Second-Order Analysis of Plane Frames with One Element Per Member
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Volume 137, Issue 11
Abstract
A corotational element is developed directly from the governing second-order differential equations of beam theory. The corotational element includes not only the effect of axial force on the bending moment (-delta effect) but also the additional axial strain caused by end rotations. Hinged and semirigid end conditions are also included so that plastic hinges could be considered. The resulting local element tangent stiffness matrix is compared to traditional local element elastic and geometric stiffness matrices. The method is implemented and executed on two example problems in which only one element per member is used. Results compare favorably to those from a nonlinear commercial program in which several elements per member are used. A third example problem includes both geometric and material nonlinearity to develop a pushover curve.
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References
ABAQUS. (2008). Analysis User’s Manual, Version 6.8. Simulia, Providence, RI.
Albermani, F. G. A., and Kitipornchai, S. (1990). “Nonlinear-analysis of thin-walled structures using least element member.” J. Struct. Eng., 116(1), 215–234.
Argyris, J. H., et al. (1979). “Finite element method—The natural approach.” Comput. Methods Appl. Mech. Eng., 17–18, 1–106.
Belytschko, T., and Glaum, L. W. (1979). “Applications of higher order corotational stretch theories to nonlinear finite element analysis.” Comput. Struct., 10, 175–182.
Chandra, R., Trikha, D. N., and Krishna, P. (1990). “Nonlinear analysis of steel space frames.” J. Struct. Eng., 116(4), 898–909.
Crisfield, M. A. (1991). Non-linear finite element analysis of solids and structures, Vol. 1, Wiley, Chichester, UK.
Haktanir, V. (1994). “New method for element stiffness matrix of arbitrary planar bars.” Comput. Struct., 52(4), 679–691.
Izzuddin, B. A. (2006). “Simplified buckling analysis of skeletal structures.” Proc., ICE Struct. Build., 159(6), 631–651.
Leu, L. J., Yang, J. P., Tsai, M. H., and Yang, Y. B. (2008). “Explicit inelastic stiffness for beam elements with uniform and nonuniform cross sections.” J. Struct. Eng., 134(4), 608–618.
Morán, A., Oñate, E., and Miquel, J. (1998). “A general procedure for deriving symmetric expressions for the secant and tangent stiffness matrices in finite element analysis.” Int. J. Numer. Methods Eng., 42, 219–236.
Nanakorn, P., and Vu, L. N. (2006). “A 2D field consistent beam element for large displacement analysis using the total Lagrangian formulation.” Finite Elem. Anal. Des., 42, 1240–1247.
Neuenhofer, A., and Filippou, F. C. (1998). “Geometrically nonlinear flexibility-based frame finite element.” J. Struct. Eng., 124(6), 704–711.
Oran, M. C. (1973a). “Tangent stiffness in plane frames.” J. Struct. Div., 99(6), 973–984.
Oran, M. C. (1973b). “Tangent stiffness in space frames.” J. Struct. Div., 99(6), 987–1001.
So, A. K. W., and Chan, S. L. (1991). “Buckling and geometrically nonlinear analysis of frames using one element/member.” J. Constr. Steel Res., 20(4), 271–289.
Wang, F., and Liu, Y. (2010). “Total incremental iterative force recovery method and the application in plastic hinge analysis of steel frames.” Int. J. Adv. Steel Constr., 6(1), 567–577.
Wempner, G. (1969). “Finite elements, finite rotations and small strains of flexible shells.” Int. J. Solids Struct., 5, 117–153.
Yang, Y. B., and Chiou, H. T. (1987). “Rigid body motion test for nonlinear-analysis with beam elements.” J. Eng. Mech., 113(9), 1404–1419.
Yang, Y. B., and Kuo, S. R. (1994). Theory and analysis of nonlinear framed structures, Prentice-Hall, Englewood Cliffs, NJ.
Yang, Y. B., Kuo, S. R., and Wu, Y. S. (2002). “Incrementally small-deformation theory for nonlinear analysis of structural frames.” Eng. Struct., 24(6), 783–798.
Yang, Y. B., Lin, S. P., and Wang, C. M. (2007). “Rigid element approach for deriving the geometric stiffness of curved beams for use in buckling analysis.” J. Struct. Eng., 133(12), 1762–1771.
Zhao, D. F., and Wong, K. K. F. (2006). “New approach for seismic nonlinear analysis of inelastic framed structures.” J. Eng. Mech., 132(9), 959–966.
Zhou, Z. H., and Chan, S. L. (2004a). “Elastoplastic and large deflection analysis of steel frames by one element per member. I: One hinge along member.” J. Struct. Eng., 130(4), 538–544.
Zhou, Z. H., and Chan, S. L. (2004b). “Elastoplastic and large deflection analysis of steel frames by one element per member. II: Three hinges along member.” J. Struct. Eng., 130(4), 545–553.
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Published In
Journal of Structural Engineering
Volume 137 • Issue 11 • November 2011
Pages: 1350 - 1358
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Apr 8, 2009
Accepted: Dec 27, 2010
Published online: Dec 29, 2010
Published in print: Nov 1, 2011
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