(S) descibres the
shape elasticity of a
material. Suppose that
equal and opposite tangential forces
F act on a
rectangular block. These
shearing forces distort the block, but its
volume remains unchanged.
Shearing stress = tangential force acting / area of surface being sheared, or just simply σ s = F / A
Shearing strain = distance sheared / distance between surfaces, or just simply εs = ΔL / L0
Then...
S = F / A / [ ΔL / ΔL0 ] = FL0 / AΔL
Since ΔL is usually very small, the ratio ΔL / L0 is equal approximately to the shear angle Θ in radians. In that case
S = F / AΘ