A Treatise On The Principles And Practice Of Dock Engineering

412 DOCK ENGINEERING. ting, in the first instance in general terms, and tlien, as far as practicable, in some brief detail, the fundamental problems which present themselves to the engineer in designing movable bridges, in so far as they are connected with the equipment of docks. Excluding fioating and lifting bridges as too remotely related to the subject for general application, we may divide our considération of the stresses in the remaining kinds of bridge into four cases, representing the different conditions in which any of them may be found. (1) A double cantilever resting upon a central support. (^) A single cantilever supported at two points, or a cantilever and beam combined. (3) An arch. (4) A continuous girder resting upon three supports. The first case represents a single swinging bridge with two equal wings. The second embraces generally all cases of bridges in one or two leaves projecting over an opening, with certain exceptions, as under. The third applies to those double-leaved bridges which afford one another mutual support at their meeting faces ; and the fourth is the normal condition of a single-leaf bridge in a state of rest. Case I. A double cantilever w O w -----a --------,,. _ _ a ------------^ resting upon a central support (fig. 396). This is an extremely simple case and need not be the cause of more than a R, moment’s detention in passing. If the Fig. 396. imposed load be w per foot run, and, assuming that the bridge is symmetrical, the central reaction is obviously_ RX = 2wa, ............................................................(81) and the shearing stress increases from zéro at each extremity to one-half of the above amount on each side of the support. The bending moment at O is— M0 ww (82) and at each end it is zero. The curve of moments for each half of the bridge is parabolic, with its origin at the extremity and its axis vertical. Where the arms are of unequal length, the stresses are clearly those due to the longer arm, a counterpoise being added to the shorter arm to produce an equal effect. Case II. A single cantilever in combination with a beam (fig. 397). Let A C be a girder of total length (a + b) supported at two points, B and C, of which only one is at an ex- tremity. The reactions, RB and ROj at B and A -------w, -------B w2 C * -------a --------■ b----------*] »s Rc Fig. 397. C may be determined by taking moments about the points C and B, respectively, thus—