Chapter 1, Problem 38E

In the structure shown below, the temperature of element 2 is 50°C above the reference temperature. An external force of 20.000 N is applied in the x direction (horizontal direction) at node 2. Assume $E={10}^{11}Pa,A={10}^{-4}\text{m}$, and $a=2\times {10}^{-6}/°\text{C}$

a. Write down the stiffness matrices and thermal force vectors for each element.

b. Write down the global matrix equations.

c. Solve the global equations to determine the displacement at node 2.

d. Determine the forces in each element. State whether it is tension or compression.

e. Show that force equilibrium is satisfied at node 2.