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Basic Plate Question

Basic Plate Question

Basic Plate Question

(OP)
Hi Everyone, I have a basic question on plates and was hoping one of you know the answer. This is an academic question, if we have two cases where:

Case 1: A steel plate with a hole in the center experiences pure tension of force F on both sides.

Case 2: A steel plate with a hole in the center is fixed on one end and experiences tension of force F on ONE side.

Are these two cases considered equivalent? I.E. the stress seen in the plate will be analytically the same? Or is the force applied to Case 2 required in increase by two to match the stresses seen in Case 1? I am confused.

Does anyone know the answer? Thank you.

RE: Basic Plate Question

same

RE: Basic Plate Question

Draw a free body diagram for both cases....the answer will be clear.

RE: Basic Plate Question

same - but only if the tension force F is applied as a uniform load along the plate edge. If the load is a concentrated load attached to a single point on the plate edge then the sides are a bit different.

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RE: Basic Plate Question

I vote equivalent. The fixed boundary condition in the one case should provide the same tension that you had in the other case as an applied load. The one caveat is that, modelled as a true plate with FEM or elasticity, Poissan's ratio would mess with the symmetry a bit unless you can eliminate in plane restraint at the fixed boundary.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Basic Plate Question

actually i see a small difference between the two scenarios.

reacting the applied tesnion with a tension force permits the loaded edge to conform to poisson effects, a 1D stress field.

reacting the applied tension with a constraint usually inhibits poission induced displacements, creating a 2D stress field.

another day in paradise, or is paradise one day closer ?

RE: Basic Plate Question

(OP)
Thank you for all the replies! I appreciate it.

RE: Basic Plate Question

The problem is not properly stated if you mean what I think you mean. The way it is stated, there is a huge difference between Case 1 and Case 2. In Case 1, the plate is in pure tension. In Case 2 with one end fixed and one side loaded there are shears and bending moments introduced in the plate.

BA

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