DEFLECTION OF BEAMS 129 
It is required to construct the bending moment and shearing 
ree diagrams for one girder, 
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Fig, 171. 
Bending Moments at Supports.—Using the notation of the preceding 
_ Articles, the theorem of three moments gives the equations :— 
4, Li + },L) + L,M, + 2(L,+L,)M,+L,M,=0 for the spans AB 
and BC, and 4w,L}+4w,L}+L,M,+2(L,+L,)M,+L,M,=0 for the 
_ spans BC and CD, where w,=1}, w,=4, w,=4, L,=160, L,=200, 
_ L,=160, M,=0, and M,=0. Loads being in tons, lengths in feet, 
_ and bending moments in foot-tons. 
Solving the above equations, M,= — 2799, and M,= — 1322. 
_ Shearing Forces at Supports.— 
Fe ae 5 wl Pe a0 A * 160 Zen 
Ys ae wins 3 ae + oe 117°5 tons. 
Ei= Masel Yi * 0 te 79788 tona, 
F, = M- Mo 5 a8 ee te tons. 
F,= = + Mas. 198 4 HO 48-26 tons. 
yp Mc-M, twyLy__ 1322 160 _,. 
