20 BROOM ALL : 



A horizontal shear, however, necessarily requires the pre- 

 sence of an equal vertical shear at each point. And together 

 with these shears there exist the transverse direct stresses 

 already referred to, acting in all directions at right angles to 

 the axis, and which may be resolved vertically and horizon- 

 tally for convenience. Hence, the total of forces in the cross 

 section may be represented after the fashion of Figure 5. 



^ I *4* 



FIGURE 5 



Let us examine now the effect of these forces on the shape 

 of the cross section. The direct stresses alone would produce 

 no change in shape other than the change from rectangular to 

 trapezoidal, since the lateral stress and accompanying unit 

 deformations vary as the distance from the neutral axis. In 

 the case of the shears, however, a different result is to be pre- 

 dicted. As already noted, a horizontal shear at any point 

 necessarily requires the presence of an equal vertical shear. 

 So much for points in the interit)r of the body. When, how- 

 ever, points near or at the boundary of the body are consid- 

 ered, one of the two right angle shears is seen to disappear 

 because of the absence of material on the outside. Thus, 



