4 ,of steel bridges little can be said1 because of the limited time this material has been in use2 but the generally acknowledged belief1 quite in agreement with the author's observation1 that steel rusts more freely than wrought iron1 suggests that such bridges will have a shorter lease of life1 the more so that the surface-to-section ratio is also greater for higher unit stresses1 though other adverse influences are much the same for one material as for the other4 ,of cast-iron structures but few cases have been given2 of these1 cast-iron arches have been noticed as developing defects which led to reconstruction1 or to limiting the loads to be carried4 ,plain cast-iron girders1 on the other hand1 have never1 under the author's direct observation1 been removed for any other reason than because they were cast iron1 or from over-stress1 due to the growth of loads2 never from defects or wasting1 though it is not suggested no such cases exist4 ,the author has no evidence which points to what may be the limit of life of a good cast-iron girder fairly treated4 ,examples of ,life of ,metallic ,bridges4 ---------------------------------------- -------------------------- ,description4 ,span4 ,age4 ,defect4 ,reference4 ---------------------------------------- -------------------------- ft4 in4,years4 ,wrought ,iron4 ,plate girders 787 #ab ,loose rivets 99,ditto #ce #j #ab ,ditto p4 #eb ,ditto #ee #j #ad ,rust4 ,distortionpp4 #gh #ig ,trough girders #aa #j #af ,loose rivets4 p4 #ej ,cracked webs ,plate girders 787 #bb ,loose rivets ,twin girders #ca #f #bc ,weak4 ,cracked p4 #ac webs ,ditto #ce #f #bc ,weak4 ,distorted4p4 #gd ,plate girders #db #j #bc ,loose rivets4 p4 #ba ,cracked webs ,ditto #gb #j #bi ,weak4 ,loose p4 #ec rivets ,ditto #dg #j #bd ,distortion p4 #i ,ditto #cb #j #cb ,rust4 ,cracked p4 #ad webs 99,ditto #be #j #cf ,weak p4 #fc ,steel4 99,trough girders #ae #h #cb ,weak4 ,rusted pp4 #fh #ih ,cast ,iron4 99,girders #cb #j #cf ,weak p4 #ada ,girders1 cast-iron piles 787 #dd ,ditto ,arches #de #j #ee ,crack4 ,settle- p4 #ade ment ,ditto #ajj #j #fb ,crack4 ,deforma- pp4 #hj #ade tion ---------------------------------------- -------------------------- ,with timber bridges the length of life appears to be about twenty-five years1 but this is very largely dependent upon the question of maintenance1 and may range from fifteen to thirty-five years4 ,it is manifest that repairs1 when extensive and consisting of the renewal of the more essential parts of the structure1 border upon reconstruction1 and may be continued indefinitely4 ,the length of life in ordinary cases1 and for the timbers commonly used in this country1 may1 for railway bridges1 be taken as stated1 though for highway bridges possibly longer4 ,of masonry bridges little is to be said but that it is only in cases of bad work or material--with1 perhaps1 vibration or settlement--that these have a shortness of life comparable with that of defective metallic bridges4 ,where these adverse conditions obtain1 heavy repairs may be necessary before the structure is many years old2 but1 under reasonably fair conditions1 bridges of masonry may be expected to outlast structures in any other material4 ,apart from road-bridges which are admittedly long-lived1 there are a large number of railway bridges and viaducts of masonry which1 despite heavy loads and vibration1 have been in use for the past seventy years4 ,dealing with the cost of maintenance1 this with bridges of wrought iron or steel should result simply from scraping and painting1 with such other incidental work as may be necessary on the subsidiary materials used in the structure4 ,the cost of painting will vary with the height and character of the bridge1 and the amount of scaffolding1 if any1 and may be from #e;d4 to #as4 or more per square yard2 this if distributed over five years1 a not unusual interval between each painting1 works out at an appreciable figure1 which may vary from one-third to one per cent4 of the first cost1 per annum4 ,the yearly cost of painting steel-work will1 for shorter intervals1 come to a somewhat higher figure4 ,serious occasional items of expense are those which should not be necessary1 repairs and possibly strengthening1 which may raise the total cost of maintenance very considerably4 ,cast-iron bridges1 being less liable to rust1 cost less for painting than other metallic bridges2 and if the cast iron is closed in by masonry1 