Fig.11.
Fig.11.
Fig.12.
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 appreciableextent 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.
Fig.13.Fig.14.Fig.15.Fig.13.,Fig.14. andFig.15.
Fig.13.Fig.14.Fig.15.
Fig.13.,Fig.14. andFig.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, and15give 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 inFig. 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 andflexure 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.
Figs.16, 17, 18.
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 (seeFigs. 16and18). 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 occasionallyloosen, 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, about1⁄4inch thick, a movement of1⁄8inch 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 shouldslope 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 inFig. 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 thefloor edge, and attached to each girder-web, the whole of the more important parts being open to the painter.
Fig.19.
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 metalin 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 timberthat 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.
Fig.20.
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 inFig. 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 theneighbourhood 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.
Fig.21.
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 of3⁄10inch, equivalent to a force of 71⁄2tons, 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,of3⁄4ton 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, of1⁄29inch, 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 31⁄2inch pitch and3⁄4inch 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 tillthe 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.
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 thebridge 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. 22to25give 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.
Fig.22.Fig.24.Fig.22. andFig.24.Fig.23.Fig.25.Fig.23. andFig.25.
Fig.22.Fig.24.
Fig.22. andFig.24.
Fig.23.Fig.25.
Fig.23. andFig.25.
Somewhat similar straining to that first indicated may occur in bracings placed between the girders of a bridgemuch 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 tothe 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 inFig. 26.
Fig.26.
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 stiffU-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.
Fig.27.
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, inFig. 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 memberis 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 tomaintain 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 tokeep 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.
Fig.28.
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 (seeFig. 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.
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 andenlargement 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 (seeFig. 26).
The girders, which were 6 feet 9 inches deep, had a bearing upon the abutments of 4 feet; the rivets were7⁄8inch in diameter and 4 inches pitch. There is in a case of this kindsome 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 barely1⁄2inch 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).