Chapter 7, Problem 40P

A structural engineer is designing a crane that is to he used to unload barges at a dock. She is using a technique called finite element analysis to determine the displacement at the end of the crane. The finite element idealization of the crane structure picking up a 2000 lb load is shown in Fig. F7.40. The displacement in the horizontal and vertical directions at the end of the crane can be determined from the system of equations:

$2.47u+1.08v=0$ $(7.154)$ $2.47u+1.08v=0$, $(7.155)$

1. Find $u$ and $v$
2. using the substitution method.
3. Write the system of equations $(7.154)$ and $(7.155)$
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.