Plane stress
From Wikipedia, the free encyclopedia
In real engineering components, stress (and strain) are 3-D tensors but in thin-walled structures such as plates subject to in-plane loading or thin cylinders subject to pressure loading, the thickness of the material is much less than the other two dimensions. The stresses associated with thickness, i.e the normal stress σ33 and the shear stresses σ13 and σ23 (if the thickness is the 3-direction) are not able to develop within the material and are small compared to the in-plane stresses. The stress tensor can then be approximated by:
.
in which the double underline indicates a second order tensor. This stress state is called plane stress. The corresponding strain tensor is:
in which the non-zero ε33 term arises from the Poisson's ratio effect. This strain term can be temporarily removed from the analysis to leave only the in-plane terms, effectively reducing the 3-D problem to a much simpler 2-D problem.
See also plane strain.
