P$2-(30$pts$)$ Design the width $b$ of a rectangular link that is to carry a maximum compressive load of $5000$ lbf as indicated with arrows. The material selected has a minimum yield strength of $75$ ksi and a modulus of elasticity $E=30,000$ksi. Use a design factor of $5$ and an end condition constant $C=1$ for buckling in the weakest direction. Design for a length of $15$ in with a thickness $h=0\mathrm{.}5in.$ Round$-$up your proposed width to the nearest $\frac{1}{2}in.$ Using slenderness ratio, determine if your proposed design is a long, intermediate$-$length, or short column. Determine the maximum compressive load on the link using the proposed width.

Determine the width $b,$ rounded up to the nearest $\frac{1}{2^{\text{'}\text{'}}}$

Is your design is long, intermediate or short?

Determine the maximum compressive load of your Proposed design.