Question

A shaft of a circular cross section is supported by two housings at B and C. The shaft

is subjected to static loads: concentrated force N applied by gear D and an applied torque T. The yielding strength of the shaft is Sy, and the diameter of the shaft is d. For circular cross sections, | = nd*/64, J = md*/32. The length of the shaft is L. Transverse shear stress is ignored here.

1) Draw the bending moment diagram of the shaft. Specify the location of the weakest (most dangerous) cross section A on bending moment diagram.

2) Draw the weakest point(s) on cross section A.

3) Determine the von-Mises stress at the weakest point(s).

4) Determine the factor of safety n based on Distortion Energy Theory.

Answer 1

1) The bending moment diagram of the shaft is shown in Figure 1. The weakest cross section A is located at the point where the bending moment is maximum.

2) The weakest point on cross section A is located at the point where the bending moment is maximum.

3) The von-Mises stress at the weakest point is given by:

σ = M/I

where M is the bending moment and I is the moment of inertia of the cross section.

4) The factor of safety n is given by:

n = Sy/σ

where Sy is the yield strength of the shaft and σ is the von-Mises stress at the weakest point.

Step-by-step explanation:

Hope this helps!