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Reactive moments in a cantilever beam modeled with 3-D elements

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Bharathsf

Bharathsf

Aerospace
Feb 5, 2012
35
I have a doubt in the formulation of 3-D HEXA elements. I know for a fact that HEXA elements cannot take applied moments as it has only 3 translational dofs. In the case of a completely constrained cantilever beam with a point load at one end, there will be a reactive moment where it is constrained. How does the 3-D HEXA elements which cannot take moments, take this reactive moments into the picture for stress analysis? Can anyone please explain

Bharat
 
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Dear Bharat,
Simply horizontal reactions in top & bottom of constrained beam end will equilibrate the moment of the load.
Here you are an example (an image is better than thousand words):
• A cantilever beam of say 20x50x300 mm is loaded in the free end with a vertical loading of FY=-1000 N.
• Vertical reaction force should be RFY=1000N, and the moment of the load will be RMX=1000x300=3e5 Nmm.

cantilever_chexa_mesh.png


Let´s see the results:

• Here you are the resultant vonMises stress (MPa) distribution in the cantilever beam, is maximum near of the fixed end.

cantilever_beam_nodal_stress.png


• And here you are the FREE BODY DIAGRAM to see the ccntribution of reaction forces in the constrained end of cantilever beam. As you can si the equilibriuem between forces & reactions is fully satisfaced, the resultant moment RMX is exactly 300e3 Nmm, and the resultant Vertical reaction force RFY=1000N, OK?.

cantilever_beam_free_body.png


Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48011 BILBAO (SPAIN)
WEB: Blog de FEMAP & NX Nastran:
 
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