The figure below shows a round shaft of diameter (1.5 mathrm{in}). loaded by a bending moment (M_{z})

Question:

The figure below shows a round shaft of diameter $1.5 \mathrm{in}$. loaded by a bending moment $M_{z}$ $=5,000 \mathrm{lb} \cdot$ in., a torque $T=8,000 \mathrm{lb} . \cdot$ in., and an axial tensile force $N=6,000 \mathrm{lb}$. If the material is ductile with the yielding stress $\sigma_{Y}=40,000 \mathrm{psi}$, determine the safety factor corresponding to yield using

(a) the maximum shear stress theory and

(b) the maximum distortion energy theory.

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