professor ben schafer's thin-walled structures research group - johns hopkins university
Generalized Beam Theory (GBT)
Note: This page was created by, and is hosted at, the Thin-walled Structures research group, but the source of the technical contributions provided on this page (with his encouragement and permission) is Dinar Camotim and his students and colleagues.
Generalized Beam Theory is an extension to conventional engineering beam theory that allows cross-section distortion to be considered. Stability analysis of thin-walled members may also be performed using GBT. GBT was originally developed by Schardt in Germany, then extended by Davies and his colleagues in Britain, and has over the last several years been an active focus of Camotim and his colleagues in Portugal (see references). Currently, no code exists in the public domain for the application of GBT; however, Camotim and Silvestre have recently supplied code focusing on distortional buckling of C and Z sections common in cold-formed steel. This code, provided by the original authors, is available here. A particular advantage of this implementation is the ability to consider the impact of different end conditions (pinned, fixed, sliding, ...) on the solution.
GBTUL a new user friendly code for GBT calculations
Generalized Beam Theory finally has a user friendly program for your use thanks to the hard work of the research group at the Technical University of Lisbon in Portugal. Bebiano, Pina, Silvestre and Camotim provide their program - GBTUL at their site. We look forward to many interesting comparisons between GBTUL and our own program CUFSM and congratulations to our friends in Portugal.
Camotim and Silvestre's code for distortional buckling calculation by GBT
The computer code supplied here is a specialized and simplified version of GBT focused specifically on distortional buckling of C and Z sections. The references which include full development of this algorithm, including verification are provided at:
Distortional buckling formulae for cold-formed steel C and Z-section members: Part I - Derivation Silvestre, N. (Department of Civil Engineering, IST/ICIST, Technical University of Lisbon); Camotim, D. Source: Thin-Walled Structures, v 42, n 11, November, 2004, p 1567-1597 (DOI:10.1016/j.tws.2004.05.001)
Distortional buckling formulae for cold-formed steel C-and Z-section members: Part II - Validation and application Silvestre, N. (Department of Civil Engineering, IST/ICIST, Technical University of Lisbon); Camotim, D. Source: Thin-Walled Structures, v 42, n 11, November, 2004, p 1599-1629 (DOI:10.1016/j.tws.2004.05.002)
The code is a simple text in text out - but the F90 source may be readily modified to your needs. Please reference the above papers when using this code. This code is distributed as open source under the Academic Free License v 1.2. Enjoy!
Brief users manual: code.doc
Fortran 90 source code: DBF.for
Compiled version for Linux: DBF.tar (untar and run)
Abbreviated Reference list for learning more about GBT
Davies, J.M., Leach, P. (1994). “First-order generalised beam theory.” J. of Constructional Steel Research, Elsevier. 31 (2-3) 187-220.
Davies, J.M., Leach, P., Heinz, D. (1994). “Second-order generalised beam theory.” J. of Constructional Steel Research, Elsevier. 31 (2-3) 221-241.
Schardt, R. (1989). Verallgemeinerte Technische Biegetheorie, Springer-Verlag, Berlin, (in German)
Silvestre, N., Camotim, D. (2002a). “First-order generalised beam theory for arbitrary orthotropic materials.” Thin-Walled Structures, Elsevier 40 (9) 755-789.
Silvestre, N., Camotim, D. (2002b). “Second-order generalised beam theory for arbitrary orthotropic materials.” Thin-Walled Structures, Elsevier, 40 (9) 791-820.
Silvestre, N., Camotim, D. (2003). “Nonlinear Generalized Beam Theory for Cold-formed Steel Members.” International Journal of Structural Stability and Dynamics. 3 (4) 461-490.
last edited 07/21/2008