ABSTRACT
SHEAR, BOND AND TORSION 5.1 SHEAR FORCES In beams, a change in bending moment involves shear forces. Shear force at a section gives rise to diagonal tension in the concrete and leads to cracking. Shear failures are very brittle and therefore should be avoided. All beams should always be designed to fail in a ductile manner in flexure rather than in shear. 5.1.1 Shear in a Homogeneous Beam According to engineers’ theory of bending, in a beam a state of pure shear stress exists at the neutral axis. This causes principal tensile and compressive stresses of the same magnitude as the shear stress and inclined at 45o to the neutral axis. This is shown in Fig. 5.1(b) and Fig. 5.1(c) on an element at the neutral axis. In an elastic rectangular beam shown in Fig. 5.1(a), the distribution of shear stress is parabolic as shown in Fig. 5.1(d). The maximum elastic shear stress at the neutral axis is given by
where V = shear force at the section. In a T-beam or an L-beam, most of the shear force is resisted by the web and therefore for all practical purposes in shear calculations, flanged beams can be considered as rectangular beams of dimensions bw h, where bw = width of the web.
