CHAP. Xm.] ANALTTIOA.L FOEMTTKS. 231 



^ = M 2 -M 3 + p (1 _ Q or s 2 =P (1 - 3 # + 2 #), 



(j 



S 3 = " 7 MZ + P or S 8 =P(3# J -2#). 







For a load anywhere, we have simply to give the proper value 

 to &, and we have at once the reactions and moments. Thus, 

 for a load at the span from the left, k = , and 



For a load in centre, T& = , and 



[Compare Supplement to Chap. VIL, Arts. 16 and 17.] 

 Ex. 2. For a uniform load over the same beam, what are the 



end moments and reactions f 



We have simply to introduce the proper values of A and A' 



for this case, and we have at once 



Mg = -jig. w P = Ma and S 2 = S 3 = w I. 



Ex. 3. A girder of three equal spans is " walled in " at the 

 ends, and has a concentrated load in the first span. What are 

 the moments^ shears, and reactions at the ends and intermediate 

 supports ? 



In this case, 8 2 = 3, and hence * = 5, r = 2, n = 0, 

 p = l, and therefore 



_ GZ A Cs + A' g 4 



C 4 Ac, + A f fr _ fr AQ, + A'fr 



8 1 c< + 2c 5 ' M< - C4 + 2, 5 ' 61 



also, <\ = ,0 cfe = .1, Cg = 2, c 4 = 7, c 5 = 26, etc. 



Inserting these values and the values of A and A' for con- 

 centrated load, we have 



P 7 91 



3^ = ^ (45 -78 # + 33 3), Mg = ff PZ (# - y^), 

 40 45 



M 4 = - L (3 P - 3 If), M, = i (3 & - 3 #). 



