Chapter 1, Problem 46E

The truss shown in the figure supports the force $\text{F}=\text{1},000\text{N}$. Both elements have the same axial rigidity of $AE=10N$, thermal expansion coefficient of $a=2\times {10}^{-6}/°\text{C}$, and length $\text{L}=\text{1 m}$. While the temperature at element i remains constant, that of element 2 is dropped by 50 C.

a. Write the $4\times 4$ element stiffness matrices [k] and the $4\times 1$ thermal force vectors $\left(f_T\right)$ for elements 1 and 2. Show the row addresses clearly.

b. Assemble two elements and apply the boundary conditions to obtain the global matrix equation in the form of $\left[K\right]\left\{Q\right\}=\left(F\right)+\left(F_T\right)$.

c. Solve for the nodal displacements.