Question 3 [7+7+7 = 21 pts]. A cylindrical geometry under combined loading
Consider a solid round long slender bar with one end fixed and more than one type of load
acting on the other end, as shown in Figure 2.
a) Consider only the axial force F (along the z-axis in a cylindrical coordinate system) and
the torsion/twisting torque T are acting on it (no bending moment). Write the 3D stress
tensor for material points at the outermost fibers and the material points at the central
axis using a cylindrical coordinate basis {êr, êe, êz}.
b) Consider only the axial force F (along the z-axis in the cylindrical coordinate system) and
bending moment M (in the plane of the paper) are acting on it (no torsion). Write the 3D
stress tensor for material points at the outermost fiber at the very bottom considering
{êr, êe, êz} coordinate basis.
c) For a point at the outermost fiber at the very bottom, write the 3D stress tensor when all
three axial force F, torsional moment T, and bending moment M are acting.
L
R
Force F
E
Bending
Moment M
Torsion T
Figure 2. Spherical approximation of intracranial saccular aneurysm