practically nothing2 they do1 indeed1 involve very little expenditure in the maintenance4 ,not being very amenable to repair or strengthening1 cast-iron bridges commonly remain very much as built1 or are reconstructed4 ,the proper care of timber bridges may become costly as the structure gains in age1 and soon grow to a very wasteful expenditure4 ,this is evident when it is considered that repairs may be necessary after ten years1 and that whatever may have been the cost of any part when new1 it cannot be replaced for the same amount1 having regard to the labour expended in removing the old member1 and the special precautions to be observed in dealing with an old structure carrying its load4 ,in addition to ordinary repairs1 there will be paint or other protective coating to be applied1 though this is not always done4 ,the upkeep charges of masonry bridges will be practically nothing in favourable cases2 but1 on the other hand1 where extensive repairs become necessary1 may reach a considerable amount4 ,exceptional outlays are1 however1 infrequent1 and may be spread over a large number of years1 in those rare instances in which they become imperative4 ,durability4 ,maintenance ,first ,cost4 ,charges4 ,masonry ,masonry ,timber ,cast ,iron ,cast iron ,masonry ,wrought iron ,wrought iron ,steel ,steel ,steel ,cast iron ,timber ,timber ,wrought iron ,for purposes of ready comparison1 placing bridges of the materials under review in order of durability1 they would appear as in column #a of the table above2 in order of low maintenance charges1 generally as in column #b2 and in order of low first cost1 as in column #c4 ,with respect to the question of first cost1 the arrangement of the third column applies only to small bridges1 say1 up to #gj-;foot span2 and1 being liable to variation with the conditions1 is but approximately correct4 ,the less costly descriptions of masonry are alone considered in this connection4 ,it may be added that the total yearly charge of interest on first cost1 redemption1 and maintenance1 appears to be for masonry bridges1 about one-half only of the corresponding totals for bridges of wrought iron1 steel1 or timber2 those of cast iron taking an intermediate place4 ,summarising the above considerations1 and dealing with the relative merits of bridges in the different materials1 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 bridges4 ,one pronounced advantage of such bridges with respect to length of life1 is that they are but little affected by increase of loads4 ,the mass of a masonry arched structure is so great1 and the margin of strength commonly so liberal1 that considerable increments of load may have but little effect upon the reliability of the structure4 ,cast iron has1 for bridges of simple design1 a strong claim to the second place1 though its want of ductility is a demerit4 ,it can1 however1 have but a limited use in bridge construction1 being applicable only to small girder spans and skilfully-designed arched structures4 ,for bridges of moderate span in which the question of cost does not control the matter1 wrought iron should probably come next1 steel being best reserved for those of a larger size1 in which weight of the structure greatly affects economy4 ,timber may be regarded as a material rarely to be used in this country for structures to occupy a permanent place1 unless for urgent economic reasons of the moment4 ,while expressing this general view of the matter1 it is to be admitted that the propriety of these conclusions is somewhat discounted by the difficulty there now is in obtaining cast iron of the desired toughness1 or wrought iron with promptitude and sufficient variety of section at a reasonable price4 ,it is apparent1 also1 that the choice of material may be largely influenced--even determined--by considerations of headway1 construction depth1 or character of foundations2 so that no very definite rules can be usefully laid down1 though the adoption of unsuitable materials has not been so unusual as to make these suggestions altogether purposeless4 ,,chapter ,,xvi4 ,,reconstruction ,,and ,,widening--,,conclusion4 ,the need for the reconstruction of bridges1 arising from various causes which have been treated in the preceding chapters1 original weakness or faults in design1 decay or defects1 may also be caused by such extraneous considerations as the growth of loads1 widening of the openings spanned1 or improvement