A rectangular concrete beam has a width of 300 mm and a depth of 500 mm. It is subjected to a shear force of 20 kN. What is the shear stress at a depth of 150 mm from the neutral axis?

A) 1.33 N/mm2
B) 2.67 N/mm2
C) 4 N/mm2
D) 5.33 N/mm2

Reference:
As per IS 456:2000, the shear stress formula is:
τ = VQ/Ib
Where,
τ – Shear stress
V – Shear force
Q – First moment of area above or below the neutral axis
I – Moment of inertia
b – Width of beam

For a rectangular section, I = bd3/12
Q = A x centroidal distance from neutral axis

Here,
b = 300 mm
d = 500 mm
V = 20 kN
Depth at which shear stress is required = 150 mm

∴ I = (300 x 5003)/12 = 7.5 x 108 mm4
Q = (150 x 300) = 45 x 104 mm3

τ = (20 x 103 x 45 x 104) / (300 x 7.5 x 108)

∴ τ = 1.33 N/mm2

Therefore, option A is the correct answer.