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How to apply end moments to a box-section beam under axial load for buckling analysis?

How to apply end moments to a box-section beam under axial load for buckling analysis?

How to apply end moments to a box-section beam under axial load for buckling analysis?

(OP)
Hi all,

The beam is subjected to an axial load and end moments and I’m trying to find the critical end moment loads (Mcr) that cause buckling.

I have a thin-walled hollow 2ply-composite beam (modelled with shell elements in Abaqus) that is simply supported (LHS is pinned, RHS is a roller support). The beam is subjected to an axial load and end moments.
When no end moments are applied I am able to find the critical buckling load (Pcr, axial load), but as soon as soon as I start incorporating end moments I am running into issues.

Does any one have any experience with applying end moments to a thin walled beam for buckling analysis?

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

What kind of issues do you encounter, specifically ? Is that a linear (eigenvalue) buckling analysis or nonlinear (postbuckling) simulation ?

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

(OP)
Hi FEA way,
It's a linear eigenvalue buckling analysis that I'm looking at - trying to find the critical axial buckling load (Pcr) and critica end moments (Mcr).

Initially, the box section beam is analysed to estimate the critical buckling loads (Pcr) with no end
moments being applied. Following this, I'm trying to calculate the critical end moments (Mcr)for three different values of axial preloads; P0 = 0.5Pcr , P0 = 0, and P0 = +0.5Pcr.

My issue is trying to apply both the axial load and the end moments.

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

I never use FEA tools for buckling analysis because I was under the impression that the linear buckling results were widely inaccurate, especially for a short to medium span, where buckling effects may be non-linear in nature

“Any idiot can build a bridge that stands, but it takes an engineer to build a bridge that barely stands.”

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

how are you applying moment to the beam ? (using an RBE spider to distribute the load around the box ?) applying a couple to two faces ??

Are you trying to solve case 2 (no axial load) first ?

Have you reviewed the classical analysis of this beam (called a beam-column) ?

How does your Pcr compare to Euler ? (i'd've thought they'd be very similar)

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

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

(OP)
Hi rb1957,

For the moments, I used a distributing coupling constraint at each end - control point as an RP at the centre, edges selected as surfaces. I applied the boundary conditions to the RP, along with the loads (bending moment and axial force).

For axial force only, my Pcr is ~90% accurate against theoretical. However when I try moments only (no axial) I'm far off.

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

I don't know Abaqus and I don't recognise the words (!?) you're using.

"RP" sounds like the dependent (or is it independent) node at the center of a rigid element (a "spider").

"coupling constraint" is an odd term in my vocabulary for "applying a moment" but maybe you're applying a moment at one end and reacting it (through a constraint) at the other.

But is that the same thing ? you want to apply a moment at each end, so the beam deflects (hogs/sags) symmetrically. But a moment constraint is also a fixity, so zero slope at that end. Maybe apply equal and opposite moments … any imbalance (very small mathematical differences) would show in slightly different shear reactions at your two supports.

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

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

Check the "Buckling analysis of beams" example in Benchmarks Guide of Abaqus documentation. It should be helpful for you.

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

Well, OC, please post:
Picture of model with loads and bc’s
Picture of mode shape
Buckling load, moment
Theoretical solution, with reference (how do you know this is correct?)

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

And run a static analysis with just a moment load, and provide plot of deformed shape.

RE: How to apply end moments to a box-section beam under axial load for buckling analysis?

You can use normal non-linear analysis with material and geometric non-linearity enabled. You can assess buckling by reviewing nodal displacements relative to your supports or a fixed point. If you can view the "element nodal forces", the information can be used to develop the various loads over the cross section. There should be a tool on your software that does the post processing for you.

Keep in mind that using normal buckling analysis which is linear will only give you buckling due to axial loads.

If you can share an image of the actual scenario I can try and give some advice on the application of the loads, as the setup of the model may/will impact the manner in which the loads should be applied.

If you want to go the route of hand calculations check out the below reference book.

https://www.wiley.com/en-us/Guide+to+Stability+Des...

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