The Anatomy of Bridgework

Transcriber's Notes:

Text between underscores represents _italics_, small capitals have been transcribed as ALL CAPITALS.

Curly brackets indicate {subscripts}; letters between square brackets (such as [T] and [U]) represent the shape rahter than the letter itself.

More Transcriber's Notes may be found at the end of this text.

The Anatomy Of Bridgework

The Anatomy Of Bridgework

By

William Henry Thorpe Assoc. M. Inst. C. E.

With 103 Illustrations

[Illustration]

London E. & F. N. SPON, LIMITED, 57 HAYMARKET New York SPON & CHAMBERLAIN, 123 LIBERTY STREET

1906

Preface

In offering this little book to the reader interested in Bridgework, the author desires to express his acknowledgments to the proprietors of “Engineering,” in which journal the papers first appeared, for their courtesy in facilitating the production in book form.

It may possibly happen that the scanning of these pages will induce others to observe and collect information extending our knowledge of this subject--information which, while familiar to maintenance engineers of experience, has not been so readily available as is desirable.

No theory which fails to stand the test of practical working can maintain its claims to regard; the study of the behaviour of old work has, therefore, a high educational value, and tends to the occasional correction of views which might otherwise be complacently retained.

60 WINSHAM STREET, CLAPHAM COMMON, LONDON, S.W. _October_, 1906.

Contents

Chapter I.

Introduction--Girder Bearings.

Page

Pressure distribution--Square and skew bearings--Fixed bearings-- Knuckles--Rollers--Yield of supports 1

Chapter II.

Main Girders.

_Plate webs_: Improper loading of flanges--Twisting of girders-- Remedial measures--Cracks in webs--Stiffening of webs--[T] stiffeners 9

_Open webs_: Common faults--Top booms--Buckling of bottom booms-- Counterbracing--Flat members 17

Chapter III.

Bridge Floors.

Liability to defects--Impact--Ends of cross and longitudinal girders--Awkward riveting--Fixed ends to cross girders--Plated floor--Liberal depths desirable--Type connections--Effect of “skew” on floor--Water-tightness--Drainage--Timber floors--Jack arches-- Corrugated sheeting--Ballast--Rail joints--Effect of main girders on floors 20

Chapter IV.

Bracing.

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 34

Chapter V.

Riveted Connections.

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 45

Chapter VI.

High Stress.

Elastic limit--Care in calculation--Impact--Examples of high stress --Early examples of high stress in steel girders--Tabulated examples--General remarks 61

Chapter VII.

Deformations.

Various kinds--Flexing of girder flanges--Examples--Settlement deformations--Creeping--Temperature changes--Local distortions-- Imperfect workmanship--Deformation of cast-iron arches 73

Chapter VIII.

Deflections.

Differences as between new work and old--Influence of booms and web structure on deflection--Yield of rivets and stiffness of connections--Working formulæ--Set--Effect of floor system-- Deflection diagrams--Loads quickly applied--“Drop” loads--Flexible girders--Measuring deflections--New method of observing deflections --Effect of running load 85

Chapter IX.

Decay And Painting.

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 96

Chapter X.

Examination, Repair, And Strengthening Of Riveted Bridges.

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 107

Chapter XI.

Strengthening Of Riveted Bridges By Centre Girders.

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 122

Chapter XII.

Cast-Iron Bridges.

Limitations of cast iron--Stress examples--Advantages and disadvantages--Foundry stresses--Examples--Want of ductility of cast iron--Repairs--Restricted possibilities 141

Chapter XIII.

Timber Bridges.

Perishable nature--Causes of decay--Sag--Lateral bracing--Piles-- Uncertainty respecting decay--Examples--Conditions and practice favourable to durability--Bracing--Protection--Repair--Piles--Cost 149

Chapter XIV.

Masonry Bridges.

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 157

Chapter XV.

Life Of Bridges--Relative Merits.

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 165

Chapter XVI.

Reconstruction And Widening Of Bridges.

Conclusion.

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 172

Index 187

The Anatomy Of Bridgework.

Chapter I.

Introduction.

No book has, so far as the author is aware, been written upon that aspect of bridgework to be treated in the following pages. No excuse need, therefore, be given for adding to the already large amount of published matter dealing with bridges. Indeed, as it too often happens that the designing of such constructions, and their after-maintenance, are in this country entirely separated, it cannot but be useful to give such results of the behaviour of bridges, whether new or old, as have come under observation.

In the early days of metallic bridges there was of necessity no experience available to guide the engineer in his endeavour to avoid objectionable features in design, and he was, as a result, compelled to rely upon his own foresight and judgment in any attempt to anticipate the effects of those influences to which his work might later be subject. How heavily handicapped he must have been under these conditions is evident from the mass of information since acquired by the experimental study of the behaviour of metals under stress, and the growth of the literature of bridgework during the last forty years. That many mistakes were made is little occasion for surprise; rather is it a cause for admiration that some very fine bridges, still in use, were the product of that time. Much may be learned from the study of defects and failures, even though they be of such a character that no experienced designer would now furnish like examples.

Modern instances may, none the less, be found, with faults repeated, which should long since have disappeared from all bridgework, and are only to be accounted for by the unnatural divorce of design and maintenance already referred to. As the reader proceeds, it may appear that details are occasionally touched upon of a character altogether too crude and objectionable to need comment; but the consideration of these cases is none the less interesting, and, so far as the author’s observation goes, not altogether unnecessary.

Most of the instances cited are of bridges, or parts of bridges, of quite small dimensions; but it is these which most commonly give trouble, both because the effects of impact are in such cases most severely felt, and possibly because the smaller class of bridges is very generally designed by men of less experience, than large and imposing structures.

The particulars given relate in all cases to bridges of wrought iron, unless otherwise described.

An endeavour has been made to secure some kind of order in dealing with the subject, but it has been found difficult to avoid a somewhat disjointed treatment, inseparable, perhaps, from the nature of the matter. Finally, the reader may be assured that every case quoted has come under the writer’s personal notice.

Girder Bearings.

In girder-work generally, and more particularly in plate-girders, considerable latitude obtains in the amount of bearing allowed. Clearly, the surface over which the pressure is distributed should be sufficiently ample to avoid overloading and possible crushing or fracture of bedstones where these exist; but if no knuckles are introduced, this is an extremely difficult matter to insure. A long bearing may deliver the load at the extreme end of the surface on which it rests, or, more probably, near the face.

If the girder is made with truly level bearings, and the beds set level, it will certainly, when under load, throw an extreme pressure upon that part of the bearing surface immediately under the forward edge of the bearing-plate. These considerations probably account for bedstones frequently cracking, in addition to which possibility there is the disadvantage that the designer does not know where the girder will rest, and cannot truly define the span. The variation of flange-stress due to this cause may, in a girder of ordinary proportions, having bearings equal in length to the girder’s depth, be as much as 15 per cent. above or below that intended.

If great care be taken in setting beds, in the first instance, to dip toward the centre of the span an amount depending upon the anticipated girder deflection, it may be possible to insure that when under full load the girder bearing shall rest equally upon its seat; but this is evidently a difficult condition to obtain practically, is good only for one degree of loading, and may at any time be nullified by a disturbance of the supports, as, for instance, the very common occurrence of a slight leaning forward of abutment walls.

Double or treble thicknesses of hair-felt are sometimes placed beneath girder bearings, with the object of securing a better distribution of pressure, no doubt with advantage; but this practice, though it may be quite satisfactory as applied to girders carrying an unchangeable load, hardly meets the case for loads which are variable. Notwithstanding the faulty nature of the plain bearing ordinarily used for girders of moderate span, its extreme simplicity commends it to most engineers. It must be admitted that no serious inconvenience need be anticipated in the majority of cases, particularly if the bearings are limited in length, do not approach nearer than 3 inches to the face of bedstones, and are furnished with hair-felt or similar packing.

[Illustration: FIG. 1.]

Whether with long or short bearings, the forward edge should be at right angles to the girder’s length. In skew bridges it is sometimes seen that this edge follows the angle of skew. The effect on the girder is to twist it, as will be clear from a little consideration. In evidence of this the case may be quoted of a lattice girder of 95 feet effective span and 7 feet deep, which, resting on a skew abutment right up to the masonry face at a rather bad angle (about 15 degrees), was, after twenty years, found canted over at the top to the extent of 4 inches, with the further result of springing a joint in the top flange at about the middle of the girder, causing some rivets to loosen. The bedstone was also very badly broken at the face, and had to be replaced in the course of repairs (Fig. 1). This girder had, in addition to the canting from the upright position at its end, and the distortion of the top flange, a curvature in the same direction, though less in amount, at the bottom--an effect very common in the main girders of skew bridges, and possibly accounted for in part by a tendency of the girder end to creep along the abutment away from the point at which it bears hardest, under frequent applications and removals of the live load, and accompanying deflections.

This tendency to travel may be aggravated in bridges carrying a ballasted road, in which there may be a considerable thickness of ballast near the bearings, by the compacting and spreading of this material taking effect upon the girder end, tending to push it outwards, being tied only by a few light cross-girders badly placed for useful effect. The movement may be prevented in new work for moderate angles of skew by carrying the end cross-girders well back, and securing them in some efficient manner; or by the introduction of a diagonal tie following the skew face, and attached to cross and main girder flanges (Fig. 2)--a method which may be applied to existing work also.

[Illustration: FIG. 2.]

For such a case as that cited it is imperative that ballast pressure at the girder end should be altogether eliminated.

The fixing of girder ends by bolts--a practice at one time usual--hardly calls for remark, as it is now seldom resorted to unless for special reasons; but it may be well to point out the weakening effect of holes for any purpose in bedstones. Bed-plates commonly need no fixing; the weight carried keeps them in position, or if, in the case of very light girders upon separate plates, it is considered well to secure these from shifting, it may best be done by letting the plate in bodily a small amount, or by means of a very shallow feather sunk into a chase.

[Illustration: FIG. 3.]

As an improvement upon the plain bearing usually adopted, it is an easy matter so to design girder-ends as to deliver the load by a narrow strip of bearing-plate carried across the bottom flange, distributing the pressure upon the stone, if there be one, by means of a simple rectangular plate of sufficient stoutness (Fig. 3). An imperfect knuckle will by this means result, with freedom to slide, and the girder span be defined within narrow limits. A true knuckle is, of course, the best means of securing imposition of the load always in the same place; but this by itself is not sufficient where the girder is of a length to make temperature and stress variations important, in which case rollers, or freedom to slide, become necessary. Bridges exist in which roller-bearings have been adopted without the knuckle, or its equivalent, but this is wholly indefensible, as it is obvious that the forward roller will in all probability take the whole load, and cannot be expected to keep its shape and roll freely under this mal-treatment. It is sometimes asserted that rollers are never effective after some years’ use; that they become clogged with dirt, and refuse to perform their office.

There is no reason why rollers should not be boxed in to exclude dirt by a casing easily removed, some attention being given to them, and any possible accumulation of dirt removed each time the bridge is painted.

To test the behaviour of rollers under somewhat unfavourable conditions for their proper action--that of the bearings of main roof trusses of crescent form, 190 feet span--the author, some thirty years since, took occasion to make the necessary observations, and found evidence of a moderate roller movement, though there was in this case no direct horizontal member to communicate motion. With girders resting upon columns, particularly if of cast iron, a roller and knuckle arrangement is most desirable for any but very small spans, as, if not adopted, the result will be a canting of the columns from side to side--a very small amount, it is true, but sufficient to throw the load upon the extreme edges of the base, though the knuckle alone will relieve the top of this danger. The author at one time took the trouble to examine, so far as it could be done superficially and without opening out the ground to make a complete inspection possible, a number of bridges crossing streets, in which girders rested upon and were secured to cast-iron columns standing in the line of kerb; and he found cracks, either at the top or bottom, in about one of every four columns.

When girders passing over columns are not continuous, it may be difficult to find room for a double roller and knuckle arrangement; but this inconvenience may be overcome by carrying one girder-end wholly across the column-top, and securing the next girder-end to it in a manner which a little care and ingenuity will render satisfactory, one free bearing then serving to carry the load from both girders.

Though the wisdom of using rollers is apparent in spans exceeding some moderate length, say 80 feet--as to which engineers do not seem quite decided--and varying with the conditions, it need not be overlooked that in some cases masonry will be sufficiently accommodating to render them unnecessary; piers, if sufficiently tall and slender, will yield a small amount without injury, and though shorter, if resting upon a bottom not absolutely rigid, will rock and give the necessary relief; but it is obvious, if the resistance to movement is sufficiently great, and the girder cannot slide or roll on its bearings, bedstones will probably loosen, as, indeed, frequently happens.

Chapter II.

Main Girders; Plate-Webs.

It is seldom that girders of this description--or, indeed, of any other--show signs of failure from mere defect of strength in the principal parts, even though somewhat highly stressed; and instances tending to support this statement will be given in a later chapter. For the present, it is proposed to indicate peculiarities of behaviour only, generally, but not always, harmless.

Though now less often done, it was at one time common practice to load plate-girders on the bottom flange by simply resting floor timbers, rails, troughs, or cross-girders upon them. In outside girders one result of this is to cause the top flange to take a curve in plan, convex towards the road, every time the live load comes upon the floor of the bridge, upon the passing of which the flange resumes its figure, though still affected by that part of the load which is constant.

A bridge of 47 feet span, carrying two lines of way, having one centre and two outside girders, with a floor consisting of old Barlow rails, resting upon the bottom flanges, showed the peculiarity named in a marked degree.

The outside girders, under dead load only, were, as to the top flanges (see Figs. 4 and 5), 1-1/4 inch and 1-1/16 inch respectively out of straight in their length, but upon the passing of a goods engine and train curved an additional 1-1/8 inch, or 2-3/8 inches in all, for one outside girder, and 2-3/16 inches for the other.

