0
Let us assume a member with uniform cross section A and of lenth l, be subjected to external axial load W as shown in the figure.
As the load is gradually applied the load is incresed from 0 to W, due to which the member is gradually extended by Δ.
Work done due to load is given by the product of avarage load and the displacement Δ.
work done = 1/2 * W * Δ
Let the tenstion developed in the member be T, @ Equilibrium W = T
Tensile stress (ƒ) = T/A
Tensile strain(e) = ƒ/E = T/AE
Δ = el = S/AE *l]
Strain Energy Stored = Work Done = 1/2*W*Δ = 1/2*T*Tl/AE = T2l/2AE
Strain Energy Stored per unit volume = (T2l/2AE)/V =T2/2A2E=ƒ2/2E)
