Consider a member of constant cross sectional area A, subjected to axial force Pas shown in Fig. 2.8. Let E be the Young’s modulus of the material. Let the member be under equilibrium under the action of this force, which is applied through the centroid of the cross section. Now, the applied force P is resisted by uniformly distributed internal stresses given by average stress σ =P/A as shown by the free body diagram (vide Fig. 2.8). Under the action of axial load P applied at one end gradually, the beam gets elongated by (say) . This may be calculated as follows. The incremental elongation of du small element of length dx of beam is given by,
Now the work done by external loads W= 1/2XPu (3.0)
In a conservative system, the external work is stored as the internal strain energy. Hence, the strain energy stored in the bar in axial deformation is,
Substituting equation (2.0) in (4.0) we get,
