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Strain Energy Stored Due To Axial Loading

Raviteja
22/02/2017 0 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)

                                        

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