of the headway4 ,in any case1 a precise survey or measuring up of the structure and its immediate surroundings is required1 in the execution of which the greatest care is desirable1 and with respect to which it may be well to give a few hints4 ,the surveying chain1 when used1 should be tested1 the measure of accuracy required rendering this imperative in a degree peculiar to work of this class4 ,linen tapes should also be compared with a reliable steel tape1 and used only where sufficiently accurate for the particular purpose4 ,a careful and observant man may do very good work with a linen tape1 making just that allowance in the sag of the tape which corrects for the inevitable stretch2 but there is still some uncertainty involved in its use1 and the author prefers to rely upon a steel tape1 notwithstanding the inconvenience commonly experienced from its intractable nature and liability to damage4 ,instruments used must also be in the best adjustment2 as errors1 which in ordinary field work may not be of great importance1 are inadmissible in bridge work4 ,it is not necessary here to enter upon the methods of small survey work1 but it may be desirable to point out that abutment walls should be plumbed for verticality2 girders1 which are liable to be leaning1 defined in position by reference to their bearings2 and generally that it should never be taken for granted that there is truth in old work1 or that this may be assumed as to line or level4 ,in cases where disputes with any local authority as to headway are likely to arise1 it is prudent to supplement the information as to level of soffits by rods cut to length in strict agreement with the clear height1 before removing the old superstructure4 ,it is apparent that in cases where the superstructure is already condemned1 the detail measurements may be confined to that part of the structure which is to remain1 securing only such information as to the work superseded which may be required in arranging for the new work4 ,in taking particulars of skew bridges1 needless as the warning may seem1 it is yet necessary to remark that there may be right or left-hand skews which will not reverse4 ,the author has known a disregard of this to make serious trouble in two instances4 ,dealing first with reconstruction of the superstructure of railway under-bridges1 these1 if small1 may not give much trouble1 though the demand for greater strength will1 perhaps1 involve some difficulty in working to the limiting construction depth--i4e41 the distance from the top of rail to soffit of bridge--particularly as many old bridges have a very niggardly allowance in this respect4 ,it may be1 and quite commonly is1 necessary to raise the rails a small amount1 or1 if headway is not restricted1 to lower the soffit4 ,clearances between the running gauge and girder-work may also be difficult to secure1 more liberal allowances being now required than formerly4 ,complications in the character of the permanent way1 so frequently found upon old bridges1 should1 of course1 be got rid of1 if possible2 but the endeavour may introduce further difficulties4 ,regard must throughout be had to the methods to be adopted in removing old work and in erecting the new4 ,perhaps the simplest case to deal with is that where girders lie parallel to1 and under the rails1 with a timber floor upon which the permanent way is carried1 as sections of the road involving pairs of girders may be readily removed1 and replaced by the new girder-work 7see ,fig4 #ic74 ,if the deck be of trough flooring or old rails1 the matter may not be so simple1 as regard must then be had to the position of joints in the existing floor1 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 road4 ,a slight slewing of rails may sometimes be resorted to on occasion1 where this has the effect of releasing some part of the work not otherwise to be dealt with4 ,illustration3 ,,figs4 #ic and #id4 ,bridges having main girders1 with timber or trough flooring resting upon the bottom flanges1 or suspended by bolts1 will1 if carrying many roads1 cause some little difficulty1 as the dismantling of any one span involves the disturbance of others2 where1 however1 many lines are concerned1 it may be feasible to put one or more temporarily out of use1 preserving the continuity of traffic over those which remain1 but refraining from any diversion of the more important roads4 ,somewhat similar troubles