Question

The figure above shows a shaft mounted in bearings A and D and having pulleys at B and C. The shaft is 20 mm in diameter and made of AISI 1020 CD steel. The forces shown acting on the pulley surfaces represent the belt tensions. The shaft is concerned with yielding and fatigue failure.

 [Stress analysis)

 (1) Draw the free body diagrams and find reaction forces at A and D in the xy and xz planes.

 (2) Draw the shear force and moment diagrams for each plane.

 (3) Find Me and Mc by combining the moments on the planes. Which of positions B and C governs? Calculate Omux at the position

 (4) Calculate Tmax due to torque between B and C.

[Yielding] Suppose the position C governs, and 6 -170 MPa and Timex - 40 MPa.

 (5) Calculate the von Mises stress at C for combined bending and torsional stress.

 (6) Estimate the safety factor based on the distortion energy theory.

[Fatigue] Suppose the position C governs, and Omax = 170 MPa and Tmax = 40 MPa. Assume Kf= Kfs = 1 and reliability = 99%

 (7) Calculate the endurance limit modification factors ka, kb and kc. With kc=kd=kf= 1, find sc Is the life of this shaft infinite in fatigue? Explain your answer.

 (8) If not, use Eqs. (6-55) and (6-56) to find σ'a and σ'm. 

 (9) Estimate the safety factors for yielding (or the first-cycle yielding) based on the Langer theory and fatigue failure based on the modified Goodman theory. 

 (10) Estimate the life of this shaft in number of cycle based on the modified Goodman theory. (10 points)

Answer 1