Practice question
Question
A rectangular slab of length 0.4 m, width 0.2 m, and thickness 0.1 m is subjected to a shearing force of 8 × 104 N. If the shear modulus is 4 × 109 N/m2, what is the displacement of the upper face relative to the lower face?
Explanation
Shear modulus: G = (Shear stress) / (Shear strain) = (F / A) / (Δx / L). Rearrange: Δx = (F L) / (A G). Area A = 0.4 × 0.2 = 0.08 m2, L = 0.1 m. Substitute: Δx = (8 × 104 × 0.1) / (0.08 × 4 × 109) = 8000 / (3.2 × 108) = 2.5 × 10-5 m.