The centre girder, having a broader and heavier top flange, curved 5/8 inch towards whichever road might be loaded. The effect of such horizontal flexure is clearly to induce stresses of tension and compression in the flanges, which, being (for the top flange) compounded with the normal compressive stress due to load carried, results in a considerable want of uniformity across the section.

[Illustration: FIG. 4.]

In the case under notice, the writer estimates the stresses for an outer girder top flange at 4·5 tons per square inch compression for simple loading, and 5·5 tons per square inch of tension and compression, on the inner and outer edges, due to flexure, resulting when compounded in a stress of 1 ton per square inch tension on the inside, and 10 tons per square inch compression on the outside edge. In this rather extreme case the stress on the inner edge, or that nearest the load, is reversed in character.

The effect described appears to be not wholly due to the twisting moment. It is apparent that whatever curvature may be induced by twisting alone must be aggravated in the compression flange by its being put out of line.

The writer does not attempt here to apportion the two effects in any other way than to say that the greater part of the flexure appears to be due to the secondary cause. Consistent with this view of the matter is the fact that the inclination of the girder towards the rails greatly exceeded the calculated slope of the Barlow rail-ends when under load, being about five times as great. The inference is that the floor rails bore hard at their extreme ends, at which point of bearing the calculated twisting moment accounts for less than one-half of the flexure observed in the flanges.

[Illustration: FIG. 5.]

The girders upon removal in the course of reconstruction again took the straight form, showing that the very frequent development of the stresses named had not sensibly injured the metal, though the bridge carried as many as three hundred trains daily in each direction, and had done so for very many years.

The deformation of the top flange only has been noticed, yet the same tendency exists in the bottom, though the actual amount is much less, both because the lower flanges are in tension, and are also in great degree confined by the frictional contact of the cross bearers, even where no proper ties are used. In the case dealt with the bottom flanges of the outer girders curved 1/8 inch outwards only.

With the broad flanges commonly adopted in English practice, twisting of the girders, under conditions similar to the above, will not generally be a serious matter; but with narrow flanges possessing little lateral stiffness it might be a source of danger.

[Illustration: FIG. 6. FIG. 7.]

The twisting may be limited in amount by introducing a cross-frame between the girders, from which they are stiffened; by strutting the girders immediately from the floor itself, in which case they cannot cant to a greater extent than that which corresponds to the floor deflection; or by designing the top flange to be unsymmetrical with reference to the web, as in Figs. 6 and 7, with the object of insuring that under the joint effect of vertical loading and twisting, the stress in the flange shall at maximum loads be uniform across the section, and allow it to remain straight. This may be secured by making the eccentricity of the flange section equal to that of the loading. For instance, if the load be applied 3 inches away from the web centre, the flange should have its centre of gravity 3 inches on the other side of the centre line. It can be shown that this is true throughout the length of the girder, and irrespective of the depth. An instance in which flange eccentricity being in excess, curvature outwards resulted, will be found in a later chapter on deformations, etc. It will not generally be necessary to make the bottom flange eccentric, as it is commonly tied in some way; but if done, the eccentricity should be on the same side as for the top. The flanges remaining straight under these conditions are not subject to the complications of stress referred to in the case first quoted. The author has adopted both the last named details in bridges where he has been obliged to accept unfair loading of the kind discussed.

It should be remarked that by the two first methods, if the stiffening frames are wide apart and attached direct to the web, there is a liability for this to tear, under distress, rather than keep the girder in line.

There is one other possible consequence of throwing load upon the flanges of a girder of a much more alarming nature. In girders not very well stiffened, it may happen that the frequent application of load in this manner finally so injures the web-plate, just above the top edge of the bottom angle-bars, as to cause it to rip in a horizontal direction. More likely is this to happen with a centre girder taking load first on one side, then on the other, and again on both together. Cases may be cited in which cracks right through the webs 3 feet or more in length have resulted from this cause. It is very probable, however, that in some of these cases the matter was aggravated by the use of a poor iron in the webs, as at one time engineers, from mistaken notions of the extreme tenuity permissible in webs near the centre of a girder, would, if they could not be made thin enough, even encourage the use of an indifferent metal as being quite good enough for that part of the work.

An instance of web-fracture from somewhat similar causes may be here given.

In a bridge of 31 feet 6 inches effective span, and consisting of twin girders carrying rails between, as shown in Figs. 8 and 9, the load resting upon the inner ledges, formed by the bottom flange, induced such a bending and tearing action along the web just above the angle-bars, as to cause a rip in one of the girders, well open for some distance, and which could be traced for 14 feet as a continuous crack.

[Illustration: FIG. 8.]

[Illustration: FIG. 9.]

It will be noticed in the figure that the [T] stiffeners occur only at the outer face of the web, and that the inner vertical strips stop short at the top edge of the angles, the result being that under load the flange would tend to twist around some point, say A, at each stiffener, inducing a serious stress in the thin web at that place, while away from these stiffeners the web would be more free to yield without tearing. The fact that at a number of the stiffeners incipient cracks were observed, some only a few inches long, suggests this view of the matter.

A case of web-failure from other influences coming under notice showed breaks at the upper part of the web extending downwards.

In this bridge, of 32 feet span, which had been in existence thirty-two years, the webs--originally 1/4 inch thick--were, largely because of cinder ballast in contact with them, so badly wasted as to be generally little thicker than a crown-piece, and in places were eaten through; in addition to which, the road being on a sharp curve, the rail-balks had been strutted from the webs to keep them in position, the effect of which would be to exert a hammering thrust upon the face of the web at the abutting ends, and assist in starting cracks in webs already much corroded. A feature of this case, tending to show that the breaks resulted as the joint effect of waste and ill-usage by the strut members, rather than by excessive stress in the web as reduced, is to be found in the fact that the girders when removed were observed to be in remarkably good shape--i.e. the camber, marked on the original drawings to be 1-1/2 inch, still showed as a perfectly even curve of that rise, which would hardly have been the case if the lower flange had been let down by web-rupture, the result of excessive web-stresses.

Occasionally webs will crack through the solid unwasted plate, in a line nearly vertical; not where shear stress is greatest, but generally at some other place, and from no apparent cause, either of stress or ill-usage. The writer has observed this only in the case of small girders not exceeding 2 feet in depth; and, for want of any better reason, attributes these cracks to poor material, coupled with some latent defect. In a bridge having some thirty cross-girders, each 26 feet long, about every other one had a web cracked in this manner after many years’ use.

Web-cracks of the kind first indicated, are perhaps, the most probable source of danger in plate-girders, of any which are likely to occur. The fault is insidious, difficult to detect when first developed, and perhaps not seen at all till the bridge, condemned for some other reason, has the girders freely exposed and brought into broad light. The manner in which old girders are sometimes partly concealed by timberwork, or covered by ballast, makes the detection of these defects an uncertain matter, unless sufficient trouble is occasionally taken to render inspection complete.

The manner in which girders with wasted and fractured webs will still hang together under heavy loading seems to warrant the deduction that, in designing new work, it can hardly be necessary to provide such a considerable amount of web-stiffening as is sometimes seen; experience showing that defects of the web-structure do not commonly occur in the stiffening so frequently as in the plate, and then in the form of cracks.

A case of web-buckling lies, so far, without the author’s experience. There is no need to introduce, for web-stresses alone, more stiffening than that which corresponds to making the stiffeners do duty as vertical struts in an openwork girder; in which case it is sufficient to insure that the stiffeners occurring in a length equal to the girder’s depth shall, as struts, be strong enough in the aggregate to take the whole shear force at the section considered, in no case exceeding this amount on one stiffener. For thin webs in which the free breadth is greater than one hundred and twenty times the thickness, the diagonal compressive stress may be completely ignored, and the thickness determined with reference to the diagonal tension stress only.

There is one fault which frequently shows itself in stiffeners though not the result of web-stresses, and when performing an additional function--viz., the breaking of [T] stiffener knees at the weld, where brought down on to the tops of cross-girders, due to the deflection of the floor, as shown in Fig. 10. When such knees are used, the angle may properly be filled in with a gusset-plate to relieve the weld of strain and prevent fracture.

[Illustration: FIG. 10.]

There is some little temptation in practice to make use of the solid web as a convenient stop for ballast, or road material. Special means, perhaps at the cost of some little trouble, should be adopted, where necessary, to avoid this.

Main Girders; Open Webs.

With these, as with plate-girders, deficiency of strength--i.e. of section strength--is seldom so marked as to be a reasonable cause of anxiety. In particular instances faults in design may result in stresses of an abnormal amount, though rarely to an extent occasioning any ill effects. The practice of loading the bottom flanges at a distance from the centre, the bad effects of which have already been dealt with as applied to plate-girders, is not commonly resorted to in girders having open webs, nor are these so liable to be heaped with ballast in immediate proximity to essential members of the structure.

Some defects are, however, occasionally seen which may be remarked. Top booms of an inverted [U] section are sometimes made with side webs too thin, and having the lower edges stiffened insufficiently, or not at all. Where this is the case, the plates may be seen to have buckled out of truth, showing that they are unable, as thin plates, to sustain the compressive stress to which the rest of the boom is liable. The practice of putting the greater part of the boom section in an outer flange, characteristic of this defect, has the further disadvantage of throwing the centre of gravity of the section so near its outer edge as to make impracticable the best arrangement of rivets for connection of the web members. Further, since all the variation in boom section is thrown into the flange-plates, the centre of gravity of the section has no constant position along the boom--an additional inconvenience where correct design is aimed at.

These considerations indicate the propriety of arranging the bulk, or all, of the section at the sides, thus reducing or getting rid of the objections named.

Where the bottom boom consists of side plates, only one point demands attention. It is found that, though nominally in tension, the end bays are liable occasionally to buckle, as though under compressive stress, and need stiffening, not excepting girders which at one end are mounted on rollers. This might seem to indicate that the rollers are of no use; but it is conceivable the resistance arises from other causes, such as wind forces, or as in the case of a bridge carrying a railway, in which the rigidity of the permanent-way may be such that the bridge-structure, in extending towards the roller end, cannot move it sufficiently, causing a reversal of stress on the lighter portions of the bottom boom at the knuckle end; or by the exposed girder booms becoming very sensibly hotter than the bridge floor, and by expanding at a greater rate, cause this effect, from which rollers cannot protect them.

In counterbracing consisting of flat bars it is desirable either to secure these where they cross other members, or stiffen them in some manner to avoid the disagreeable chattering which will otherwise commonly be found to occur on the passage of the live load.

Occasionally diagonal ties are made up of two flat bars placed face to face, to escape the use of one very thick member. Where this is done, the two thicknesses, if not riveted together along the edges, will be liable to open, as the result of rusting between the bars in contact, when the evil will be aggravated by the greater freedom with which moisture will enter the space.

Other matters relating to open-web girders will be more conveniently dealt with under their separate headings, particularly a further consideration of the relationship subsisting between the booms and floor structure.

Chapter III.

Bridge Floors.

The floors of bridges commonly give more trouble in maintenance, and their defects are more frequently the cause which renders reconstruction necessary, apart from reasons not concerning strength, than any other part of such structures. When it is considered that this portion of a bridge is first affected by impact of the load which comes upon it, and is usually light in comparison with the main girders further removed from the load, and to which the latter is transferred through the more or less elastic floor, the fact will be readily appreciated by those not already familiar with it.

The end attachments of cross and longitudinal girders are very liable to suffer by loosening of rivets, or, more rarely, by breaking of the angle-irons which commonly make such a connection. A not unusual defect of old work, which may also sometimes be seen in work quite new, where the cross-girder depth has from any cause been restricted, is the extremely cramped position of the rivets securing the ends. There is small chance of these ever being properly tight, if the act of riveting is rendered difficult by bad design. This is the more objectionable if it happens that cross-girder ends abut against opposite sides of the web of an intermediate main girder, and are secured by the same rivets passing through. At the best such rivets will not be well placed to insure good workmanship, and the severe treatment to which they become subject, as the cross-girders take their load and deflect under it, will be very apt to loosen them. The author has seen a case of this kind (see Figs. 11 and 12)--rather extreme, it is true--in which nearly the whole of the cross-girder end rivets were loose, some nearly worn through, thus allowing the cross-girders to be carried, not by their attachments, but by resting upon the main-girder flanges, which in turn, by repeated twisting, tore the web for a length of 4 feet; there was also pronounced side flexure of the top booms. The movements generally on this bridge (of 42-feet span), whether of main or cross-girders, were very considerable and disturbing. It was removed after about twenty-three years’ use.

[Illustration: FIG. 11.]

[Illustration: FIG. 12.]

There is no necessity, as a rule, for the ends of cross-girders attached to the same main girder at opposite sides to be placed in line. The author prefers to arrange them to miss, by which device each connection is entirely separate, the riveting can be more efficiently executed, erection is simplified, and the rivets will be more likely to keep tight. Other special cases of cross-girder ends will be dealt with under the head “Riveted Connections.”

It is sometimes contended that cross-girders attached at their ends by a riveted connection should be designed as for fixed ends, in which case they are usually made of the same flange section throughout, with a view to satisfy the supposed requirements. But a girder to be rightly considered as having fixed ends must be secured to something itself unyielding. With an outer main girder of ordinary construction, and no overhead bracing, this is so far from being the case as to leave little occasion for taking the precaution named. As the cross-girders deflect, the main girders will commonly yield slightly, inclining bodily towards the cross-girders, if these are attached to the lower part of the main girders. The force requisite to cant the main girders in this manner is usually less than that which corresponds to fixing the cross-girder ends, and is, generally, slight. It is, of course, necessary that this measure of resistance at the connection should be borne in mind for the sake of the joint itself, quite apart from any question of fixing.

Possibly, in quite exceptional cases, where very stiff main girders are braced in such a manner as to prevent canting, it may be proper to consider the cross-girder ends as fixed, or for those near the bearings of heavy main girders; but the author has not met with any example where cross-girders, apart from attachments, appear to have suffered from neglect of this consideration.

