STRESS AND STRAIN. 



23 



As we have seen, in the cross section of a beam under 

 flexure there exist horizontal and vertical shears and a gen- 

 eral direct compression or tension in all directions. The effect 

 of the shears is to produce tension and compression at 

 angles of 45° with the shears. These would be superposed 

 upon the general direct stress, as indicated in Figure 10 (the 

 general direct stresses being resolved for this consideration at 

 45°). In each quadrant of the cross section one of the direct 

 stresses due to shear is opposed by the general direct stress. 



X X 

 XiX 



FIGURE 10 



The prevailing maximum direct stresses would, therefore, 

 be at angles of 45°, and at the same time there would exist 

 the two right angle shears already noted. We may indicate 

 the general nature of these stresses as in Figure 11. 



Having called attention, in the case of a beam subjected 

 to flexure, to the transverse or lateral stresses in the plane of 

 the cross section brought into a play by the process of deform- 

 ation, the question of their magnitude presents itself. The 

 evaluation of these stresses is problematical, yet by certain 

 approximate methods it is possible to show they have a not 

 inconsiderable value. 



