1.A material subjected to a simple tension test shows an elastic limit of 240 MN/ m². Calculate the factor of safety provided if the principal stresses set up in a complex two-dimensional stress system are limited to 140 MN/m² tensile and 45 MN/m² compressive. The appropriate theories of failure on which your answer should be based are:

 (a) The maximum shear stress theory;                                          

 (b) The maximum shear strain energy theory.

2. Write Short Note on necessity and significance of theories of failure.