Art. 79. 



STRESSES IN GIRDERS. 



119 



of equation (12), which must be solved by trial, as there are 

 no tables of section moduli as there are for I beams. In order 

 to avoid the labor of calculating the moment of inertia of each 

 section which may be tried, the calculation is much simplified 

 by making two assumptions. 



1. The stresses in the flanges (tension and compression) 

 are uniformly distributed over their areas and their resultants, 

 therefore, act at the centers of gravity of the flanges. 



2. That the depth of the web, h, may be set equal to d, the 

 distance between centers of gravity of the flanges. 



/V 



&*0ffF&n &f fofa/ equ/'vofenf 11 * X 

 "" tfrett-s ^ ^ w 



Fig. 88. 



Fig. 88 (a) shows the actual distribution of the intensity of 

 bending stress over the cross section, while Fig. 88 (b) shows the 

 effect of the assumptions, with the diagrams for the intensities 

 of stress in flanges and web superimposed. Fig. 88 (a) corre- 

 sponds with the formula M =s ; so does Fig. 88 (b) so far as 



the web is concerned, except that the second assumption changes 

 its depth a little. The depth of the web is sometimes equal to 

 that of the cross section; it is sometimes less and sometimes 

 greater than d. The diagram for each flange is a rectangle, 

 which results from the first assumption, and which is the same ' 

 thing as neglecting the moment of inertia of the flange about its 

 own axis, in comparison with that about the neutral axis of the 

 whole cross section; equation (16) becomes J x =Ad? = 



2A t (\d)\ and from equation (10), M R =s 2At ^ d) * = sA,d. 

 That this is true may be easily seen by reference to Fig. 88 (6) ; 



