STRESS AND STRAIN. 



19 



Let us return, however, to the more or less trapezoidal 

 section of Figure 3. Every point above the neutral axis 

 expands, and we may consider, hence, that it is subjected at 

 each point to a uniform dilating stress in all directions at 

 right angles to the axis. Likewise, every point below the 

 neutral axis is subjected to a uniform compressive stress in 

 all directions. These stresses have a real existence in the 

 plane of the cross section. Further, it will be noted that the 

 lateral expansion and cpntraction are different at different 

 levels, since the longitudinal stresses increase as the distance 

 from the neutral axis increases. It is to be noted, also, that 

 the lateral deformations are symmetrically disposed as regards 

 the vertical axis of the cross section. As a result of the dif- 

 ferent value of this lateral strain at different levels, it follows 

 that successive horizontal lamina in the cross section must 

 have slid laterally one upon the other. In other words, hori- 

 zontal shearing deformation has taken place, that is, a hori- 

 zontal lateral shearing stress must exist in the plane of the 

 cross section. This shear will vary as the distance from the 

 middle vertical line, being in opposite directions on opposite 

 sides, as shown in F'igure 4. 



FIGURE 4. 