occur where main girders with cross-girders at the lower flanges are found1 particularly if the cross-girders are arranged in line1 the ends abutting on each side of the same main girder webs4 ,it is seldom1 however1 that this construction is used in bridges of small span carrying many roads2 but where it does occur1 it may necessitate the use of timbering below1 to carry the ends of cross-girders when freed from their supporting main girders4 7,see ,fig4 #id47 ,illustration3 ,,fig4 #ie4 ,if it is proposed to use new main and cross-girders1 it is desirable to arrange these in the manner already recommended1 the cross-girders not in line2 this has peculiar advantages in reconstruction work1 as the bolting up and riveting of the cross-girder ends is not hampered by other cross-girder attachments1 leaving each piece of floor complete in itself4 ,twin main girders are occasionally used with the same object1 and present the advantage of simplicity in erection and independence of one span from those adjoining 7see ,fig4 #ie72 but the method is wasteful of space1 and involves a somewhat greater total weight in the main girders4 ,the foregoing observations apply more generally to small single-span bridges1 the operations on which may be effected without any material disturbance of traffic arrangements2 though this can seldom be wholly avoided1 it should be confined1 where practicable1 to a few hours on a ,sunday4 ,the reconstruction of bridges over #gj-;feet span may have to be dealt with under more elaborate arrangements1 if carrying two lines only1 possibly with single-line working for a period more or less protracted2 or it may be necessary1 having regard to the weight of main girders to be removed1 to carry the whole structure upon temporary staging1 supporting the road independently1 cutting up and removing the old work1 and later putting the new work in place1 either by detailed erection in its ultimate position1 or by erection at one side and drawing across4 ,the latter method is1 however1 commonly reserved for cases in which no special staging is used under the old structure4 ,bridges of a number of openings are usually dealt with by securing full possession of one road at a time1 which for double-line bridges necessitates single-line working4 ,it is commonly out of the question1 even with moderate spans1 to deal with some of these only at a time1 and so avoid continuous possession of one road1 for a lengthened period2 and it can only1 as a rule1 be managed where the ends of the new main girders do not in any way interfere with those of the old1 and where it is not necessary to reset bed-stones1 or make other alterations in the bearings which necessitate the complete clearance of the pier-tops4 ,in exceptional cases it may be found possible to arrange for the complete removal of a small number of moderate spans on a ,sunday1 and the putting in place of the new work1 as in the case of small single spans4 ,spans erected to one side of the final position1 to be later travelled across1 are commonly mounted upon gantry staging1 and up to #ej tons weight may rest directly upon rails well greased4 ,the power adopted to move the span is usually that of screw or hydraulic jacks1 or occasionally engine haulage1 special tackle being in that case necessary to apply the engine power in the right direction4 ,if the time is limited1 or weight considerable1 a more elaborate arrangement by which the load is supported upon wheels1 may be necessary1 with a view to reducing the resistance to a manageable amount4 ,all work which it is possible to do before shifting into place1 including the permanent way1 where this is of a special character1 should be executed in advance1 leaving only the rail connections to be made good when the span is in position4 ,where timber staging is used to carry the permanent way before dismantling an old structure1 it is convenient to begin by placing stout balks of timber under the sleepers from end to end of the bridge1 or directly under the rails if space is limited2 the staging is then arranged to give support to the running timbers4 ,metallic under-bridges of ample headway1 perhaps over coal-workings 7since settled down71 or for some less sufficient reason made of metal1 may be cheaply replaced by brick arches built below the old superstructure1 the springings of the arch being checked into the face of the existing abutments4 ,with stout walls1 careful