Sidesway unprevented frame in CISC

[burtonli]

In CISC handbook, you can't get effective length of columns in a sidesway unprevented frams. It really suprise me. I wonder if I could consult other codes, let say, AISC?

 

[VoyageofDiscovery]

Hi burtonli,

The CSA S16 has moved away from the approximate method using k values larger than 1.0 in the case of sway permitted. Now you have to follow the current CSA S16 which does allow you an amplification factor in lieu of a second order analysis for the Pdelta effects.

This move occured in the 1989 edition of the S16.

With regards to your question, at the risk of sounding cheeky, sure you can consult other codes but if you are designing a building in Canada you will have to follow the current CAN CSA S16. Typically most structural programs can easily do Pdelta effects. In such a case you wouldn't have a problem finding your actual moments.

Regards

VOD

 

[burtonli]

Thanks, VOD.

I understand your means, but the problem is how to calculate
the effective length factor k. P-delta analysis can't solve the problem.

For example, a column with 1000 kN axis force and 10 kN.m moment. If consisting P-delta effect and M change to 20 kN.m, it did not change a lot. But if the column change for "sidesway prevent" to "sidesway permit", k maybe change from 0.9 to 3.0, it will be a big problem.

It's a stability problem, not a strength problem.

 

[VoyageofDiscovery]

From my experience for a sway permitted rigid frame K=1.0

For a building with beams and columns coming in together at every connection, I use the nomograph for sway prevented to determine my K after I have accounted for Pdelta effects. You will have to find this nomograph in one of the past versions CISC Steel Handbook.

Regards

VOD

 

[burtonli]

Hi, VOD;
In CISC appendix B, k=1, 2, 2 for three special situation of sway permitted column, so I don't thank k=1 is suitable for sway permitted column.

k is a theory value for structure, no matter what kind of method to calculate, it should be almost same, if not completely equal.

CISC handbook only has a nomograph for sidesway prevented frame, it's same as in AISC or other code. But it didn't have another for sidesway permitted. I don't know why.

 

[VoyageofDiscovery]

Hi burtonli,

I knew that was coming as I wasn't specific enough. A rigid frame with fixed bases, the theoretical K=1.0 as seen in Fig. B1 (d) in Appendix B of the current CISC. Yes, in any other situation K=2.0.

Regards

VOD

 

[burtonli]

Hi, VOD,

My friend told me they use k=2.0 for sidesway permitted, I thank it will waste material in most situation.

It make me confuse that Appendix B told us k should be greater than 1.0 for sidesway permitted, but did not tell us how to calculate it.

I contacted one member of CISC committee and asked that question. He told me U2 is used to deal with "sway permitted effect", he still did not give the answer how to get k value according to Appendix B.

 

[VoyageofDiscovery]

Hi burtonli,

The recommended value you should use for the theoretical K=1.0 situation is K=1.2 as shown in Appendix B. There is no need to calculate this value.

Regards

VOD

 

[trainguy]

Since the early-to-mid-1990's, columns in Canada are designed with k=1, regardless of the sidesway. It is up to the analyst to incorporate the P-delta effects into the analysis. One of the ways to do this is to utilize the U2 factor to effectively amplify the moments from first-order analysis. Another way is to do an actual p-delta analysis with your analysis package. Either way, remember that your treatment of p_delta effects must account for plastic deformations if you're designing for seismic loads.

Before these methods, the old way of considering moment amplification due to sway was to consider effective length factors greater than 1.

The underlying concept is that a column's axial capacity is reduced by the applied moment, and that moment must be amplified due to the sway of the frame.

The U2 factor is derived (if I remember) from applied lateral loads, 1st order deflections etc, so this inherently reflects the degree of sway that is happening.

MOST IMPORTANTLY:
Please don't take my word for it, it's been approx. 5 years since I've worked on buildings, but check the CISC Steel handbook commentary carefully, there should be design examples.

 

[burtonli]

Hi, trainguy,
k was not deal with moment amplification due to sway in stability analysis. k is a effective length factor for no-simple support member that compare with ideal simple support member with axial compress, it means, in that support condition, member with l length have same stability resistance as that of simple support member with kl length.

In fact, Appendix B give k>1 for sway permitted column, but it only three situation for Ig=0 and Ic/Ig=0. In actual structure, Ic/Ig is alway a limit value and greater than 0.

P-delta calculation in computer can tell us if the structural is stable or unstable, but it's not enough for design. we need to know a critical value.

 

[trainguy]

Burtonli:

My post was somewhat unclear, I agree that k is the column's effective length factor. However, when you check a column for strength interaction and stability interaction, you have axial and moment effects to consider, and the overall check of the column is largely dependent on how you treated the stability effects.

I need some help here from some other practicing Canadian engineers to shed some light on this: it's just not that fresh in my memory.

The U2 factor, by the way, can be used instead of a P-delta analysis, especially if your computer program only iterates on the elastic displacements - this could underestimate them in case of seismic loads, where the code requires you to multiply your elastic displacements by R to get the anticipated plastic values.

As far as I can remember, there is no need to consider k-factors greater than 1.0. but then again, I haven't read the CISC handbook since the 1992 (approx) edition...

Remember, having the top end of your column sway increases the effective length, so the 2 concepts (eff. length for bucklng and moment magnification) are somewhat related.

tg

 

[burtonli]

Hi, tg;

No all structural engineer paid enough attention to stability because most time they deal with the concrete structure and concrete columns are "short column" in general.

U2 is a simplified method to consider P-delta effect, it is used in both moment-resistant frame and braced frame. k is a theoretic value.

"For out-of plane buckling the effective length deponds on the end restaints", and "when subjectted to axial load only, the axial compressive resistance, Cr, depends on the maximum slenderness ratio" (CISC commentary 13.8)

I can not find in anywhere that CISC decare it's not need to consistent k for sway permitted column. So I wish we can find a way to solve this problem.

Anyway, thanks you and VOD

 

[calculor]

I agree with Trainguy, there is no need to determine a k value. You have to calculate U2, which is used to amplify the first order translational moments at a joint rather than performing a second order analysis. U2 must be less than 1.4; a large U2 is an indication that the structure is unusually flexible. The standard requires, therefore, the designer to increase the stiffness of the frame and thereby reduce the deflections or perform a second order elastic-plastic analysis. The exception to this requirement is when considering earthquake forces.

 

[burtonli]

Hi, Calculor;

I have been thought that U2<1.4 can control Cf small enough, it seems wrong.

here is a result using SAP2000 to calculate a cantilever column (it's easy to check ), W14X665.
P=1192kip, Vx=6.5kip, My=-2000kip-in, L=500in
Result: U2=1.1, stress ratio=0.502 for k=1.
According to Eular, Ce=1193.5kip for k=2, and if using P-delta analysis, you'll see the column is fail.

May be it's not common. If cantilever column need to consider k, why we don't need to consider k for other sway permitted situation?

I think U2 is one way to calculate P-delta effect. P-delta effect will big enough only when P is almost equal Eular strengt, but the structure fail before that time because material and member have fault and Cr is small the Ce.