Chapter 24, Problem 41P

A rod subject to an axial load (Fig. P24.41a) will be de-formed, as shown in the stress-strain curve in Fig. P24.41b. The area under the curve from zero stress out to the point of rupture is called the modulus of toughness of the material. It providesa measure of the energy per unit volume required to cause the material to rupture. As such, it is representative of the material's ability to withstand an impact load. Use numerical integration to compute the modulus of toughness for the stress-strain curve seen in Fig. P24.41b.

FIGURE P24.41: (a) A rod under axial loading and (b) the resulting stress-strain curve where stress is in kipsper square inch $\left({10}^3{\text{lb/in}}^2\right)$ and strain is dimensionless.