90 



BROOMALL : 



the horizontal shear, as before, does not reduce to zero. 

 As regards the lines of stress in the web, another method 

 of reasoning must be used. In the first place, we will 

 encounter longitudinal shear with vertical shearing planes, as 

 only in this way can the two flanges be tied together to work 

 in harmony with the web. The planes of shearing for the 

 whole section are more or less as indicated in Figure 4. 



iiMniiiii iilllHIIIIIIINIIIITTTmTi 



FIGURE 4. 



The distribution of forces acting on the elements of the 

 body in the four quadrants of the web and their variation in 

 value are indicated in Figure 5. 



The resolution of these forces will give lines of maximum 

 internal stress for the plane of the web after the manner 

 shown to the left in the figure. 



The lines of direct stress cut the middle line of the beam 



at 0° and 90°. They cut the edges of the web at angles dif- 



s 

 fering from 45° a certain amount, since the ratio — — does 



2 V 



not reduce to zero. 



The lines of shear cut the middle line at 45° and approach 

 0° and 90° at the edges of the web. 



As mentioned, the lines of stress cut the boundaries in cer- 

 tain cases at angles diflfering more or less from limiting 

 values. These angles may be found by substitution of the 

 proper values in Formulas (i) and (2). They will depend, 

 of course, upon the relative values of the unit direct stress 

 and unit horizontal shear. 



If the flange and web are of same thickness, the shear 

 and direct stress, at A and B, Figure 4, have nearly the same 



