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Buckling of column in SAP2000
2

Buckling of column in SAP2000

Buckling of column in SAP2000

(OP)
Hi , all. This is a steel frame made up of I-beam on top and I-beam column.

The I-beam on top is connected thru moment connection to the I-beam column below to restrain the major axis bending.

I understand that in major axis bedning of column (x axis), it's pinned (bottom) , fixed (top) connection, so that k factor for buckling = 0.7 .

However, for minor axis bending ( y axis) , it's pinned free. In free condition, the frame shall be unstable, right ? But it seems that the SAP2000 still somehow detect it as pinned-pinned condition.

I have checked the buckling capacity of column, it's rather similar to the results that the SAP2000 gave. What's wrong with the model, can anyone help ?

RE: Buckling of column in SAP2000

(OP)
I have checked the buckling capacity of column in the weak axis when Lcr = 1.0L , it's rather similar to the results that the SAP2000 gave. It's clearly show that SAP2000 detect it as pinned -pinned conidition. ...What's wrong with the model, can anyone help ?

RE: Buckling of column in SAP2000

Quote (dccd)

I understand that in major axis bedning of column (x axis), it's pinned (bottom) , fixed (top) connection, so that k factor for buckling = 0.7 .

I feel that K > 2.0 given that the column appears to be a sway column with its bottom pinned and its top partially fixed.

Quote (dccd)

However, for minor axis bending ( y axis) , it's pinned free. In free condition, the frame shall be unstable, right ? But it seems that the SAP2000 still somehow detect it as pinned-pinned condition.

I suspect that your joist members are acting somewhat like a moment frame beam with respect to weak axis column behavior. The response chain would be something like this:

1) When the tops of the columns try to rotate weak axis, they engage and rotate the wide flange girders in torsion.

2) When the wide flange girders try to twist, they engage and flex the attached joist members in strong axis bending.

You could adjust the model to behave as you'd like by releasing the torsional restraint at the ends of the girders. But, then, the model should be unstable as you said and you'd have to add some other kind of lateral restraint to make a go of it.

RE: Buckling of column in SAP2000

(OP)
Do you mean the secondary member along the x axis act as restraint for the column in the minor axis bending ?

The seocndary member doesnt connect directly to the top of column, that's weird. How can the secondaty member act as minor axis bending moment restraint for the column ?

How to modify the model so that it will become more realisitic ???Since for the minor axis bending of column, it's clealy unstable because of the piined free condition, (no restraint against minor axis bedning on top of column)

RE: Buckling of column in SAP2000

(OP)
By the way, if for major axis bending column is in pinned partially pinned condtion, the k shall be = 0.85, am i right ? The max k is only 2.0 ( free, cantilever condition)

RE: Buckling of column in SAP2000

Quote (I understand that in major axis bedning of column (x axis))


Look to your picture carefully ... the major axis is X axis for the columns on the left and Y axis for the right columns..Regarding the joists; I suspect that the joists rigid connected to I beams..

RE: Buckling of column in SAP2000

(OP)
Even if the joist (secondary beam) rigidly connected to the primary beam, will it have effect on the column ? The joist isn't directly connceted to the column. Will the joist act as restraint to minor axis buckling of column ?

RE: Buckling of column in SAP2000

Quote (dccd
...Even if the joist (secondary beam) rigidly connected to the primary beam, will it have effect on the column ? The joist isn't directly connceted to the column. Will the joist act as restraint to minor axis buckling of column ?)


The answer is yes... the torsional resistance of primary beams will provide some limited necessary restraint...But how the rigid connection will be provided and detailed is another issue..
Another question, is it reasonable to assume and model that rigid connection ?..


RE: Buckling of column in SAP2000

(OP)
Do you mean the primary beam provide the bending moment restraint of the minor axis bending of the column ? There's only rigid moment connection between the beam and the column (in major axis of column) ...Will this affect the minor axis restraint ? Will the program detect the primary beam as minor axis restraint for column buckling ??



