ABSTRACT

This chapter establishes the definitions of stress and strain. Further, Hooke’s law relating stress to strain is discussed. The determination of principal stresses and strains is shown, and the application of Mohr’s circle is elaborated. The state of stress in polar coordinates is shown, and the concept of stress concentration around holes in plates is discussed. Numerical examples are provided to elaborate the concept and theory presented here.

Stress is defined as an application of a load over a finite area, where the area is an extension of a three-dimensional (3-D) element. The state of stress is normally defined in terms of the stresses due to normal and shear loads acting on a structural body. It can be represented in either Cartesian or polar coordinate systems; however, preference is given to the Cartesian system for general-shaped bodies. The state of stress on a body in threedimensions is shown by Figure 2.1, where σx, σy, and σz are defined as normal stresses and τxy, τyx, τyz, τzy, τxz, and τzx as the shear stresses present on a body. When the 3-D element is in equilibrium, the shear components reduce as follows: