252 



STRESSES IN A SIMPLE WARREN TRUSS. Art. 131. 



It is evident that the lower chord is in tension, and the upper 

 chord and end posts in compression. Since there are two diago- 

 nals in each panel, a section may be taken through either, and 

 its vertical component must be equal to the shear in the panel. 

 Since all diagonals have the same inclination, the stresses in the 

 two diagonals of a panel must be equal, for a particular loading; 

 but since they are inclined in opposite directions, their stresses 

 will be of opposite kind. For full load, D is in compression; D 2 

 is in tension ; D s is in compression ; Z) 4 is in tension ; Z> 5 is in com- 

 pression. Those near the middle of the truss may reverse under 

 partial live load. 



The diagonal length=j/7 > 2 2 -|-10 2 =12.5 ft. 





Tan. *= 



D. L. P.=200X 15=3,000 Ibs. L. L. P.=700X 15=10,500 Ibs. 

 D. L. P. sec 0= 3,000X1.25= 3,750 Ibs. 

 L. L. P. sec 0=10,500X1.25=13,125 Ibs. 

 D. L. P. tan 0= 3,000X0.75= 2,250 Ibs. 

 L. L. P. tan 0=10,500X0.75= 7,875 Ibs. 



The dead load shear in the middle panel is zero and, there- 

 fore, there is no dead load stress in Z) 5 . The maximum plus and 

 minus shears in the middle panel are the same and, therefore, the 

 maximum compression in D 5 is equal to the maximum tension in 

 it. The maximum negative live load shear in panel 3-4 is 

 y 5 XlO,500= 2,100 Ibs.; the dead load shear is+lX3,000 

 =-f3,000 Ibs. ; there is no reversal in D 4 or D 3 . 

 Diagonal Stresses. 



D^=2P sec 0=2X 3,750=+ 7,500 D. L. 

 = do =2X13,125=+26,250 L. L. 



+33,750 Total. 

 J> 2 same as D^ but sign is 

 +D 3 =-Z> 4 = P sec 0=1 X 3,750= 3,750 D. L. 

 r=fp sec 0=fKl3,125=15,750 L. L. 



19,500 Total. 



=jp sec 0=4X13,125=2,625 L. L. 

 and as stated above there is no reversal. 



Z> 5 =|P see 0=|X13,125=7,875 L. L. and Total. 

 If one-third of the dead load be taken at each upper joint 

 and two-thirds at each lower joint, the dead load coefficients of 

 Z> 1} Z) 3 and Z> 5 will be increased by one-sixth and of D. z and J> 4 , 