Or do you mean the secondary beam provide the bending moment restraint of the minor axis bending of the column ?

RE: Buckling of column in SAP2000

Quote (dccd)

Do you mean the secondary member along the x axis act as restraint for the column in the minor axis bending ?

Yes, and I believe that HTRUKAK is saying more or less the same thing.

Quote (dccd)

How can the secondary member act as minor axis bending moment restraint for the column ?

Like this if the torsion connection between the girders and columns is modelled as rigid.

Quote (KootK)

The response chain would be something like this:

1) When the tops of the columns try to rotate weak axis, they engage and rotate the wide flange girders in torsion.

2) When the wide flange girders try to twist, they engage and flex the attached joist members in strong axis bending.

Quote (dccd)

How to modify the model so that it will become more realisitic ???

Like this, if my assumption about the girder torsion connection is correct.

Quote (KootK)

You could adjust the model to behave as you'd like by releasing the torsional restraint at the ends of the girders. But, then, the model should be unstable as you said and you'd have to add some other kind of lateral restraint to make a go of it.

Quote (dccd)

By the way, if for major axis bending column is in pinned partially pinned condition, the k shall be = 0.85, am i right ? The max k is only 2.0 ( free, cantilever condition)

I don't believe that you are right if this is a sway frame, as your model suggests. For a sway frame with a pinned base and a partially fixed top: [2.0 > K >= Infinity].

I'd recommend supplying us with some more information:

1) Is your frame intended to be a sway frame in the X direction?

2) Is your frame intended to be a sway frame in the Y direction?

3) Can you post the deflected shape of your frame acting under an X direction load?

4) Can you post the deflected shape of your frame acting under a Y direction load?

5) Can you upload your SAP model so that we can review it it?

RE: Buckling of column in SAP2000

(OP)
Do you mean that for when the column buckle in minor axis direction , the wide flange of primary beam is enagaged, so, somehow the buckling is prevented by the torsion resistance of the flange of the primary beam ?

However, in reality, is it reasonable to assume the wide flange of primary beam to act as restraint for minor axis buckling of column ??



As for the deflection shape of the column under the applied lateral load in x and y direction, please refer to teh attachment posted.



RE: Buckling of column in SAP2000

(OP)

RE: Buckling of column in SAP2000

(OP)
The frame is intended to sway in x direction, for y -direction, they are rigidly connected.

RE: Buckling of column in SAP2000

You've said twice that you expect the structure to be unstable. What are you trying to achieve by modelling it? It seems as though half the story is missing.

RE: Buckling of column in SAP2000

(OP)
Ya, I expect the model to be unstable . However, the model seems to be stable in the analysis software. I am confused now .

RE: Buckling of column in SAP2000

As per the comments above, you need to put more pin joints into the model to make it act the way you're thinking about it. Something like the picture below. You could also use master-slave node connections. You can't just put a pin in the secondary beams because they need to be continuous over the primary beams so the cantilever outstands remain stable.

Also, when a structure is a sway frame, the *minimum* value of K is 1.0. The maximum can be more than 2.0 as KootK said. 2.0 is just the largest number usually given in tables of idealised situations. The 2.0 case is for pin base with *ideal* rigid moment restraint at the top, but with the top free to sway. A real connection can't achieve perfect rigidity so K>2.0 in real structures.


RE: Buckling of column in SAP2000

(OP)
@steveh49 , I have tried to model a dummy member connecting the primary beam and the secondary beam to avoid the column detect the secondary beam as restraint of minor axis buckling of column ....

However, it seems the program still doesnt shows the real life situtaion, ( No member to restraint minor axis buckling of column, the column should fail in minor axis buckling , (due to pinned -cantilever condition in minor axis of column) .....

