## Shear, bond and torsion

Shear forces accompany a change in bending moment in beams and give rise to diagonal tension in the concrete and bond stresses between the reinforcement and the concrete.

In a homogeneous elastic beam a vertical shear force causes complimentary shear stresses and diagonal tensile and compressive stresses of the same magnitude. This is shown in Figs 5.1(a) and 5.1(b) where the stresses are shown on the small element A near the neutral axis. The beam section is shown in 5.1(c) and the parabolic shear stress distribution in 5.1(d). The maximum shear stress at the neutral axis of the section is given by max

vmax=1.5V/bd

Shear in a reinforced concrete beam without shear reinforcement causes cracks on inclined planes near the support as shown in Fig. 5.2. The cracks are caused by the diagonal tensile stress mentioned above. The shear failure mechanism is complex and depends on the shear span ratio av/d. When this ratio is large the failure is as shown in Fig. 5.2.