Problem $4$

Numerical Problem $(20$ points$)$: The materials $($typically steel$)$ for the roof or the bridge have a limit on how much force they can take before they rupture$/$fail$/$break$/$fracture$.$ This maximum force limit is different if the member is in compression or in tension. For instance, steel has a higher limit $($or strength$)$ in tension than in compression. You will learn a lot more about the rupture stresses$/$forces in Mechanics of Materials course $($ENG$104).$ For now, you are tasked with calculating the maximum force a structure can take given some limits to the maximum force in material of the structure.

Calculate the magnitude of maximum load $P,$ that is applied at point $D$ and has a vertically downwards direction, such that the maximum force any member can support is $16kN$ in tension and $12kN$ in compression. Also, all the angles of the truss are $60.$ Use any method $($joint or section$)$ you like for final solution, but I would recommend practicing this problem using both.