## Buckling un-braced length of uniformly loaded axial member

## Buckling un-braced length of uniformly loaded axial member

(OP)

Hi all,

I did a search and didn't find any discussion so I'm starting this new thread. Hope I'm not creating a duplicate topic. For buckling un-braced length of a column with point load at the top, it is clear that the un-braced length equals the length of the column (assuming pin-pin top and bottom). My question is what is the un-braced length when the column is loaded uniformly throughout it's length and not a point load at the top? The axially force & stress diagram would increase linearly. Intuitively, I sense the two loading conditions would affect the buckling behavior of a column differently but I'm not sure how to take the uniform axial load into consideration in an analysis. I understand a conservative assumption to treat it as a point load at the top can be made.

Please chime in.

Thanks

D2

I did a search and didn't find any discussion so I'm starting this new thread. Hope I'm not creating a duplicate topic. For buckling un-braced length of a column with point load at the top, it is clear that the un-braced length equals the length of the column (assuming pin-pin top and bottom). My question is what is the un-braced length when the column is loaded uniformly throughout it's length and not a point load at the top? The axially force & stress diagram would increase linearly. Intuitively, I sense the two loading conditions would affect the buckling behavior of a column differently but I'm not sure how to take the uniform axial load into consideration in an analysis. I understand a conservative assumption to treat it as a point load at the top can be made.

Please chime in.

Thanks

D2

## RE: Buckling un-braced length of uniformly loaded axial member

## RE: Buckling un-braced length of uniformly loaded axial member

-5^2 = -25

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## RE: Buckling un-braced length of uniformly loaded axial member

I've checked beams like this before when they're supporting grating panels that wouldn't act as a diaphragm...seismic weight of the grating goes to each joist, each joist applies a seismic axial point load to its girder, check the girder as a beam-column.

## RE: Buckling un-braced length of uniformly loaded axial member

## RE: Buckling un-braced length of uniformly loaded axial member

However, if the applied load is coming into the column via some structural element that has strength and stiffness capable of bracing the column either nodally or relatively to some other stable structural fixity, then it may indeed brace your column.

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## RE: Buckling un-braced length of uniformly loaded axial member

## RE: Buckling un-braced length of uniformly loaded axial member

It's a good question because it points out how silly the concept of effective length really is. This is a good example why AISC has moved more towards the Direct Analysis Method, which does a better job of capturing the geometric non-linearity of the structure. Now, for use in the Direct Analysis method, I would say that the effective length is really the same for the loaded at the top and the uniformly loaded method.

It's a poor question if you're looking for this effective length to tell you a lot about the structure the way it does for a pin-pin column with a point load at the top. There are, however, ways to calculate the theoretically correct euler buckling load load for a column loaded this way. Asking the difference between this load the euler buckling point load is probably a better question. The AISC design guide on tapered members gives a method in an appendix that works for tapered members under various loading conditions. This is the method of successive approximations. I believe it could be used easily for this example to solve for the euler buckling load for a given column, length load arrangement.

## RE: Buckling un-braced length of uniformly loaded axial member