With cross-girders placed on either side of a main girder, and in line, it may also, for new work, be desirable to regard the ends as fixed, and to detail them with this in view. It does not, however, appear wise to carry this assumption to its logical issue, and reduce the flange section to any appreciable extent on this account. The fixity of the ends will, in any such case, be imperfect; and when one side only of an intermediate main girder is loaded, it can have but a moderate effect in reducing flange stress at the middle of the loaded floor beam.

[Illustration: FIG. 13. FIG. 14. FIG. 15.]

Similar reasons affect the design of longitudinal girder attachments to cross-girders, which, if intended to support rails, cannot of necessity be schemed to come other than in line. Where the floor is plated as one plane surface, there will not usually be any trouble resulting if no special precautions are used, as the plate itself will insure that the longitudinals act, in a measure, as continuous beams, relieving the joints of abnormal stress. If the plating is, however, designed in a manner which does not present this advantage, or if the floor be of timber, it is better to decide whether the connections shall be considered as fixed, and made so; or avowedly flexible, and detailed in such a manner as to possess a capacity for yielding slightly without injury. Those connections are most likely to suffer which are neither of the one character nor the other, offering resistance without the ability to maintain it. Figs. 13, 14, and 15 give representations of three “spring joint” methods of insuring yield in a greater or less degree. For small longitudinals it is, perhaps, sufficient to use end angles with very broad flanges against the cross-girder web; these to be riveted in the manner indicated in Fig. 15.

Liberal depth to floor beams is distinctly advantageous where it can be secured, rendering it easier to design the ends in a suitable manner, by giving room near mid-depth of the attachment to get in the necessary number of rivets; or where the ends are rigidly attached direct to vertical members of an open-work truss, the greater depth is effective in reducing the inclination of the end from the vertical, with a correspondingly reduced cant of the main girders and flexure of the vertical member, with smaller consequent secondary stresses. In any case deep girders will contribute to stiffness of the floor itself, favourable in railway bridges to the maintenance of permanent-way in good order.

[Illustration: FIGS. 16, 17, 18.]

A point in connection with skew-bridge floors occasionally overlooked is the combined effect of the skew, and main girder camber, in throwing the floor structure out of truth, if no regard has been paid to this. The result is bad cross-girder or other connections; or, in the case of bearers running over the tops of main girders, a necessity for special packings to bring all fair (Fig. 17). The author has in such cases, where cross-girders are used, set the main girder beds at suitable levels, in order that the cross-bearers may all be horizontal (see Figs. 16 and 18). This may not always be permissible; but, however the difficulty may be met, it should be dealt with as part of the design. For small angles of skew only may it be neglected.

Rivets attaching cross-girder angles to the web will occasionally loosen, probably due in most cases to bad work, together with some circumstance of aggravation, as in the case of a bridge floor consisting of girders spaced 3 feet 6 inches apart, with short timber bearers between, carrying rails. In many girders the top row of rivets, of ordinary pitch and size, had loosened, allowing the web, about 1/4 inch thick, a movement of 1/8 inch vertically. The rails being very close down upon the cross-girder tops, though not intended to touch, had at some time probably done so, and by “hammering” produced the result described.

Plated floors are often found which are objectionable on account of their inability to hold water, arising sometimes from bad work, as often from wide spacing of rivets. With rivets arranged to be easily got at, and pitched not more than 3 inches apart, a tight floor may be expected; but it is still necessary to drain the floor by a sufficient number of holes, provided with nozzles projecting below the underside of the plate, and sufficiently long to deliver direct into gutters, where these are necessary. Drain-holes should not be less frequent than one to every 50 square feet of floor, if flat, and may advantageously be more so. Gutters should slope well, and care be taken to insure practicable joints and good methods of attachment--a matter too often left to take care of itself, with considerable after-annoyance as a result.

The use of asphalt, or asphalt concrete, to render a plated floor water-tight is hardly to be relied upon for railway bridges, though no doubt effective for those carrying roads. It is extremely difficult to insure that it shall stand the jarring and disturbance to which it may be subject, and under which it will commonly break up, and make matters worse by holding moisture, and delaying the natural drying of the floor. In bulk, as in troughs, it may be useful, but in thin coverings on plates it cannot be depended upon.

Floors having plated tops are sometimes finished over abutments or piers in a manner which is not satisfactory, either as regards the carrying of loads or accessibility for painting. If the plates are carried on to a dwarf wall with the intention that the free margin of the plate shall rest upon it, there will be a difficulty in securing this in an efficient manner. Commonly such a wall is built up after the girder work is in place, making it difficult to insure that the wall really supports the plate, the result being that this may have to carry itself as best it can. In any case, severe corrosion will occur on the underside, and the plate rust through much before the rest of the floor; the masonry also will usually be disturbed.

It appears preferable to form the end of the floor with a vertical skirting-plate having an angle or angles along the lower edge. This may come down to a dwarf wall, but preferably not to touch it, the skirting being designed to act as a carrying girder. A convenient arrangement is shown in Fig. 19, which may be used either for a square or skew bridge. It will be seen that the plate-girders have no end-plates, the skirting referred to being carried continuously along the floor edge, and attached to each girder-web, the whole of the more important parts being open to the painter.

[Illustration: FIG. 19.]

Trough floors consisting of one or other of the forms of pressed or rolled section present the objection that it is almost impracticable to arrange an efficient connection at the ends, if they abut against main girders, and but little connection is, as a rule, attempted, and sometimes none. The result is that the load from these troughs is delivered in an objectionable manner, and the ends being open or imperfectly closed, water and dirt escape on to the flange, or other ledge, which supports them. A description of pressed floor which promises to overcome this objection, and provide a ready means of attachment to the webs of plate-girders, or of booms having vertical plate-webs, has within the last few years been introduced. This has the ends shaped in such a manner as to close them and provide a flat surface of sufficient area for connection by rivets. Each hollow is separately drained by holes with nozzles. Whether this type of trough will develop faults of its own, due to over-straining of the metal in the act of pressing, remains to be seen; but as it appears possible to produce the desired form without any material thinning or thickening of the metal, the contention that no severe usage accompanies the process appears to be reasonable.

That form of troughing in which the top and bottom portions are separately formed, and connected by a horizontal seam of rivets at mid-depth, is found in use upon railway bridges to be very liable to loosening of those rivets near the ends; less surprising, perhaps, because the sloping sides are usually thin.

It is a distinctly difficult matter to join two or more lengths of any trough flooring having sloping sides, in a workmanlike manner; the fit of covers is apt to be imperfect, and some rivets, being difficult of access, are likely to be but indifferently tight, so that if the joint occurs where it will be more than lightly stressed, trouble will probably follow. A bad place for such joints is immediately over girders supporting the troughs, as there the stress will be most severe, any leakage come directly upon the girder, and remedial measures be more difficult to carry out.

Timber floors of the best timber, close jointed, are more durable than might be supposed. The disadvantage is a difficulty in ascertaining the precise condition of the timber after many years’ use. The author has seen timbers, 9 inches by 9 inches, forming in one length a close floor, carried by three girders, and supporting two lines of way, which, when taken out, could as to a considerable part be kicked to pieces with the foot; whilst in another case, with the same arrangement of girders and close-timbered floor, the wood, after being in place for thirty-two years, was, when taken out, found to be perfectly sound, with the exception of a very few bad places of no great extent. In this instance, however, it is known that the floor--pitch-pine--was put in by a contractor who prided himself upon the quality of the timber that he used; the floor being also covered with tar concrete, which had in this instance so well performed its office as to keep the timber quite dry on the top.

Jack arches between girders make an excellent floor for road bridges, though heavy; and for small bridges may be used to carry rails, if the girders are designed to be stiff under load. The apprehension that brickwork or concrete will separate from the girder-work, or become broken up under even moderate vibration, does not seem to be well founded, if the deflection is small and the brickwork or concrete good.

The use of corrugated sheeting as a means of rendering the underside of a bridge drop dry cannot be too strongly deprecated. If it must be adopted, the arrangement should be such as to permit ready removal for inspection and painting. It is evident that by boxing up the floor structure, rust is favoured, and serious defects may be developed, not to be discovered till the sheeting is removed, or something happens.

[Illustration: FIG. 20.]

A case may be instanced in which it was found, on taking down sheeting of this description, that the floor girders, previously hidden, were badly wasted in the webs. One of these girders had cracked, as shown in Fig. 20, and others were in a condition only less bad.

In any floor carrying ballast or macadam, if means are not adopted to keep the road material from the structure of the floor, or from the main girders, corrosion may be serious in its effects. Cinder ballast is, perhaps, the worst in this respect, in its action upon steel or ironwork, being distinctly more damaging than any other kind commonly used.

Rail-joints upon bridge floors are to be avoided where practicable by the use of rails as long as can be obtained; if the bridge is small enough, crossing it in one length. At each joint there is likely to be hammering and working extremely detrimental to floor members and connections; indeed, it may happen that loose rivets will be found in the neighbourhood of such joints, and nowhere else on the bridge. Where rail-joints cannot be avoided, their position should, if there be any choice, be judiciously selected, and the plate-layers taught to close the joints and jam the fish-bolts.

[Illustration: FIG. 21.]

As rail-joints upon a bridge may injuriously affect the floor, so also will a weak floor be very trying to the rails. A remarkable instance of this has come under the writer’s notice, where a bridge (Fig. 21) of three 33-feet spans, having outer and centre main girders, with cross-girders spaced 3 feet apart, resting upon the girder flanges, but not attached, and carrying two roads, had the permanent-way in a very bad state. The rails proper, with supplementary angle-plates, rested direct upon the cross-girders, which were decidedly light, and the whole floor had much “life” in it, the ill-effect of which was shown in thirteen breaks in the angle-plates, in each case near their ends, generally at holes.

It appears probable that severe stresses may be thrown upon the parts of a floor, whether placed at the level of the bottom booms or of the top, by changes of length in the booms due to stress. The author has, unfortunately, no direct evidence to offer in reference to this, tending either for or against the contention. If an unplated floor of cross and longitudinal girders of usual arrangement be at the bottom boom of a large bridge, as the boom lengthens with the imposition of load upon the bridge, all the cross-girders from the centre towards the abutments will be curved horizontally, the middle portion being restrained by the longitudinals from moving bodily with the ends. Each cross-girder except that at the centre, if there be one, will thus present a figure in plan, concave towards the abutment to which it is nearest. This will be accompanied by stressing of the connections, and a transfer to the longitudinals of as much of the tensile stress properly belonging to the booms as the stiffness of the cross-girders may communicate.

This in itself will hardly be considerable, and will be the less on account of a slight yielding which may be expected at the end connections of each longitudinal; but the effect upon the cross-girders by horizontal bending will be much marked. If the case be supposed of a 200-feet span in steel at ordinary loads and stresses, carrying one line of way, with cross-girders 20 feet apart, and having no floor-plates, it may be ascertained, neglecting for the moment any slight yielding of the longitudinal girder connections, that upon the bridge taking its full live load there will be the following approximate results: Movement at each end of the end cross-girders of 3/10 inch, equivalent to a force of 7-1/2 tons, tending to bend them horizontally, and a mean stress on the outer edges of the girders, 12 inches wide, of 8 tons per square inch due to flexure, which, compounded with the ordinary flange stresses, will seem to give rather alarming results. There will also be a longitudinal stress in the rail-girders, at centre part of bridge, of 3/4 ton per square inch. Normal elongation of the longitudinal girder bottom flanges, and compression of the top, modifies the figures unfavourably as to the cross-girder top flange. Yielding of the connections named before has been neglected in arriving at these stresses. If they are sufficiently accommodating to give freely, to a mean extent, as between the top and bottom of each joint, of 1/29 inch, these results will disappear. It is evident, however, that we cannot rely upon good work yielding without the existence of considerable forces to cause it. In the issue it is justifiable to apprehend that the flexing and stressing of the cross-girders will be considerable.

The most favourable case has been taken; if now it is assumed that the floor has continuous plating, the results would seem to be much more astonishing. It will appear on this supposition that the boom stresses, instead of being taken wholly by the booms, are about equally divided between these and the floor structure, each cross-girder connection communicating its share of boom stress to the floor, which for the end cross-girders will approach 40 tons at each connection--considerably more than the vertical reaction under normal loads.

Palpably, these conclusions must be greatly modified by the yield of longitudinal girder ends, and slip of the floor rivets in transverse seams. If these rivets be 3-1/2 inch pitch and 3/4 inch in diameter, the stress at each, as estimated, would be sufficient to induce shear of about 6 tons per square inch--more than enough to cause “slip.” After making this allowance, it is still evident there must be very serious forces at work about the ends of cross-girders under the conditions supposed, probably not less than one half the amounts named, as with this reduction the floor rivets should not yield, given reasonably good work. It is to be observed that the effect of live load only has been introduced, on the presumption that the longitudinals and floor-plating have not been riveted up till the main girders have been allowed to carry the major part of the dead load; but even this cannot always be conceded. The deduction appears to be that the floor and cross-girder connections should be studied with special reference to these possible effects, either with the object of rendering the communication of these forces harmless, or making the floor so that it shall take little or no stress from the main booms, by arranging joints across the floor specially designed to yield, the ends of longitudinals being schemed with the same object. Where there is no plating, the case is, perhaps, sufficiently provided for by making the cross-girders narrow, and the longitudinal girder connections flexible, or by putting these girders upon the top of the cross-girders, when stretching of the bottom flanges of the rail-bearers under load may be expected, within a little, to keep pace with the lengthening of the main booms.

It would appear that light pressed troughs running across the longitudinals would, by yielding in every section, also furnish relief, as compared with the rigidity of flat plates.

By placing the floor at a level corresponding to the neutral axis of the main girders, the communication of stress to the floor may be avoided; but it seldom happens that there is so free a choice as to floor height relative to the girders. This solution is, therefore, of limited application.

It is obvious that somewhat similar effects must obtain to those considered in detail, when the floor structure lies at the level of top booms, but with forces of compression from the booms to deal with, instead of tension.

Chapter IV.

Bracing.

