A bone specimen is to be tested under 3-point bending. A model of the test set up in the figure below. The bone is modeled as a prismatic beam with a hollow cylindrical cross-section that has an inner diameter of 10 mm and outer diameter of 20 mm. Assume for this problem that the bone is a homogeneous, linearly elastic and isotropic material.

(a) Draw a free-body diagram of the test setup and clearly label all relevant loads, reactions and geometry. (Recall that a triangle denotes a pin support and a circle denotes a roller support.)

(b) Compute the reaction forces at the two supports.

(c) Draw the shear and moment diagrams for the test setup. Clearly label all key points in the diagrams with the appropriate values. Use Newtons (N) as the unit for the y-axis in the shear diagram and Newton millimeters (Nmm) as the unit for the y-axis in the moment diagram.

(d) Indicate the point on the bone that experiences the largest normal compressive stress and calculate the normal stress at that point. Report your answer in megapascals (MPa). Recall that the second moment of area of a hollow cylinder is given by: I = ?^4 (r^4O ? r^4i ), where rO is the outer radius and ri is the inner radius.

100 mm 100 N 50 mm 200 mm 50 mm 10 mm 20 mm z