RANKINE’s THEORY

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MAXIMUM PRINCIPLE STRESS THEORY (or RANKINE’s THEORY)


                  According to this theory, when the maximum principle or normal stress reaches the limiting strength of the material, then it undergoes elastic failure. Since the limiting strength for ductile materials is yield point stress and for brittle materials is ultimate stress, the maximum or principle or normal stress (σ1) is given by
                        σy  
σ1   =           ----------           (Ductile materials),
             Factor of Safety

                        σu
        =          ----------           (Brittle materials),
             Factor of Safety

                                              where,  σy = yield stress
                                                           σu = ultimate stress


                This theory is not feasible for ductile materials since while using this equation, the possibility of failure due to shearing stress is not considered.

                However, for brittle materials which are relatively strong in shear but weak in tension or compression, this theory is generally used.  

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