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RE: question on K factors and P-delta analysis
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- Subject: RE: question on K factors and P-delta analysis
- From: "Eric Ober" <eober(--nospam--at)holbertapple.com>
- Date: Thu, 16 Oct 2003 08:55:20 -0400
If you check the archives from August 2002 (I believe) you will find a response to this same question by Geschwinder (thru Charlie Carter) regarding this issue. Also, Geschwinder's 2000 T.R. Higgins paper on the subject explains the issue (available on EPubs on AISC website from conference proceedings). I will try to explain my understanding of the issue and welcome any comments if I am in error. The gist of the issue is that you must use a K-factor if using the AISC specifications, regardless of the P-Delta analysis. The P-Delta analysis will give the increased moments and axial loads on the rigid frames due to lateral loads, 'leaning' columns, etc. However, it does not account for the impact of the leaning columns on the sway stability of the story. The AISC specification is calibrated to rely on use of the K-factor at this time. The so-called 'Advanced Analysis' with notional lateral loads, accounting for initial out-of-straightness, P-little delta, etc., would be required to be able to use K=1 (I guess Canadian code provides for this). Picture a rigid portal frame, equal columns, with equal axial loads, P. This frame has a sway buckling capacity, say it is 2P, so we have the frame designed to be exactly critical. Now add a 'leaning' column, same column size, attached to the rigid frame by a pinned end beam, with the same vertical load P applied. The sway buckling capacity is unchanged, 2P. To be able to design the 'leaning' column with K=1, the rigid frame must provide the lateral restraint at the top of the 'leaning' column. Sway instability requires all columns in a story to buckle simultaneously. This means that the rigid frame w/ leaning column must resist 3P to be 'sway-stable' but only has capacity for 2P. If you perform a second order analysis on both of these frames, the analysis results will be the same as if you only did a first order analysis (since no deflection). But the frame with the leaning column will want to buckle in a sway mode at a lower load, 2P/3 on each column, than the one without the leaning columns. How do you account for this without using a modified K-factor (or some equivalent means - see AISC commentary to LRFD) to reflect the actual buckling capacity of the rigid frame? My advice to all, do not use K=1 for rigid frames if using AISC specification, and don't forget the leaning columns. Clearly SSRC 3rd edition was incorrect (else why change it?). Eric Ober Holbert Apple Associates -----Original Message----- From: Haan, Scott M. [mailto:HaanSM(--nospam--at)ci.anchorage.ak.us] Sent: Tuesday, October 14, 2003 3:56 PM To: seaint(--nospam--at)seaint.org Subject: RE: question on K factors and P-delta analysis Clifford: It has been my understanding that the UBC used to specifically say that K could be taken equal to 1 for seismic resisting moment frames and the reasoning was that the code had drift limits and required a P-Delta analysis. The effective length factor is a way of designing for stability and if your stability is already accounted for with a P-Delta analysis and drift limits then K>1 is conservative. If you are not checking drift and doing a P-Delta analysis then K should be determined to ensure stability. If you are designing with drift limits and a P-delta analysis and want to be conservative you could use a K greater than 1. Respectfully, Scott Haan -----Original Message----- From: Clifford Schwinger [mailto:clifford234(--nospam--at)yahoo.com] Sent: Tuesday, October 07, 2003 5:15 AM To: seaint(--nospam--at)seaint.org Subject: question on K factors and P-delta analysis I've heard people say that when you do a second-order analysis on a moment frame, you can use a K-factor of 1.0 for the column design. I'm trying to find an explanation of this concept, and I am trying to find out whether the idea of using K=1 when you do a second-order analysis is correct or not. I don't understand how doing a second-order analysis to compute the P-delta moments would allow you to automatically toss the K-factor out the window (and use K=1). As I understand it, the K-factor is a modification you make to the Euler buckling equation to adjust that equation to account for column end conditions different from the ideal pinned-pinned ends assumed for the "perfect" Euler column. I have a copy of a book called "Is Your Structure Suitably Braced". This publication is a compilation of papers from