232 CONTINUOUS GIRDER. [CHAP. XIIT. 



Observe that the moments are positive at each end of the 

 loaded span and alternate in sign from that span, varying as 

 the numbers 1, 2, 7, or as the numbers c [Art. 140]. A positive 

 moment always denotes compression in lower fibre. For the 

 shears we h&Ve, then, from Art. 150, 



S-j r= (45 - 99 W + 54#), S' 8 = . (99 - 54 #). 



TtO 4:5 



S, = l (27 & - 27 #), S' 4 = (- 27 #> + 27 V), 



S 4 = - (- 9 # + 9 #), S' 5 = (9 - 9 



For the reactions, then, 



R, = S 2 , R,, = S' 8 + S 8 = i (126 ^ -81 0), 



Observe that the reactions as also the shears are positive at 

 the supports of the loaded span, and alternate in sign from 

 those supports. A positive shear or reaction acts always up- 

 wards. Disregarding, then, for the present, the weight of the 

 beam itself, it would have to be held down, at first pier from 

 right end. 



If the weight is in the centre of first span from left, 7c = |-, and 



216 171 36 9 



The reactions add up to P, as they should. 

 If P = 100 tons, and I = 15 ft., we have 



M 2 = 237.5 ft. tons, M 8 = 87.5, M 4 = - 50, M s = 25 ft. tons. 

 Hz = 60 tons RB = 47.5, R 4 = - 10, Rg = 2.5 tons ; 



S 2 = 60 tons, S' 8 = 40, S 8 = 7.5, S' 4 = - 7.5, 



S 4 = -2.5, S' 5 = 2.5. 



Ex. 4. A beam of five spans, free at ends ; centre and adja- 

 cent spans 100 ft., end spans each 75 ft., has a uniform load 

 extending over the whole of the second span from left. What 

 are the moments at the ends and supports f 



