Determine contact area

[abaqususer1981]

Imagine you have two block with square cross sections with side length a. One is fixed and cannot deform. The other is free to move and rotate.
Both blocks have initially two surfaces in full contact and no sliding is allowed between these two surfaces.

A bending moment in each principal inertia axis are applied to the block free to rotate, M1 and M2 bending moments, as well as a axial tensile force, Nt, so that this block deforms over the fixed block.

My question is: How can I determine the contact area? To make things easy assume that only one bending moment, M, is applied plus the axial tensile force.

I'm struggling to find how the axial tensile force changes the contact area by an analytical equation. Anyone can help?

Thanks

Joao

 

[paddingtongreen]

One last time! If Nt > W, there is no contact.

I think I know what you are trying to do. I think you are calculating the plus/minus pressures from overturning and thinking that if the plus is bigger than the average uplift "pressure" it will maintain contact over that small area. THIS IS NOT TRUE.

Foe equilibrium, ΣF=0 and ΣM=0. If your W-Nt <0 you don't have equilibrium.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[CELinOttawa]

Sketch. Show us all that we're wrong, or go away.

 

[BAretired]

BA

 

[3DDave]

Looking at the original problem statement, there is cause to wonder:
1) Why is the first block a square and not a planar surface?
2) What prevents sliding?
3) The first block is infinitely rigid, but no information is provided about the properties of the second block.
4) There is no mention of where the moments are applied. Do you mean couples?
5) There is no mention of weight or other force to offset the tensile load.
6) There is no mention of any means to react the moment load (couple?)
7) There is no mention of where the Tensile load acts. Does it change position as the moment (couple) is applied?

Since this is a fundamental problem, the inability to find it already solved would indicate there is no general purpose equation.

You have access to FEM/FEA. Create test cases for your example and run contact analyses, then use the output contact area and input loads to develop an equation that predicts contact area based on the loads and all the other assumptions you are making in posting the problem. This is the way experimentally derived formulae are created and should work for this case.

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Imagine you have two block with square cross sections with side length a. One is fixed and cannot deform. The other is free to move and rotate.
Both blocks have initially two surfaces in full contact and no sliding is allowed between these two surfaces.

A bending moment in each principal inertia axis are applied to the block free to rotate, M1 and M2 bending moments, as well as a axial tensile force, Nt, so that this block deforms over the fixed block.

My question is: How can I determine the contact area? To make things easy assume that only one bending moment, M, is applied plus the axial tensile force.

I'm struggling to find how the axial tensile force changes the contact area by an analytical equation. Anyone can help?

Thanks

Joao