ALGEBRAIC MOMENTS 45 



To find the stresses in the members of the truss in (a) Fig. 28, 

 proceed as follows : Cut the truss by means of plane A A, as in (b), and 

 replace the stresses in the members cut away with external forces. 

 These forces are equal to the stresses in the members in amount, but 

 opposite in direction, and produce equilibrium. 



To obtain stress ^-x take center of moments at L. 2 , and take 

 moments of external forces 



4-jr x a + P x d 7^ x 2 d = o 



4^= * X2 *- f '* = !** (compression) 

 a a 



To obtain stress in 4-5 take center of moments at L , and take 

 moments of external forces 



4-5 X 6 2 AX 1^=0 



4_ 5 = 3 p * d (tension) 



To obtain the stress in 5-3; take center of moments at joint U z in 

 (c), and take moments of external forces 



$-y x h R! x 3 d + 3 P x d o 

 5 ^3^-3P^ = 9Aj (tension) 



To Determine Kind of Stress. If the unknown external force is 

 always taken as acting from the outside toward the cut section, i. e. 

 is always assumed to cause compression, the sign of the result will in- 

 dicate the kind of stress. A plus sign will indicate that the assumed 

 direction was correct and that the stress is compression, while a minus 

 sign will indicate that the assumed direction was incorrect and that the 

 stress is tension. 



In calculating stresses by algebraic moments, therefore, always 

 observe the following rule: 



Assume the unknown external force as acting from the outside 

 toward the cut section ; a plus sign for the result will then show that 

 the stress in the member is compression, and a minus sign will indi- 

 cate that the stress in the member is tension. 



The stresses in the web members 3-4, 2-3, 1-2, are found by 



