COE 3001 Lecture 12: 12+Hooke_s+Law+for+Plane+Stress
Document Summary
So far, our study of plane stress has been based solely on arguments using equilibrium of forces, so the derived relationships are relevant for any material. However, for all of our special cases of plane stress (uniaxial loading, pure torsion, and bending), at some point we assumed that the object was made of a linear elastic material to relate stresses and strains. We will now do the same for the more general case of plane stress. For the strain in the x-direction, we have the strain generated by the normal stress in the x-direction, as well as the strain caused by the normal stress in the y-direction due to the poisson effect: An identical argument can be made for the strains in the y- and z-directions (remember that while there are no stresses in the z-direction in plane stress, there can still be strains in the z-direction):