m' = b d3 = 357-659. Because b d3 = b ď2 × d, 357·659 = With a solid bar of this size there would be prohibitive difficulties in the way of making a satisfactory joint with the cross girders, and if the material be expanded into an open section, the difficulty of obtaining the proper moment of resistance, together with the requisite deflection and suitable sections of metal to build up the distributing girder, will be experienced. In practice a girder stiffer than that indicated by theory has to be adopted; hence the load on the idle girder is greater than 0.268 W, but it can never exceed 0.3125 W, which would be its value were the distributing girder absolutely rigid; hence by adopting this coefficient perfect safety is secured, and as this is equivalent to twice the weight equally distributed, the saving is 10.625 0.375, or 37 per cent. of the area required by the running load, using a distributing girder. Many other cases arise in practice in which the distributing or equalising girder is found advantageous; for instance, in bridges carrying ordinary roads, on which the moving load is generally of a uniform character, but is occasionally varied by heavy concentrated loads, such as that presented by a heavy traction-engine or steam-roller. Instead of making each roadway girder heavy and strong enough to carry this load, should it come upon it, by means of a distributing girder, the concentrated load is distributed over several of the ordinary girders. CHAPTER XII. PRACTICAL APPLICATION OF FORMULÆ. HAVING So far elucidated the principles upon which structures should be designed, it seems advisable to show the method of applying them in practice, as although the calculations once explained present in themselves no difficulties, the reproduction of their results in the form of working drawings is not always obvious to the student. The drawings necessary are: a general plan; side elevation; cross section; longitudinal section; and enlarged views and sections of details. These drawings should be accompanied by a specification stating the quality of materials to be used, and the kind of workmanship to be put into the work. The specification should be very carefully drawn up and adhered to, for if the specification is drawn by a competent engineer, there should be nothing in it to require modification after the agreement for the execution of the work is signed. Let a design be required for the superstructure of a railway bridge (the piers or abutments will be treated of under the head of Structures of Stability), to carry a double line of railway, the headway being sufficient to allow a suitable depth to be given to the cross girders, but not enough to allow of the main girders being put under the rails, so that two main side girders will be used, cross girders 4 feet apart between them, combined by a central H distributing girder, and the floor being made of buckled plates. All the girders to be plate girders. The span of the bridge 130 feet. In order to allow a sufficient clearance on each side of the railway trains, the girders must be 4 feet 6 inches from the outer rail, giving for the clear width between the side girders 25 feet. To determine the running load, the actual strain produced by a string of locomotives of the heaviest type running on the line should be calculated, and the load per lineal foot capable of producing an equal strain determined for various spans, so as to have the data for any span at hand. For the present case I shall take 1 tons per line of railway as the running load for the main girders, and 15 tons per pair of driving wheels for running load on the cross girders. For the large side girders and for the shallower girders the effective depth will be the depth between the centres of gravity of the flange area. The working strains allowed will be-tension, 4 tons; compression, 3 tons; shearing, 4 tons per sectional square inch. In fixing the dead load it is necessary to have some means of estimating the weight of a girder, arch, or chain, to carry any given live load; such weight in the arch to include the spandrels and road girder, and in the chain to include the suspension rods and road girder; the following table will supply these data for carefully designed structures. = 2 If W weight of girder, or arch, or chain, in tons per foot run; W2 = total load on girder (not including weight of girder); c = coefficient taken from the table; W = W2 x c. = The cross girders must first be designed. Each cross girder will carry as dead load its own weight and its share of ballast, floor plates, and permanent way. As running load there will be 15 tons on each pair of rails for every alternate girder: taking the wheel bases of a tank engine at 8 feet, this will be a maximum load for any cross girder, and of this (as shown in the chapter on Combinations of Girders) a part only will act on one cross girder. The top flanges of the side girders for such a span should be made 2 feet 6 inches wide; hence the effective span of the cross girder from web to web will be 27 feet 6 inches, and the load will be placed as shown in Fig. 65. What will *The versine is the rise of the arch from springing to crown, or the fall of the chain from level of supports in towers to centre. be the equally distributed load, giving a maximum strain equal to that produced by the 7.5 tons on each rail? Treating these as symmetrical loads, the maximum strain is (using our former notation) 7.5 (5.75 + 10·75), The strain from a distributed load is d WI 8 d = 123.75 d at the centre; W x 27.5 123-75; W = 36 tons, and of this the 8 d = d proportionate equally distributed load carried by one girder will be 36 × 625 = 22.5 tons. The weight of 4-inch buckled floor plates, including their joints, strips, and rivets, is 12 lbs. per superficial foot; of ballast 1 foot thick, 120 lbs. per superficial foot; of per manent way, 400 lbs. per yard of double line. The area carried by each cross girder is 27·5 × 4 = 150 square feet; the loads will be which, added to 22.5 tons running load, gives 29.22 tons, to which must be added the weight of the cross girder. The girder will be of uniform section, its depth in the centre of its span; hence its weight will be, taking the coefficient from the table, 29.22 × 0·00213 = 0·06224 ton |
