Effective Buckling Length for Post Restrained at Midheight 2

[Maturin]

Can anybody tell me how I would determine the "K" value for a post fixed at it's base and laterally supported at midheight? The axial load is applied at the top of the post.

 

[JAE]

If the top and bottom are pinned and the restraint at mid-height is only for lateral translation (and not any moment connections) then I would use a k would be 1.0 since the column will buckle in an "S" shape and each segment would be a pure simple curve. Your L is 1/2 the total length (base to restraint at mid-height or mid-height to top).

 

[Maturin]

Sorry, I should have specified that the top of the post is unbraced, (like a propped cantilever running vertically). The restraint at midheight is only for lateral translation.

 

[Tomfh]

The easiest thing is to let a computer solve it.

I did so and got K = 2.7, where L is half the total length.

 

[JAE]

Tomfh - I would wonder what computer program you used and what its basis is?

Maturin - if the top of the column is cantilevered above the floor, then the lower half would still be k=1 but I would think the upper section would be at least 2.0 as Tomfh suggests. Check the AISC nomographs for sway condition and no beam stiffness.

 

[GregLocock]

As a practical point, does it have to be pinned at the exact mid point, I suspect that moving the restraint up a bit would help.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Tomfh]

I used Microstran and ran a linear buckling analysis.

I should point out that K=2.7 is for a pinned base. A rigid base gives K=2.5

These values make sense if you draw your buckled shape. The tip to crest distance will be approximately 1/2 of your effective length.

 

[Maturin]

Thanks for all the input.

Tomfh, I agree with your values. I ran a model to determine the section displacement due to a lateral load applied at the tip assuming that this deflected shape would approximate the buckled shape. Using tip to crest distance as 1/2 of the buckled length gave approximate values of K=2.75 (pinned) and K=2.58 (fixed).

 

[rb1957]

is the mid-support constrinaing lateral deflections in both directions (x- and y-, assuming z- is along the column) ?

 

[Maturin]

The mid-support is restraining in one direction only. Cross-bracing restrains the post in the other lateral direction so that the K-value is 1.0.

 

[rb1957]

if the column is fixed at the ground, isn't k=2 (assuming that you use k as L' = (L/k)^2.

if the mid-support is effective in one lateral direction only, is there something different happening between the two directions (loads?, geoometry?) ? if there isn't, then does this mid-support affect the column buckling at all ?

 

[miecz]

I wouldn't trust a computer program to solve for this, unless I could verify it with a hand calc.

Looking at the AISC nomograph for sidesway uninhibited, with infinite GB,and replacing the lower column with a girder of the same I and L, so GA=1, K=2.3. I don't see why it should be any greater than that.

 

[Maturin]

jmiec - Good suggestion, I didn't think of manipulating the nomograph that way but it makes sense. Thanks.

 

[haynewp]

It seems like the G equation in AISC is kind of being violated by using the lower part of the column as a girder to resist buckling of the upper part of the column.
I thought the idea was that all columns buckle simultaneously on a floor. How can the lower column offer resistance if it buckles at the same time as the upper floor? Also for this case, how do you know the column will necessarily buckle in an "S" shape, since the cantilevered end is free to translate?
I am just trying to justify this for myself.

 

[JAE]

haynewp - I don't think they are thinking "S" shaped buckling anymore - that was my statement prior to Maturin clarifying that the top was free to translate.

This specific condition doesn't appear to be strictly dealt with in the AISC specification as I somewhat agree that using the lower portion of the column as a pseudo girder in the calculation of G may not be totally proper (but its not a bad thing to do to at least get a handle on k for this situation).

You might want to read the last section of Commentary for Chapter C in the newest (13th edition) AISC specification where it states the following:

[red]Some Conclusions Regarding K.

It is important to note that column design using K-factors can be tedious and confusing for complex building structures containing leaning columns and/or combined framing systems, particularly where column inelasticity is considered. This confusion can be avoided if the Direct Analysis Method of Appendix 7 is used, where Pn is always based on K = 1.0. Also, the first-order elastic design-analysis method of Section C2.2b is based on the Direct Analysis Method, and hence also uses K = 1.0 in the determination of Pn.

Furthermore, under certain circumstances where B2 is sufficiently low, a K-factor of 1.0 may be assumed in design by second-order analysis as specified in Section C2.2a (4). For frames that satisfy this clause, it is not appropriate to use K = 1.0 in the calculation of B2 using Equations C2-6a and C2-3. The use of Equation C2-6b is recommended for the calculation of B2 within this context.[/red]

So in addition to trying to determine a K for your condition, you try to do a second order analysis on your model - (including both P[Δ] AND P[δ] effects)
where you can simply use k = 1.0.

 

[haynewp]

If we do that, wouldn't there have to be some modification to how the lower column is now designed. I was thinking about what K value you should use for designing the lower portion of the column now that you have used the lower stiffness as contributing to the upper section's stability. For a normal multi-story frame, the G is calculated at the top and bottom of a story column but the column stiffness is normally at the numerator instead of the denominator of the G equation.

I am thinking the lower column could be modeled as fixed-pinned with an applied moment at the top. I think you have to justify the lower column working as an influence to the upper column now prior to the lower column buckling.
What do you think? Or am I way off here?

I have to get the 13th manual to get into it. I don't have a copy yet. I would have hoped they would have made things less confusing, but that does not seem to be the trend.

 

[JAE]

haynewp, my friend! Less confusing? I really can't think of any spec or code that has gone in that direction for a long while.

I think that using the second order analysis, you'd have results that would either converge or diverge, telling you whether you have an inherent instability. Use K=1.0 as they say.

I might add that the direct method uses reduced EA and EI values for the members as well.

 

[haynewp]

I read in a magazine previously where some of the code writers were trying to figure out how things have gotten so difficult. It was kind of funny in a sad way for me.

 

[JAE]

Plot the complexity of the codes/specs against the number of engineers with drinking problems....correllation do you think?

 

[haynewp]

It was a linear increase for me up until 2000, but since then my drinking has gone up exponentially with the introduction of the IBC. The owner of the last company I worked for always kept a bottle of Vodka in his bottom drawer.