Vol. 8, No. 2, pp. 183-198 (2012)
HIGHER-ORDER NON-LINEAR ANALYSIS OF STEEL STRUCTURES PART II : REFINED PLASTIC HINGE FORMULATION
C.K. Iu * and M.A. Bradford
Centre for Infrastructure Engineering and Safety
School of Civil and Environmental Engineering
The University of New South Wales, UNSW Sydney, NSW 2052, Australia
*(Corresponding author: E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.)
Received: 31 May 2011; Revised: 10 October 2011; Accepted: 14 November 2011
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ABSTRACT
In the companion paper, a fourth-order element formulation in an updated Lagrangian formulation was presented to handle geometric non-linearities. The formulation of the present paper extends this to include material non-linearity by proposing a refined plastic hinge approach to analyse large steel framed structures with many members, for which contemporary algorithms based on the plastic zone approach can be problematic computationally. This concept is an advancement of conventional plastic hinge approaches, as the refined plastic hinge technique allows for gradual yielding, being recognized as distributed plasticity across the element section, a condition of full plasticity, as well as including strain hardening. It is founded on interaction yield surfaces specified analytically in terms of force resultants, and achieves accurate and rapid convergence for large frames for which geometric and material non-linearity are significant. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. In addition to the numerical efficiency, the present versatile approach is able to capture different kinds of material and geometric non-linearities on general applications of steel structures, and thereby it offers an efficacious and accurate means of assessing non-linear behaviour of the structures for engineering practice.
KEYWORDS
Beam-column, Frames, Interaction surface, Material non-linearity, Refined plastic hinge method, Strain hardening
REFERENCES
[1] Iu, C.K. and Bradford, M.A., “Higher-order Non-linear Analysis of Steel Structures”, Part 1: Elastic second-order formulation, (???? Year).
[2] King, W.S., White, D.W. and Chen, W.F., “On Second-order Inelastic Analysis Methods for Steel Frame Design”, Journal of Structural Engineering, ASCE, 1992, Vol. 118, No. 2, pp. 408-428.
[3] Duan, L. and Chen, W.F., “Design Interaction Equation for Steel Beam-columns”, Journal of Structural Engineering, ASCE, 1989, Vol. 115, No. 5, pp. 1225-1243.
[4] Liew, J.Y.R., White, D.W. and Chen, W.F., “Second-order Refined Plastic-hinge Analysis for Frame Design”, Part I, Journal of Structural Engineering, ASCE, 1993, Vol. 119, No. 11, pp. 3196-3216.
[5] Liew, J.Y.R., White, D.W. and Chen, W.F., “Second-order Refined Plastic-hinge Analysis for Frame Design”, Part II, Journal of Structural Engineering, ASCE, 1993, Vol. 119, No. 11, pp. 3217-3237.
[6] American Institute of Steel Construction, Load and Resistance Factor Design Specification for Structural Steel Buildings, AISC, Chicago, 1986.
[7] Yau, C.Y. and Chan, S.L., “Inelastic and Stability Analysis of Flexibly Connected Steel Frames by Springs-in-series Model”, Journal of Structural Engineering, ASCE, 1994, Vol. 120, No. 10, pp. 2803-2819.
[8] Chan, S.L. and Chui, P.P.T., “A Generalized Design-based Elastoplastic Analysis of Steel Frames by Section Assemblage Concept”, Engineering Structures, 1997, Vol. 19, No. 8, pp. 628-636.
[9] Iu, C.K. and Chan, S.L., “A Simulation-based Large Deflection and Inelastic Analysis of Steel Frames under Fire”, Journal of Constructional Steel Research, 2004, Vol. 60, pp. 1495-1524.
[10] Iu, C.K., Chan, S.L. and Zha, X.X., “Material Yielding by Both Axial and Bending Spring Stiffness at Elevated Temperature”, Journal of Constructional Steel Research, 2007, Vol. 63, pp. 677-685.
[11] Zhou, Z.H. and Chan, S.L., “Elastoplastic and Large Deflection Analysis of Steel Frames by One Element per Member I: One Hinge along Member,” Journal of Structural Engineering, ASCE, 2004, Vol. 130, No. 4, pp. 538-544.
