80 BOVEY ON THE BENDING MOMENTS IN GIRDERS. 



Case III. — The same general principle still holds true when the two cud spans are 

 of different length. 



E.G. — Let the length of the first span be k.l, k being a numerical coefficient, and 

 put 2{\ + k) = x. 



Eq. 1 now becomes, 



7nj.x+m^=0 



Proceeding as before, 



m^ v\ wi,, m^ 



the coefficients b^, b.^, b^, . . . . being given by the same law as before, viz., 



b, = x 



b,= 4:.b.-b^=4:.X-l 



b^=4.b,— b.^=15.x — 4: 

 b, = 'i.b, — b,= 56.x-lb 



The two sets of coefficients (a) and (b) are identical when x^4, and when x>4 all the 

 coefficients h except the first (61 = 1) are numerically increased.. 



Hence, the same general results will follow. 



N.B. — The equations giving w, are simple and easily applicable in practice. They 

 may be written, 



?K„= H — ^ — r— - — T if fl is on the left of r, 



~' a,.i b.c — 1 



^ ^ g g 



and m„^ + ""'"'" ' • '— if q is on the right of r. 



If there are several weights on the rib span, 



.-. A = :S-"^-f^' and B = 2 .w^ ■ ï^.2.l—p. 



The author proposes to extend the above investigation on a future occasion. 