Bracing, whether to strengthen a structure against wind, to insure the relative positions of its parts, or for any other purpose, cannot be arranged with too great care and regard to its possible effects. Forces may be induced which the connections will not stand, with loose rivets as a consequence, and inefficiency of the bracing itself; or, the connections holding good, stresses in the main structure may, perhaps, be injuriously altered.

To take a not uncommon case, let us suppose a bridge consisting of four main girders placed immediately under rails of ordinary gauge, and braced in vertical planes only, right across from one outer girder to the other. If the roads were loaded always at the same time, nothing objectionable would result; but, as a fact, this will be the exception. When one pair of girders only takes live load, and deflects, the bracing under the six-foot will endeavour to communicate some part of this load to the other pair of girders. If the bracing is so designed that some correctly calculated portion of the load can be transferred in this manner, without over-stressing the bars and riveted connections, there will be no harmful consequences; but if not, the bracings will most probably work at the ends; this, indeed, is what frequently happens. There is one other effect which will ensue, if the bracing is wholly efficient; a certain twisting movement of the bridge will occur, which increases the live load upon the outer girder on the loaded side of the bridge to the extent of 10 per cent., with a corresponding lifting force at the outer girder on the unloaded side. These amounts are not serious, but wholly dispose of any advantage it is conceived will be gained by causing the otherwise idle girders to act through the medium of the bracing. In road bridges of similar arrangement, over which heavy loads may pass on any part of the surface, it is clear that the use of bracing between girders should not be taken as justifying the assumption that the load is distributed over many girders, and correspondingly light sections adopted, unless the effect of twisting on the whole bridge is also considered, and justifies this view; for, as already stated in the case of the railway bridge, the net result may be to increase the girder stresses instead of reducing them. Generally, it may be deduced that the better plan for railway bridges is to brace the girders in pairs, leaving, in the case supposed, no bracing between the two middle girders, though there will be no objection to connecting these by simple transverse members of no great stiffness, to assist in checking lateral vibration. For road bridges of more than five longitudinal girders, equally spaced, it may be advantageous to brace right across, the twisting effect with this, or a greater, number of girders not, as a rule, leading to any increase of load on any girder. Figs. 22 to 25 give the distribution of live load, placed as shown, for 3, 4, 5, and 6 girders.

It is to be observed that these statements do not apply to cases where there may be also a complete system of horizontal bracing, the effect of which, in conjunction with cross diagonals, may be greatly different, with considerable forces set up in the bracing, and a modification of girder stresses.

These effects may be so considerable as to call for special attention in design where such an arrangement is adopted.

[Illustration: FIG. 22.]

[Illustration: FIG. 24.]

[Illustration: FIG. 23.]

[Illustration: FIG. 25.]

Somewhat similar straining to that first indicated may occur in bracings placed between the girders of a bridge much on the skew. If this is, on plan, at right angles to the girders, as is commonly and properly the case, the ends will evidently be attached to the girders at points on their length at different distances from the bearings, which points, even with both girders loaded, deflect dissimilar amounts, and the bracing will, if at one end attached near a rigid bearing, transfer some part of the load from one girder to the other, notwithstanding that both girders may be of the same span and equal extraneous loading. It would not be difficult to ascertain the amount of load so transferred from a consideration of the relative movements if free, and the loads on the two girders necessary to render these movements equal, if the deflections were simply vertical; but as there will be some twisting and yielding of the girders on their seats, the calculation becomes involved. If the bracing is placed at about the middle of the girders, the effects noted will be greatly reduced; first, because the difference of movements near the centre will be less; second, any given difference will correspond to a smaller transference of load; and, third, because each girder will there be more free to twist than at the ends. It therefore appears that bracings between the girders of a skew bridge should not be placed near the bearings, though they may be put, with much less risk of injury, near the middle.

Cross-girders on a skew bridge are subject to forces somewhat similar to those which may affect bracing, rendering it desirable to design their attachments in a manner which shall not aggravate the matter, but rather reduce the effects of unequal vertical displacement of their ends where secured to the main girders.

Crossed flat bars as bracing members are objectionable on account of their tendency to rattle, after working loose; but as this effect only ensues in bracing which has first become loose (it being assumed that the bars in any case are connected where they cross), this objection is not itself vital, though greater rigidity is easily obtained by making all such members of a stiff section.

Defective bracing between girders, from neglect of the very considerable forces it may be called upon to communicate, is very common; the writer has seen many such cases, of which one is here illustrated in Fig. 26.

[Illustration: FIG. 26.]

This bridge, of the section shown, and 85 feet span, had very light web structure. The bracings, of which there were two sets, were wholly inefficient, the end rivets being loose in enlarged holes. Upon the passage of a train there was a positive lurching of the girder tops from side to side. The integrity of the bridge was really dependent upon such stiffness as there was in the girders, and unplated floor.

A common but indifferent method of keeping the top members of main girders in line is by the use of overhead girders alone, frequently curved to give the requisite clearance over the road. This cannot be considered as wholly inefficient, as sometimes maintained, since it is evident that the closed frame formed by the floor beams, the web members of the main girders, and the overhead girder itself, must take a greater force to distort it than would be necessary to cause deformation of a corresponding degree, in an open frame formed by the omission of the overhead girder; but it is not a method to be recommended, its precise utility is difficult to estimate, and, if the cross-girder attachments are of a rigid character, tends to increase the stresses induced at those connections. The latter consideration is, however, not applicable to this arrangement alone. All overhead bracing favours this by restraining the tendency of the top booms to cant inwards when the floor beams are loaded; and though this restraint may be quite harmless, it is desirable that close attention be given to these effects in designing bridges which make a complete frame more or less rigid in its character. “Sway” bracing, sometimes introduced at right angles to the bridge between opposite verticals, tends to emphasise these effects by rendering the cross-section of the bridge still stiffer, besides making it a matter of difficulty to ascertain how much of the wind forces on the top boom is carried to the abutment by the top system of bracing, and how much by the floor. The author does not, however, mean to suggest that it cannot be used with propriety, but rather that extreme care is desirable in considering its ultimate effect on the rest of the structure.

For girders of moderate depth there may be on these grounds a distinct advantage in abandoning overhead bracing, and securing rigidity of the top boom, and adequate resistance to wind forces, by making the connection between the cross-girders and the web members sufficiently good to insure, as a whole, a stiff [U]-shaped frame; but this, with the ordinary type of rocker arrangement under the main girder bearings, will not be entirely free from objection, as canting of the girders due to floor loading will throw extreme pressure on the inner end of each rocker. There appears to be no reason why the cylindrical knuckle should not in this case be supplanted by a cup hinge, allowing angular movement of the girder bearing in any plane.

[Illustration: FIG. 27.]

The efficient stiffening of light girders, as in the case of foot-bridges, from the floor, where this is at the bottom flanges, renders very narrow top booms permissible. This is a decided advantage where lightness of appearance is aimed at; but it is not unusual to see an attempt made in this direction by introducing gusset plates of very ample proportions between vertical members of the girders, and the projecting ends of flimsy transoms, carried beyond the width of the bridge proper, these being of a section wholly out of proportion to the brackets they are supposed to secure. Whatever may be the amount of strength necessary at the point A, in Fig. 27, there should not be less throughout the transom from one girder to the other. The degree of strength and stiffness required in this member, and in the vertical stiffeners is not, as a rule, great. Information to enable this question to be dealt with as a matter of calculation is somewhat scanty; but it would appear to be sufficient to insure safety that, for an assumed small amount of curvature in the compression member, the forces outwards corresponding to this curvature, due to thrust, should be resisted by verticals and transoms of strength and stiffness sufficient to restrain it from any further flexure. It will, of course, be necessary also to take care that the compression member is good as a strut between the points of restraint. A simple and sufficiently precise method of dealing with this question is much needed. In cases where the floor weight rests on the flange projection, it is also necessary to give the transom additional strength to an extent enabling it to resist the twisting effort between any two of these transverse members; further, resistance to wind on the girder has to be provided in both transoms and verticals.

It may be hardly necessary to insist that bracing intended to stiffen a structure against wind, local crippling, or vibration, should be made complete, not stopping short at some point, because it cannot conveniently be carried further, as is sometimes done, unless the strength of those parts of the structure through which the forces from the bracing must be communicated to the abutments is sufficiently great, considered with reference to other stresses in those parts which have also to be endured.

Bracing stopped short in this way, making only the central part of a bridge rigid, may have the effect of increasing the forces to which the unstiffened end members would otherwise be liable. Such a structure would evidently be much stiffer against wind-gusts than if no bracing existed--the resistance to a blow would be increased; but the power to maintain that greater resistance being confined to the intermediate bays, the unbraced ends would be subject to greater maximum forces than if bracing were wholly omitted. The net effect may still be better than with no bracing, the point raised being simply that of an increase of stress in particular end members.

In the bracing of tall piers, the rising members of which will be subject to any considerable stress, if the diagonal members are not finally secured when the piers are under their full load, or an initial stress of proper amount induced in those members, the effect of loading will be to render them slack; so that an appreciable amount of movement at the top may occur before it can be limited by the efficient action of the bracings. This effect under blasts of wind or continual passage of trains may, indeed, be dangerous. Similar considerations apply to the top wind bracing of deep girder bridges, influencing also the bottom bracing in a contrary manner, which calls for attention in fixing the unit stresses for such members.

The bracing of sea-piers is very liable to slacken if made with pin-and-eye ends, as is often done for round rods. The detail presents advantages in erection, but is not altogether satisfactory in practice. Such connections are continually working. In the finest weather, with the sea quite smooth but for an almost imperceptible wave movement, the lower parts of such structures will be found, as a rule, to have some slight motion. This is very trying to bracing; nor is there room for surprise when it is considered that these oscillations, occurring at about ten to each minute, never wholly cease, and amount in the course of one year to over five million in number.

Bracing attached in such a manner that there can be no initial slack, or slack due to wear under endless repetitions of small amounts of stress, will have a much better chance to keep tight. The advantage presented by round rods in offering little surface to the water, is more than negatived by inefficiency of the usual attachments for such rods.

The author has observed that bracing of members possessing some stiffness, and with good end attachments to ample surfaces, appears to stand best in ordinary sea-pier work. For such structures the bracing should consist of a few good members, with a solid form of attachment, rather than of a multiplicity of lighter adjustable members, which will commonly give great trouble in maintenance; being very possibly also, in the case of sea-pier work, in unskilled hands. If round rods must be used, they will stand much better if made of large diameter.

Before leaving the subject of bracing, it may not be out of place to refer to wind pressure, as this may so much affect the proportioning of the members.

Some years since the author had occasion to examine a number of structures with respect to their stability. Of foot-bridges from 60 feet to 120 feet long, three or four, when calculated on the basis recommended by the Board of Trade as to pressures upon open-work structures, worked out at an overturning pressure of from 18 lb. to 22 lb. per square foot. These bridges had been many years in existence; it is, therefore, fair to assume that no such wind in the direction required for overturning had expended its force upon them as to the whole surface.

[Illustration: FIG. 28.]

Particulars were taken in 1895 of a notice-board, presenting about 12 square feet of surface, which was blown down in the great storm of March 24 of that year, at Bilston, in Staffordshire. It was situated at the foot of a slight slope, over which the wind came, striking the obstruction at right angles. The board was mounted on two oak posts of fair quality and condition, which broke near the ground at bolt holes (see Fig. 28). The force required to do this, at 9000 lb. modulus of rupture--a moderate value--corresponds to 50 lb. per square foot on the surface exposed above the break.

In the same neighbourhood, at the same time, considerable damage was wrought in overturning chimney stacks, to buildings and roofs; the general impression in the locality being that the storm was of exceptional, even unprecedented, violence. Bilston, it should be noted, lies high.

At Bidston Hill, near Birkenhead, on the same occasion, a pressure of 27 lb. was registered. In another part of the country it is said to have been 37 lb. Wind is so capricious in its effects over small areas as to render it probable that the maximum pressures have never been recorded; but this is a matter of little importance where general stability and strength only are concerned. The instances cited, though by themselves insufficient to throw much light on the question, may be of use in connection with other known examples.

Chapter V.

Riveted Connections.

Considerable latitude is observable in the practice of engineers in the use of rivets. Numberless experiments to determine the resistance of riveted connections have from time to time been made, but these are not to be considered by themselves as final, when the results of experience in actual construction, are available for further enlightenment.

The class of workmanship so largely influences the degree in which rivets will maintain their integrity that it is only by the observation of a large number of cases, including all degrees of workmanship, that any reliable conclusions may be drawn. In this respect laboratory experiments have an apparent advantage, as the conditions may be kept sensibly the same; but, on the other hand, no such investigation reproduces the circumstances of actual use, which alone must in the end determine the utility of any inquiry for practical application.

The author has studied the particulars of a number of cases to ascertain under what conditions as to stress, having due regard to the effects of vibration, rivets will remain tight, or become loose. Every loose rivet that may be found cannot, of course, be taken as being due to excessive stress; the more frequent cause is indifferent work, evidenced by the fact that neighbouring rivets will frequently be found quite sound, though the failure of some will cause a greater stress upon the remainder. When rivets loosen as the direct result of over-stress, it is usually by compression of the shank and enlargement of the hole, or by stretching of the rivet and reduction of its diameter. Instances of failure by partial or complete shear are extremely rare; indeed, the author has never yet found one, though when a rivet has first worked loose, as a result of excessive bearing pressure or bad work, it is not uncommon to find it cut or bent as an after consequence.

In estimating stresses at which rivets have remained tight, or loosened, as the case may be, examples have generally been chosen in which there could be no reasonable doubt as to the amount of those stresses by the ordinary methods of computation. This is clearly most important, as, if any appreciable uncertainty remained as to the degree of stress, the results deduced would be of little value. For this reason those instances in which the loads upon girders, or parts of girders, may find their way to the supports by more than one route, are to be regarded with caution, as are those in which full loading possibly never obtains, but which may, on the other hand, perhaps have been frequent. The working diameter of the rivet as it fills the hole has been used in making the computations; in some cases from direct measurement from particular rivets, in others with a suitable allowance for excess diameter of hole, according to the class of work under consideration.

