A bar of length \(L\) and cross-sectional area \(A\) is made of a material whose stressstrain diagram is shown in Figure P2.16. If the internal force developed in the bar is such that \(\sigma\sigma_{p}\). Let \(P=\sigma_{p} A+\delta P\) be the applied load which results in a deflection of \(\Delta=\frac{\sigma_{p} L}{E}+\delta \Delta\).

(a) The work done by the applied force is equal to the strain energy developed in the bar. The strain energy per unit volume is the area under the stress-strain curve. Use this information to relate \(\delta P\) to \(\delta \Delta\).

(b) What is the equivalent stiffness when the bar is approximated as a linear spring for \(\sigma>\sigma_{p}\) ?

FIGURE P 2.16

Transcribed Image Text:

E = f(E) FIGURE P 2.16 (a) W