Question

A rectangular block of plastic material 500 mm long by 20 mm wide by 300 mm high has its lower face glued to a bench and a force of 200 N is applied to the upper face and in line with it. The upper face moves 15 mm relative to the lower face. Determine (a) the shear stress, and (b) the shear strain in the upper face, assuming the deformation is uniform.

Answer 1

(a) Shear stress, τ = force/area parallel to the force

Area of any face parallel to the force

= 500 mm × 20 mm

= (0.5 × 0.02) m² = 0.01 m² 

Hence, shear stress

τ = 200 N/0.01 m²

= 20000 Pa or 20 kPa

(b) Shear strain, γ = x/L (see side view)

= 15/300 = 0.05 (or 5%)