Dealing first with main girders, it may be said that rivets attaching the webs of plate girders to the flange angles rarely loosen, though subject to considerable stress. In illustration of this may be named a bridge for two lines of way, 85 feet effective span, having two main girders with plate webs, and cross-girders resting on the top flanges, previously referred to (see Fig. 26).

The girders, which were 6 feet 9 inches deep, had a bearing upon the abutments of 4 feet; the rivets were 7/8 inch in diameter and 4 inches pitch. There is in a case of this kind some little uncertainty as to what is the stress on the flange angle rivets at, or very near to, the bearings; but, taking the vertical rows of rivets at the web joints near the ends as presenting less uncertainty, the stress per rivet works out at 4·8 tons, being 4 tons per square inch on each shear surface, and 11 tons per square inch bearing pressure upon the shank in the web plate, which was barely 1/2 inch thick. This bridge was frequently loaded upon both roads, but with one road only carrying live load, the stresses in the more heavily loaded girder would be fully 90 per cent. of those obtaining as a maximum. There was on this bridge, which had been in use 31 years, considerable movement and vibration.

It is by no means uncommon to find cases of rivets in main girders taking 11 tons per square inch bearing pressure--occasionally more--and remaining tight. As furnishing an instructive, though slightly ambiguous, instance of rivets in single shear, may be cited a bridge not greatly less than that just referred to, of about 65 feet span, carrying two lines of way, there being two outer and one centre main girder of multiple lattice type, with cross-girders in one length 4 feet apart, riveted to the bottom booms of the main girders; these rivets, by the way, were in tension. The floor was plated, the road consisting of stout timber longitudinals, chairs, and rails (Fig. 29).

[Illustration: FIG. 29.]

It should be noted that there is in this case some difficulty in ascertaining the precise behaviour of the cross-girders, affecting the proportion of load carried by the outer and the inner main girders. Strict continuity of all the cross-girders could only obtain if the deflection of the main girders were such as to keep the three points of suspension of each cross-girder in the same straight line. A close inquiry showed that this was very far from being the case, and that while each cross-girder at the centre of the bridge would, under load, by relative depression of the middle point of support, be reduced to the condition of two simple beams, those at the extreme ends of the span would behave as continuous girders.

With both roads carrying engine loads equal to those coming upon the bridge, the author estimates that for the centre main girder the shear on the rivets of the end diagonals, secured by one rivet only, was 14·9 tons per square inch, and the bearing pressure 16·3 tons; the flange stress being 7·1 tons per square inch net. The outer main girders are most heavily stressed when but one road, next to the outer girder considered, carries live load. For this condition the stresses work out at 9 tons per square inch shear on the rivets of the end diagonals, and 9 tons bearing pressure, the flange stress being 5·7 tons per square inch on the net section.

Without intending to throw any doubt upon the substantial truth of these results, it must be admitted that instances of greater simplicity of stress determination are much to be preferred. For purposes of comparison, but not as having any other value, the results have also been worked out on the supposition of all cross-girders acting each as two simple beams, and also for strict continuity, and are here tabulated, together with the conclusions given above.

The cross-girders were moderately stressed, and the tension on the rivets attaching them to the main girders probably did not exceed 3 tons per square inch.

It should be pointed out that the traffic over the bridge was small. The centre main girder but seldom bore its full load, though at all times liable to receive it. Much importance cannot, therefore, be attached to the results for this girder, other than as showing how a structure may stand for many years, though liable at any time to the development of stresses which would commonly be regarded as destructive, or nearly so.

Examples Of Rivet Stresses, Etc., In Lattice Girders.

---------------------------------+-----------+------------+--------- | Cross- | Cross- | | Girders | Girders as | Correct | as Simple | Continuous | Results. -- | Beams. | Beams. | +-----------+------------+--------- | Stress in Tons per Square Inch. ---------------------------------+-----------+------------+--------- Centre girder, 63 ft. span (both | | | roads loaded): | | | Rivets in diagonals--Shear | 13·7 | 17·2 | 14·9 Do. Bearing | | | pressure | 15·0 | 18·8 | 16·3 Flange | | | stress | 6·8 | 8·5 | 7·1 | | | Outer girder, 66 ft. span (near | | | road loaded): | | | Rivets in diagonals--Shear | 9·6 | 8·2 | 9·0 Do. Bearing | | | pressure | 9·6 | 8·2 | 9·0 Flange | | | stress | 5·9 | 5·1 | 5·7 ---------------------------------+-----------+------------+---------

The material and workmanship of the bridge were good. The rivets of the centre girder end diagonals, 1 inch in diameter, were originally 7/8 inch, but on becoming loose were cut out, the holes reamered, and replaced by the larger size, which remained tight, and to which the stress figures apply. The rivets in the diagonals near the centre, 7/8 inch in diameter, which were subject to reversal of stress, occasionally worked loose, and were more than once replaced. The riveting in the outer girder diagonals, subject to smaller stresses, much more frequently developed, also gave trouble, particularly those liable to counter stresses.

Apart from looseness of rivets, the general appearance and behaviour of the bridge, which had been in existence about twenty years, was not suggestive of any weakness.

Of smaller girders, an example showing the necessity for care in discriminating, if it be possible, between looseness of rivets resulting from over-stress and that due to other influences may first be quoted. Two trough girders, of 11 feet effective span, each of the section shown in Fig. 30, 11-1/2 inches deep at the ends, 14 inches at the middle, with 1/4-inch webs, and rivets 3/4 inch in diameter, of 4-1/2-inch pitch, showed certain defects, of which one, it may be incidentally mentioned, was a cracked web (Fig. 31). From the nature of the arrangement the lower web rivets, which were loose, would receive the first shock of the load coming upon the span, but there were evidences indicative of original bad work. The angle bars gaped, suggesting that these had first been riveted to the bottom plate, and left sufficiently wide to allow the web to be afterwards inserted, the rivets failing to pull the work close, and then readily working loose. Here there is considerable uncertainty as to how much of the loosening is to be attributed to bad work, and how much to stress. It may, however, be remarked that whatever bearing stress was the ultimate result of the load hammering on the lower angle flanges, loosening rivets never perhaps really tight, the stress of 7 tons per square inch bearing pressure on the upper rivets, though aggravated by considerable impactive force, was not sufficient to loosen these. The girders were taken out after being in place sixteen years.

[Illustration: FIG. 32.]

[Illustration: FIG. 30.]

[Illustration: FIG. 31.]

An instance of undoubted excessive bearing pressure was found in the cross-girders of a bridge, mentioned on p. 15, of which so many web plates were cracked. This bridge, carrying two lines of way, had outer main girders, and long cross-girders with 1/4-inch webs and 3/4-inch rivets, 4 inches pitch. The rivet stresses work out at 4·3 tons per square inch on each shear surface, and 24 tons per square inch bearing pressure. For one road only being loaded, the latter figure falls to 18·5 tons. The traffic over this bridge, twenty years old, was considerable, rapid, and heavy. It is hardly necessary to add that a large number of the rivets were loose, one of which is shown in Fig. 32.

[Illustration: FIG. 33.]

To take another case relating to a floor system of extremely bad design (Fig. 33). The main girders were 11 feet apart, 35 feet span, the floor having two cross-girders only, spaced at 11 feet 3 inches, and 9 inches deep, supporting hog-backed trough longitudinals. The cross-girders were at their ends but 6-3/4 inches deep, the distance from the bearing of cross-girders to centre of longitudinals carrying a rail being 2 feet 10 inches, in which length were eight rivets in the web and angles at the top, and six at the bottom, all 3/4 inch in diameter.

The shear stress on the upper rivets works out at 7·3 tons per square inch on each shear surface, the bearing pressure 20·6 tons per square inch. On the lower rivets the shear stress becomes 9·7 tons, and the bearing pressure 27·4 tons, per square inch. Care was exercised in computing these stresses, that part of the bending moment carried by the web being allowed for, but it must be admitted that the result is, probably, approximate only. The sketch here given shows the cross-girder end and section. The rivets, though in double shear, were, as might be expected, loose, notwithstanding that the traffic over the bridge was moderate, and quite slow. The floor system was remodelled after twelve years’ use.

In illustration of the behaviour of rivets in the ends of long cross-girders, both shallow and weak, and many years in use under heavy traffic, may be cited connections having end angle bars to the cross-girders, with six rivets through the web of main girders. The bearing pressure worked out at 7·8 tons per square inch. Many rivets were loose, but it should be remarked that the workmanship was not of the best class, and the cross girders flexible: a characteristic very trying to end rivets, and inducing a stretch in some, already referred to as a possible cause of loosening. This will be apparent if the probable end slope of weak girders be considered. The author concludes that this inclination should not, for ordinary cases, exceed 1 in 250; but the ratio must largely depend upon the degree of rigidity of the part to which the connection is made. It is commonly regarded as bad practice to submit rivets to tension, yet this is frequently, though unintentionally, permitted in end attachments, without any attempt to limit the amount of tension. With suitable restrictions, there appears no serious objection to rivet tension for many situations.

Another instance of cross-girder end connections of a different type is illustrated in Fig. 34.

The main girders of the bridge were 12 feet apart, each cross-girder end carrying its share of the half of one road. The mean bearing pressure upon the rivet shanks works out at 5·8 tons per square inch for the six rivets of the original joint, but in the particular joint shown some of the rivets had loosened, making the bearing pressure upon the remainder about 8·7 tons per square inch. It is apparent there must have been considerable stress on the top and bottom rivets which loosened. These two rivets would also, because of difficult access, be in all likelihood insufficiently hammered up. The joints worked rather badly; the loose rivets had “cut” to a considerable extent, a process materially assisted by the gritty nature of the ballast (limestone), particles of which, getting into the joint, contributed to the sawing action; this had clearly been taking effect for some considerable time. (See Fig. 35.)

[Illustration: FIG. 34.]

[Illustration: FIG. 35.]

The two cases of cross-girder ends given are both rather exceptional in character, and in each case the defects appear to be due to general bad design and workmanship rather than to any serious excess of bearing pressure. This may be illustrated by taking the common case of cross-girders, 2 feet deep, carrying two roads, and having end angle irons riveted to the web and stiffeners of the main girders by ten rivets in single shear at each end. In this example, which is, for old work, simply typical, and does not relate to any specific instance, the bearing pressure on the rivets will work out at from 6 to 8 tons per square inch, and will seldom be accompanied by looseness of rivets, and then only as a result of faulty work.

Some sketches of rivets taken from old bridges have already been given in connection with the cases to which they belong; a few others are here shown (Figs. 36 to 40) to further illustrate what may be the actual condition of rivets after some years’ use, and how different from the ideal rivet upon which calculations are based. These are, however, bad instances.

[Illustration: FIG. 36.]

[Illustration: FIG. 37.]

[Illustration: FIG. 38.]

[Illustration: FIG. 39.]

[Illustration: FIG. 40.]

It should be noticed that rivets may, if in double shear, be loose in the middle thickness, due to enlargement of the hole in the central part and compression of the rivet, and yet show no sign of this by testing with the hammer. There is, however, generally marked evidence of another kind in the “working” of the inner part, as, for instance, the web of a plate girder, in which case a discoloration due to rust is to be found along the edges of the angle bars, or a movement may be detected on the passage of live load. Red rust is, in fact, frequently an indication of something wrong, when no other evidence is apparent. In plate girders having [T] or [L] bars brought down and cranked on to the top of shallow cross-girders, it is not uncommon to find the rivets attaching these bars to the cross-girder tops loose, due to causes already dealt with. The riveted connection should, as to strength, bear some relation to the strength and stiffness of the parts secured, if the rivets are to remain sound.

It may be well to give here a summarised statement of the results already named, for purposes of ready reference. These by themselves are not sufficient to enable working stresses to be deduced, though they are instructive. The author has found many instances of shear and bearing stresses in excess of those usually sanctioned, under which the rivets behaved well, but is not now able to give precise particulars of these.

Examples Of Rivet Stresses.

---------+-----+---------+------+------+--------+----------------- -- |Span | Where |Shear |Single|Bearing | Tight or Loose. | in | Found. |Stress| or |Pressure| |Feet.| | in |Double|in Tons | | | | Tons |Shear.| per | | | | per | | Square | | | |Square| | Inch. | | | |Inch. | | | ---------+-----+---------+------+------+--------+----------------- Main {| 85 | Web | 4·0 | D | 11·0 | Tight. girders {| 66 |Diagonals| 9·0 | S | 9·0 | Many loose. {| 63 | „ | 14·9 | S | 16·3 | Tight generally. | | | | | | {| 11 | Web | 1·4 | D | 7·0 | Tight. Small {| 26 | „ | 4·3 | D | 24·0 | Many loose. girders {| 11 | „ | 7·3 | D | 20·6 | Loose. {| 11 | „ | 9·7 | D | 27·4 | Loose. | | | | | | End {| 27 | Ends | 5·4 | S | 7·8 | Loose. connec- {| 12 | „ | 1·8 | D | {5·8 |}Many loose. tions {| | | | | {8·7 |} | | | | | | (Type | | | | | | case) | 26 | „ | 4·8 | S | 7·0 | Tight. ---------+-----+---------+------+------+--------+-----------------

It is probable that the fact of a rivet being in single or in double shear largely affects its ability to resist the effects of bearing pressure, as commonly estimated. In the first case, the rivet-shank must bear heavily on the half-thickness of the plates or bars through which it passes, rather than on the whole thickness; and it is to be supposed that under this condition it will work loose at a lower average stress than if it were in double shear, and the pressure better distributed.

[Illustration: FIG. 41.]

[Illustration: FIG. 42.]