a 1993 conference organized by the SSRC, AISC, AISI and MBMA. In the back of the book is a transcript of a panel discussion where someone asked the following question: What is your recommendation on the K-factor when a second-order elastic analysis is performed? Can K be taken as 1.0 in all these cases? Dr. Joseph Yura (one of the panelists) responded as follows: "If you are using the AISC Specification, and you are using a second-order elastic structure analysis, you must use a K-factor. The SSRC Third Edition indicated that you can do a K=1.0. If you check the Fourth Edition, you'll see that's been removed and you still must use a K factor because the checks that we had done indicated that in high gravity load situations, that procedure will not cut it." Surfing the internet for the source of the "you can use K=1 when you do a second-order analysis" concept, I found a paper by Dr. Edward Wilson (of CSI?) titled "Geometric Stiffness and P-Delta Effects". In that paper he says: "...The application of the method of analysis presented in this chapter should lead to the elimination of the column effective length (K-) factors, since P-Delta effects automatically produce the required design moment amplifications. Also, the K-factors are approximate, complicated, and time-consuming to calculate. Building codes for concrete and steel now allow explicit accounting of P-Delta effects as an alternative to the more involved and approximate methods of calculating moment magnification factors for most column designs..." (Here is the url to the paper: www.comp-engineering.com/downloads/technical_papers/CSI/11.pdf So now I am really confused. Section C1.2 in the Third Edition AISC Manual says: "In structures designed on the basis of elastic analysis, Mu for beam-columns....shall be determined from a second order elastic analysis or from the following approximate second order analysis procedure: Mu = B1 x Mnt + B2 x Mlt..." A similar methodology to the one in the AISC Manual is specified in ACI 318-02-318 for concrete structures. The way I see it, engineers have the option of accounting for P-delta effects by either doing a second-order analysis or by computing the moment magnification factors as described in the AISC Manual or ACI 318, but whichever method is used (for computing P-delta moments) you still have to use the appropriate K-factor. I'm confused by the comment made by Dr. Yura (see above) where he said that SSRC Third Edition said to use K=1 but the SSRC Fourth Edition said to use the actual K-factor. Was the Third Edition incorrect, or did something else change when the Fourth Edition was published. What is the theory (please explain in simple terms so that my aging mind can understand) that would allow you to ever use K=1 for an unbraced moment frame when you do a second-order analysis? Here's an example that's reinforcing my "brain-lock" on this issue: Let's say you have a single cantilevering "flag-pole" column with an axial load and horizontal load applied at the top of the column. You compute the first-order moment and deflection. You then compute the second-order moment and deflection, and then design the cantilevered column using K=2. Is there any way you could ever use K=1 on a cantilevered column just because you did the second-order analysis? A similar example is where you have a moment frame with two identical columns with perfectly pinned bases and connected to an infinitely rigid beam at the top. Each column has an identical axial load and there is a single horizontal load applied at the top of one of the columns acting parallel to the beam span. This example is virtually identical to the previous cantilevered flag-pole example except that the cantilevering flag-pole columns are upside down. How could you ever justify using K=1 just because you do a second-order analysis? I would be most grateful if someone could explain where the "you can use K=1 when you do a second-order analysis" idea came from and whether or not it is a structural engineering "urban legend". There must have been some justification to the K=1 concept if it was in the SSRC Third Edition. Thanks. Cliff Schwinger __________________________________ Do you Yahoo!? The New Yahoo! Shopping - with improved product search http://shopping.yahoo.com ******* ****** ******* ******** ******* ******* ******* *** * Read list FAQ at: http://www.seaint.org/list_FAQ.asp * * This email was sent to you via Structural Engineers * Association of Southern California (SEAOSC) server. 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- RE: question on K factors and P-delta analysis
- From: Haan, Scott M.
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