work and good material will make this an efficient and durable job4 ,it being a primary condition of reconstruction work to interfere but little with ordinary traffic arrangements1 single-line working is avoided wherever practicable2 as this1 always objectionable1 may necessitate the erection of special signals and signal apparatus1 besides the temporary remodelling of the roads1 and in this country may involve also a ,board of ,trade inspection--altogether a troublesome and expensive business4 ,any bridgework which is accompanied by breaking or blocking the road can only be undertaken by arrangement with the traffic department1 after notice duly given and published in the periodical record of such matters2 it is generally fixed for a ,sunday4 ,preparatory to this1 it is necessary to make all ready by getting as much done beforehand as is possible4 ,wherever practicable and prudent1 the whole work is released from its surroundings1 masonry cut away1 rivets cut out and replaced by good bolts1 nuts removed from holding down bolts1 or the bolts cut through1 etc4 ,particular care should be exercised to ascertain what remains to be done immediately prior to removal4 ,it is necessary further to arrange for trucks to be in readiness to receive old material1 and others containing new girder work to be conveniently stationed1 having been loaded up to come right end foremost2 engine power1 cranes1 empty and loaded trucks1 being all marshalled and so placed as to be available in proper order1 and as wanted4 ,there must be no mistake as to what roads will be fouled by swinging the crane with its load1 or as to the reach of the crane in effecting its work4 ,the whole operation to be conducted on any ,sunday should be well within the resources of the men and plant engaged in it1 or so managed that it is a matter of no serious importance if the whole cannot be completed as originally desired4 ,possession of the roads to be blocked having been secured between certain hours1 if some part only of the work to be carried out has been completed as the time grows short1 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 considerable4 ,in scheming any reconstruction1 it may be insisted that at least one feasible method of carrying out the work must be secured1 though it is the author's experience that frequently some other method than that contemplated is in the end adopted1 when1 some months later1 the final arrangements for fixing are made4 ,the tendency of a zealous erector is commonly to take full advantage of any facilities offered1 with a view to a moderate amount of work being done at any one time1 and to achieve as much more as he can himself secure by scheming1 or a liberal use of labour2 all ,sunday work1 with attendance of engines and cranes1 being of necessity expensive4 ,railway over-bridges do not commonly present any particular difficulties4 ,the spans to be dealt with are usually small1 and the weights to be lifted moderate4 ,the height above rails may1 however1 be above the lift of any crane2 and1 for the purpose of raising main girders1 a derrick may become necessary1 the rearing and guying of which may block many roads during the time it is in use4 ,the girders of larger spans1 too unmanageable to be lifted whole1 may be erected upon staging2 to secure the requisite headway it may be necessary to build the girders at a level above that at which they will finally be1 lowering them into position when self-supporting1 and after the removal of the staging4 ,the widening of railway under-bridges is1 as a rule1 a matter of no special difficulty1 but some remarks may be of use4 ,widenings should be planned with a regard to later reconstruction of the original bridge1 if that is at all likely to be necessary1 and with the object that1 when complete1 the whole should be a consistent piece of work4 ,it may1 indeed1 happen that widening of a bridge may involve the remodelling or reconstruction of the old work1 to enable the new roads to be laid down as desired2 this is more likely to be necessary where there exist main girders not competent to take any additional load1 and to duplicate which would sacrifice space between the new and old roads2 or it may be unavoidable because of slewing of the old rails1 as part of a general rearrangement4 ,illustration3 ,,fig4 #if4 ,dealing with widenings simply1 there is often some little trouble in contriving a connection between the new and