4.19 a human femur is mounted in a torsion testing device and loaded to failure. assuming that one end is fixed and the other rotated, failure (fracture) occurs when t¼180 nm and θ(l)¼20 . assume that l¼37 cm and that the failure occurs at 25 cm from the fixed end, where the inner and outer radii are 7 mm and 13 mm, respectively. find the value of the shear stress at which fracture occurs; estimate the shear modulus g. finally, note that "torsional fractures are usually initiated at regions of the bones where the cross-sections are the smallest. some particularly weak sections of human bones are the upper and lower thirds of the humerus, femur, and fibula; the upper third of the radius; and the lower fourth of the ulna and tibia" (o¨ zkaya and nordin 1999).