(Solved): 2. (50) The photo at right shows the cross-section at a-a of a human femur bone. The scan below the ...

2. (50) The photo at right shows the cross-section at a-a of a human femur bone. The scan below the photo shows the same cross-section after the bone's center was reamed in preparation for insertion of a titanium intramedullary rod. The radius of the circular hole produced by reaming is \( 9.2 \mathrm{~mm} \). Plane 1-3 is a plane of symmetry. Also: For titanium \( \mathrm{E}=116 \mathrm{GPa} \) For cortical bone \( \mathrm{E}=15 \mathrm{GPa} \) For the reamed bone: \[ I_{1}=6.4 \times 10^{4} \mathrm{~mm}^{4}, I_{2}=4.2 \times 10^{4} \mathrm{~mm}^{4} \text {, Area }=603 \mathrm{~mm}^{2} \] For a circle, \( \mathrm{I}=\pi r^{4} / 4 \) for a diameter through its centroid The bone with perfectly bonded implant is subjected to an \( 800 \mathrm{~N} \) force along the dashed line, which is the centroidal axis of the bone after reaming but before insertion of the rod. Point \( C_{B} \) is the centroid of the reamed bone cross-section a-a without the implant. \( C_{H} \) is the centroid of the hole. The bone is fixed at its lower end. (a) Determine the centroid \( \mathrm{C} \) and neutral axis at a-a of the bone with implant. Sketch the neutral axis on the crosssection. (b) Determine the internal force-moment system at \( \mathrm{C} \). (c) Determine the stress in the bone at the bone-implant interface Point D. \( \quad{ }_{\sigma_{D}}=0 \)