58 PRACTICAL STRUCTURAL DESIGN 



The stress in c = - - = 12,000 Ibs. tension, for the stress 



d Zi 



acts away from the point B. 



bP = 8.246 x 3000 = 24,738 ft. Ibs. 



for member b. 



bP 24 7*^8 

 The stress in b = = ^ = 12,369 Ibs. compression, for the 



stress acts toward the point C. 



In Fig. 49 cP = bP = 8.062 x 3000 = 24,186 ft. Ibs. 



Stress in c = stress in 6 = - - = 12,093 Ibs., the character of 



m 



the stress in each member being determined by whether the mem- 



ber pulls from the point of fastening or pushes toward the support. 



In Fig. 50 cP = 8.246 x 3000 = 24,738 ft. Ibs. Stress in 



c = = = 



a 2 



bP = 8 x 3000 = 24,000 ft. Ibs. 



Stress in b = - - = '-= = 12,000 Ibs. compression. 



The examples show that the stress at any point in a horizontal 

 member of a frame is equal to the bending moment at the point divided 

 by the depth of the frame at that point. The stress in an inclined 

 member is equal to the stress in the corresponding horizontal member 

 times the ratio of their respective lengths. 



A frame is so made that certain members are in tension and 

 other members are in compression, the shear being carried by the 

 vertical and inclined members. The lines of travel of the stresses 

 are plainly exhibited. The same lines exist in a solid beam, so in 

 a beam it is also true that the horizontal stress is equal to the 

 bending moment divided by the depth of the beam. On one side 

 of the neutral axis the stress is tension and on the other side the 

 stress is compression. This will be fully explained later. 



Assume that the frame is made of some material, wood for 

 example, in which a fiber stress of 500 Ibs. per square inch can be 

 used in either tension or compression. Referring to Fig. 49, where 

 the stress in each member is equal, each member will require an 



12 093 



area = ' = 24.186 sq. ins. Extracting the square root gives 

 500 



the dimensions of each piece as 5.85 ins. x 5.85 ins., which, of course, 



