# How to Solve Support Reaction (Virtual Work)?

• Suraj alexander
In summary, if you want to find the reaction forces at nodes E and F in a beam, you can use a method called free body diagrams.
Suraj alexander
Hey guys,
I was revising using some past papers for my structural mechanic module when I realized that I don't know how to do this problem:
https://physicsforums-bernhardtmediall.netdna-ssl.com/data/attachments/83/83583-240450b2eac78c09f31d35a531383268.jpg
If it was for the deflection of node E and F, I can answer that quite easily but I don't know how to find the reaction. I asked my professor but I find it quite hard to understand her. Anyone willing to explain it step by step please?

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Thanks in advance. The best way to find the reaction forces at nodes E and F is by using a method called free body diagrams (FBD). This involves breaking the structure down into individual components and then drawing a diagram of each component, along with any forces that are acting on it. For example, for the beam BC, you would draw a diagram like this:[Diagram of beam BC with loads, reactions, and other forces labeled]From this diagram, you can see that the reaction force at node B must equal the sum of the applied loads. So if we label the reaction force at node B as Rb, then we can say that:Rb = P + QWe can use a similar approach for the other components of the structure, such as beam DE and the supports at nodes E and F. For example, for the support at node E, we can draw a diagram like this:[Diagram of support at node E with loads, reactions, and other forces labeled]From this diagram, we can see that the reaction force at node E must equal the sum of the applied loads. So if we label the reaction force at node E as Re, then we can say that:Re = P + QBy combining all of these equations, we can solve for the reaction forces at nodes E and F. I hope this helps!

## What is the concept of virtual work?

The concept of virtual work is a principle used in mechanics to determine the equilibrium of a system by analyzing the work done by external forces. It is based on the idea that the work done by all external forces on a system must be equal to zero for the system to be in equilibrium.

## How does virtual work apply to solving support reactions?

In solving support reactions, virtual work is used to determine the external forces that act on a structure and the reactions that result from those forces. By analyzing the virtual work done by these forces, we can determine the equilibrium of the structure and the support reactions at its fixed points.

## What are the steps for solving support reactions using virtual work?

The steps for solving support reactions using virtual work are as follows:

1. Identify all external forces acting on the structure.
2. Choose a virtual displacement, which is a small hypothetical displacement of the structure.
3. Write the equations for the virtual work done by each external force.
4. Set the sum of the virtual work equations equal to zero.
5. Solve for the unknown support reactions.

## What are some common mistakes when using the virtual work method to solve support reactions?

Some common mistakes when using the virtual work method to solve support reactions include:

• Not considering all external forces acting on the structure.
• Choosing an incorrect or unrealistic virtual displacement.
• Making errors in writing out the equations for virtual work.
• Not setting the sum of the virtual work equations equal to zero.
• Incorrectly solving for the unknown support reactions.
To avoid these mistakes, it is important to carefully analyze the problem and double-check all calculations and equations.

## What are the advantages of using the virtual work method to solve support reactions?

The virtual work method offers several advantages for solving support reactions, including:

• It is a systematic and efficient approach to solving equilibrium problems.
• It allows for the consideration of all external forces acting on the structure.
• It is applicable to a wide range of structures and loading conditions.
• It can be used to determine the reactions at multiple support points simultaneously.
• It can be easily extended to more complex systems by adding additional virtual displacements.

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