9. (10 Points) The cantilevered shaft in the figure is made from a ductile material and is statically loaded as shown.
a. Find the torque on the shaft.
b. Find the bending moments on the shaft around the y and z axes at A.
c. Calculate the axial, bending and torsional shear stresses on the shaft. Neglect the VQ/It shear stress.
d. Sketch the critical stress element and show the stresses acting on it.
e. Find the principal and maximum shear stresses for the critical stress element.
[Answers: Torque = 800 lb-in, My = -1600 lb-in, Mz = 960 lb-in, axial stress = 0.255 ksi, bending = 19.006 ksi, torsion = 4.074 ksi, principals 20.18, 0, -0.82 ksi, max shear 10.50 ksi]
1-in dia.
1/4 in
1 1/2 in
2 in
160 lb
100 lb
200 lb
6 in
5 in