In this study, the stability-based beam-column element has been proposed to consider the geometric second-order effects and material inelasticity, and to take advantage of the computational efficiency of the second-order analysis. A new force interpolation function matrix is developed to consider a moment magnification due to the axial force and lateral displacement. The constitutive behaviour of the cross-section is formulated by integration of the uniaxial stress-strain response of fibres to model the material inelasticity. The generalized displacement control (GDC) method incorporating the incremental secant stiffness method is applied to solve the nonlinear equilibrium equations with multiple limit points. Evaluation of the results of this study shows that the proposed method consistently predicts well the nonlinear inelastic behaviour of steel and composite structures, and gives good efficiency.
AlemdarB.N. and WhiteD.W. (2005). “Displacement, flexibility, and mixed beam-column finite element formulations for distributed plasticity analysis”, Journal of Structural Engineering, ASCE, Vol. 131, No. 12, pp. 1811–1819.
3.
AyoubA. and FilippouF.C. (2000). “Mixed formulation of nonlinear steel-concrete composite beam element”, Journal of Structural Engineering, ASCE, Vol. 126, No. 3, pp. 371–381.
4.
ChanS.L. and GuJ.X. (2000). “Exact tangent stiffness for imperfect beam-column members”, Journal of Structural Engineering, ASCE, Vol. 126, No. 9, pp. 1094–1102.
5.
ChanS.L. and ZhouZ.H. (1998). “On the development of a robust element for second-order non-linear integrated design and analysis”, Journal of Constructional Steel Research, Vol. 47, No. 1–2, pp. 169–190.
6.
ChanS.L. and ZhouZ.H. (2000). “Non-linear integrated design and analysis of skeletal structures by 1 element per member”, Engineering Structures, Vol. 22, pp. 246–257.
7.
ChanS.L. and ZhouZ.H. (2004). “Elastoplastic and large deflection analysis of steel frames by one element per member. II: Three hinges along member”, Journal of Structural Engineering, Vol. 130, No. 4, pp. 545–553.
8.
ChenH. and LiewJ.Y.R. (2005). “Explosion and fire analysis of steel frames using mixed element method”, Journal of Engineering Mechanics, ASCE, Vol. 131, No. 6, pp. 606–616.
9.
ChenW.F. and LuiE.M. (1987). Structural Stability: Theory and Implementation, Elsevier, New York.
10.
HjelmstadK.D. and TacirogluE. (2003). “Mixed variational methods for finite element analysis of geometrically non-linear, inelastic Bernoulli-Euler beams”, Communications in Numerical Methods in Engineering, Vol. 19, pp. 809–832.
11.
KentD.C. and ParkR. (1971). “Flexural members with confined concrete”, Journal of Structural Division, ASCE, Vol. 97, No. 7, pp. 1969–1990.
12.
KimS.E.ParkM.H. and ChoiS.H. (2001). “Direct design of three-dimensional frames using practical advanced analysis”, Engineering Structures, Vol. 23, pp. 1491–1502.
13.
KimS.E.UangC.M.ChoiS.H. and AnK.Y. (2006). “Practical advanced analysis of steel frames considering lateral-torsional buckling”, Thin-Walled Structures, Vol. 44, pp. 709–720.
14.
LeeS.ManuelF.S. and RossowE.C. (1968). “Large deflections and stability of elastic frames”, Journal of Engineering Mechanics Division, ASCE, Vol. 94, No. 2, pp. 521–547.
15.
LiewJ.Y.R. (2004). “Performance based fire safety design of structures – A multi-dimensional integration”, Advances in Structural Engineering, Vol. 7, No. 4, pp. 111–133.
16.
LiewJ.Y.R.ChenH.ShanmugamN.E. and ChenW.F. (2000). “Improved nonlinear plastic hinge analysis of space frames”, Engineering Structures, Vol. 22, No. 10, pp. 1324–1338.
17.
ManderJ.B.PriestlyJ.N. and ParkR. (1988). “Theoretical stress-strain model for confined concrete”, Journal of Structural Engineering, ASCE, Vol. 114, No. 8, pp. 1804–1826.
18.
NeuenhoferA. and FilippouF.C. (1998). “Geometrically nonlinear flexibility-based frame finite element”, Journal of Structural Engineering, ASCE, Vol. 124, No. 6, pp. 704–711.
19.
OpenSees (2008). OpenSees User Command-Language Manual, Pacific Earthquake Engineering Research Center, University of California, Berkeley.
20.
PopovicsS. (1973). “A numerical approach to the complete stress-strain curves for concrete”, Cement and Concrete Research, Vol. 3, No. 5, pp. 583–599.
21.
RanganB.V. and JoyceM. (1992). “Strength of eccentrically loaded slender steel tubular columns filled with high-strength concrete”, ACI Structural Journal, Vol. 89, No. 6, pp. 676–681.
22.
SpaconeE.CiampiV. and FilippouF.C. (1996a). “Mixed formulation of nonlinear beam finite element”, Computers and Structures, Vol. 58, No. 1, pp. 71–83.
23.
SpaconeE.FilippouF.C. and TaucerF.F. (1996b). “Fibre beam column model for nonlinear analysis of R/C frames: Part I. formulation”, Earthquake Engineering and Structural Dynamics, Vol. 25, pp. 711–725.
24.
StroudA.H. and SecrestD. (1966). Gaussian Quadrature Formulas, Prentice Hall, New Jersey.
25.
SusanthaK.A.S.GeH. and UsamiT. (2001). “Uniaxial-stress-strain relationship of concrete confined by various shaped steel tubes”, Engineering Structures, Vol. 23, No. 10, pp. 1331–1347.
26.
TangJ.HinoS.KurodaI. and OhtaT. (1996). “Modeling of stress-strain relationships for steel and concrete in concrete filled circular steel tubular columns”, Steel Construction Engineering, JSSC, Vol. 3, No. 11, pp. 35–46.
27.
TaucerF.F.SpaconeE. and FilippouF.C. (1991). A Fiber Beam-Column Element for Seismic Response Analysis of Reinforced Concrete Structures, Report No. EERC 91–17, Earthquake Engineering Research Center, University of California, Berkeley.
28.
UsamiT. and GeH.B. (1998). “Cyclic behaviour of thin-walled steel structures – numerical analysis”, Thin-Walled Structures, Vol. 32, pp. 41–80.
29.
YangY.B. and KuoS.R. (1994). Theory and Analysis of Nonlinear Framed Structures. Englewood Cliffs, Prentice Hall.
30.
YangY.B. and ShiehM.S. (1990). “Solution method for nonlinear problems with multiple critical points”, AIAA Journal, Vol. 28, No. 12, pp. 2110–2116.
31.
YangY.B.LinS.P. and LeuL.J. (2007). “Solution strategy and rigid element for nonlinear analysis of elastically structures based on updated Lagrangian formulation”, Engineering Structures, Vol. 29, pp. 1189–1200.
