But it may be asked, Can the precise load which is coming upon any structure be exactly fixed? are not the circumstances under which bridges are loaded very different? Bridges in different localities are certainly subjected to very different loads, and under very different conditions; but the proper loads to be provided for have been fixed by the best authority for all cases within narrow enough limits for all practical purposes. Few persons are aware of the weight of a closely packed crowd of people. Mr. Stoney of Dublin, one of the best authorities, packed 30 persons upon an area of a little less than 30 square feet; and at another time he placed 58 persons upon an area of 57 square feet, the resulting load in the two cases being very nearly 150 pounds to the square foot. "Such cramming," says Mr. Stoney, "could scarcely occur in practice, except in portions of a strongly excited crowd; but I have no doubt that it does occasionally so occur." "In my own practice," he continues, "I adopt 100 pounds per square foot as the standard working-load distributed uniformly over the whole surface of a public bridge, and 140 pounds per square foot for certain portions of the structure, such, for example, as the foot-paths of a bridge crossing a navigable river in a city, which are liable to be severely tried by an excited crowd during a boat-race, or some similar occasion." Tredgold and Rankine estimate the weight of a dense crowd at 120 pounds per square foot. Mr. Brunel used 100 pounds in his calculations for the Hungerford Suspension Bridge. Mr. Drewry, an old but excellent authority, observes that any body of men marching in step at from 3 to 3-1/2 miles an hour will strain a bridge at least as much as double the same weight at rest; and he adds, "In prudence, not more than one-sixth the number of infantry that would fill a bridge should be permitted to march over it in step." Mr. Roebling says, in speaking of the Niagara Falls Suspension Bridge, "In my opinion, a heavy train, running at a speed of 20 miles an hour, does less injury to the structure than is caused by 20 heavy cattle under full trot. Public processions marching to the sound of music, or bodies of soldiers keeping regular step, will produce a still more injurious effect."
Evidently a difference should be made in determining the load for London Bridge and the load for a highway bridge upon a New-England country road in a thinly settled district. A bridge that is strong enough is just as good and just as safe as one that is ten times stronger, and even better; for in a large bridge, if we make it too strong, we make it at the same time too heavy. The weight of the structure itself has to be sustained, and this part of the load is a perpetual drag on the material.
In 1875 the American Society of Civil Engineers, in view of the repeated bridge disasters in this country, appointed a committee to report upon The Means of Averting Bridge Accidents. We might expect, when a society composed of some hundreds of our best engineers selects an expert committee of half a dozen men, that the best authority would be pretty well represented; and such was eminently the case. It would be impossible to have combined a greater amount of acknowledged talent, both theoretical and practical, with a wider and more valuable experience than this committee possessed. The first point taken up in the report is the determination of the loads for which both railroad and highway bridges should be proportioned. In regard to highway bridges, a majority of the committee reported that for such structures the standard loads should not be less than as shown in the following table:—
Class A includes city and suburban bridges, and those over large rivers, where great concentration of weight is possible. Class B denotes highway bridges in manufacturing districts having well-ballasted roads. Class C refers to ordinary country-road bridges, where travel is less frequent and lighter. A minority of the committee modified the table above by making the loads a little larger. The whole committee agreed in making the load per square foot less as the span is greater, which is, of course, correct. It would seem eminently proper to make a difference between a bridge which carries the continuous and heavy traffic of a large city, and one which is subjected only to the comparatively light and infrequent traffic of a country road. At the same time it should not be forgotten, that, in a large part of the United States, a bridge may be loaded by ten, fifteen, or even twenty pounds per square foot by snow and ice alone, and that the very bridges which from their location we should be apt to make the lightest, are those which would be most likely to be neglected, and not relieved from a heavy accumulation of snow. In view of the above, and remembering that a moving load produces a much greater strain upon a bridge than one which is at rest, we may be sure, that, as the committee above referred to recommend, the loads should not be less than those given in the table. We can easily see that in special cases they should be more.
There is another point in regard to loading a highway bridge, which is to be considered. It often happens that a very heavy load is carried over such bridges upon a single truck, thus throwing a heavy and concentrated load upon each point as it passes. Mr. Stoney states that a wagon with a crank-shaft of the British ship "Hercules," weighing about forty-five tons, was refused a passage over Westminster iron bridge, for fear of damage to the structure, and had to be carried over Waterloo bridge, which is of stone; and he says that in many cases large boilers, heavy forgings, or castings reach as high as twelve tons upon a single wheel. The report of the American Society of Civil Engineers, above referred to, advises that the floor system be strong enough to carry the following loads upon four wheels: Class A, 24 tons; Class B, 16 tons; Class C, 8 tons; though it is stated that these do not include the extraordinary loads sometimes taken over highways. "This provision for local loads," says Mr. Boller, one of the committee, "may seem extreme; but the jar and jolt of heavy, spring-less loads come directly on all parts of the flooring at successive intervals, and admonish us that any errors should be on the safe side."
