2 - Shear force, bending moment, and bending stress

Abstract

This chapter describes shear force, bending moment, and bending stress. The terms “shear force” and “bending moment” are applied to beams, a beam being part of a structure that supports transverse loads, that is, loads that are perpendicular to the length of the beam. For a horizontal beam to be at rest when acted upon by transverse forces, the following conditions must be satisfied: (1) the sum of the clockwise moments about any point must equal the sum of the anticlockwise moments about the same point and (2) the sum of the forces acting upwards must equal the sum of the forces acting downwards. The bending moment at any section of a beam that is in equilibrium is defined as the algebraic sum of the moments of all the external forces that are acting either to the left of the section or to the right of the section being considered but not both together. The beam bends under the force, causing the fibers of a plane to be compressed and the fibers of the other plane to be stretched, and setting up associated compressive and tensile stresses, called “bending stresses,” in the beam material. At a plane in the beam cross-section, known as the “neutral plane” or “neutral axis,” there would be no change in the length of the fibers and, thus, no bending stress, that is, the neutral axis is a plane of zero bending stress.