Chapter 1, Problem 32E

The truss structure shown in the figure supports the force F. The finite element method is used to analyze this structure using three truss elements as shown. The area of cross- section (for all elements) $\text{A}=\text{2}{\text{in}}^{\text{2}}$. Young’s Modulus $E=\text{3}0\times \text{1}{0}^{\text{6}}\text{psi}$. The lengths of the elements are: $L_{\text{1}}=L_{\text{3}}=\text{1}0\text{ft}.,L_{\text{2}}=\text{14}.\text{14 ft}$.

a. Determine the stiffness matrix of element 2.

b. It is determined after solving the final equations that the displacement components of node 1 are: $u_1=-0.5\times {10}^{-2}\text{in}.$ and $v_1=1.5\times {10}^{-2}\text{in}.$. Using the four equations for this element, compute the forces acting on element 2 at nodes 1 and 3. Are these two forces collinear?

c. What is the change in length of element 2?