the old work1 as this may have to be made under1 or close to1 the sleeper ends of the existing roads4 ,it is desirable to arrange this part so that no drilling of old work for rivets or bolts shall be necessary1 there being1 in fact1 no strict connection4 ,by judicious scheming1 this may be effected1 whilst securing freedom from leakage of water at the joint4 7,see ,figs4 #if and #ig47 ,if tying of the new and old structure is desired1 this can usually be done quite simply1 well below the floor at some more accessible level4 ,illustration3 ,,figs4 #ig and #ih4 ,the strict jointing-up of trough flooring1 new to old1 at right angles to the troughs1 cannot be contemplated1 but may be dealt with by treating each part independently1 the ends being near together1 separated by the space of an inch or so4 ,each trough end being closed up by a diaphragm or oak block to prevent ballast dropping through1 the top of the space may be covered by a loose strip1 secured to prevent it shifting1 the bottom provided with a gutter of liberal dimensions to take away leakage1 as it is practically impossible to make this arrangement 8drop dry0 under the conditions common in executing work of this kind 7see ,fig4 #ih74 ,illustration3 ,,figs4 #ii and #ajj4 ,where trough flooring1 new and old1 has to be made good parallel to the troughs1 the difficulty of making a direct connection is less marked1 and it is not unusual to introduce a strip cover simply2 but if accessible1 the work is still troublesome1 as there is commonly a want of strict alignment and truth as to level1 between the new and the old troughs4 ,it is preferable to arrange for junctions of a more convenient type1 as in ,figs4 #ii and #ajj4 ,when widening masonry arch bridges by girder-work1 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 executed4 ,the space remaining between the girder and the arch may then be bridged by floor-plates1 or an extension of the timber floor if that is adopted4 ,in effecting a junction such as this1 the author has used the arrangement shown in ,fig4 #aja1 the advantage being that the piece of connecting-floor is sufficiently wide1 and also sufficiently flexible1 to allow the girder-work freedom to deflect without doing harm4 ,the load carried by the width of floor is1 as to one part1 delivered well on to the old masonry1 in preference to being imposed near to the face4 ,if it should for any reason be imperative to place the girder close to the arch face1 it is preferable to scheme the floor so that there shall be no actual contact1 the new floor in that case slightly overhanging the masonry1 as in ,fig4 #ajb1 or dealt with as in ,fig4 #ajc1 if depth is restricted4 ,the widening of masonry arch bridges by masonry1 calls for no other remark than that the new work should be free from the old2 though it may be advisable1 when the widening is narrow1 to tie the new work to the old in such a way as to permit independent settlement4 ,if the widening is exceptionally narrow1 there may be no choice but to bond the new and old work together1 and in the best manner1 with the object of minimising the risk of separation4 ,illustration3 ,,figs4 #aja and #ajb4 ,illustration3 ,,fig4 #ajc4 ,the above matters relative to widenings1 though apparently trifling1 may by neglect cause much trouble and expense in maintenance4 ,they principally concern small bridges1 the extension of larger structures coming rather in the category of independent works4 ,,conclusion4 ,in bringing these chapters1 dealing largely with questions affecting maintenance1 to a close1 it may be well to draw attention to the fact that economy in design 7apart from improper reduction of sections7 goes hand-in-hand with economy of upkeep4 ,given good material1 that which favours low first cost1 simplicity of detail1 fewness of parts1 absence of smithing1 the use of rolled sections1 and good depth to girders1 favours also small expenditure in maintenance4 ,the less complex the design1 the easier will it be to keep the structure in order2 the less the number of parts1 the fewer will be the connections4 ,freedom from smithing eliminates liability to failure at cranks1 or other work which has been subject to fire4 ,it is apparent also that the free use of rolled instead of built-up sections1 reduces the liability to trouble from bad riveting1 or from good riveting overstressed4 ,a liberal depth to all girders1 by reducing deflections1 limits the