120 STRESSES IN GIRDERS. Art. 79. 



sA t is the stress in each flange, and d is the lever arm of a couple, 

 whose moment is the moment of resistance of the flanges. 



The moment of resistance of the web ==s = s^-r- = 



v $h 



i s th 2 = J -s A w h = I s A?, d by the second assumption. 

 The total moment of resistance is 



M R =s(A t +j.A w )d = M (34) 



which shows that one-sixth of the area of the web may be treated 

 like flange area, that is, the couple formed by the stresses in the 

 web may be replaced by an equivalent couple (IsA^d) whose 

 forces GJ-M W ) act in the centers of gravity of the flanges, so 

 that there results a stress diagram as shown in Fig. 88 (c). Now 

 it is plain that the 



Equivalent flange stress = ^- (35) 



_, . , equiv. flange stress ,nn< 



Equivalent flange area = - y (36) 



Flange area proper (net one flange) = 



equiv. flange area -J- A w (37) 



Flange area proper (net one flange) = 



equiv. flange area -J- A w (38) 



Equation (37) is used when there is no allowance to be made 

 for rivet holes in the web; equation (38) makes an approximate 

 allowance for a vertical line of rivet holes in the web; (these 

 occur at stiffen ers) ; an exact allowance can be made by deduct- 

 ing the moment of inertia of the areas cut out of the web by 

 the rivet holes on the tension side from the total moment of 

 inertia of the web. 



The moment of resistance of the web is sometimes neglected, 

 in which case the equivalent flange stresses and areas become the 

 actual ones, and the term in A w drops out of equations (37) 

 and (38). 



Since d, the effective depth, can not be calculated until the 

 flanges are known, an approximate value, or the depth of the 

 web, may be used for the first trial. Two or three trials will 

 usually give a flange that is exact. 



Equation (36) determines the net area of the tension flange, 

 that is, the gross area less that cut out by the rivet holes. 



The top flange is usually made the same as the bottom 

 flange (gross areas alike), but it must be held against sidewise 

 buckling, if it is long. There are many points in the design of 



