Unsymmetrical bending of Beams and shear center

Stress Invariants and Principal stresses

To determine the roots of a cubic equation using calculator, follow the steps in the video below

Equilibrium equations - Relationship between stress components

 Equilibrium equations - Relationship between stress components

When a body is subjected to loads, stresses are developed in all portions of the body. But, the stresses should develop in such a way that the sum of all forces should be zero, i.e the force balance should be satisfied in all directions, including along x-, y- and z- directions. In the following paragraphs, the relationship between various stress components of a DIFFERENTIAL ELEMENT is derived based on the equilibrium conditions. The resultant relationships are thus referred to as equilibrium equations in 3D.

In addition to the stresses on all the six faces, there can be body forces, which are developed within the volume. For example, the gravity force is developed in proportion to the volume of the differential element considered. Such volume-proportional forces are referred to as body forces. Their contribution is to be considered in the EQUILIBRIUM equations.