The transverse loads on a beam segment cause a bending moment and a shear force that vary across the beam cross section and along the beam length. At point (1) in a beam shown in Figure 16.1, these contribute to the bending (flexure) stress and the shear stress, respectively, expressed as follows:

f My

I b = (16.1a)


f VQ

Ib v = (16.1b)

where M is bending moment at a horizontal distance x from the support y is vertical distance of point (1) from the neutral axis I is moment of inertia of the section V is shear force at x Q is moment taken at the neutral axis of the cross-sectional area of the beam above point (1) b is width of section at (1)

The distribution of these stresses is shown in Figure 16.2. At any point (2) on the neutral axis, the bending stress is zero and the shear stress is maximum (for a rectangular section). On a small element at point (2), the vertical shear stresses act on the two faces balancing each other, as shown in Figure 16.2. According to the laws of mechanics, the complementary shear stresses of equal magnitude and opposite sign act on the horizontal faces as shown, so as not to cause any rotation to the element.