Art. 129. LIVE LOAD FOR MAXIMUM WEB STRESSES. 



243 



shear; neither does its stress necessarily reverse when the shear 

 reverses. In Fig. 179 



S 2 =R 1 P=U 2 cos 2 'D 2 cos 2 

 U 2 can not reverse ; its sign, in the equation, 

 will always be plus. Should D 2 be in ten- 

 sion, its sign will be plus and the shear, S 2 , 

 will be positive. When D 2 is in compres- 

 sion, however, S 2 may be positive or nega- 

 tive, according as U 2 cos 6 2 is greater or less 

 than Z> 2 cos 2 ; "the stress in D 2 may be re- I ' 

 versed without reversing the shear or vica- Fig. 179. 



versa. Evidently, when the chords are inclined, the maximum 

 stresses in a web member do not depend upon the shear in such 

 a way that the above rule for positions of live load may be confi- 

 dently applied. It will now be shown that this rule does give the 

 positions for maximum web stresses also, with certain exceptions. 



The maximum stress in D 3 occurs when the moment about a 

 (Fig. 180) is a maximum, because 



Djb=M a of external forces. 



Considering the part to the left of the section, and no loads 

 on this part, R l is the only external force. The moment of R l 

 about a is anti-clockwise, and therefore that of D 3 must be clock- 

 wise. D 3 is in tension for any load to the right of the section. 

 Considering the part to the right and loads to the left of the 

 section only, K 2 is the only external force. The moment of R 2 

 about a is anti-clockwise and therefore that of Z> 3 must be clock- 

 wise. Z> 3 is in compression for any load to the left of the section. 

 A similar analysis for V 2 will show that V 2 is in compression for 



