1. A hollow shaft 105mm outside diameter, 85mm inside diameter is subjected to a maximum bending moment of 4 kN-m. If the yield stress of the material is 400MPa, calculate the maximum torque which can be applied under these conditions assuming a safety factor of 3 and the Tresca failure criterion.
2. A component is subjected to loading conditions which result in the following stress conditions at a point on the surface, σx = -40MPa, σy = 50MPa and ζxy = 35 MPa.
Determine :-
(a) the magnitude and orientation of the principal stresses
(b) the magnitude and orientation of the maximum shear stress
(c) the stresses acting on a plane whose normal makes angle of 30o clockwise from the x-axis.
3. An 80mm diameter transmission shaft projects 300mm from a bearing housing. The shaft is subjected to a torque of 7 kN.m and a vertical cantilever load of 10 kN at the end of the shaft.
(i) Show, by means of a sketch, the critical positions on the surface of the shaft, where the maximum stresses occur.
(ii) Determine the principal stresses at the critical positions.
(iii) If the yield stress of the material in simple tension is 280 MPa, determine the Factor of Safety according to:
a) the Tresca yield criterion and
b) the Von Mises yield criterion.
4. A rectangular beam, cross section 60mm x 110mm as shown in Fig. Q3, is subjected to a bending moment of 35 kN.m about the horizontal axis a-a.
Determine the thickness of the elastic core x assuming the material is elastic perfectly plastic with a yield strength of 240MPa.