The author has no very definite information in support of this contention, but suggests that for double shear the permissible bearing pressure may probably be as much as 50 per cent. greater than for rivets in single shear; the difference being made rather in the direction of increasing the allowable load on double-shear rivets, than in reducing that upon rivets in single shear. The propriety of this is evident when it is considered that the practice has commonly been to make no distinction, so that whatever bearing pressures are found to be sufficient for both cases may be increased for those capable of taking the greater amount. Figs. 41 and 42, here given, illustrate the behaviour of rivets under the two conditions.

With reference to the amounts of the stresses to which rivets may be subject, the author concludes, as a result of his experience, coupled with a consideration of known laboratory tests, that for all dead load these may be quite prudently higher than is frequently taken. For iron the shear stress to be 10 per cent. less than the stress of parts joined; and the bearing pressure--for single-shear rivets, 20 per cent.; and for double-shear rivets, 80 per cent. greater. For ordinary mild steel the shear stress to be 20 per cent. less than the stress in parts connected, and the bearing pressure equal to it for single-shear rivets; and 50 per cent. more for rivets in double shear, though the two latter values may probably approach those for wrought iron in steel of the higher grades sometimes used in bridge-work. For live load, or part live and part dead load, the same rules may apply, the reduction of the nominal working stress, arrived at by any one of the methods in use which may be adopted, affecting both the parts connected, and the rivets connecting them. For reverse stresses it is advisable to keep the shear stress in any rivet so low, say 3 tons per square inch, that the frictional resistance of the parts gripped by the rivets shall be sufficient to prevent any tendency to slip under the influence of the smaller of the two forces to which the part is liable, to insure that, if brought to a bearing in one direction by the greater force, it shall not go back with reversal of stress. This requirement may be open to some question with respect to good machine-riveted work, but for hand-riveted connections it may certainly be adopted with wisdom.

The following table will show at a glance how the stresses proposed vary with the unit stresses governing the main sections.

Proposed Table Of Rivet Stresses.

-----------+-------------+----------------+---------------- Unit Stress| |Bearing Pressure|Bearing Pressure in |Shear Stress.|for Single-Shear|for Double-Shear Member. | | Rivets. | Rivets. -----------+-------------+----------------+---------------- _Wrought Iron.--Tons per Square Inch._ 3·0 | 2·7 | 3·6 | 5·4 4·0 | 3·6 | 4·8 | 7·2 5·0 | 4·5 | 6·0 | 9·0 6·0 | 5·4 | 7·2 | 10·8 7·0 | 6·3 | 8·4 | 12·6 _Steel.--Tons per Square Inch._ 4·0 | 3·2 | 4·0 | 6·0 5·0 | 4·0 | 5·0 | 7·5 6·0 | 4·8 | 6·0 | 9·0 7·0 | 5·6 | 7·0 | 10·5 8·0 | 6·4 | 8·0 | 12·0 9·0 | 7·2 | 9·0 | 13·5 -----------+-------------+----------------+----------------

NOTE.--Tension on rivets to be limited to one-half the permissible shear stress, the holes being slightly countersunk under snap-head.

It may be objected that the shear stresses in the proposed table are somewhat high for wrought iron and steel. This feature is intentional, and is supported by the consideration that whereas there may be loss of strength in the members of a structure by waste, there is no such loss in rivets, if the work is so designed that there shall be no loosening. Any allowance that may be desirable for loose or defective field rivets is left to be dealt with as may be considered advisable for each particular case, the table as it stands being applicable only to riveting not below the standard of first-rate hand work.

Cases of loose rivets in main girders over 50 feet span, due to any cause but bad work, are extremely rare, unless resulting from the action of some other part of the structure. It may be stated broadly that for railway bridges of less than perfect design, the nearer the rail, the more loose rivets, generally at connections. This is, no doubt, largely due to the severe impact of the load, the effects of which are greater near the rail, both because of the small proportion of dead load, and because this effect has been but little modified by the elasticity of any considerable length of intervening girder-work. In addition to this, it is quite usual to find the rivets more heavily stressed, even though the load be considered as “static,” in the floor system than in the main-girders, though the reverse should be the case. It is unfortunate that those parts which require the best riveting--viz., the connections--are commonly dealt with by hand; and for this reason it is the more necessary to design these with the greatest care.

Any arrangement which favours the gradual acceptance of stress by one part from another will contribute to the integrity of riveted connections, and lessen the liability of the material to develop faults. In other branches of design this is well recognised, but appears in much old bridge work to have been entirely overlooked.

Bridges carrying public roads very seldom furnish examples of loose rivets; the conditions are generally much more favourable, impact being practically absent, full loading infrequent, and the proportion of dead load to live, high.

It is, perhaps, hardly necessary to insist upon rivets being, apart from mere considerations of strength, sufficiently near together to insure close work and exclude moisture. Outside edge seams should never be more widely spaced than 16 times the thickness of the plates; 12 thicknesses apart is better. In the case of angle, tee, and channel sections, the greater stiffness of the section makes wider spacing allowable up to, say, 20 times the thickness; but this must be governed largely by the amount of riveting required to pull the parts close together. Where more than four thicknesses are to be gripped by the rivets, 3/4 inch in diameter is hardly sufficient to insure tight work, and quite unsuitable if the plates exceed 5/8 inch thick.

Chapter VI.

High Stress.

High stress, provided it be well below that at which immediate injury results, or possible failure, is not uniformly objectionable. It may be first considered relative to the absolute and elastic limits of strength, next with respect to the range of stress, and, finally, with regard to the frequency of application. For practical purposes--that is, for the continued efficiency of a structure--the limit of elasticity must be considered to be the limit of strength, or, more strictly, the limit for all those parts of the structure which must, so long as it lasts, be liable to the original measure of stress. There may be places in a bridge, however, over-stressed only in the earlier period of its existence, which, by being over-stressed and suffering deformation, permit the origin of this distortion to be harmlessly met in some other way. In such a case the injury done to that part does not, of necessity, lead to any culminating disaster; indeed, were it not for this plasticity it is probable a large number of bridges would fail after being in use but a short time. As for riveting, so in dealing with the amount of stress to which a member is supposed to be liable, it should be clearly understood by what method this has been arrived at, whether the value assigned is the actual measure of the stress, or simply the conventional amount arrived at in the conventional way; perhaps neglecting web section in plate girders, or without regard to the various influences which may reduce or increase the nominal amount of stress, or including only a partial recognition of those influences. In any case quoted the stress named is that at which the author arrives by the ordinary methods of computation carefully applied, where these appear to be sufficiently precise, unless any qualifying remark be added. Extreme flange stress is in special cases computed, first on the gross section by estimating the moment of inertia on that basis, and deducing the stress at the holes from the ratio of net to gross section at the extreme fibres; a method more correct than by reference to the moment of inertia of the net section. Any exhaustive refinement in the study of stresses is not attempted, both because it is beyond the author’s powers of analysis, and for the reason that such results are not comparable with the results of ordinary methods of calculation in practice. Effective spans are taken at moderate values, and all exaggeration is avoided.

The effects of impact in any part vary so much with nearness to, or remoteness from, the living load, and the frequency of development of the maximum stress from all causes acting together is so much affected by the same consideration, that it is apparent a nominal stress which may be harmless in one part of a bridge may be destructive in some other, a statement borne out by observation. Stress, as ordinarily stated--i.e., at so much per square inch, uniform across a section--is seldom a cause of trouble. In nearly all cases of failure there is an accompanying localised destructive stress, either in rivets or elsewhere, with crippling or deformation of some essential part. In the tension flanges of main girders with uncomplicated stress, this may run up to an amount very considerably beyond the ordinary limits without producing signs of distress. The same remark applies to the compression flanges, if these be in themselves sufficiently stiff, or properly restrained from side flexure. In support of the above statement may be quoted the following instances relating to wrought-iron structures:--

A bridge of 60 feet effective span, having girders immediately under the rails, had a flange stress of 6·3 tons per square inch. Another of 64 feet span, carrying two lines of way, with outside main girders and cross-girders, had the flanges of the former stressed to 6·8 tons per square inch. A third, of 76 feet span, of similar construction to the last, was stressed in the main girder flanges to 7·5 tons per square inch. The webs were not included in the computation; the figures, therefore, compare with ordinary practice. In these three cases the main girders showed no signs of distress, referable to the results stated, though the top flanges in the last case were curved inwards. The effect of this flexing of the flange would be, of course, to increase the amount of compressive stress along one edge, though to what degree cannot now be stated.

[Illustration: FIG. 43.]

[Illustration: FIG. 45.]

[Illustration: FIG. 44.]

A further instance of considerable flange stress occurred in a bridge of seven nearly equal continuous spans, 25 feet generally, the end and greatest span being 29 feet 6 inches, centre to centre of bearings. Some details of the bridge are given in Figs. 43 to 45. The four inner main girders under rails were 2 feet deep, with webs 1/2 inch thick over piers, and 3/8 inch at abutments, having flanges of two [L] bars, 3 inches by 3 inches by 5/8 inch. There were also two outer girders of the same depth, with single [L] bars. Plate diaphragms of full girder depth and particularly stiff were carried right across the bridge at the centre of the spans, and over the piers. The girders, though evidently designed to be continuous, had very poor flange joints at each bearing, of little more than one half the flange strength (see Fig. 45). It is doubtful if the girders acted with strict continuity for long after erection, as the excessive stress in the rivets of the flange joint would, for that condition, have been nearly sufficient to shear them. It is probable that this being so, the joints first yielded, relieving the bending moment over the piers, and increasing it near mid-span. Whether the end spans be considered as strictly continuous with the rest, or as simple beams, the maximum bending moments would not greatly differ, though occurring for continuity over the pier, for free beams at the centre. There is, however, an intermediate condition which makes the moments at these two places less than either maximum, but equal to each other; a condition of semi-continuity agreeable to a partial efficiency of the joints referred to. It is this state which has been calculated, giving the minimum stress value that can be accepted. The diaphragm has been assumed to transfer to the outer girders a due proportion of the load. With this explanation it may now be stated that, under engine loads corresponding to those running, the flange stress worked out at 7·4 tons per square inch tension, web included, or 9·7 tons per square inch without considering the web; which stresses, it is more than probable, may have been greater. The figures include the consideration of anything which may contribute to lowering the stress, and are hardly to be compared with those worked to in ordinary design of new work, in which it would be quite usual to neglect the assistance of the outer girders and the webs, to work to heaviest engine-loads, and possibly include an allowance for the effects of settlement. Dealt with in this way the girders would seem to be of about one-fourth the strength that would be required in the design of a new bridge, in which certain elements of strength would be deliberately ignored.

The ironwork was in good condition, there was no ordinary evidence of weakness apart from the calculated results, the vibration was distinctly moderate, and the deflection, though not recorded, was certainly small. The bridge did, indeed, seem somewhat inert under load, and favours a suspicion, the author entertains, that old girderwork long overstressed may have a sensibly higher modulus of elasticity than newer work at more moderate stresses. The traffic was not very considerable, and both roads, of the same spans, but seldom loaded at the same time; though with this construction of bridge there would in either case be very little difference. The author recalls no reason for supposing that the piers had yielded in any sensible degree. The bridge was rebuilt after some thirty-six years’ use.

Stress of considerable amount in the flanges of a latticed main girder of 63 feet span has already been noticed in the chapter on “Riveted Connections,” which for the tension boom worked out to 7·1 tons per square inch, the flanges in this case showing no signs of weakness. An instance has also been given in dealing with a case of side flexure in which the extreme fibre stress was calculated to be 10 tons per square inch, the girder recovering its form when relieved of load.

As to stress in cross-girder flanges, an example may be quoted of a bridge of 109 feet span, carrying two roads, having outside main girders, with cross-girders between; these latter were stressed in the flanges to 6·7 tons per square inch (webs not included), if the partial distribution among the girders (which were spaced 6 feet apart) by the rails and longitudinal timbers be neglected. There is some reason to think in this instance that distribution had the effect of reducing the stress quoted, as the observed deflection of the cross-girders was materially less than that calculated for girders acting independently of each other, though this may be in part due to a cause already hinted at. Rigidity of the cross-girder ends, where attached to the heavy main girders, would also tend to moderate the stress. No very definite conclusion can therefore be deduced from this instance.

To take another case of less uncertainty, the bridge of 35 feet span (see Fig. 33), referred to in “Riveted Connections,” may again be cited. The extreme fibre stress in the cross-girder flanges worked out at 6·3 tons per square inch, web included, or 6·5 tons, exclusive of the web. It cannot be said in this example that the girders showed no signs of weakness, as the deflection under live load was 1/2 inch on the span of 11 feet, in addition to a permanent set of 3/4 inch, largely due, however, to “working” rivets.

A better and altogether conclusive case of the way in which cross-girders may occasionally suffer considerable stress, and show no sign, is furnished by two cross-girders, of which some particulars are here given. These girders occurred in the floor of a very acute angled skew bridge, riveted at one end to the main girders in a manner which was very far from fixing the ends, resting at the other end on a masonry abutment. The first girder was about 19 feet effective span, 12 inches deep in the web, with angle bar and plate flanges. The girders were spaced 6 feet apart, and were connected under the rails by [T]-bars, cranked down to face the webs, and riveted through. Though these [T]’s had little stiffness, yet the frequent vertical movements of the girders relative to each other, under passing loads, had broken the majority of the [T]-bars at the bends, so that no notice need be taken of these as transferring load from any one cross-girder to its neighbour. The floor covering consisted of timbers about 4 inches thick, also incompetent to transfer any sensible proportion of the load on a girder to others 6 feet distant. Upon the floor was cinder ballast, with sleepers, chairs, and ordinary bull-headed rails. The stress to which the girder was liable works out at 8·4 tons per square inch, on the extreme fibres of the net section, web included; or 9·1 tons, neglecting the web, under engine-loads of a common amount. The other girder had an effective span of about 22 feet, as before 12 inches deep in the web, with angle bar and plate flanges. The stress per square inch was 10·5 tons, web included, or 11·1 tons per square inch, neglecting the web. This girder carried three rails, one of which was near to the abutment bearing, so that there was no great difference in the stress induced whether all three rails were loaded or the pair only. The traffic over the bridge was very great, but of moderate speed. It must have been a common occurrence for the girders to take the full loads. The heavier engines passed scores of times in a day--lighter engines probably one hundred times. The bridge was about twenty years old, yet these cross-girders, when removed, showed no other sign of age and wear than that due to rust.

