## 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?

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?

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

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?

“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?

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?

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?

"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?

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

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?

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

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...