The cylindrical bar in the figure has a total length L=1.2 m, a diameter d=15 mm, and is confined by fixed supports at the walls A and B. A concentrated axial load FC=30 kN is applied to the bar at point C as indicated in the figure, with LACLBC. The bar is homogenous with Young’s modulus E. The material will fail if the magnitude of axial stress in the material exceeds σf=226 MPa.

Question

The cylindrical bar in the figure has a total length L=1.2 m, a diameter d=15 mm, and is confined by fixed supports at the walls A and B. A concentrated axial load FC=30 kN is applied to the bar at point C as indicated in the figure, with LAC>LBC. The bar is homogenous with Young’s modulus E. The material will fail if the magnitude of axial stress in the material exceeds σf=226 MPa.

If you apply the force at the center of the shaft ( LBC=LAC ), what safety factor SFmid would you have against failure? Provide a numerical (dimensionless) value:

If you want to apply the force FC as close as possible to the wall at B, but you also want to maintain a minimum safety factor SFmin=2 against failure, what is the minimum (LBC/LAC) that you can have? Provide a numerical (dimensionless) value: