Constrained Finite Strip Method for Thin-Walled Members with General End Boundary Conditions
Publication: Journal of Engineering Mechanics
Volume 139, Issue 11
Abstract
The objective of this paper is to provide the theoretical background and illustrate the capabilities of the constrained finite strip method (cFSM) for thin-walled members with general end boundary conditions. Based on the conventional finite strip method (FSM), cFSM provides a mechanical methodology to separate the deformations of a thin-walled member into those consistent with global, distortional, local, and other (e.g., shear and transverse extension) modes. For elastic buckling analysis, this enables isolation of any given mode (modal decomposition) or quantitative measures of the interactions within a given general eigenmode (modal identification). Existing cFSM is only applicable to simply supported end boundary conditions. In this paper, FSM is first extended to general end boundary conditions, including simply–simply, clamped–clamped, simply–clamped, clamped–guided, and clamped–free. Next, with the conventional FSM for general end boundary conditions in place, the derivation of the constraint matrices for global, distortional, local, and other modes that play a central role in cFSM are summarized. Several bases (i.e., the constraint matrices) are presented for general end boundary conditions involving, in particular, different orthogonalization conditions. For modal identification, normalization schemes for the base vectors as well as the summation method employed for the modal participation calculation are also provided. Numerical examples of modal decomposition and identification are illustrated for a thin-walled member with general end boundary conditions. Recommendations on the choice of basis, orthogonalization, and normalization are provided.
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Acknowledgments
This paper is based in part upon work supported by the U.S. National Science Foundation under Grant No. 0448707. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
References
Ádány, S. (2004). Buckling mode classification of members with open thin-walled cross-sections by using the finite strip method, Johns Hopkins University Press, Baltimore.
Ádány, S., and Schafer, B. W. (2006a). “Buckling mode decomposition of single-branched open cross-section members via finite strip method: Application and examples.” Thin-Walled Struct., 44(5), 585–600.
Ádány, S., and Schafer, B. W. (2006b). “Buckling mode decomposition of single-branched open cross-section members via finite strip method: Derivation.” Thin-Walled Struct., 44(5), 563–584.
Ádány, S., and Schafer, B. W. (2008). “A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method.” J. Constr. Steel Res., 64(1), 12–29.
Ádány, S., Silvestre, N., Schafer, B. W., and Camotim, D. (2009). “GBT and cFSM: Two modal approaches to the buckling analysis of unbranched thin-walled members.” Adv. Steel Constr., Int. J., 5(2), 195–223.
American Iron and Steel Institute (AISI). (2006). Direct strength method design guide, Washington, DC.
American Iron and Steel Institute (AISI). (2007). “North American specification for the design of cold-formed steel structural members, 2007 Ed.” AISI S100-07, Washington, DC.
Bebiano, R., Pina, P., Silvestre, N., and Camotim, D. (2008). “GBTUL: Buckling and vibration analysis of thin-walled members, DECivil/IST.” Technical Univ. of Lisbon, Lisbon, Portugal 〈http://www.civil.ist.utl.pt/gbt〉 (Jul. 8, 2008).
Bradford, M. A., and Azhari, M. (1995). “Buckling of plates with different end conditions using the finite strip method.” Comp. Struct., 56(1), 75–83.
Camotim, D., Silvestre, N., Basaglia, C., and Bebiano, R. (2008). “GBT-based buckling analysis of thin-walled members with non-standard support conditions.” Thin-Walled Struct., 46(7–9), 800–815.
Davies, J. M., and Jiang, C. (1998). “Design for distortional buckling.” J. Constr. Steel Res., 46(1–3), 174–175.
European Committee for Standardization (CEN). (1996). “Design of steel structures, part 1.3: General rules.” Eurocode 3, Brussels, Belgium.
Gonçalves, R., Ritto-Corrêa, M., and Camotim, D. (2010). “A new approach to the calculation of cross-section deformation modes in the framework of generalized beam theory.” Comput. Mech., 46(5), 759–781.
Hancock, G. J. (1997). “Design for distortional buckling of flexural members.” Thin-Walled Struct., 27(1), 3–12.
Lau, S. C. W., and Hancock, G. J. (1987). “Distortional buckling formulas for channel columns.” J. Struct. Eng., 113(5), 1063–1078.
Li, Z. (2009). Buckling analysis of the finite strip method and theoretical extension of the constrained finite strip method for general boundary conditions, Johns Hopkins University Press, Baltimore.
Li, Z., Hanna, M. T., Ádány, S., and Schafer, B. W. (2011). “Impact of basis, orthogonalization, and normalization on the constrained finite strip method for stability solutions of open thin-walled members.” Thin-Walled Struct., 49(9), 1108–1122.
Li, Z., and Schafer, B. W. (2009). “Finite strip stability solutions for general boundary conditions and the extension of the constrained finite strip method.” Chapter 6, Trends in civil and structural engineering computing, Saxe-Coburg, Stirlingshire, U.K., 103–130.
Li, Z., and Schafer, B. W. (2010a). “Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM: Conventional and constrained finite strip methods.” Proc., 20th Int. Specialty Conf. on Cold-Formed Steel Structures: Recent Research and Developments in Cold-Formed Steel Design and Construction, Missouri S&T, St. Louis, 17–31.
Li, Z., and Schafer, B. W. (2010b). “The constrained finite strip method for general end boundary conditions.” Proc., 2010 Annual Stability Conf., Structural Stability Research Council, Chicago, 573–591.
Schafer, B. W., and Ádány, S. (2006). “Buckling analysis of cold-formed steel members using CUFSM: Conventional and constrained finite strip methods.” Proc., 18th Int. Specialty Conf. on Cold-Formed Steel Structures: Recent Research and Developments in Cold-Formed Steel Design and Construction, Missouri S&T, St. Louis, 39–54.
Schafer, B. W., and Peköz, T. (1999). “Laterally braced cold-formed steel flexural members with edge stiffened flanges.” J. Struct. Eng., 125(2), 118–127.
Silvestre, N., and Camotim, D. (2002a). “First-order generalised beam theory for arbitrary orthotropic materials.” Thin-Walled Struct., 40(9), 755–789.
Silvestre, N., and Camotim, D. (2002b). “Second-order generalised beam theory for arbitrary orthotropic materials.” Thin-Walled Struct., 40(9), 791–820.
Silvestre, N., and Camotim, D. (2003). “GBT buckling analysis of pultruded FRP lipped channel members.” Comput. Struct., 81(18–19), 1889–1904.
Silvestre, N., Camotim, D., and Silva, N. F. (2011). “Generalized beam theory revisited: From the kinematical assumptions to the deformation mode determination.” Int. J. Struct. Stab. Dyn., 11(05), 969–997.
Standards Australia/Standards New Zealand (AS/NZS). (1996). “Cold-formed steel structures.” AS/NZS 4600, Joint Technical Committee BD-082, Sydney, Australia.
Steel Stud Manufacturers Association (SSMA). (2001). “Product technical information.” ICBO ER-4943P, Chicago.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 139 • Issue 11 • November 2013
Pages: 1566 - 1576
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jun 29, 2012
Accepted: Jan 4, 2013
Published online: Jan 7, 2013
Published in print: Nov 1, 2013
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