a) Assume the maximum shear stress that bone (as a material) can withstand is tau Max = 57 MPa prior to failure. Determine the maximum torsional torque that can be carried prior to failure for each of the following
a) A solid circular cylindrical bone of radius r = 2 cm
b) A hollow circular cylindrical bone with outer radius ro = 4 cm and inner radius, ri, chosen to have the same total cross-sectional area as the bone in (a).
c) A hollow circular cylindrical bone with outer radius ro = 6 cm and inner radius, ri, chosen to have the same total cross-sectional area as the bone in (a).
d) Which of these bones is strongest against torsional loads? Why?
b) A vertical force of F = 2500 N is applied to the femoral head as shown. This force is applied at a distance b = 65 mm laterally from the long shaft of the femur and a distance h = 250 mm above section a-a, which is at the mid shaft (half way between the hip and knee joints). Assume the long shaft of the femur is a hollow circular cylinder with inner radius ri = 200 mm and outer radius ro = 250 mm.
a) Assuming the femur is in static equilibrium, what are the reaction forces and moments that occur at section a-a?
b) What maximum axial stresses (compression and/or tension) arise at section a-a due to purely axial loading?
c) What maximum axial stresses (compression and/or tension) arise at section a-a due to purely flexural loading (i.e., bending)?
d) What then are the net axial stresses on the medial and lateral borders of the femoral shaft at section a-a? Are they different?
e) If bone (as a material) is generally stronger in compression than in tension, does having an axial compressive load, in combination with bending, increase or decrease the chances of fracture in this situation? Why or why not?