RE: Buckling of column in SAP2000

I don't use SAP so can't look at your model. It should be unstable if you've put those pinned dummy members in so the analysis should fail before even getting to the code check. Some programs will stabilise an unstable structure by applying some arbitrary restraint. I don't know whether SAP follows this unsavoury practice though. Check the analysis log for any warnings or comments about stability.

RE: Buckling of column in SAP2000

(OP)
Surprisingly, no warning message popped out. Whole structure is stable, that's weird.

RE: Buckling of column in SAP2000

Release all end moments on joists. Should work.

RE: Buckling of column in SAP2000

(OP)
@kostast88, releasing all moment on secondary clearly doesnt work. It made things worse, as you can see in the photos earlier, secondary joist is cantilever at both ends and simply supported in betweens

RE: Buckling of column in SAP2000

Quote (dccd

Surprisingly, no warning message popped out. Whole structure is stable, that's weird.)



Will you post the deformed shape with nominal horizontal tip loads? and model showing the support conditions , joint releases with the set up that Mr. steveh49 proposed?..

I am familiar with old versions if the model is correct , the program should terminate with giving fatal error message. If the stability is provided by program , ( for some modelling with FEM and Push -over is valid) , the output will not be reliable...

With your modelling, ( the columns pin supported in X and Y direction, the joists supported to main beams with fictious column elements having length half of the heights of main beam + joist and pin connected to one of the beams either joist or beam ) the frame is unstable in X direction.. There is no way..

Regarding the frames with pin supported , the stability is provided with fixity of beam -column connection and there is no way that the buckling length can be less than 2* L .. And 2xL is valid for infinite rigid of the beam..


I will suggest you to look tutorials for the modelling issues..

RE: Buckling of column in SAP2000

(OP)
@HTURKAK , I have posted the deformed shape under lateral load in x and y direction earlier, please refer to the attached image for your reference again .





RE: Buckling of column in SAP2000

Remove the cantilever bit from your model and substitute them with a load representing the weight. Leave only the simply supported joists.

RE: Buckling of column in SAP2000

(OP)
For the secondary member, I have removed the cantilever part and released the moment at the simply supported part, the program detect the system as unstable. (This is what I expected in real situtaion, the whoel strcuture isn't stable because it's pinned free condition in minor axis...) But the column still pass in the analysis. Surprisingly, the column doesnt fail due to minor axis buckling...


Why would release moment of the secondary member can render the whole structure unstable ?? ( When the secondary beam not released, the program detect it as restraint of the column against minor axis buckling) ??


The secondary member doesnt connect directly to thw column, how can the program detect it as restraint for minor axis buckling ??

RE: Buckling of column in SAP2000

Your first photo shows that 2 columns are rotated 90 degrees.Is that right? Or did you rotate them to get different buckling resistances on the 2 grids?

Therefore you effectively have a 3D structure. The pinned joists still provide some restraint to the beam which is rigidly connected to the columns (and they should). Since your model is 3D, these are activated when forces act in the X and Y direction respectively.

Try rotate all columns accordingly and you may get a complete failure this time.

Finally, since it passes strength and fails in stability, it fails.

RE: Buckling of column in SAP2000

(OP)
My questions are still the same.....


Why would release moment of the secondary member can render the whole structure unstable ?? ( When the secondary beam not released, the program detect it as restraint of the column against minor axis buckling) ??


The secondary member doesnt connect directly to thw column, how can the program detect it as restraint for minor axis buckling ??

RE: Buckling of column in SAP2000

Quote (dccd)

My questions are still the same.....

So are our answers.

Quote (dccd)

Why would release moment of the secondary member can render the whole structure unstable ??

Because it interrupts the second step in this response chain.

Quote (KootK)

1) When the tops of the columns try to rotate weak axis, they engage and rotate the wide flange girders in torsion.

2) When the wide flange girders try to twist, they engage and flex the attached joist members in strong axis bending.

Quote (dccd)

The secondary member doesnt connect directly to thw column, how can the program detect it as restraint for minor axis buckling ??

