Effective Length (K factor) 2

[PostFrameSE]

When desiging a steel column that is free to move at the top (rotation not fixed and translation free) but its movement at the top is limited to only 1% of the length of the column (ie 2" translation on a 200" tall column) and the column is anchored to a concrete pier with four anchor bolts, what K value should be used? I recognize that the base is not truly fixed, but it's probably more than just pinned. At the top, with it being allowed to translate approximately 1% of the total height, can the top be considered "pinned" or not? What K-value should I use? Is it reasonable to assume that since I'm not obviously pin-pin, I'm kind of fixed-base/pin-top and maybe fixed-base/translation free top that I just resort to the middle-of-the-road K value of 1.0?

Thanks.

 

[ishvaaag]

Presumably a moderate degree of fixity at the base won't be able to enforce double curvature in the member when starting to buckle, hence it seems the convenient and conservative assumption is that it will buckle in single curvature.

Since buckling is sudden it will impart likely in the order of 2% of the standing (buckling) load to the support that forbids the top end displace more than H/100.

So the likely scenario is that under the (theoretical, factored) load the column buckles as a cantilever with partial restraint at the base (with restraint 0 at the base, pinned, it would equate to the column leaning till finding support atop) to origin a member to buckle in single curvature with more or less pins bottom and atop and so in the situation K=1 seems reasonable using the length H.

 

[structSU10]

Is this column a part of a LFRS or is it a leaning column? if the column is not a part of a LFRS but is braced by one, a K = 1 should be used.

If the column is part of a braced frame, such as an x brace, you can check the brace stiffness and strength per appendix 6 of AISC. If you meet that criteria, a K = 1 can be used.

For a moment frame, the nomographs can be used, or for more accuracy, a second order analysis can be performed to determine your K.

 

[asixth]

What software are you using to determine the K-factors? I have had mixed results using frame analysis programs to calculate K-factors. I'm not sure whether I have posted this topic before?

If you build a model with pin top and btm and run the elastic critical load it will tell you k=1.0. If you run a fixed-end model it will tell you k=0.7, and some degree of rotational fixity will vary from 0.7 to 1.0.

Only time I have used this is to calculate k-factors for rc columns in braced frames. Columns near the core had k-factors around 0.8 and at the extent of the diaphragm the k factors increased to 0.9.

 

[JoshPlumSE]

Hard to tell. K factors can be pretty tricky for the odd or unusual cases. I'd use AISC's Direct Analysis Method with a K = 1.0. The whole point of the Direct Analysis Method is that the extra analysis requirements should lead to a more reasonable prediction of buckling than you get by arbitrarily assuming a particular K value.

 

[charliealphabravo]

A few thoughts...

I wouldn't normally consider a column with 4 anchor bolts to be a fixed connection unless it were detailed something like a wind column or moment frame. The fact that the column is on a pier is a further discouragement.

I think the K factor will depend on the stiffness of the column relative to the base connection. The deflected shape of a slender column will look more like the base is fixed. For heavier columns, more load can be transferred to the base and it is more likely to resemble a pinned connection. Also note that the k value changes once the loaded cantilever column makes contact with the deflection limiter.

As ishvaaag pointed out, what really matters is what happens at failure. The column may behave like it is fixed at the base in the elastic zone under service loads, but behave like the base is pinned at ultimate failure.

Have you done a sensitivity study to see what the effect is at the extremes (fixed and pinned)? That will tell you if there is any value in trying to determine base fixity rather than just assuming it is pinned.

 

[PostFrameSE]

Sorry I posted a question and haven't responded to any of YOUR questions. I've had problems accessing this site lately, and even my own post. Not sure what I did wrong. At any rate, I appreciate your responses.

The columns that I'm referring to are NOT part of the LFRS. A typical scenario is a 40' column spacing with "braced frames" at 120' o.c. Therefore, these two intermediate columns "propped" by a fairly rigid roof diaphragm that is supported laterally at 120' o.c. Therefore, since I'm not counting on these to carry lateral loads, they are strictly compression columns with a slight translation at the top.

I have not used software to determine K-values. These are more hand calcs.

As charliealphabravo points out, as the cantilever column makes contact with the deflection limiter, the K-value changes. In my case, it is partially acting as a cantilever only because the roof diaphragm has forced it to move. Since that movement is relatively small, I'm gathering from everybody's response that a K-value of 1.0 is adequate. I'm just wanting to make sure that I shouldn't be using some value between 1.0 and 2.0 that can radically affect the axial load-carrying capacity of my column.

Thanks.

 

[structSU10]

Since this is a leaning column:

Columns in gravity framing systems shall be designed based on their actual length (K=1.0) unless analysis shows that a smaller value may be used. The lateral stability of gravity framing systems shall be provided by moment frames, braced frames, shear walls, and/or other equivalent lateral load resisting systems. P Delta effects due to load on gravity columns shall be transferred to the lateral load resisting systems and shall be considered in the calculatio of the required strengths of the lateral load resisting systems.

So since it is not part of the LFRS, it can be designed with K=1, with any P-Delta (large delta) effects being transfered to the LFRS.

 

[PostFrameSE]

Perfect. Thanks.