PHYS 270 Chapter Notes - Chapter 5: Shear Stress, Stress Concentration, Rotational Symmetry
Document Summary
Shear stress can be replace by an equivalent torque using an integral over the cross-sectional area. Let p represent the radial coordinate (the radius of the circle where the shear stress acts). The moment at the center due to the shear stress on the differential area is. By integrating over the entire area we get the total internal torque at the cross section. Equation independent of the material model as it represents static equivalency between shear stress on the entire cross section and the internal torque. For composite shaft cross section or nonlinear material behaviour, it would affect the value and distribution of across the cross section. Theory objectives: to obtain a formula for the relative rotation in terms of the internal torque t, to obtain a formula for the shear stress in terms of the internal torque t. This permits us to use arguments of axisymmetry in deducing deformation.
