an anchor span, a cantilever arm, a suspended span, a cantilever arm, and an anchor arm, being similar to Class C at one end and to Class B at the other. For the purpose of plotting weights of metal the following ratios have been assumed, as indicated in Fig. 55aaa. They are as nearly as may be the economic ones. Calling L the length of main opening, or that of a suspended span and two cantilever arms, the length of the suspended span is 3L, that of each cantilever arm and of each anchor arm is 16 L, and that of the anchor span is 5%L. 5 The average weights of metal per lineal foot for total length of structure have been carefully figured for main openings varying in length from 300 to 1,800 feet, and have been plotted on the diagrams shown in Figs. 55bbb to 55mmm, inclusive. Figs. 55bbb, 55eee, 55hhh, and 55kkk give the weights of the floor system, lateral system, and metal in anchorages and on piers, for each of the four types of cantilevers. These weights are practically the same for riveted and for pin-connected spans. Figs. 55ccc, 55fff, 55iii, and 55ll record the weights of trusses and total metal in bridge for riveted structures; and Figs. 55ddd, 55ggg, 55jjj, and 55mmm, afford the same information for pin-connected bridges. It should be noted that Type C gives the least weight per lineal foot for total length of structure; but this does not necessarily mean that it is the most economic, for the main opening provided is only eleven-sixteenths of that in the other types. A discussion of the economics of the four types of cantilevers will be found on page 587, et seq. The curves for the weight of the pin-connected trusses were obtained by the direct designing of the trusses for a number of span lengths. Those for the riveted trusses were figured from the pin-connected curves, taking due account of the high percentage of details in heavy riveted trusses, which in the case of the Fratt Bridge over the Missouri River at Kansas City ran as high as fifty per cent, instead of the usual thirty-five per cent for ordinary spans. The curves for the pin-connected spans have been carried out to a length of 1,800 feet, and those for riveted spans to 1,400 feet. The use of riveted trusses for spans as long as the latter limit is very unlikely. TRANSFORMATION FORMULÆ It is often advantageous to know how to obtain the weight of metal per lineal foot of span for any portion of a bridge when the corresponding weight for that portion of a similar bridge is known. For instance, if the truss weight or the floor weight for a certain bridge and a certain loading be given, what would be the corresponding weight for a similar bridge having a heavier or a lighter load? Or, if the truss weight per lineal foot of span for a certain live load and a certain span length be known, what would be the corresponding weight per foot for the same live load in a longer or a shorter span? Or, if the truss weight or the Average Weight of Metal in Pounds per Lineal Foot of Entire Bridge 200 400 600 800 1000 1200 1400 1600 1800 Length of Main Opening in Feet FIG. 55eee. Double-track-railway, Cantilever Bridges, Type B-Metal in Floor System, Laterals, and on Piers. FIG. 55fff. Double-track-railway, Riveted, Cantilever Bridges, Type, B-Metal in Trusses and Total Metal in Bridge. Average Weight of Metal in Pounds per Lineal Foot of Entire Bridge 200 400 600 800 1000 1200 1400 1600 1800 Length of Main Opening in Feet FIG. 55ggg. Double-track-railway, Pin-connected, Cantilever Bridges, Type B-Metal in Trusses and Total Metal in Bridge. floor weight per lineal foot of span for a carbon steel bridge be known, what would be the corresponding weight for a similar bridge manufactured from an alloy steel of a certain elastic limit? Average Weight of Metal in Pounds per Lineal Foot of Entire Bridge 200 400 600 800 1000 1200 2000 1000 1400 1800 Length "L'in Feet (See Fig. 55 aoa) FIG. 55hhh. Double-track-railway, Cantilever Bridges, Type C-Metal in Floor System, Laterals, and on Piers. For many years the author has studied deeply the theory of such weight variation and from time to time has given some of the results |