Instructions: Complete the following problem. Working in groups is permitted; however, copying homework is NOT permitted. Homework must be written or typed clearly, include a problem statement $($reiteration or summary of the assigned problem$),$ correctly drawn free$-$body diagram$($s$)$ as necessary, and boxed final answer$($s$).$ All homework problems should be scanned and converted into a single PDF for upload to Canvas.

The simple truss crane below is composed of weightless beams, with a weight of $W=40,000kg$ hanging from the tip of the crane at point $K.$ It is supported at point $C$ by a pin and at point $H$ by a rolling pin $.$ Relevant lengths are given in the figure. You may assume that vertical and horizontal members are oriented orthogonally to each other.

a$)$ Find $4$ zero$-$force members. For each case, explain why the member is a zero$-$force member $($you may draw a free body diagram in your explanation$).$ Sketch the truss again, removing those members.

b$)$ Determine the force in members EK and HK$.$ Are they in tension or compression?

c$)$ Each truss member is a square beam with side length $100$ mm $.$ The pinholes connecting the members have diameter $50$ mm $.$ The members can bear, at most, an ultimate strength of ${}_{ut}=60$MPa before failing. Determine if members EK or HK will fail under the given loading.