To pass now to railroad bridges, we find here a very heavy load coming upon the structure in a sudden, and often very violent, manner. Experiment and observation both indicate that a rapidly moving load produces an effect equal to double the same load at rest. This effect is seen much more upon short bridges, where the moving load is large in proportion to the weight of the bridge, than upon long spans, where the weight of the bridge itself is considerable. The actual load upon a short bridge is also more per foot than upon a long one, because the locomotive, which is much heavier than an equal length of cars, may cover the whole of a short span, but only a part of a longer one. The largest engines in use upon our railroads weigh from 75,000 to 80,000 pounds on a wheel-base of not over twelve feet in length, or 2,800 pounds per foot for the whole length of the engine, and from 20,000 to 24,000 pounds on a single pair of wheels. The heaviest coal-trains will weigh nearly a ton to the foot, ordinary freight-trains from 1,600 to 1,800 pounds, and passenger-trains from 1,000 to 1,200 pounds per foot. Any bridge is liable to be traversed by two heavy freight-engines followed by a load of three-quarters of a ton to the foot; so that if we proportion a bridge to carry 3,000 pounds per foot for the total engine length, and one ton per foot for the rest of the bridge, bearing in mind that any one point may be called upon to sustain 24,000 pounds, and regarding the increase of strain upon short spans due to high speeds, we have the following loads for different spans exclusive of the weight of the bridge:—
The above does not vary essentially from the English practice, and is substantially the same as given by the committee of the American Society of Civil Engineers.
The load which any bridge will be required to carry being determined, and the general plan and dimensions fixed, the several strains upon the different members follow by a simple process of arithmetic, leaving to be determined the actual dimensions of the various parts, a matter which depends upon the power of different kinds of material to resist different strains. This brings us to the exceedingly important subject of the nature and strength of materials.
It has been said that we know what one square inch of iron will hold. Like the question of loads above examined, this is a matter which has been settled, at any rate within very narrow limits, by the experience of many years of both European and American engineers. A bar of the best wrought-iron an inch square will not break under a tensile strain of less than sixty thousand pounds. Only a small part of this, however, is to be used in practice. A bar or beam may be loaded with a greater weight applied as a permanent or dead-load than would be safe as a rolling or moving weight. A load may be brought upon any material in an easy and gradual manner, so as not to damage it; while the same load could not be suddenly and violently applied without injury. The margin for safety should be greater with a material liable to contain hidden defects, than with one which is not so; and it should be greater with any member of a bridge which is subjected to several different kinds of strain, than for one which has to resist only a single form of strain. Respect, also, should be had to the frequency with which any part is subjected to strain from a moving load, as this will influence its power of endurance. The rule in structures having so important an office to perform as railroad or highway bridges, should be, in all cases, absolute safety under all conditions.
The British Board of Trade fixes the greatest strain that shall come upon the material in a wrought-iron bridge, from the combined weight of the bridge and load, at 5 tons per square inch of the net section of the metal. The French practice allows 3-8/10 tons per square inch of the cross section of the metal, which, considering the amount taken out by rivet-holes, is substantially the same as the English allowance. The report of the American Society of Civil Engineers, above referred to, recommends 10,000 pounds per inch as the maximum for wrought-iron in tension in railroad bridges. For highway bridges a unit strain of 15,000 pounds per square inch is often allowed. A very common clause in a specification is that the factor of safety shall be four, five, or six, as the case may be, meaning by this that the actual load shall not exceed one-fourth, one-fifth, or one-sixth part of the breaking-load. It is a little unfortunate that this term, factor of safety, has found its way into use just as it has; for it by no means indicates what is intended, or what it is supposed to. The true margin for safety is not the difference between the working-strain and the breaking-strain, but between the working-strain and that strain which will in any way unfit the material for use. Now, any material is unfitted for use when it is so far distorted by overstraining that it cannot recover, or, technically speaking, when its elastic limit has been exceeded. The elastic limit of the best grades of iron is just about half the breaking-weight, or from 25,000 to 30,000 pounds per inch. A poor iron will often show a very fair breaking-strength, but, at the same time, will have a very low elastic limit, and be entirely unfit for use in a bridge. A piece of iron of very inferior quality will often sustain a greater load before breaking than a piece of the best and toughest material, for the reason that a tough but ductile iron will stretch before giving way, thus reducing the area of section, while a hard but poor iron will keep nearly its full size until it breaks. A tough and ductile iron should bend double, when cold, without showing any signs of fracture, and should stretch fifteen per cent of its length before breaking; but much of the iron used in bridges, although it may hold 40,000 or 50,000 pounds per inch before failing, will not bend over 90 degrees without cracking, and has an elastic limit as low as 18,000 pounds. It is thus full as important to specify that an iron should have a high elastic limit as that it should have a high breaking-weight. A specification which allowed no material to be strained by more than 10,000 pounds per inch, and no iron to be used with a less elastic limit than 25,000 pounds, would, at the same time, agree with the standard requirement, both in England and in the United States, and would also secure a good quality of iron.