(Solved): 2. A human femur is mounted in the grips of a torsion testing machine (Fig. 2(a)). The length of t ...

2. A human femur is mounted in the grips of a torsion testing machine (Fig. 2(a)). The length of the bone between the rotating (D) and stationary (E) grips is measured as \( L=37 \mathrm{~cm} \). The femur is subjected to a torsional loading until fracture, and the applied torque vs. angular displacement (deflection) graph is obtained (Fig. 2(b)). The femur is fractured at a cross-section that is \( l=25 \mathrm{~cm} \) away from the stationary grip. The geometry of the bony tissue at the fractured section is approximated as a circular ring (Section a-a in Fig. 2(a)) with inner radius \( r_{\mathrm{i}}=7 \mathrm{~mm} \) and outer radius \( r_{\mathrm{o}}=13 \mathrm{~mm} \). Find the maximum shear stress and shear strain at the fractured section. Also calculate the shear modulus of the femur. Figure 2(a): Bone in Figure 2(b): Torque vs. angular torsion testing device displacement diagram