The key to this is to recognize that the framing shown below, with the offset, IS a functional moment frame. Do you see it? If not, let us know and we'll keep hammering away at it.

Quote (dccd)

Do you mean that for when the column buckle in minor axis direction , the wide flange of primary beam is enagaged, so, somehow the buckling is prevented by the torsion resistance of the flange of the primary beam ?

Yes, the tops of the columns will be rotationally restrained by the torsional strength and stiffness of the primary girders.

Quote (dccd)

However, in reality, is it reasonable to assume the wide flange of primary beam to act as restraint for minor axis buckling of column ??

Given that your question in this thread is about the behavior of your model, it doesn't much matter whether or not it's reasonable in reality. That said, most common moment frame connections in one plane will in fact result in significant rotational column restraint in the orthogonal plane. It is, however, uncommon for engineers to rely upon that restraint. One thing to keep in mind is that many software programs will accurately model St. Venant torsional stiffness but neglect warping torsional stiffness, thus underestimating aggregate torsional stiffness.

Quote (dccd)

As for the deflection shape of the column under the applied lateral load in x and y direction, please refer to the attachment posted.

Thanks. Your Y-axis plot confirms my expectation that K > 2.0 here. Your X-axis plot is showing no visible, relative deformation between the column ends. It may be that you need to amplify the plot scale in order to make that show up.



RE: Buckling of column in SAP2000

(OP)
Do you mean somehow with the secondary beam rigidly connected to the primary beam, the effect it just like the addtiional horizontal member joining directly to the column in x direction of your figure above to restrain buckling of column about y axis ?? Eventhough the secondary beam is at some ECC away from the column, as long as the secondary member is rigidly connected to the primary beam, the effect is still the same ? (In this case, we can assume , pinned, pinned condition for buckling about y axis ??


Or do you mean both the torsional restraint of the primary beam and the fixed connection between the secondary beam and primary beam contribute to the restraint of the buckling of column ?



RE: Buckling of column in SAP2000

(OP)
@KootK

In realility, can I depend on the torsional restraint of the primary beam and the fixed connection between the secondary beam and primary beam contribute to the restraint of the buckling of column about the minor axis ?


Is it safe to do so ? So I must provide horizontal member in another direction to restraint the buckling (so that it became pinned-piined condition) ?

RE: Buckling of column in SAP2000

Quote (dccd)

Do you mean somehow with the secondary beam rigidly connected to the primary beam, the effect it just like the addtiional horizontal member joining directly to the column in x direction of your figure above to restrain buckling of column about y axis ?? Eventhough the secondary beam is at some ECC away from the column, as long as the secondary member is rigidly connected to the primary beam, the effect is still the same ?

Yes, so long at the primary beam's torsional degree of freedom is rigidly connected to the column's flexural degree of freedom about the same rotational axis.

Quote (dccd)

In this case, we can assume , pinned, pinned condition for buckling about y axis ??

No, not pin-pin, k=1.0. The column would be pinned at the bottom, partially fixed at the top, and free to translate at the top. So, again, K>2.0

Quote (dccd)

Or do you mean both the torsional restraint of the primary beam and the fixed connection between the secondary beam and primary beam contribute to the restraint of the buckling of column ?

Yes, I mean that as well.

Quote (dccd)

In realility, can I depend on the torsional restraint of the primary beam and the fixed connection between the secondary beam and primary beam contribute to the restraint of the buckling of column about the minor axis ?

It's rare to do that but, yes, so long as your analysis, design, detailing, and application are all appropriate for utilizing such a load path.

RE: Buckling of column in SAP2000

(OP)

Quote (KootK)




In my case , the connection of the primary beam and the column is fixed, the connection of the secondary beam and the primary beam is fixed, is it safe to ignore the horizontal member bracing (red member in the diagram) in the x direction ?? For modelling wise, it seems ok. (The column passed , and without failed in the analysis software). In reality, can I depend on them to provide the resistance against minor axis buckling ??

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