[Illustration: FIG. 46.]

All the foregoing instances relate to wrought-iron bridges. Two cases of steel construction are here added, the first of these furnishing an example of high girder stress somewhat remarkable. This was found in a trough girder of a strange pattern, of which a section is here given (Fig. 46). The bridge to which it belonged carried a siding, over which engines of less than the heaviest class sometimes passed at a crawling pace. The larger of the two girders carrying the rails was 15 feet 8 inches effective span. The sides of the trough consisted each of two vertical plates, originally 1/2 inch thick, but wasted to an aggregate thickness of 5/8 inch. These plates 6 inches deep, were connected at their lower edges to angle bars, 3 inches by 3 inches by 1/2 inch, which again were riveted to a bottom plate 16 inches wide, originally 1/2 inch thick, wasted to 3/8 inch. Lying in the bottom of the trough, and riveted through the inner angle flanges, was a bridge-rail. Assuming that the metal retained its elastic properties from top to bottom of the section, at whatever stress, this works out at 32 tons per square inch at the extreme top fibre, and 15 tons at the bottom, on the net section. As puddled steel, of which the girders were made, may have a tenacity of 45 to 55 tons per square inch, the assumption is probably correct. The author has no record of the deflection, but it may be remarked it was such that to stand under the girder, with a tank engine passing over, required some determination.

A point of additional interest in this little bridge is that, though made of steel, it dates as far back as 1861, having been in use thirty-two years when removed. The particular variety of steel used was known as Firth’s puddled. The evidence of this consists in correspondence showing that permission had been asked of the controlling authority, by the only users of the siding, to apply this material, with no evidence of any refusal. At about the same time this steel was also used upon the railway concerned in the top flanges of some girders of considerable span. The appearance of the trough girders to which the foregoing particulars apply was distinctly different to that which might be expected in ordinary wrought iron. The top edges of the vertical plates were wasted away, smooth, and rounded in a manner strongly suggestive of a steely character. Finally, the way in which the girders held up to their work for so long is, by itself, conclusive on the point. The bridge-rail appeared to be of wrought iron, the different modulus of elasticity of which has been included in the calculation upon which the preceding results are based. That these girders stood so well is, perhaps, largely due to the fact that the load carried by them was, though varying within wide limits, practically free from impact, which, had the load passed over quickly, would, with girders so small, shallow and flexible, have been very sensible.

The second instance of steel construction in which somewhat high stress is manifest is that of some steel troughing of the Lindsay pattern, used in a bridge built in 1885. The troughs ran parallel to the rails, having an effective span of 18 feet 8 inches. The depth of the section (which is shown in Fig. 47), was 8-1/2 inches, making a ratio of depth to span of 1/28. The road was of ballast, sleepers, chairs, and 85-lb. rails.

[Illustration: FIG. 47.]

Assuming this to be carried on six troughs, which corresponds to 11 feet 3 inches of width, the extreme fibre stress works out at 7·5 tons per square inch, under usual engine-loads. The bridge when examined after fourteen years’ use was in good condition, and at that time but little rusted; but the end seam rivets were, as is not uncommon with such troughing, loose. The traffic over the bridge was considerable, but not at great speed.

On the opposite page are set out the results which have been given, in tabulated form, as was done for rivet stresses, to enable ready comparison to be made.

Examples Of High Stress.

--------------+-----+---------+---------------+--------+----------- |Span | Part | Stress per |Tension |Condition. | in |Stressed.| Square Inch. | or | |Feet.| +-------+-------+Compres-| -- | | | Webs | Webs | sion. | | | | In- | not | | | | |cluded.| In- | | | | | |cluded.| | --------------+-----+---------+-------+-------+--------+----------- Wrought-iron | | | | | | main girders, |60·0 |Flange | .. | 6·3 |Tension | Good. plate | | | | | | | | | | | | Wrought-iron | | | | | | main girders, |64·0 | „ | .. | 6·8 | „ | Good. plate | | | | | | | | | | | | Wrought-iron | | | | | | main girders, |76·0 | „ | .. | 7·5 | „ | Fair. plate | | | | | | | | | | | | Wrought-iron | {| „ | 7·4 | 9·7 | „ |} main girders, |29·5{| „ | 6·3 | 8·3} |Compres-|}Good. plate | {| | | } |sion |} | | | | | | Wrought-iron | | | | | | main girders, |63·0 | „ | 7·1 |Tension | Fair. lattice | | | | | | | | | | | | Wrought-iron | | | | | | main girders, |47·0 |Flange | 10·0 | .. |Compres-| Fair. plate | |edge | | |sion | | | | | | | Wrought-iron | | | | | | cross-girders,|26·0 |Flange | .. | 6·7 |Tension | Fair. plate | | | | | | | | | | | | Wrought-iron | | | | | | cross-girders,|11.0 | „ | 6·3 | 6·5 | „ | Bad; loose plate | | | | | | rivets. | | | | | | Wrought-iron | | | | | | cross-girders,|19·0 | „ | 8·4 | 9·1 | „ | Good, but plate | | | | | | rusted. | | | | | | Wrought-iron | | | | | | cross-girders,|22·0 | „ | 10·5 | 11·1 | „ | Good, but plate | | | | | | rusted. | | | | | | Steel trough | {| „ | 15·0 | „ |}Fair, girder |15.7{|Top edge | 32·0 |Compres-|}but | {| | | |sion |}rusted. | | | | | | Steel |18·7 |Flanges | 7·5 | .. |Tension | Fair, troughing | | | | |and Com-| but | | | | |pression| rusted. --------------+-----+---------+-------+-------+--------+-----------

It would be unwise to infer from the instances which have been quoted that high stress may be regarded with complaisance. In the most conscientious engineering work there should still be a liberal margin for material possibly defective, or even bad, for waste and deterioration, and for the aggregate effect of minor errors in design, any one of which considerations, except the first, by itself might not be of great importance. The conclusion which may, however, be derived from this and the previous chapters is, that bridge failures are less likely to occur from high stress of a kind readily calculated than from failure in detail, obscure and little suspected, the reason for which is not perhaps apparent, till the attention is forcibly directed to it by the refusal of the structure to sustain the forces to which it may be liable.

Chapter VII.

Deformations.

Instructive lessons are to be had from a study of the various alterations in form to which metallic bridgework is liable, which alterations may be due simply to the development of stress of ordinary amount, and are then generally small; or to abnormal stresses, the result of some distortion in the bridge structure itself not originally intended, and possibly extreme. In addition to these there may be deformations due to settlement, to “creeping” of parts of the structure relative to the rest, to temperature changes, to rust, and to original bad workmanship. In any instance quoted below the methods adopted to ascertain the amounts of such alterations were quite simple, even crude; but as care was exercised, and no attempt made to measure any very minute changes, the results may be accepted as practically correct.

Dismissing for the present changes of form such as are to be expected, and touched upon in other places in this work, with respect to the particular parts of bridge structures affected by them, a few instances will be adduced of alterations which, though not very surprising, are such as in the design of the work are hardly likely, in most instances, to have been contemplated.

A case has already been referred to in which, owing to eccentric loading of main girders, these were, as to the top flanges, flexed sideways a considerable amount. It is proposed to supplement this by further remarks relative to somewhat similar cases. A like effect is frequently to be observed in trough or twin girders, in which the rails are supported upon longitudinal timbers resting upon projecting ledges formed by the bottom angle-bars of such troughs. In old forms of this arrangement it is common to find the two girders forming the trough connected only by bolts passing through the timbers, or just above them and below the rails; or connected by narrow strips, which serve no other purpose than to prevent the sides spreading at the bottom. The top flanges in such cases commonly curve inwards on the passage of the running load, accompanied of necessity by an increase of compressive stress upon the outer edges of the flanges, and perhaps by the working of any flange-joint which may exist. This, both as to flexing of the top flange and the working of a joint, was noticed in the case of a bridge twenty-three years old, very similar to that illustrated in Figs. 8 and 9, and described on pages 13 and 14. The top flange consisted, however, of a bridge rail riveted to the top edge of the web, butting at a joint, and covered by thick cover strips (see Fig. 48). The joint itself was poor, and depended largely upon the character of the butt, which was not sufficiently good to prevent the top member kinking at this point, under the joint influence of transverse effort and compressive stress, with possibly some help from bolts passing through timber and webs, though these being loose, the author does not think them at all responsible. Although not strictly relevant, it may be remarked in passing that it is very objectionable to use bolts as was done in this instance; for as the timber settles down on its seat, taking the bolts with it, these bear hard in the webs, enlarging or even, as in this case, tearing the holes, accompanied by injury to the bolts themselves. The practice is now almost obsolete, but the example is instructive as showing the impropriety of securing timbers by bolts passing through them at right angles to the action of the load, unless these bolts are quite free to move with the timber as it compresses.

If trough girders must be used, the better plan is to connect the two sides by a continuous bottom plate, the trough thus formed being properly drained, if the timber is not bedded in asphalt concrete; or to introduce stiff diaphragms at intervals beneath timbers, if the depth suffices.

In the case just quoted the curvature of the top members of the girders was inwards, but in the instance given below, of twin girders 26 feet effective span, with longitudinal timbers between, resting, as before, upon the inner ledge formed by the bottom flanges, the curvature was observed in three out of four girders to be 1/2 inch in a contrary direction, the fourth remaining straight.

[Illustration: FIG. 48.]

[Illustration: FIG. 49.]

An inspection of the accompanying section, Fig. 49, will, perhaps, render the reason evident when it is noticed that the top members are very unsymmetrical in form, the effect of this being to give these members, under stress, a strong tendency to flex outwards, apparently more than sufficient to counteract the tendency of an eccentric application of load on the bottom flange to bring them inwards. It is to be observed that the eccentricity of the flange appears to be not materially in excess, and is actually so, only because the thinness of the web--1/4 inch--renders it incompetent to keep the bottom flange up to its work, and so secure the full effect of the eccentric loading in limiting the outward tendency, due to the section of the top member, the effects of which are thus more apparent than would have been the case with a stiffer web. Ties across from one bottom flange to the other prevent the want of symmetry noticed in these--which, by the way, is on the wrong side for utility--from having any particular effect.

To give one other example of the consequences of eccentric loading, a bridge of 48 feet effective span may be quoted. This bridge carried four lines of way supported by five main girders, trussed by kicking-struts in such a manner as to form a bastard arch. A part section and plan are given in Figs. 50 and 51.

[Illustration: FIG. 50.]

[Illustration: FIG. 51.]

The floor consisted of Lindsay’s troughing resting upon the lower flanges of the main girders, the three middle girders, subject to eccentric loading, sometimes on one side, sometimes on the other, were, with dead load only, straight; but the two outer girders, liable to loading only on one side, had, under repeated applications of such a load, assumed a permanent curve towards the rails--13/16 inch in one case and 1 inch in the other--which curvature, no doubt, increased when a live load came upon the contiguous roads, though this was not measured. It should be remarked in passing that, owing to settlement and the canting of the abutments, the three middle girders were also “down”--in one case 3/4 inch. The girders, with one near road loaded, deflected 1/8 inch--greatly less than would have been the case had the main girder not been trussed. The bridge, at the time these particulars were obtained, had been in existence six years.

Deformations due to settlement may be very considerable. The author recalls two instances affecting continuous girders. In the first of these, a bridge twenty years old, of two spans of about 50 feet each, and with girders 4 feet 6 inches deep, the centre pier had sunk 4 inches, reducing the spans, as respects the dead load, practically to the condition of simple beams, just resting, but hardly bearing, upon the piers when free of live load.

In the second case, also of two openings of about 55 feet each, with girders 8 feet deep, one abutment had sunk about 3 inches, more than doubling the stresses over the centre pier. It is manifest that continuous girders should only be adopted where settlement of the supporting points is not likely to occur to any material degree. If this cannot be relied upon, the theoretical flange sections may hardly be worked to with any prudence; it being then advisable to make a liberal allowance for settlement stresses, in which case any economical advantage that should exist will probably disappear. It is, however, to be acknowledged that so long as the girders are in touch, under dead load, with the bearings intended to support them, the stresses due to a live load are unaltered, the principal effect in this case being that the variation in stress due to the live load ranges between limits that are higher or lower in the scale of stress than is the case with bearings undisturbed; still, if it is desired that the maximum stress shall not exceed, say, 6 tons per square inch, it can hardly be a matter of indifference that settlement shall induce a maximum of, perhaps, 10 tons, as in that case the stress must be 4 tons nearer the limit of statical strength.

Before leaving this matter it may be well to point out that in the case of continuous girders of uniform section a moderate settlement of the piers may even be advantageous by reducing the moments over the piers, and possibly making them equal to those obtaining near the middle of the spans, in which case there will be less inequality of stress in the booms and a reduction of the maximum stress.

Bridges consisting of simple main girders connected by cross-girders may be very prejudicially affected by unequal settlement; for instance, if one girder bearing settles more than the others, a twist is put upon the structure very trying to the floor-girder connections, and possibly to the main girders; to the web if a plate girder, or to the verticals if an open-webbed truss with rigid cross-girder attachments. Indeed, settlement of this kind may be much more destructive to a metallic bridge than to an arch of brick or masonry, the commonly accepted opinion notwithstanding.

Instances of deformations due to the creeping of some part of the structure away from its work, are within the author’s knowledge, rare; except in the case of the ends of main girders in skew bridges, already referred to.

Distortion, the result of temperature changes, is frequently to be observed in any considerable length of girder flange or parapet where there is not freedom of movement, unless due provision is made to check it.

