Chapter 1, Problem 47E

The finite element method as used to solve the truss problem shown below. The solution for displacements was obtained as ${\text{u}}_{\text{2}}=\text{1}.\text{5 mm}.{\text{ v}}_{\text{2}}=-\text{1}.\text{5mm}.{\text{ u}}_{\text{3}}\text{=3mm}$, and ${\text{v}}_{\text{3}}=-\text{1}.\text{5mm}$. Note: the displacements are given in mm.

a. Determine the axial forces P in elements 2 and 4.

b. The forces in elements 3 and 5 are found to be as follows: $p^{\left(3\right)}=-2,000\text{N}$, $p^{\left(5\right)}=7,070\text{N}$. Determine the support reactions $R_{y4}$ at node 4 using the nodal equilibrium equations. The element properties are listed in the following table.