A rectangular beam is of size 230 mm × 350 mm (effective depth). The factored shear force acting at a section is 80 kN. If the permissible shear stress in concrete is 0.25 MPa, the design shear force is nearly

Concept:

Recent laboratory experiments confirmed that reinforced concrete in beams has shear strength even without any shear reinforcement. This shear strength (τ_c) depends on the grade of concrete and the percentage of tension steel in beams and this is known as the permissible shear stress in concrete.

On the other hand, the shear strength of reinforced concrete with the reinforcement is restricted to some maximum value τ_cmax depending on the grade of concrete.

The amount of shear reinforcement to be provided is determined to carry a shear force Vus equal to

V_us = V_u – τ_c ×  b × d

Where b is the breadth of rectangular beams or b_w in the case of flanged beams.

d = effective depth of beam

V_us = Design shear force

V_u = Factored shear force and τ_c = permissible shear stress in concrete.

Calculation:

Given,

b = 230 mm           

d = 350 mm

V_u = 80 kN = 80,000 N

τ_c = 0.25 MPa

Design shear force is 

V_us = 80,000 – (0.25 × 230 × 350) = 59.875 KN = 60 kN