## Strain Energy Axial Load Effects

Consider an axially loaded structural member of length 'L', cross-sectional area 'A', and of material with modulus of elasticity 'E' as shown in Figure 3.12(a)

### Figure 3.12

When an axial load 'P' is applied as indicated, the member will increase in length by '5L' as shown in Figure 3.12(b). Assuming linear elastic behaviour 5L this relationship is represented graphically in Figure 3.13. Figure 3.13

The work-done by the externally applied load 'P' is equal to:

(average value of the forcexdistance through which the force moves in its line of action)

.e. Work-done yxSL

For linearly elastic materials the relationship between the applied axial load and the change in length is: This work-done by the externally applied load is equal to the 'energy' stored by the member when it changes length and is known as the strain energy, usually given the symbol 'U'. It is this energy which causes structural members to return to their original length when an applied load system is removed; (Note: assuming that the strains are within the elastic limits of the material).

Strain energy=Work-done by the applied load system u=

+1 0