A SINGLE CANTILEVER.
RB0 = wxa 12 + /+ Wi 2 '
R0 o = ^ ^ - w2 ^, . .
413
• (83)
• (84)
Ro being measured downwards. The amount of counterpoise required to'
prevent the cantilever end overbalancing is, accordingly, the positive term
a2
in the value of RC in (84) — viz., -^—•
At any point distant æ to the left of B, the shearing stress is—
^^w^Ça-x), .......................(85)
and the bending moment—
MX = W1 b -----4.........................(86)
XU (Il
These become w^ a and ——, respectively, at B.
At any point distant x to the right of B, the shearing stress is—-
8*2 = w2 (b - x) + Ro
= w2(b - x) + w1 ^ - w2^, . . . (87)
and the bending moment—
M2 = + Rc (6 - x)
= b-^ FM2(6 - ^ + wiy " w26~|
At B, these become w2- + w^^ and —, respectively.
The same equations necessarily hold good whether a closed cantilevei
bridge be supported at one point by the pivot, or by bearing blocks located
nearer the edge of the quay, the only difference being in the respective
lengths of the two portions of the bridge. The general practice is to raise
the tail end of the bridge with wedges, screws, rams, or other contrivances,
so as to throw the forward pressure on to bearing blocks and relieve the
pivot and rollers of unnecessary stress. In this way the length of the
overhanging or cantilever portion of the bridge is reduced, and it is even
possible that the reduction in length of the closed bridge may more than
compensate for the increased load which it incurs in that position.
When the bridge is swinging the pressure on the pivot is that due to
the ordinary weight of the structure plus the counterpoise, which, computed
to balance the bridge under the condition of maximum load, generally
throws some excess of pressure upon the rollers.