Understanding the Reciprocal Theorem for Beam Deflection: Examples and Tips

[EngNoob]

I am trying to learn and figure our the reciprical theorem when applied to beans and the deflection on a beam when a load is applied.

The beam would be x long, say 10m and would have a weight/load applied at 5m, or dead center. There would be point A (Dead Center) point B (Half way between dead centre and end) or 1/4 beam. Load applied to A and deflection at a and b needed, and then load applied at B and deflection and A and B.

I need to create a graph with a slope of load cases to varify the theorem.

I am a little lost on this one, i know what the theorem is, but i am not sure how to apply it to beam deflection and how to create a graph.

Does anyone know any good links to learn further or some examples.

This is needed for a test in 48 hours, and i am lost on it completely, the graph part especially

Thanks for any help

 

[Achy47]

or advice!

Hello! I am a fellow scientist and I would be happy to help you understand the reciprocal theorem and its application to beams and deflection.

First, let's start with the reciprocal theorem. This theorem states that the work done by a force acting at a point A and producing a displacement at point B is equal to the work done by the same force acting at point B and producing a displacement at point A. In other words, the effect of a force at point A on point B is the same as the effect of the same force at point B on point A.

Now, to apply this to your specific scenario, we can consider the beam as a system with two points of interest - point A (dead center) and point B (halfway between dead center and end). The load applied at point A will cause a deflection at both points A and B. Similarly, the load applied at point B will also cause a deflection at both points A and B.

To create a graph with a slope of load cases, you can plot the deflections at points A and B on the y-axis and the load cases on the x-axis. The slope of this graph will represent the relationship between the load and deflection at points A and B. You can also plot different load cases to see how they affect the deflection at points A and B.

As for learning resources, there are many online tutorials and examples available that can help you understand and apply the reciprocal theorem. Some good links to start with are:

1. https://www.engineeringtoolbox.com/reciprocal-theorem-d_1808.html
2.
3. https://www.mathalino.com/reviewer/engineering-mechanics/lesson-11-reciprocal-theorem
4. https://www.sciencedirect.com/topics/engineering/reciprocal-theorem

I hope this helps you in your understanding of the reciprocal theorem and its application to beams and deflection. Don't hesitate to reach out if you have any further questions. Good luck on your test!