Using Reciprical Theorem With Beams

[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

 

[anathema]

and suggestions

Hello there,

Thank you for reaching out for help with understanding the reciprocal theorem and its application to beam deflection. Let me try to break down the concept and provide some resources that might help you understand it better.

Firstly, the reciprocal theorem is a principle in mechanics that states that the work done by a load on a structure is equal to the work done by the same load acting in reverse on the same structure. In simpler terms, it means that if you apply a load to a structure, the resulting deflection at one point is the same as if you applied the same load at a different point on the structure.

In your case, you have a beam of length 10m and you are applying a load at the center (5m). This means that the deflection at point A (center) and point B (halfway between center and end) should be the same. To verify this, you will need to perform two load cases: one with the load applied at point A and one with the load applied at point B.

To create a graph, you will need to plot the deflection values at points A and B for each load case. The x-axis will represent the load applied and the y-axis will represent the corresponding deflection values. The slope of the graph will show the relationship between the load and deflection, which will help verify the reciprocal theorem.

Here are a few resources that may help you understand this concept better and provide examples:

1. Engineering Toolbox: This website provides a detailed explanation of the reciprocal theorem and its application to beam deflection, along with examples and graphs. You can also use their beam deflection calculator to get values for your graph.

2. Khan Academy: This video from Khan Academy explains the concept of the reciprocal theorem and its application to structural analysis, including beam deflection.

3. MIT OpenCourseware: This course material from MIT provides a thorough explanation of the reciprocal theorem and its application to beam deflection, along with practice problems and solutions.

I hope these resources will help you understand the concept better and prepare for your test. Remember to also practice solving problems and creating graphs to get a better grasp of the concept. Good luck!

 

[Moetasim]

I can provide some guidance and resources to help you understand and apply the reciprocal theorem to beams and their deflection.

First, let's review what the reciprocal theorem is. It states that the work done by a force on a structure is equal to the work done by the same structure on the force, regardless of the location of the force and the structure's response. In simpler terms, this means that the effect of a force on a structure is the same as the effect of that structure on the force.

Now, let's apply this to beams and their deflection. When a load is applied to a beam, it will deflect or bend in response. The amount of deflection can be measured at different points along the beam, such as at the center (point A) or at a quarter of the beam's length (point B). The reciprocal theorem tells us that the work done by the load on the beam at point A will be equal to the work done by the beam on the load at point A. The same applies for point B.

To create a graph with a slope of load cases, you will need to plot the deflection at point A and point B for each load case. The x-axis can represent the different load cases, and the y-axis can represent the deflection at points A and B. You can then calculate the slope of the line connecting these points to verify the reciprocal theorem.

As for learning more about this topic and finding examples, I recommend checking out engineering textbooks or online resources that cover beam deflection and the reciprocal theorem. Some helpful keywords to search for could be "beam deflection", "reciprocal theorem", and "load cases". Additionally, you may want to consult with a professor or a tutor for further assistance.

I wish you the best of luck on your test in 48 hours. Remember to take breaks and stay calm while studying, as it will help you retain the information better. Good luck!