Chapter 2, Problem 22E

The stepped bar shown in the figure is subjected to a force at the center. Use the finite element method to determine the displacement field $u\left(x\right)$, axial force distribution $P\left(x\right)$, and reactions $R_L$ and $R_R$. Assume: $E=100\text{GPa}$, the areas of cross sections of the three portions shown are, respectively, ${10}^{-4}{\text{m}}^{\text{2}}$, $2\times {10}^{-4}{\text{m}}^{\text{2}},$ and ${10}^{-4}{\text{m}}^{\text{2}}$, and $F=10,000\text{N}$.