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.

Stress Transformations in 3D

 Stress Transformation in 3D

Unit I of Theory of Elasticity

Question Bank for UG students- topic wise links

QUESTION BANK

Topic 1.Static and Kinemetic indeterminacy

 

Topic 2.SFD and BMD of determinate beams 

 These problems are solved by applying equilibrium to suitably cut sections

Topic 3.Beam deflection problems

These problems can be solved by Double integration method, Macaulay's method, Moment area method, Conjugate beam method or strain energy (Castigliano's method or unit Load method)

Topic 4.Determinate Truss Analysis

These problems can be solved by method of joints, method of sections or tension coefficient method

 Topic 5. Truss deflection problems

These problems can be solved by Castigliano's method or unit Load method

Topic 6. Indeterminate beam problems

Answers to the above problems