Chapter 1, Problem 18E

A stepped bar is clamped at both ends. A force of $F=10,000\text{ N}$ is applied as shown in the figure. Areas of cross sections of the two portions of the bar are $1\times {10}^{-4}\text{m}$ and $\text{2}\times \text{1}{0}^{-\text{4}}{\text{m}}^{\text{2}}$, respectively. Young’s modulus =10 GPa. Use three bar elements to solve the problem.

a. Sketch the displacement field $u\left(x\right)$ as a function of x on an x-y graph.

b. Calculate the stress at a distance of 2.5 m from the left support.