State of Stress – Stress Tensor

State of stress at a Point (Stress Tensor)

Consider a three dimensional body in equilibrium under the action of a set of external forces P1,P2,P3.. , the stresses developed in different planes vary. To study the magnitude of these forces at any point let the body be divided into 2 parts A&B by a cross section “mm” . Any of these parts may be said to be in equilibrium under the action of the external forces and the internal forces distributed over the c/s “mm” . Please download the pdf file for complete note

Three Dimensional Stresses

Figure shows an elemental stress block subjected to three dimensional stress. Each stress component in it is represented by its magnitude , direction as well as position of the plane on which it is acting.

In order to represent these stresses a double subscript notation system is used

Stress Tensor, Three Dimensional Stress, Stresses on an Axi-Symmetric Plane, Problems & Solutions, Principle Planes, Principle Stresses, Shear stress, Max. Shear Stress, Equations Of Equilibrium, Compatibility Conditions & Equations, Boundary Conditions, State of Pure Shear, Hydro Static State, Octahedral Stresses & Planes, Derivation for Transformation Of Stresses, Generalised Hooke’s Law