Reaction at 4 Points in Rectangle with Force in x-Direction

In summary: Anyway, enough of that … here's your summary:In summary, the conversation discusses determining the reaction at four points arranged in a rectangle with a force acting in the x direction. The term "statically indeterminate" is mentioned and it is noted that this applies to the situation. It is questioned whether there is a way to calculate the forces at each of the corners. The conversation then explains that the problem can be solved with one more equation, and this can be achieved by knowing the bendy-ness or modulus of the table. It is suggested that tensors may be used in solving this problem.
  • #1
larocket83
1
0
I'm pretty rusty on my statics. I'm wondering how I could determine the reaction at four points arranged in a rectangle, with a force acting in the x direction at a distance away from the plate I have shown in this graphic. I seem to remember the term statically indeterminate, I think this applies, but is there any way to figure out the forces that each of these corners see? (Assume the points are fixed to the floor.)

Thanks in advance.

x.png
 
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  • #2
Welcome to PF!

Hi larocket83! Welcome to PF! :smile:
larocket83 said:
… I seem to remember the term statically indeterminate, I think this applies, but is there any way to figure out the forces that each of these corners see? (Assume the points are fixed to the floor.)

You're right, it is statically indeterminate … you can calculate the forces for a table on three legs, but not on four legs (basically because if you take one leg away, the table will still stand up … or, mathematically, because you have more unknowns than equations).

Of course, you can solve it, but you need one more equation …

in this case, you need to know how bendy the table is. :wink:
 
  • #3
wow, this is incredibly awesome. if the bendy-ness were given, what kind of quantity would that come as?

also, are tensors used to solve this problem?
 
  • #4
frustr8photon said:
wow, this is incredibly awesome. if the bendy-ness were given, what kind of quantity would that come as?

A modulus … see http://en.wikipedia.org/wiki/Modulus_of_elasticity" :smile:
also, are tensors used to solve this problem?

Maybe … bendy-ness depends on lots of things (it's flexible :wink:).
 
Last edited by a moderator:

1. What is the significance of the reaction at 4 points in a rectangle?

The reaction at 4 points in a rectangle refers to the force exerted on the four corners of the rectangle when a force is applied in the x-direction. It is important because it helps to determine the stability and strength of the rectangle structure.

2. How is the reaction at 4 points in a rectangle calculated?

The reaction at 4 points in a rectangle can be calculated using the principles of statics and the equations of equilibrium. The forces acting at each point must be balanced in order to determine the reactions at the four corners.

3. What factors can affect the reaction at 4 points in a rectangle?

The reaction at 4 points in a rectangle can be affected by various factors such as the magnitude and direction of the applied force, the dimensions and material properties of the rectangle, and any external forces or constraints acting on the structure.

4. How does the reaction at 4 points in a rectangle impact the overall stability of the structure?

The reaction at 4 points in a rectangle helps to distribute the applied force evenly throughout the structure, which can increase its stability. If the reactions at the four corners are not balanced, it can lead to an unstable structure and potential failure.

5. Can the reaction at 4 points in a rectangle be applied to other shapes or structures?

Yes, the concept of the reaction at 4 points in a rectangle can be applied to other shapes or structures as well. Any structure that experiences a force in one direction can be analyzed using the principles of statics and the equations of equilibrium to determine the reactions at its support points.

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