Problem $4$:

An engineer is designing a knee metallic replacement, based on the bending moment $M$ which is transmitted by the tibial bone. The cross$-$section of bone is schematically illustrated in the figure below, where $(,)$ are principal directions of inertia.

Neglecting the component acting along $,$ determine the bending moment $M$ knowing the maximum $($absolute$)$ stress ${}_{\text{m}\text{a}\text{x}}.$

Compute the radius $R$ of the metallic stem, such that it has the same moment of inertia $I_{}$ of the tibial bone.

Find the maximum bending stress acting in the circular stem.

Given: $I_{}=15820m{m}^4,I_{}=10820m{m}^4,{}_0=35,{}_{\text{m}\text{a}\text{x}}=130$MPa.