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The beam shown is made of a nylon for which the allowable stress is $20$ MPa in tension and $50$

MPa in compression. Determine the largest couple $M$ that can be applied to the beam after

following steps $(30$ points$)$:

a$)$ Divide the cross$-$section geometry to simple geometries. Start with coordinate $x-y$

identified in below figure and determine the centroid for the cross$-$section geometry $(8$

points$)$

b$)$ Determine the moment of inertia for the neutral axis $(8$ points$)$

c$)$ Determine the maximum tensile and compressive stresses and calculate the largest

couple $M$ for tensile and compression failures $(12$ points$)$

d$)$ Determine the largest couple $M$ that can be applied to the beam. Explain why? $(2$ points$)$

Moments of Inertia of Common Geometric Shapes

Rectan