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  1. For Brittle Materials, Max Principal stress theory is suitable as it considers Uni-axial tension or compression and fact that brittle material fails at tension For Ductile Materials, there are two theories applicable depending on loading condition/application Max. Shear stress theory is suitable for all conditions of loading as it considers yielding as design criteria and the fact that ductile material is weak or yield at shear first and fails at tension. Shear strain energy/Von-mises theory suits when there is no uni-axial loading ie, when we have multiaxial loading on the system, and it considers equivalent max normal/shear stress and fall little below satisfactorial design.
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