Manchester Memoirs, Vol. lix. (1915), No. %. 11 



i' 9". The maximum height of the parabolic free ended 



bending moment diagrams is equal to 



wi 2 40 x 4*67* c . 1U 



— = " — '- = 100 ft. lbs. 



8 8 v 



The maximum bending moment on the cantilever 

 portion will amount to 



wl 2 40 x 17c 2 ,. ., 



= _ L±- = 6 1 -3 ft. lbs. 



2 2 



The characteristic points are shown in s y /, u, v {Fig. 5), 

 their heights above the free ended base line being 

 obtained by joining the extremity of the maximum 

 ordinate of the parabola to the points at the extremities 

 of each span, the point where the vertical at one-third 

 and two-thirds the span cuts this line, being the charac- 

 teristic point for the nearer support. The true base line 

 p, q, r, E has been drawn so that sl=at and ub = vc. 

 From this diagram the moments at the equivalent points 

 of support are scaled off as 70 ft. lbs. at n and 92 ft. lbs. 

 at 0. We have therefore, taking moments round n 

 (see Fig. 3^), 



„ 40 x 6*42* 



2 

 A = 5 14 lbs. 



Taking moments round 0, 



r> n , 40 X I I "o8 2 



r 1 X2 , 09 + r l X2 -96 = — - 9 2 



2 



^ = 404 lbs. 



Taking the moments round E, 



P, x3' 3 o + ^ 1 x4 4 4 + ^x4-17 = 3 2_1A 



2 



/>„ = 304 lbs. 

 The horizontal component of 7^ = 488 lbs., and there- 

 fore the moment it induces at /> = 8r4lbs. Similarly the 

 moments induced by P t and P., at C and D will be 

 60*4 ft. lbs. and 360 ft. lbs. respectively. 



