Second-Order Direct Analysis of Domelike Structures Consisting of Tapered Members with I-Sections
Publication: Journal of Structural Engineering
Volume 142, Issue 5
Abstract
A new and advanced beam-column element, namely the curved tapered-three-hinges (TTH) beam-column element, is proposed in this paper. The present element can perform large deformation analysis and explicitly simulate the initial member curvature, which is essential for the second-order direct analysis using one-element-per-member models. Another distinct feature of the element is to analytically express the flexural rigidity of tapered I-sections in the stiffness matrix through a series of tapered stiffness factors such as the and factors. Unlike the conventional models using the approximated distributions (e.g., linear, parabolic, or cubic) or stepped-elements modeling approaches in an analysis, the present study gives an accurate simulation solution on nonprismatic beam-column elements. Herein, the element derivations and formulations are given in detail. To consider the large deflection effect in the analysis, the incremental tangent stiffness method is adopted and the kinematic descriptions are presented. Finally, several examples are employed to validate and verify the reliability and accuracy of the proposed element.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors are grateful to the financial supports by the Research Grant Council of the Hong Kong SAR Government on the project “Second-order and advanced analysis of arches and curved structures (PolyU 152012/14E)” and by the Innovative Technology Fund for the project “Advanced design of flexible barrier systems by large deflection theory (ITS/032/14).” This first author would like to appreciate the financial support by the Faculty of Construction and Environment through the project “FCE Postdoctoral Fellow Scheme.”
References
AISC (American Institute of Steel Construction). (2011). “Specification for structural steel buildings.” Chicago.
Al-Gahtani, H. (1996). “Exact stiffnesses for tapered members.” J. Struct. Eng., 1234–1239.
Andrade, A., and Camotim, D. (2005). “Lateral-torsional buckling of singly symmetric tapered beams: Theory and applications.” J. Eng. Mech., 586–597.
Argyris, J. (1982). “An excursion into large rotations.” Comput. Method. Appl. Mech. Eng., 32(1), 85–155.
Banerjee, J. R., and Williams, F. W. (1986). “Exact Bernoulli-Euler static stiffness matrix for a range of tapered beam-columns.” Int. J. Numer. Method. Eng., 23(9), 1615–1628.
Bradford, M., and Cuk, P. (1988). “Elastic buckling of tapered monosymmetric I-beams.” J. Struct. Eng., 977–996.
Building Department of Hong Kong. (2005). “Code of practice for the structural use of steel.” Hong Kong.
Building Department of Hong Kong. (2011). “Code of practice for the structural use of steel.” Hong Kong.
CEN (European Committee for Standardization). (2005). “Eurocode 3: Design of steel structures. Part 1-1: General rules and rules for buildings, EN 1993-1-1, Brussels, Belgium.
Chan, S. L. (1990). “Buckling analysis of structures composed of tapered members.” J. Struct. Eng., 1893–1906.
Chan, S. L. (1992). “Large deflection kinematic formulations for 3-dimensional framed structures.” Comput. Method. Appl. Mech. Eng., 95(1), 17–36.
Chan, S. L. (2001). “Non-linear behavior and design of steel structures.” J. Constr. Steel Res., 57(12), 1217–1231.
Chan, S. L., and Gu, J. X. (2000). “Exact tangent stiffness for imperfect beam-column members.” J. Struct. Eng., 1094–1102.
Chan, S. L., Huang, H. Y., and Fang, L. X. (2005). “Advanced analysis of imperfect portal frames with semirigid base connections.” J. Eng. Mech., 633–640.
Chan, S. L., and Zhou, Z. H. (1994). “Pointwise equilibrating polynomial element for nonlinear analysis of frames.” J. Struct. Eng., 1703–1717.
Chan, S. L., and Zhou, Z. H. (1998). “On the development of a robust element for second-order non-linear integrated design and analysis (nida)’.” J. Constr. Steel Res., 47(1), 169–190.
Dube, G. P., and Dumir, P. C. (1996). “Tapered thin open section beams on elastic foundation. I: Buckling analysis.” Comput. Struct., 61(5), 845–857.
Fong, M., Liu, Y. P., and Chan, S. L. (2012). “Second-order analysis and experiments of semi-rigid and imperfect domes.” Adv. Struct. Eng., 15(9), 1537–1546.
Kim, M., Chang, K., and Lee, G. (1997). “Elastic and inelastic buckling analysis of thin-walled tapered members.” J. Eng. Mech., 727–737.
Li, G. Q., and Li, J. J. (2002). “A tapered Timoshenko-Euler beam element for analysis of steel portal frames.” J. Constr. Steel Res., 58(12), 1531–1544.
Liu, S. W., Liu, Y. P., and Chan, S. L. (2010). “Pushover analysis by one element per member for performance-based seismic design.” Int. J. Struct. Stab. Dyn., 10(1), 111–126.
Liu, S. W., Liu, Y. P., and Chan, S. L. (2012a). “Advanced analysis of hybrid steel and concrete frames. Part 2: Refined plastic hinge and advanced analysis.” J. Constr. Steel Res., 70, 337–349.
Liu, S. W., Liu, Y. P., and Chan, S. L. (2012b). “Advanced analysis of hybrid steel and concrete frames: Part 1: Cross-section analysis technique and second-order analysis.” J. Constr. Steel Res., 70, 326–336.
Liu, S. W., Liu, Y. P., and Chan, S. L. (2014a). “Direct analysis by an arbitrarily-located-plastic-hinge element. Part 1: Planar analysis.” J. Constr. Steel Res., 103, 303–315.
Liu, S. W., Liu, Y. P., and Chan, S. L. (2014b). “Direct analysis by an arbitrarily-located-plastic-hinge element. Part 2: Spatial analysis.” J. Constr. Steel Res., 103, 316–326.
Ronagh, H. R., and Bradford, M. A. (1994). “Elastic distortional buckling of tapered I-beams.” Eng. Struct., 16(2), 97–110.
Valipour, H. R., and Bradford, M. A. (2012). “A new shape function for tapered three-dimensional beams with flexible connections.” J. Constr. Steel Res., 70, 43–50.
Yang, Y. B., and Chiou, H. T. (1987). “Rigid body motion test for nonlinear analysis with beam elements.” J. Eng. Mech., 1404–1419.
Zhou, Z. H., and Chan, S. L. (1995). “Self-equilibrating element for second-order analysis of semirigid jointed frames.” J. Eng. Mech., 896–902.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 142 • Issue 5 • May 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Apr 12, 2015
Accepted: Oct 28, 2015
Published online: Jan 11, 2016
Published in print: May 1, 2016
Discussion open until: Jun 11, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.