Fixed base for a column? 1

[Lion06]

In digging into the nomograph for a previous thread I posted about FMC frames I happened upon another question that I am hoping I can get some opinions and insight on.
When using the nomograph to calc k (for either sway or non-sway frames), you can assume a G of 1 for a column rigidly attached to a properly design footing. My question is what exactly is a properly designed footing?
Initially, I thought it would be any footing designed to take the greatest load effects from the combinations assuming a fixed base. When I started thinking about this more, I don't necessarily agree with this anymore.
Now I think that the footing needs to be designed to take the full moment capacity of the column. My reasoning is this: as this column is loaded and reaches the point of buckling the COLUMN needs to be fixed at the base, not just be able to transfer some value of moment. It is likely that the moment it will see when buckling could exceed the moment it sees under combined gravity and lateral loads. I guess you could say that it won't see anything higher than gravity and lateral loads, but.. that is for strength, not stability. The lower moment resistance will likely allow more rotation, true?

 

[PMR06]

Without checking an example, I would think that the axial load large enough to cause the column to buckle would contribute greatly to the P/A component of the footing, and it would not be as likely to rotate.

 

[DaveAtkins]

Technically, I think you are correct. But I am comfortable designing for the maximum load combination, and not worrying about any larger axial forces or moments that could cause buckling. I also agree with PMR06.

DaveAtkins

 

[271828]

I do not believe that the footing must be able to develop the column strength to use G=1. Why would we believe that the column base moment would be that large at the onset of bifurcation? Remember that the buckled shape has a very small amplitude at the initiation of buckling--sure it would get larger if more load was applied.

 

[lkjh345]

Agree with the above posters. I design for the maximum load combination from the footing. Not the capacity of the column.

In moment frames, frame members sometimes (often) are designed not just for strength but also so the overall frame stiffness meets drift criteria. The columns may be much stronger than required in order to control deflection.

If the loads have been computed correctly, the the column base reaction (axial and moment) is the maximum load that the footing will 'see'.

 

[Lion06]

Well, taken to the extreme case, if you have a gravity only column with no moment connection anywhere above the base, the moment at the base is going to be zero, even if you assume it fixed at the base.
Now the footing is designed for axial load only. Would you still use a G of 1 in this case, and if so why? I would look at this case and say that it is not capable of resisting any appreciable amount of moment and therefore can't be considered fixed.

 

[haynewp]

There is a formula to approximate the fixity of the footing relative to the column based on the dimensions and the subgrade reaction modulus of the soil.

You can also derive the moment required for restraint at the base from the curvature of the buckled shape.

 

[Lion06]

haynewp-
How do you go about deriving the moment required for restraint at the base from the curvature of the buckled shape?
I hope this isn't a second grade question.

 

[haynewp]

I think you have to go back to Euler's equations where the buckling load is derived. These are interesting questions you have but I don't think I know anyone that has actually included this restraining moment in the design of a footing or in the connections between the column and the girders.

 

[shin25]

ACI 318, 10.13.7-

"In sway frames, flexural members shall be designed for the total magnified end moments of the compression members at the joint."

Footing is a flexural member.

 

[haynewp]

I would happy if anyone could direct me to an example in any steel or concrete journal or text where the moment restraint required to resist column buckling is included in the design of a footing or the top connection of the column.

 

[shin25]

At least in concrete buildings, most of the structures, (braced or unbraced)by very definition fall under non-sway frames. Also, the columns usually have kl/r<22. Therefore, most of the worked out examples ignore magnified moment. But, anything else, design should consider these moments and required by code.

 

[haynewp]

What he is asking doesn't matter if it is sway or non-sway.

 

[haynewp]

So you are saying that you always include the moment required to restrain the column from buckling when designing a concrete frame's beam-column joint? (You add this moment to the unbalanced gravity moments at the joint)

 

[DaveAtkins]

In general (there are exceptions to what I am about to type), structural engineers do not concern themselves about buckling forces in a properly designed structure. If you design the structure (diaphragms, braced or portal frames, and footings) for the lateral loads imposed, then the structure should be able to resist buckling forces easily. For example, I don't know of any structural engineer who adds up all the buckling forces in all the beam compression flanges in the various floors of a building, in order to check the lateral load resisting system for these forces. What I recommend is that you design your footing for the axial load and moment it will see due to gravity and lateral loads, then assume it is a fixed base.

And then have a nice weekend and don't worry about it.

DaveAtkins

 

[shin25]

Mostly, all the computer programs account for P-delta effect for sway structure.

So, during designing the members this magnified moment is already accounted for?

 

[haynewp]

Yeah but he was not asking about P-delta moments, he was asking about buckling restraint moments. Just out of curiosity, if I get time I might try to derive the moment required to restrain a steel column from buckling. Unless someone else here already knows it.

 

[Lion06]

well, at least haynewp gets my question. It looks like daveatkins does as well.
Dave-
If you have the case of a gravity only column that is rigidly attached to a foundation designed for axial load only (no moment in the gravity only column), and it is a sway frame, what would you do? Would you consider it as a fixed base and free top? If you consider it a fixed base, how do you reasonably assume that with zero moment accounted for in design of the footing?

 

[DaveAtkins]

If it is a column that is not participating in the resistance of lateral loads, then it is what Jim Fisher calls a "leaner" column--that is, it "leans" on the lateral load resisting system for stability. For a "leaner" column, K = 1.0.

DaveAtkins

 

[haynewp]

A method for including leaning columns is shown in the example from the paper I was trying to help you with the other day.