# How to Solve Support Reaction (Virtual Work) (Past Paper)?

• Suraj alexander
In summary, if you want to determine the deflection of a node in a system, you need to set up a matrix of equations that represent the equilibrium of the system, solve for the reaction forces and moments, and use the equation of equilibrium to check your results.

#### 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/83/83930-3dbc2a331721a2497ccdff8c950df951.jpg [Broken]
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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First, you need to determine the total force acting on the system. This can be done by summing up all of the forces and moments in the x and y directions. In this case, we have the two forces at points A and B, and the moment at point C.Next, you need to determine the reaction forces and moments at each of the nodes. This is done by setting up a matrix of equations that represent the equilibrium of the system. The matrix should look like this:Fx = 0Fy = 0 Mz = 0Where Fx, Fy, and Mz are the sums of the forces and moments in the x, y, and z directions respectively.Once you have set up the matrix, you can solve for the reaction forces and moments by using the equation of equilibrium. The equations look like this:Rx = Fx - F1 - F2 Ry = Fy - Mz Rm = Mz - F1x - F2y Where Rx, Ry, and Rm are the reaction forces and moments at each of the nodes. F1 and F2 are the forces at points A and B respectively.Once you have determined the reaction forces and moments, you can calculate the deflection of node E and F. To do this, you need to use the equation:Deflection = (Rx/EI) + (Ry/GJ) Where EI and GJ are the stiffness constants of the system. Finally, you can use the equation of equilibrium to check your results. You should find that the sum of the forces and moments at each of the nodes is equal to zero. I hope this helps!