Reaction Forces of a simply supported thin plate

[gemmott]

I have a square thin plate 620mm*620mm that is simply supported on all four edges and is subjected to a uniformly distributed patch load (q0) over a central area of 58mm*58mm. I have calculated the central deflection to be (3.137x〖10〗^(-6) q0 (mm) via navier solution and the max stress in the plate (64.87q0 (〖N/m〗^2)).
However I am trying to find the reaction forces and moments at the four edges and corners of a thin plate.
Further information:
Material yeilds at 380MPa, by using von mises yield criterion is have calculated q0=5.86MN.

If I calculate the shear force Qx and Qy from
Qx=dMx/dx+dMxy/dy - then as these are the vertical forces then this givse me the reaction forces?

Will the reaction forces in the corners of the plate differ from the reaction forces on the four edges.

Any help would be much appreciated

 

[pongo38]

Please clarify whether 'simply supported' means uplift is restrained or unrestrained. If corners can lift, what will be the reactions there?

 

[Mene]

I would first like to commend you on your thorough analysis of the thin plate and your use of the Navier solution and von Mises yield criterion. It is clear that you have a strong understanding of the mechanics involved in this problem.

To answer your question, yes, the reaction forces at the corners of the plate will differ from the reaction forces on the four edges. This is due to the fact that the corners are not in direct contact with the supports, so they will experience different stresses and deflections compared to the edges.

To determine the reaction forces at the corners, you can use the same approach you used for the edges, but you will need to consider the additional moments and forces acting on the corners due to the plate's curvature and the patch load. This can be done by calculating the moment of inertia and the bending stresses at the corners.

Additionally, it is important to consider the effect of the material's yield strength on the reaction forces. If the calculated reaction forces exceed the yield strength of the material, it is possible that the plate could fail at the supports. Therefore, it is important to ensure that the reaction forces are within the yield strength limits of the material.

In summary, the reaction forces at the corners of the plate will differ from those at the edges, and further analysis is needed to accurately determine the reaction forces at the corners. It is also important to consider the material's yield strength in your analysis to ensure the stability and safety of the structure.