inclination of the ends and gives the connections a better chance of remaining intact4 ,lastly1 with work of this character1 the labour of scraping and painting is simplified and cheapened4 ,the author wishes to reiterate the statement made in the opening paragraphs of this book1 that all instances of decrepitude1 failure1 or peculiar behaviour cited1 have been under his direct observation4 ,the fact is insisted upon simply that the reader may appreciate that the information is at first hand4 ,it has not been thought necessary1 nor was it considered desirable1 to indicate the locality of each case referred to2 but it may be said that the matter of these chapters has been accumulating during many years1 and relates to structures under the control of many different bodies4 ,the study of old bridges is strongly recommended1 particularly with respect to stress and strain1 which in structures new or old1 occur possibly as may be expected--certainly as they must4 ,consideration of existing work may thus be a useful check upon the fanciful requirements of some methods of design4 ,there is a recent tendency1 for instance1 in ,english practice to over-stiffen the webs of plate-girders1 such that if the theory upon which the results are based were true1 many old bridges carrying their loads with no sign of distress1 should have failed long ago4 ,excess in riveting is a common extravagance1 to which the same criticism may in a less degree apply4 ,considerable impact allowances for girders of large span may also be referred to as an application of empiric theory not justified by experience1 which1 as in all cases where such considerations fight with facts1 should be modified or rejected4 ,,index ,abutments1 leaning1 #hb1 #agc -- movements of1 #aeh -- settlement of1 #gh ,adjustment of centre girders1 #abh -- of distributing girders1 #abj ,angular distortions1 #hh ,arches1 equilibrium of1 #afb -- repair of1 #afc ,arrangement of cross girders1 #ba1 #age ,asphalt1 #bf ,ballast1 #bi ,bearing pressure on rivets1 #dg1 #ea1 #eg ,bearings1 skew1 #d ,bottom booms1 end bays1 #ah ,bracing1 additional1 #aag -- effects of1 #cd -- flat bars1 #cg -- incomplete1 #da -- sea piers1 #db ,bridge floors1 #bj -- repairs1 #ajg -- surveys1 #ajg ,bridges1 life of1 #afe ,breaks in ,t bars1 #af ,buckling of webs1 #af ,camber1 #bd1 #hj ,cast-iron arches1 #hj1 #ade -- -- bridges1 #ada -- -- columns1 #g1add -- -- girders1 #ada -- -- in sea water1 #aja ,centre girders1 #abb ,cinder ballast1 #bi ,cold-blast iron1 #ada ,cooling stresses in cast iron1 #ade ,construction depth1 #agc ,corrugated sheeting1 #bi ,cost of centre girders1 #ace -- of maintenance1 #afh ,counterbracing1 #ai ,cracked bedstones1 #c -- columns1 #g -- web plates1 #ac1 #ad1 #ae1 #ej ,cross girder arrangement1 #ba -- girders1 fixed ends1 #bb1 #aah -- -- rusted1 #bi1 #ig -- -- weak1 #cj1 #ff ,decay and painting1 #if -- of floor plates1 #aji -- of timber1 #bh1 #aej ,deflection1 #he -- due to booms and web1 #hf -- exceptional cases1 #hh -- in new and old work1 #he -- working formul1 #hg ,deformations1 #gc ,depth of girders1 #bc1 #hi1 #ahd ,diagonal ties1 #ai1 #db ,distortion due to temperature changes1 #gi1 #hd ,distributing girders1 #abj ,drainage holes1 #be 8,drop0 loads1 #hi ,dwarf walls under floors1 #bf ,early steel girders1 #fh ,economy1 #ahd ,effect of earth slips1 #aeg -- of floor on deflection1 #hh -- -- -- on stresses1 #bc1 #cj -- of high stress1 #hf -- of permanent way on stresses1 #ah --of skew on bridge floors1 #be -- -- -- on centre girders1 #aca -- of transverse bracings1 #cd -- of vibration on masonry1 #afb -- of wave action on sea piers1 #db ,end bays1 bottom booms1 #ah ,equilibrium of masonry arches1 #afb ,examination of bridges1 #ajg ,examples of cast-iron bridges overstressed1 #ada -- of high stress1 #gj -- of life of bridges1 #afg -- of rivet stress1 #ef -- of strengthening1 #aad -- -- -- by centre girders1 #aca1 #acd ,excessive bearing pressure1 #ea ,faulty workmanship1 #hj ,fixed ends to cross girders1 #bb1 #aah ,flange stresses1 #fc1 #ff1 #fg ,flanges1 side loaded1 #i1 #gc ,flat bar bracing1 #cg ,flexing of girders1 #i1 #gd1 #gf ,flexure curves1 #ach ,fractured bedstones1 #c -- rails1 #cj -- webs1 #ac1 #ad1 #ae1 #ej ,fractures in cast iron1 #g1 #ade ,girder bearings1 #b ,girders on columns1 #g -- on masonry1 #h ,girderwork in masonry1 #aja ,headway1 #agc ,high stress1 #fa -- in cast iron1 #ada -- in rivets1 #dg1 #eb ,holes