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.
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.
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.
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]), 11⁄4 inch and 11⁄16 inch respectively out of straight in their length, but upon the passing of a goods engine and train curved an additional 11⁄8 inch, or 23⁄8 inches in all, for one outside girder, and 23⁄16 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.
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.
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.
Fig. 6. Fig. 7.
Fig. 6. and 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.
Fig. 8.
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 11⁄2 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.
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.