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Timoshenko + Second-order effects

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Anne93

Structural
Jan 20, 2023
1
Hello all,

I am modelling a Timoshenko beam in Abaqus with also an axial load.
Therefore, I also include second-order effects.

I am not sure whether I include both the shear deformation and second-order effect in a correct way.
On the internet I found that I have to use a B21 beam element for Timoshenko beams.
For second-order effects I have to include the nonlinear effects of large displacements (switched on at the step settings).
I also switched the beam element to B22, but that does not make a difference.

However, I have the feeling that the definition of to include shear is not correct. This is because I checked a Timoshenko beam with only a q-load (so without axial load) and this gives also the wrong result compared to the hand calculation.

On the internet, I found that also a transverse shear stiffness can be defined.
How does this work? What are the K13 and K23? And how do I know the Slenderness Compensation Factor?
I thought that the transverse shear stiffness is just G*A, but maybe I am wrong?
Or do I do something else wrong regarding including the shear?

Attached to this thread I uploaded the abaqus file. Here, I also made a model of an Euler beam with second order effects, and this one is exactly correct with the theory. Therefore, I also think that the addition of shear gives the problem.
 
 https://files.engineering.com/getfile.aspx?folder=ab4a0edb-149d-4252-88e9-faabca280049&file=FEM_model_deformation1.cae
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Check the documentation chapter Elements —> Structural Elements —> Beam elements —> Choosing a beam element (paragraph "Timoshenko (shear-flexible) beams"). You can also find some tests including comparison with analytical calculations in Verification —> Element Verification —> Simple load tests—> Shear flexible beams and shells.
 
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