Shear strength of concrete

Shear strength is the resistance of concrete to failure by sliding of one part over the adjacent part under forces acting parallel to the plane. In practice pure shear is rare; shear in beams occurs together with flexure, and failure is by diagonal tension.

• Direct (pure) shear strength of plain concrete is about 20 to 30% of the compressive strength (higher than the tensile strength). It is hard to test because shear and bending are mixed (the double shear test on a prism is used).
• Beam shear: the nominal shear stress is $\tau_v = V_u/(bd)$ (IS 456, Cl. 40.1). The design shear strength of concrete $\tau_c$ depends on the grade and the tension steel percentage $100A_s/bd$ (Table 19; for M20 it ranges from 0.28 N/mm$^2$ at 0.15% steel to 0.82 N/mm$^2$ at 2.5% steel and above). If $\tau_v > \tau_c$, shear reinforcement is provided (Cl. 40.4); $\tau_v$ must not exceed $\tau_{c,max}$ (Table 20, 2.8 N/mm$^2$ for M20), otherwise the section is changed.
• Factors: compressive strength, steel percentage (dowel action), aggregate interlock, depth of beam (size effect) and axial load (compression raises the shear strength, tension reduces it).
• Punching shear in footings and flat slabs: $\tau_c = k_s \cdot 0.25\sqrt{f_{ck}}$ (Cl. 31.6.3).
• Shear failure is brittle and sudden, so design is conservative, with minimum stirrups (Cl. 26.5.1.6).