Simple Bending Theory
Simple Bending Theory
(OP)
Hi all,
To test out a FEA software, I modeled a cantilever beam 6m long and 0.7m deep with a concentrated load at the tip of the beam. I compared the stresses at the support from FEA to those obtained by simple bending theory (Euler-Bernoulli), I got a difference of about 15% (FEA is larger). Mesh was fine.
I was wondering if that was a departure from simple bending theory or just a numerical approximation error? Seems quite large to be an approximation error.
Thanks,
Joe
To test out a FEA software, I modeled a cantilever beam 6m long and 0.7m deep with a concentrated load at the tip of the beam. I compared the stresses at the support from FEA to those obtained by simple bending theory (Euler-Bernoulli), I got a difference of about 15% (FEA is larger). Mesh was fine.
I was wondering if that was a departure from simple bending theory or just a numerical approximation error? Seems quite large to be an approximation error.
Thanks,
Joe






RE: Simple Bending Theory
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: Simple Bending Theory
What if you refine the mesh substantially near and at the support and also don't restrain vertical at any nodes except the bottom, i.e. all connection nodes are restrained in x and base node is x & y (or z if z is your vertical).
RE: Simple Bending Theory
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Simple Bending Theory
IDS, Yes it is a 2D analysis with plane stress elements.
If I restrain only the base node vertically, the results at the top are very close to the theoretical (1.5%). So it was a departure from simple bending theory, and the extra stresses at the support are due to the addition of shear stresses. Spot on.
Thanks guys! Much appreciated!
RE: Simple Bending Theory
The resulting loads on the support should all total up to the proper moment.
Could you have self-weight of the beam that's making a difference?
There will be a certain amount of extra deflection due to shear, and a wide flat beam can have reduced deflection due to Poisson's effects, but neither would affect stress.
RE: Simple Bending Theory
Solution by double integration is inaccurate if there is a lot of bending. According to double integration, the end of the beam travels straight down. That's not what it does in reality.
For most practical analyses, the deflections are small. Double integration is convenient, and accurate enough.
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JHG
RE: Simple Bending Theory
BA
RE: Simple Bending Theory
The self-weight is included in both theoretical calcs and model.
RE: Simple Bending Theory
so you're predicting a numerical error? This is kinda like a practical analysis tho, where loads and spans are pretty reasonable, deflections are small but a 15% difference in stress is surely not accurate enough, don't you think?
RE: Simple Bending Theory
Halfway along the beam the shear stress distribution will be approximately parabolic with zero shear at the top and bottom face.
At the support the behaviour is no longer predominantly flexural, so you wouldn't expect the stresses to match those from flexural theory.
Regarding the suggestion that the problem is due to inaccuracies in the double integration process, that would only affect the calculated deflections, and assuming the FEA was linear elastic, the computer makes the same assumptions (small deflections) anyway.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/