for drainage1 #be ,impact1 #bj1 #fb ,inclination of girder ends1 #bc1 #ec ,incomplete bracing1 #da ,initial set1 #hh ,interference with traffic1 #agg ,jack arches1 #bi1 #aja ,joints in rails1 #bi1 #aji -- in trough floors1 #bh1 #ahj ,junction between metallic and masonry bridges1 #ahc -- -- new and old masonry bridges1 #ahb -- -- new and old metallic bridges1 #ahj ,lattice girder stresses1 #dg-ff ,liberal depth to girders1 #bc1 #hi1 #ahd ,life of bridges1 #afe ,limit of elasticity1 #fa ,linen tapes1 #agb ,longitudinal floor girders1 #bc ,loose rivets1 #ba1 #be1 #ea1 #ec1 #ef1 #aji ,main girders1 #i-ag ,masonry bridges1 #aeg -- enduring character of1 #afa ,memel timber1 #aej ,methods of calculation1 #df1 #fa -- of observing deflection1 #ij -- of setting out deflection curves1 #ach ,movements of abutments1 #aeh -- of cast-iron bridge1 #hb -- of piers1 #db1 #hc1 #aei -- of rollers1 #g -- of wrought-iron bridges1 #d1 #ba1 #ch1 #gc ,new members to old work1 #aaf ,oiling steelwork1 #ii ,old drawings unreliable1 #ajh -- rivets1 #ba1 #ea1 #ed1 #ee ,open webs1 #ag ,overhead bracing1 #ci -- girders1 #aah ,painting1 #ih ,parapets1 #gi ,permissible stress in old work1 #aaj ,piers1 movements of1 #db1 #hc1 #aei -- out of plumb1 #aei ,piles1 decay of1 #ajb1 #aej ,pitch pine1 #bh ,plasticity1 #fa ,plate webs1 #i ,plated floors1 #bc1 #be1 #cj ,pointing masonry1 #afd ,proposed rivet stresses1 #eh ,quickly applied loads1 #hi ,rail joints1 #bi1 #aji ,rails1 breaks in1 #cj ,reaction of cross girder with centre support1 #abg ,red-lead1 #ih1 #ajj ,relative merits of bridges1 #afi ,relief by centre girders1 #abb ,repainting1 #ajj ,repair of bridges1 #ajg1 #adg1 #aee1 #afc -- of timber piles1 #aef ,replacing flange plates1 #aaj -- rivets1 #aaa ,resistance of cast iron to rust1 #aja ,riveted connections1 #de1 #hf ,rivets in cramped positions1 #bj -- in cross girder ends1 #ba1 #di1 #ec1 #ed -- in road bridges1 #fj -- in webs of main girders1 #df -- spacing of1 #fj1 #hj -- stresses in1 #ef ,rocking of piers1 #h1 #hc1 #aei ,roller bearings1 #g ,rubble masonry1 #afa-afd ,running load and deflection1 #ie ,rusting1 instances of1 #bi1 #if -- of steelwork1 #ii -- over sea-water1 #ih ,sag in timber bridges1 #aej -- of tapes1 #agb ,scour under piers1 #afa ,sea piers1 #db1 #ajb ,setting bedstones1 #c1 #abi1 #agf ,settlements1 #gf1 #aeg ,skew bearings1 #d -- bridges1 right and left1 #agc -- -- floors1 #be ,skirting plate1 #bf ,slope of girder ends1 #ib ,softening of cast-iron in sea-water1 #aja ,spacing of rivets1 #fj1 #gi ,spread of abutments1 #aeg ,spring joints1 #bc ,steel trough girders1 #fh -- troughing1 #gj ,stiffening girders from floor1 #ab1 #dj -- to webs1 #af1 #ch1 #ahe ,stop piers1 #aeh ,strength of light top booms1 #dj ,strengthening of bridges1 #ajg1 #abb -- bridge floors1 #aah -- cross girders1 #abc ,stress in plated floors1 #ca ,study of old bridges1 #ahe ,tall piers1 #db1 #aei ,timber bridges1 #adi -- floors1 #bg -- staging1 #agg ,top booms1 #ah ,traffic during reconstruction1 #agg ,transverse bracing1 #cd1 #aag ,trough floors1 #bg1 #ahj -- girders1 #ej1 #gd ,t stiffeners1 breaks in1 #af ,twin girders1 #ae1 #ge ,twisting of girders1 #aa1 #fh1 #gc -- -- -- corrected1 #ab ,types of reconstruction1 #agd ,u-shaped booms1 #ah ,uncomplicated stress1 #fb ,uniform pressure on bearings1 #f ,value of ,e in deflection formul1 #hg ,vibration1 #afb ,wasted webs1 #ad1 #bi1 #if ,water1 scour of1 #afa ,web buckling1 #af -- plates1 cracked1 #ac1 #ad1 #ae1 #ej -- rivets1 #df1 #ej -- stiffening1 #af1 #ch1 #ahe ,widening masonry bridges1 #ahb -- metallic bridges1 #agi ,wide spaced rivets1 #gi ,wind pressure1 #da1 #dc ,yielding of piers1 #h1 #hc1 #aei ,,london3 ,,printed ,,by ,,william ,,clowes ,,and ,,sons1 ,,limited1 ,,great ,,windmill ,,street1 ,w41 ,,and ,,duke ,,street1 ,,stamford ,,street1 ,s4,e4 ,transcriber's ,notes3 ,the text of the original work 7including inconsistent spelling1 hyphenation1 formatting etc47 has been retained1 except as mentioned below4 ,the slight differences between the ,table of ,contents and the text have not been changed4 ,changes made to the text3 ,some punctuation errors and obvious typographical errors have been corrected silently4 ,several illustrations have been moved to where they are described in the text4 ,page #abc1 formula 7#b73 the original shows an unclear superscript after the first ,l4 ,as described in the following line of the text1 this has been changed to ,ll4