Buckled Column Lateral Load Capacity

[RFreund]

I have somewhat of a hypothetical question - If a column buckles elastically, is its lateral load carrying capacity reduced after buckling (in the axis perpendicular to which it has buckled) and assuming the buckling load is removed/reduced?

Imagine 1: You push down on a yardstick in order to buckle it (about its weak axis). The force required to break it about the strong axis - is it the same or less as if it was not buckled?
Imagine 2: A slender stud has a beam above it. The beam deflects enough to buckle the stud. The stud takes no more axial load as it is picked up by the beam now. Can the stud resist more/less/same as when it was not buckled?

My thoughts are that at a minimum your capacity would be reduced due to having moments about both axis My = P*Delta (although I'm not sure what P equals??) and Mx remains the same. But I'm not sure about how the post-buckling behaviour would affect things. Maybe I'm overthinking something here...



EIT

http://www.HowToEngineer.com

 

[jayrod12]

Edit: Read too fast.

Will formulate proper response later.

 

[KootK]

Some thoughts:

1) The axial load on the column would not be reduced in the scenarios described. It's not clear to me if you're seeing this in the same way.

2) Agree with the My = P x Delta.

3) If the studs were not LTB braced, it would be difficult to assess their LTB capacity.

4) Weak axis buckling implies lateral movement and might compromise the sheathing fastening from which you derive your LTB bracing.

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.

 

[Teguci]

Check unity for bending in both directions Mx/Max + My/May <= 1. With bending in both directions, corner stresses will be higher than just one or the other. For a pipe, the bending moment will be the root of the squares.

As for bucking and then unloading, if the column stays in the elastic region, this should have no impact on column performance. Of course, if a column buckles that is usually enough of a problem to suggest something went wrong. Further, if the column stays in the elastic range it suggests that the column is not the main support member and can probably ignore the buckling stress completely (you are using ductile material - check your connections - and the load can redistribute to another load path). The only deflection concern would be the torsion caused by applying the lateral load at the buckling delta.

 

[jayrod12]

Imagine 1: You push down on a yardstick in order to buckle it (about its weak axis). The force required to break it about the strong axis - is it the same or less as if it was not buckled?

Less, think of what the tensile stresses would be at the outer corner. You'd be getting increased stresses from bending in both directions. It would have to be less.

Imagine 2: A slender stud has a beam above it. The beam deflects enough to buckle the stud. The stud takes no more axial load as it is picked up by the beam now. Can the stud resist more/less/same as when it was not buckled?

I would say the same at best. But more likely less. For the same reason indicated in scenario 1.

However, the more I think about it, if we're discussing specifically capacities in singular directions ignoring what's happening in the other direction (to a point) I don't know if the capacity itself changes.

Your unity check in each direction would still require you to calculate Mrx and Mry, and I don't feel that being at the buckling load directly affects these capacities. The overall section capacity will be less because you've now entered combined axial and bi-axial bending as opposed to the original design that assumed only Axial and strong-axis bending.

 

[KootK]

For an 8' stud to accommodate, say, 1/2" of beam deflection, it would need to bow out 4"-5" at mid-height. That would be enough to blow out any sheathing connections and, as mentioned above, cause one to start thinking about the impact of the displacement with regard to torsion and LTB under strong axis lateral load.

One could certainly use the imposed axial displacement to work out the associated weak axis moments. Then, a unity stress check could be undertaken including My, Mx, and P but omitting axial buckling concerns. If this check would somehow work out without relying on sheathing connections for bracing, I could get behind it. It's tough to imagine a practical situation where the lateral displacement would be tolerable though.

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.

 

[jayrod12]

Agreed. I don't think if you've exceeded the buckling capacity of any column that it still has any appreciable load resisting capabilities as a section.

 

[Agent666]

Agree with Jarrod, it's failed, trying to argue otherwise is flawed. Sure it will take some load after its buckled, but at that point it ceases to be of use in a real structural sense when the objective is to prevent the first failure.

 

[wannabeSE]

KootK
RFreund's question is hypothetical and assumes no sheathing. The sheathing would likely brace the member against weak axis compression buckling. Also, I don't understand the 8" stud example. Are you saying the stud has buckled 4"-5" on the weak axis at mid span and has 1/2" strong axis deflection? I am not following the point.

For RFreund's second scenario where the vertical displacement of the buckled stud is stopped (by a beam?). The axial force on the stud is equal to the critical buckling force, P_cr, provided the member stresses are less than yield (assuming ideal elastic slender column). The axial force remains constant without regard to the amount lateral displacement after buckling (the deflection is proportional to P_cre and e is equal to the deflection). But, the post buckled bending cause addition member stresses. I don't know why anyone would want to determine the strong axis bending capacity of a column buckled on the weak axis, but I guess an interaction check could be performed with M_y = P_cre

 

[KootK]

RFreund's question is hypothetical and assumes no sheathing.

How do you know this? RF made no mention of the presence or absence of sheathing. He didn't even technically specify a construction material. And the question was described as "somewhat hypothetical". In the world of structural engineers, "somewhat hypothetical" usually translates to "I've got a practical application for this wackiness but I want some feedback on it before I commit".

The problem sounded wood-ish to me so I made an assumption and ran with with it. In practice, it's pretty hard to get wind lateral load to a stud without sheathing. My perspective is probably tainted by the fact that I've dealt with this before in practice. I had a case where the owner wanted a small opening in a wood frame wall that could later be turned into a large opening without too much fuss. He had the builder install a header for the large opening and then infilled half of the opening with un-gapped stud wall. Sheathed of course.

Also, I don't understand the 8" stud example. Are you saying the stud has buckled 4"-5" on the weak axis at mid span and has 1/2" strong axis deflection? I am not following the point.

The point of the example is that, if we're discussing a case of imposed axial stud displacement resulting in weak axis buckling, it would take a great deal of weak axis lateral displacement (4"-5") to accommodate a rather small imposed axial displacement (1/2" over 8' in the example). Again, the relevance flows from my assumption that:

1) Sheathing connections would be present and;
2) Villagers would be frightened by gross curvature in the stud in question.


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.

 

[RFreund]

I missed the last few comments here. What Kootk described is along the lines of what was thinking, not that I gave many clues to this. And it was a hypothetical exercise.
The application is a Vertical Window Mullion below a steel beam.

EIT

http://www.HowToEngineer.com

 

[KootK]

Ahh. In a window million, that potential lateral deflection would be a problem.

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.