of Continuous Girders, 183 



terms in the first member shall reduce to zero except the last 

 containing M 4 ., then the value of M s is 



and the values of the multipliers are given by the equations 

 2c 2 (4 + / 2 )+c 3 / 2 = 0, 

 c 2 / 2 + 2c y (/ 2 + / 3 ) + c 4 ! 3 = 0, 



After deducing the values of c from these equations, the value of 

 M 8 then becomes known. 



Now, if we multiply the equations of moments, beginning with 

 the last, by d 2) d 3f &c, all the moments except M 2 may be eli- 

 minated, and we have 



il2 ~<4-i/ 2 +2<4 (/, + /,)' 



and the multipliers will be given by 



</ 2 4_! + 2</ 3 (4_! + 4- 2 ) + ^ 4 4_ 2 =o, 



The values x)f the indeterminate numbers need only fulfil the 

 condition that they satisfy the equations as given above. Assu- 

 ming then c 2 =l and tf 2 =l, we get the following values: — 



c, = 0, d t =0, ) 



c 2 =l, d 2 =l, 

 ^=-2-^-^ d 3 =-2 — , 



t 2 *S — 1 



c 4 =^2c 3 -^ T ^--c 2 f, d 4 ——ld 3 — dcr — , 



* 3 % c s-2 h—2 



(3 + 4 4 J 0^7 * -2 "1"4— 3 7 4-2 



C5=- 2c 4 J 7-^ -<? 8 f. ^5- -2^4 r - ^37—, 



(1) 



Since the equations of moments are of the same form as the 

 equations of the multipliers, we have 



M 3 =* 3 M 2 , M 4 = c 4 M 2 , 



