Rankine's theory
Introduction:
This is also known as maximum principal or normal stress theory.
Rankine’s Theory
- According to this theory, the failure or yielding occurs at a point in a member when the maximum principal or normal stress in a bi-axial stress system reaches the limiting strength of the material in a simple tension test.
- Since the limiting strength for ductile materials is yield point stress and for brittle materials (which do not have well defined yield point) the limiting strength is ultimate stress, therefore according to the above theory, taking factor of safety (F.S.) into consideration, the maximum principal or normal stress (st1) in a bi-axial stress system is given by
- Since the maximum principal or normal stress theory is based on failure in tension or compression and ignores the possibility of failure due to shearing stress, therefore it is not used for ductile materials.
- However, for brittle materials which are relatively strong in shear but weak in tension or compression, this theory is generally used.