It is quite common to see parapets out of line, either because the ends are not free, or because the light work of the parapet being more exposed to the sun’s rays than the girder work to which the lower part is attached, expanding to a greater degree, is subject to considerable compressive force, and buckles under its influence. The cure for this condition is obviously to provide such parapets with free or flexible joints at moderate distances apart, or to make the parapet sufficiently stiff to take the stresses developed, without crippling. A parapet may also go out of shape if directly attached to the top flange of a girder liable to heavy loading, particularly if the girder be shallower than the parapet, simply by its inability to maintain truth of line under the compressive stress, which it shares with the top flange of the girder proper.

Rivets spaced too far apart, by allowing the plates or other parts to spring open slightly, and permitting moisture to enter, results in the growth of rust, which, as it swells in forming, forces the parts asunder, and may set up considerable stress.

Flat bars riveted together by rivets spaced 12 inches apart may from this cause be forced asunder, as much as 1/2 inch, sufficient to set up a stress, with any practicable thickness of bar, much exceeding the elastic limit.

Local distortions may occur as the result of imperfect workmanship or careless erection, causing quite possibly very severe local stresses; or girder flanges may be out of straight as a result of riveting up along one side first, instead of advancing the riveting simultaneously along the whole breadth of the flange. The injury done by drifting is well known, and there is reason to think considerable damage is sometimes done to girderwork during manufacture by rough treatment to make the work come together; but the author has little to offer with respect to these matters that is not common knowledge. It may, however, be pointed out in passing that a bridge upon the design of which great care has been expended, with the idea that theoretical propriety shall not be violated, may be completely spoiled in this respect by careless construction. Fortunately, both steel and wrought iron, if of good quality, are long suffering. Incompetent erection will sometimes result in the true girder camber not appearing, or in differences as between girders supposed to be similar. This is not, of course, a deformation in the sense in which the word has previously been used, but it is desirable to bear the fact in mind as a possible cause of defective camber in dealing with questions of deformation.

The foregoing has reference chiefly to alterations of form in bridgework of wrought iron or steel, but a case of considerable interest is that of a cast-iron arched structure, of which the author made a very complete examination.

[Illustration: FIG. 52.]

[Illustration: FIG. 53.]

This bridge, built in 1839, and carrying two lines of railway, consisted of three spans, 100 feet each, of 10 feet rise, made up of four inner and two outer ribs, each rib being in three nearly equal parts; the floor was of timber, the abutments and piers of masonry. As originally constructed there was no bracing between the ribs other than the frames indicated on the plan here given (Fig. 52), stretching from outer rib to outer rib in the neighbourhood of the rib joints, which were simple butts without bolts or any equivalent means of connection. The floor was, however, braced in the horizontal plane, and the structure was also braced over the masonry piers. After forty-two years’ use supplementary distance-pieces were introduced between the ribs, but still no bracing between them, or any efficient means of checking lateral movement. A crack developing in one of the outer ribs at the crown, led to an investigation to trace the cause, the bridge then being fifty-four years old. Careful plumbing of the abutments revealed the fact that three out of four abutment pilasters were out of the vertical, as shown in Figs. 52 and 53, the greatest amount being 5/8 inch in 6 feet--at that corner from which the cracked rib had its springing; there was also other evidence of settlement in an old crack extending from the top of the abutment to the ground level, although this movement was very old, certainly as to the greater part. The ribs of this span were also out of plumb, that which was cracked being 2-1/2 inches out at the centre. The joints of the ribs, which, as already stated, were simple butts, in some cases opened and shut, as the load passed over, in such a way as to suggest that the ribs were acting, in a manner, as four-hinged arches, of which two hinges were at the springing, and the other two at the joints, one of which would for most positions of the load be out of use, reducing the rib to the three-hinged condition; in other words, as the rolling load passed over the span, one or other of the two joints of a rib would “gape” an appreciable amount at the bottom or at the top. Observations were taken by means of a theodolite placed below, either upon the bank or upon the tops of the masonry piers, sighting upon suitable scales attached to the ribs to ascertain the amounts of vertical and horizontal movement during the passage of trains over the bridge. The principal results are set forth in the following table:--

Movements Of Cast-Iron Ribs Under Live Load In A Bridge Of Three 100-Ft. Spans.

----------------------+-------+----------+----------- |Fall in| Rise in | Lateral -- |Inches.| Inches. | Movement | | |in Inches. ----------------------+-------+----------+----------- _Span No. 1._ At A. Up road loaded | ·20 | ·08 | ·04 „ A. Down road loaded| ·08 | ·03 | ·04 „ B. Down road loaded| ·14 |No record.| ·02 _Span No. 2._ At C. Up road loaded | ·40 | ·13 | Slight. „ C. Down road loaded| ·10 | ·05 | „ _Span No. 3._ At D. Up road loaded | ·22 |No record.| No record. „ D. Down road loaded| ·15 | Slight. | Slight. ----------------------+-------+----------+-----------

NOTE.--The lateral movements are to either side of the mean position.

The particulars for spans 2 and 3 were obtained with the instrument set up on the pier between these spans. The tremor of this pier was such that no useful readings for lateral movement could be obtained. Further, as the rolling load came upon these spans, the effect was to rock the pier to an extent vitiating the readings for vertical displacement; but by sighting upon the fixed abutment, and observing the amount of this rocking, suitable corrections were made in the apparent rib movements. The figures given in the table are thus corrected. The pier rocking was equivalent, as an extreme, to an inclination from the vertical of 1 in 3200. An attempt to measure the horizontal movement of the pier-top was unsuccessful, owing to the impracticability of setting up the instrument in a suitable position, sufficiently near to the pier to enable readings to be satisfactorily taken. This horizontal displacement probably amounted to about 1/16 inch either way. The rise and fall of the arches, and rocking either way of the piers, varied, as might be expected, in accordance with the position of the running load with respect to the spans. Summarising the results, the greatest vertical movements downwards were 0·20 inch, 0·40 inch, and 0·22 inch for spans Nos. 1, 2, and 3, the upward movements being 0·08 inch and 0·13 inch for the first and second spans, there being no recorded result of this kind for the third span. With adjacent ribs loaded, the movement of the ribs unloaded was one from one-third to one-half of the full amounts. It is to be noted that the lateral displacement in no case exceeded 0·04 inch either way, nor were the vertical movements exceptional; yet, as a matter of sensation, when seated upon the ironwork, it was a little difficult to believe them really so moderate. Observations were also made to ascertain the rise of the arches from winter to summer temperatures, with the result that this was found to be 0·45 inch, 0·45 inch, and 0·55 inch for the spans in order, the extreme temperatures being fairly representative of the English winter and summer. The structure was, as a consequence of the examination, efficiently braced by diaphragms between the ribs, and diagonals following the arch ribs round from springing to springing, with satisfactory results. The crack already referred to, and its probable causes, will be dealt with under “Cast-Iron Bridges.” Eventually this bridge was reconstructed to meet the requirements of growing engine-loads.

Chapter VIII.

Deflections.

Deflection, considered only as a fraction of the span, and without regard to other conditions affecting it, is of very little use as an indication of a girder’s fitness for its work; but when taken with reference to the depth of the girder, the nature and amount of the load producing flexure, and, further, with regard to the quality of the workmanship and normal properties of the material of which the beam is constructed, it may be of some little service in helping to form a reliable opinion. This consideration applies with less force, perhaps, to new work than to old, in which there may be unknown influences at work, or unknown defects which by excessive deflection may be betrayed. Though too much importance should not be attached to results of deflection tests in any one instance, yet the practice of observing such movements, and considering them with reference to each case, gives a good general idea of what may be expected in a fresh instance, any material departure from which should be a reason for specific inquiry as to the cause. A further reason with new work is found in the evidence it affords as to whether the loads carried travel to the supports really as intended, or by some route not contemplated; or, in the case of floor beams, in what way the load is distributed amongst them, if, indeed, there be any such distribution.

The author has commonly found that new work gives greater deflections than old--i.e., while calculation gives the same result for each, it does not apply equally well to both. The differences may be accidental, but are probably due to other causes, perhaps to the fact that new work has not by repeated applications of load lost the resilience of parts liable to considerable local stress, such as is very liable to occur at connections, so that the deflection is, whilst new, greater than after many years’ use, by which time such parts may develop a definite “set,” and contribute in a less degree, or not at all, to the total elastic deformation.

It is also possible, as already suggested, that repeated high stress may reduce the ratio of strain to stress, the material gradually becoming more rigid, the modulus of elasticity being, in fact, increased.

In girders of ordinary construction, the major part of the deflection is due to the booms, the remainder to the web; the latter is for plate girders a small amount only, and is commonly neglected, but for open web constructions it may be quite appreciable. For any given type of web arrangement the deflection due to the web will, for all depths, remain a constant quantity for the same span and unit stress; and though a moderate fraction of the whole deflection for a shallow girder, it may be a very considerable part for a girder of great depth, in which that part due to the booms is, of course, smaller, since the deflection due to these varies inversely as the girders’ depths.

Deflection, being dependent upon the elasticity of the material, is of necessity very largely influenced by the value of its modulus E, itself liable to considerable variation, and is increased in a small degree by the yield of joints and rivets, which effect, apart from the initial “set” of the girders, appears to be negligible. The stiffness of members in resisting angular distortion at connections must also, for open-web riveted structures, affect the result, making it somewhat less, and, finally, section excess at joints and gusset attachments has an influence in modifying deflection as compared with that due to the normal gross sections simply.

From these considerations it is apparent that any simple deflection formula must be largely empiric in its nature. For plate girders of uniform depth and flange stress, the writer has found the following to give good results:--

S^2 ----- × _f_ = deflection in inches. D × C

The span S and depth D are, as a matter of convenience, taken in feet; the constant C is for wrought iron 3500, and for mild steel 4000; _f_ is the mean of the extreme tensile and compressive stresses of the booms, in tons per square inch, estimated upon the gross sections.

This, though satisfactory for plate girders, is not so suited to girders having open webs, in which the deflection will more nearly be

(3S S^2 ) (-- + -----) × _f_, (C D × C)

the constant C being 3900 and 4450 for iron and steel respectively. The latter values of C correspond to normal values of the modulus of elasticity of 11,700 and 13,350 tons for iron and for steel, it being assumed that any slight rivet yield is off-set by any small section excess--say, 5 per cent.; it may, however, happen that section excess is greater than assumed, in which case some allowance may properly be made for this by increasing C.

To adapt the formulæ to girders other than those having parallel booms and uniform stress, the results, as deduced above, may be multiplied by constants given in column B of the Table given on page 93.

The practice of adopting for E in deflection formulæ a quantity much smaller than its nominal amount, with the object of allowing in riveted girder work for the yield of rivets and of joints, can hardly now be defended, whatever may have been a case at a time when workmanship was much inferior, when there was no machine riveting, and joints were, owing to the small weight of plates and bars, three times as numerous.

The initial “set” of a girder consequent upon first loading is a quantity quite distinct from deflection proper, and may be so small as to be negligible, or read 10 per cent. of the true deflection, varying with design and workmanship.

No estimate of girder deflection can be even approximately true if there is, at the level of the top or bottom flanges, a plated or otherwise rigid floor system which is not taken into account, as this will have the effect of very materially reducing the boom stress. To neglect this influence, where it exists, must necessarily lead to disappointing results, and it is quite practicable in many instances to include it in the calculation.

The influence of angular distortion between the various members has been neglected. It may be pointed out, however, that the resistance accompanying these movements in girders having riveted connections, though unimportant as affecting deflection, is worth some consideration in regard to secondary stress. For girders of similar type and unit stress these angular variations will be the same in amount for any span, but will generally be of less importance in large girders than in small, because in large girders the ratio of the breadth of members to their length is commonly less.

When determining the probable deflection of any girder of exceptional figure, it will be found convenient to make a strain diagram--an old device, in which the actual alterations of length being ascertained for all members, the girder is carefully set out to a suitable scale, with the lengths of members increased or reduced by the actual estimated amounts. The distorted figure resulting will then give the probable deflection. The value of E for this purpose should never be taken at less than the normal amount, and may for a considerable excess of metal in joints and gussets be made as much as 10 per cent. greater, this being a convenient means of making the necessary correction.

The effect of loads quickly applied may here be considered in connection with elastic deformations of girders of the same span, but different depths. If these be designed for similar loads and unit stresses, the deflections due to webs and booms of the girders compared will bear the same relation, each to each, as do the weights, whether in both cases the loads be inert or quickly applied, from which it follows that the mechanical “work” done by the loads in falling through the deflection heights is, neglecting inertia, always in proportion to the girderwork weights, and is a similar amount per ton, which as the total length of members remains substantially unaltered, corresponds to a similar amount of work per unit of section, or similar stress, irrespective of the depth of the girders.

But for a “drop” load, as when there is some obstruction upon a railway bridge, there will be in addition a further amount of work to be absorbed, which is to be considered the same whatever the girder’s depth, and will for deep girders be a larger amount per ton of girderwork than in those that are shallow; this, taking effect on members of the same aggregate length, but lighter, will develop a higher stress than in girders of lesser depth, more particularly in the booms.

The influence of the girder’s inertia in modifying drop-load effects will also be less marked in deep--i.e., light--girders than in girders shallow and heavy.

It is, notwithstanding all this, desirable that the depth of main girders should be liberal for economy’s sake, and also that of floor beams, for reasons already dealt with; the probability of the drop load is somewhat remote, and, though possible, would simply induce, if it occurred, an increment of stress rather more important in deep girders, making it specially desirable in these to give particular attention to the detailing of any connections liable to suffer from impact effects.

It should be remarked that for short and very flexible beams, generally outside the limits of practice, there may also be, under quickly moving loads, a material increase of stress due to the centrifugal effort of the load on running round the deflection curve, and in rising upon the steep part of the curve beyond the girder’s centre. Where advisable, these effects may be modified by cambering the rail.

For pin bridges in which there may be spring in the pins, excess stress in some eye-bars due to inequalities of length, and a want of that rigidity peculiar to riveted structures, the deflection will be greater than above indicated for gir