Chapter 7, Problem 39P

A structural engineer is performing a finite element analysis on an aluminum truss support structure subjected to a load as shown in Fig. P7.39. By the finite

element method, the displacements in the horizontal and vertical directions at the node where the load is applied can be determined from the system of equations:

$2.57u+3.33v=-0.05$ $(7.152)$ $3.33u+6.99v=0$. $(7.153)$

1. Find $u$ and $v$
2. using the substitution method.
3. Write the system of equations $(7.152)$ and $(7.153)$
4. in the matrix form $Ax=b$, where $x=\left[\begin{array}{c}u\\ v\end{array}\right]$.
5. Find $u$ and $v$
6. using the matrix algebra method. Perform all computations by hand and show all steps.

(d) Find $u$ and $v$ using the Cramer’s rule.