A Treatise On The Principles And Practice Of Dock Engineering

422 DOCK ENGINEERING. Substituting these values for MB in (122), we find— I1'KiW^1^-^-^ - ■ ’ W '’■ ■wmS!11''"''^i3i_'ii4îwi 'isi Rb = SW - (RA + RC).................(127) Having obtained the équations corresponding to a concentrated load, we now proceed a step further to obtain an expression for the bending moment due to a uniform load, w, of length, I, less than one span, b (see fig. 403). Fig. 403. (128) (129) (130) The weight on an infinitesimal length, dx, at a distance, x, from B is w.dx and, taking the sum between the limits, x = (b - 1) and x = b, Mb = rw.dx.^Æ2jL^l=. t-i 2 b(a + b) 8b(a + b) The reactions at the points of support will therefore be— ÅWl8ab(a +b)........................................ R0 = wJ 1 _ ((6^+4^- P) I lSb^a +b)}....................................... Rb = w6 - (Ra + Ro). . ....................... These results afford us all the data for dealing not only with the stresses due to the countei poise, but also with those due to a moving load covering the span to any desired extent. Having taken in detail the dead load, the counterpoise, and the moving load, it is only necessary to compute their algebraical sum in order to find the stresses due to the combined systems. It would be possible to pursue the subject much further, but we have now reached the boundary which divides movable bridges from stationary bridges. The remaining calculations are common to both forms of structure, and the student is accordingly referred, for further information, to treatises dealing with the latter subject, in a more complété and efficient manner than is possible within the limits of the present volume. Loads imposed on Movable Bridges.—Before designing the framework of a movable bridge, and in order that the stresses in the proposed members may be calculated, an estimate has to be made of the loads which the bridge will be called upon to bear. These loads may be classified as follows :_ 1. Dead Load. — (») Weight of main girders and bracing. (3) Weight of roadway or railway. 2. Moving Load.—(y) Weight of trains, vehicles, &c.