Unsymmetrical Bending. — Lesson 1

This lesson covers the concept of unsymmetric bending, a crucial topic in structural engineering. It delves into the bending of beams with asymmetric cross sections and the resulting stress distribution. The lesson explains the derivation of the stress formula and the concept of the product moment of inertia. It also discusses the impact of the moment of these stresses on the cross section about the axis of symmetry. The lesson further explores the calculation of stress distribution on a cross section when the product moment of inertia is not equal to zero. Using a beam of uniform cross section as an example, the lesson demonstrates how to find the principle directions of the cross sections and calculate the bending stresses acting on a cross section.

Video Highlights

00:10 - Introduction to un symmetric bending and the concept of stress distribution in the cross section of a beam
06:06 - Explanation of the concept of principle directions of the cross sections.
12:02 - Explanation of the concept of stress invariant
21:26 - Explanation of how to calculate the stresses in a cross section.
34:10 - Calculation of the principle moments of inertia.
43:10 - Calculation of the stresses in a cross section using the principle moments of inertia.
51:38 - Explanation of how to calculate the neutral axis and the stresses at different points on the cross section.

Key Takeaways

- Unsymmetric bending occurs when the loading is not in the plane of symmetry.
- The stress distribution in the cross section can be derived using the stress formula.
- The product moment of inertia plays a crucial role in determining the stress distribution.
- The principle directions of the cross sections can be determined using the product moment of inertia.
- The bending stresses acting on a cross section can be calculated using the principle directions and the flexure formula.