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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: "Ron Hill" <ronhill(--nospam--at)hillce.com>
- Date: Tue, 7 Oct 2003 10:17:35 -0500
Clifford, My ASD general finite element program has the following note concerning P-Delta analysis: 1. In 2d structures, analyze them in 3d and enter a small destabilization force perpendicular to the plane of the structure. 2. Keep K=1.0 unless the elements are subdivided. In this case, enter K factor such that the K*L longitude of the sub-element is equal to the length of the undivided element. I have always wondered how a small perpendicular force should be defined. I have tried structures that passed with wind but not seismic forces. Seems subject to interruption. HTH Ronald A. Hill, P.E. HILL Consulting Engineering PO BOX 26525 Birmingham, Alabama 35260 USA Phone: 205-823-4784 FAX: 205-823-4145 email: ronhill(--nospam--at)hillce.com http://www.hillce.com Email Filtered by McAfeeSpamKiller -----Original Message----- From: Clifford Schwinger [mailto:clifford234(--nospam--at)yahoo.com] Sent: Tuesday, October 07, 2003 8:15 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! 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- question on K factors and P-delta analysis
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