[12] Chan, S.L. and Zhou, Z.H., “Elastoplastic and Large Deflection Analysis of Steel Frames by One Element per Member II: Three Hinges along Member”, Journal of Structural Engineering, ASCE, 2004, Vol. 130, No. 4, pp. 545-553.
[13] Kassimali, A., “Large Deformation Analysis of Elastic-plastic Frames,” Journal of Structural Engineering, ASCE, 1983, Vol. 109, No. 8, pp. 1869-1886.
[14] Tebedge, N. and Chen, W.F., “Design Criteria for H-columns under Biaxial Loading”, Journal of the Structural Division, ASCE, 1974, Vol. 100(ST3), pp. 579-598.
[15] Iu, C.K., Bradford, M.A. and Chen, W.F., "Second-order Inelastic Analysis of Composite Framed Structures based on the Refined Plastic Hinge Method”, Engineering Structures, 2009, Vol. 31, No. 3, pp. 799-813.
[16] Iu, C.K., “Inelastic Finite Element Analysis of Composite Beams on the Basis of the Plastic Hinge Approach”, Engineering Structures, 2008, Vol. 30, pp. 2912-2922.
[17] Liew, J.Y.R., White, D.W. and Chen, W.F., “Second-order Refined Plastic Hinge Analysis of Frames”, Structural Engineering Report CE-STR-92-12, Purdue University, West Lafayette, Indiana, 1992.
[18] Trahair, N.S., Bradford, M.A., Nethercot, D.A. and Gardner, L., “The Analysis and Behaviour of Steel Structures to EC4”, 4th edn., Taylor and Francis, London, 2008.
[19] Vogel, U., “Calibrating Frames”, Der Stahlbau 1985, Vol. 10, pp. 296-301.
[20] Toma, S. and Chen, W.F., “European Calibration Frames for Second-order Inelastic Analysis”, Engineering Structures 1992, Vol. 14, No. 1, pp. 7-14.
[21] Clarke, M.J., “Plastic Zone Analysis of Frames”, In: Advanced Analysis of Steel Frames, Chen, W.F. and Toma, S., eds., CRC Press, Boca Raton, Florida, 1994, pp. 259-320.
[22] Teh, L.H. and Clarke, M.J., “Plastic-zone Analysis of 3D Steel Frames using Beam Elements”, Journal of Structural Engineering, ASCE, 1999, Vol. 125, No. 11, pp. 1328-1337.
[23] Ziemian, R.D., “A Verification Study for Methods of Second-order Inelastic Analysis”, Proceedings of Annual Technical Session, Structural Stability Research Council, Pittsburgh, Pennsylvania, 1992, pp. 315-326.
[24] Iffland, J.S.B. and Birnstiel, C., “Stability Design Procedures for Building Frameworks”, Research Report, AISC Project No. 21.62, American Institute of Steel Construction, Chicago, Illinois, 1982.
[25] Crisfield, M.A., “An Arc-length Method including Line Searches and Accelerations”, International Journal for Numerical Methods in Engineering, 1983, Vol. 19, pp. 1269-1289.
[26] Chan, S.L., “Geometric and Material Nonlinear Analysis of Beam-columns and Frames using the Minimum Residual Displacement Method”, International Journal for Numerical Methods in Engineering 1988, Vol. 26, pp. 2657-2669.
[27] Orbison, J.G., McGuire, W. and Abel, J.F., “Yield Surface Applications in Nonlinear Steel Frame Analysis”, Computer Methods in Applied Mechanics and Engineering 1982, Vol. 33, No. 1, pp. 557-573.
[28] Liew, J.Y.R., Chen, H., Shanmugam, N.E. and Chen, W.F., “Improved Nonlinear Plastic Hinge Analysis of Space Frame Structures”, Engineering Structures, 2000, Vol. 22, No. 2, pp. 1324-1338.
[29] Jiang, X.M., Chen, H. and Liew, J.Y.R., “Spread of Plasticity Analysis of Three-dimensional Steel Frames”, Journal of Constructional Steel Research, 2002, Vol. 58, pp. 193-212.