5.8. Effect of Transverse Normal Stress

When a beam is subjected to a transverse load, there is a resulting transverse normal stress. According to Eq. (5.26), this stress is not related to the normal strain ε_y and thus cannot be determined from Hooke’s law. However, an expression for the average transverse normal stress can be obtained from the equilibrium requirement of force balance along the axis of the beam. For this purpose, a procedure is used similar to that employed for determining the shear stress in Section 5.7.

Consider, for example, a rectangular cantilever beam of width b and depth 2h subject to a uniform load of intensity p (Fig. 5.12a). The free-body diagram of an isolated beam segment of length dx is shown in Fig. 5.12b. Passing a horizontal plane through this segment results in the free-body diagram of Fig. 5.11c, for which the condition of statics Σ F_y = 0 yields