Problems 1. Calculate the centroid and second area moment, I, for each of the cross-sections shown below. 10 mm w = 15 mm 5 mm 20 111111 5 mmr 20 mm | 30 mm d = 50 mm 20 mm 25 mm 2. Consider a segment of cortical bone subjected to a bending moment M = 1 Nm. Assume the cortical bone can be approximated as a hollow cylinder with outer diameter do = 2.54 cm and inner diameter d; = 1.75 cm. Assume the bone acts as a linearly elastic material with elastic modulus of 17 GPa. 3. Calculate the maximum bending stress magnitude in the bone segment. b. What are the maximum compression and tension strains in the bone segment? 3. An engineer needs to determine how thick to the stem of a titanium hip implant needs to be to ensure it can withstand a bending moment of 60 Nm. Assuming a circular cross-section, what is the minimum diameter stem that can be used. Assume a yield stress 0'}, = 45 0 MPa. 4. Consider the human femur subjected to bending during the bench test by a horizontal force F applied to the head ofthe femur at point P, as shown in the figure below. The distance it = 175 mm. Suppose the internal moment at section a: a: is known to be 91 Nm. Assume a circular geometry of the bone at section a a with inner radius 11 = 5.5 mm and outer radius 1}, = 12.5 mm. 3. Calculate the internal reaction force V at section a a. b. Draw the shear and moment diagrams for the section of femur proximal to a a. {i.e. the top of the femur) c. Calculate the maximum bending stress at section a a