Fig.29.
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 ofsupport, 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 beenworked 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.
The material and workmanship of the bridge were good. The rivets of the centre girder end diagonals, 1 inch in diameter, were originally7⁄8inch, but on becoming loose werecut 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,7⁄8inch 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 inFig. 30, 111⁄2inches deep at the ends, 14 inches at the middle, with1⁄4-inch webs, and rivets3⁄4inch in diameter, of 41⁄2-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 considerableimpactive force, was not sufficient to loosen these. The girders were taken out after being in place sixteen years.
Fig.30.Fig.32.Fig.30. andFig.32.Fig.31.
Fig.30.Fig.32.
Fig.30. andFig.32.
Fig.31.
An instance of undoubted excessive bearing pressure was found in the cross-girders of a bridge, mentioned onp. 15, of which so many web plates were cracked. This bridge, carrying two lines of way, had outer main girders, and long cross-girders with1⁄4-inch webs and3⁄4-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 inFig. 32.
Fig.33.
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 63⁄4inches 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, all3⁄4inch 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 theshear 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. Thesketchhere 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 inFig. 34.
Fig.34.
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. (SeeFig. 35.)
Fig.35.
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, whichis, 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. 36to40) 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.
Fig.36.Fig.37.Fig.36. andFig.37.
Fig.36.Fig.37.
Fig.36. andFig.37.
Fig.38.Fig.39.Fig.38. andFig.39.
Fig.38.Fig.39.
Fig.38. andFig.39.
Fig.40.
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 inthe “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 havingTorLbars 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. Theauthor 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.
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.
Fig.41.Fig.42.Fig.41. andFig.42.
Fig.41.Fig.42.
Fig.41. andFig.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. 41and42, 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.
Note.—Tension on rivets to be limited to one-half the permissible shear stress, the holes being slightly countersunk under snap-head.
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 considerationthat 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 deadload, 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,3⁄4inch in diameter is hardly sufficient to insure tight work, and quite unsuitable if the plates exceed5⁄8inch thick.
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 ofthose 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.
Fig.43.Fig.44.Fig.45.Fig.44. andFig.45.
Fig.43.
Fig.44.Fig.45.
Fig.44. andFig.45.
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 inFigs. 43 to 45. The four inner main girders under rails were 2 feet deep, with webs1⁄2inch thick over piers, and3⁄8inch at abutments, having flanges of twoLbars, 3 inches by 3 inches by5⁄8inch. There were also two outer girders of the same depth, with singleLbars. 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 (seeFig. 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 overthe 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 notgreatly 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 constructionof 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 (seeFig. 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 cannotbe said in this example that the girders showed no signs of weakness, as the deflection under live load was1⁄2inch on the span of 11 feet, in addition to a permanent set of3⁄4inch, 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 byT-bars, cranked down to face the webs, and riveted through. Though theseT’s had little stiffness, yet the frequent vertical movements of the girders relative to each other, under passing loads, had broken the majority of theT-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 wasno 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.
Fig.46.
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, originally1⁄2inch thick, but wasted to an aggregate thickness of5⁄8inch. These plates 6 inches deep, were connected at their lower edges to angle bars, 3 inches by 3 inches by1⁄2inch, which again were riveted to a bottom plate 16 inches wide, originally1⁄2inch thick, wasted to3⁄8inch. Lying in the bottomof 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, withgirders 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 inFig. 47), was 81⁄2inches, making a ratio of depth to span of1⁄28. The road was of ballast, sleepers, chairs, and 85-lb. rails.