Chapter 1, Problem 37E

The uniaxial bar shown below can be modeled as a one-dimensional bar. The bar has the following properties: $L=\text{1 m},\text{ A}=\text{1}{0}^{-\text{4}}\text{m},E=\text{1}00\text{ GPa},$ and $\text{a}=\text{2}\times \text{1}{0}^{-\text{6}}/°\text{C}$. From the stress-free initial state, a force of 5,000 N is applied at node 2, and the temperature is lowered by 50°C below the reference temperature.

a. Calculate the global matrix equation after applying boundary conditions.

b. Solve for the displacement $u_{\text{2}}$.

c. What is the element force P in the bar?