24:0 CONTINUOUS GIRDER. [OffAP. XHI. 



Ex. 9. A beam of three spans of 25, 50 and 40 feet respec- 

 tively is fixed horizontally at the right end, and has a concen- 

 trated load of 10 tons at 12 feet from the third support from 

 left. What are the moments at the supports f 



Here ^ = 25, 4 = 50, 4 = 40, J 4 = 0, P = 10, k 4 = 12, 

 k = 0.3, 5 1 = 3, s = 4, 1 4 = and r = 3. Also, c x = 0, 

 Cg = 1, Cj = 3, c 4 = 12.25 and ^ = 0, <4 = 1, 4 = 2, 

 rf 4 = 6.4, <4 = - 32.4. 



When, then, m < 4, 



(3 * - 6 # + 3 >) . 



Inserting & = 0.3 and the values of c, 



form = 1, M! = ; m = 2, M 2 =- 8.20 ; m = 3, M 8 = 24.62 ; 

 for n = 4, 



M 4 = A (_ 3 A + 12.25 B) = (6.25* + 9 > - 15.25 #), 



or M 4 = 42.29 ft. tons. 



Find the shears. Also moments and shears for uniform load 

 over third span. 



Ex. 3. A beam of four spans \ = 80, 1 8 100, 1 3 = 50, 

 1^ = 40 ft., free at the ends, has a load of 10 tons in the sec- 

 ond span at 40 ft. from left. What are the moments f 



Here 5 = 4,^ = 0, <fr = 1, c* = 3.6, c 4 = 19.6, c 5 = -83.7, 

 ^ = 0, ^ = 1, d* = - 3.6, d 4 = 10.3, &=- 41.85, r = 2. 



For m <3, M^ - - (A d, + B ^), 



m>3, M 



Hence, M t = 0, 



Find the shears. Also find the moments and shear for uni 

 form load over second span. 



