OVERVIEW

In Chapter 3 we saw that externally applied shear loads produce internal shear forces and bending moments in cross sections of a beam. The bending moments cause direct stress distributions in beam sections (Chapter 9); we shall now determine the corresponding distributions of shear stress. Initially, however, we shall examine the physical relationship between bending and shear; the mathematical relationship has already been defined in Eq. (3.8).

Suppose that a number of planks are laid one on top of the other and supported at each end as shown in Fig. 10.1(a). Applying a central concentrated load to the planks at mid span will cause them to bend as shown in Fig. 10.1(b). Due to bending the underside of each plank will stretch and the topside will shorten. It follows that there must be a relative sliding between the surfaces in contact. If now the planks are glued together they will bend as shown in Fig. 10.2. The glue has prevented the relative sliding of the adjacent surfaces and is therefore subjected to a shear force. This means that the application of a vertical shear load to a beam not only produces internal shear forces on cross sections of the beam but shear forces on horizontal planes as well. In fact, we have noted this earlier in Section 7.3 where we saw that shear stresses applied in one plane induce equal complementary shear stresses on perpendicular planes which is exactly the same situation as in the connected planks. This is...