Advanced Steel Construction

Vol. 4, No. 4, pp. 341-352 (2008)




Yu-Shu Liu 1,* and Guo-Qiang Li 2

1 Lecturer, School of Civil Engineering, Tongji University, Shanghai, China

* (Corresponding author: E-mail: ysliu@

2 Professor, School of Civil Engineering, Tongji University, Shanghai, China

Received: 18 October 2007; Revised: 11 December 2007; Accepted: 12 December 2007




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A nonlinear analysis method of steel frames using element with internal plastic hinge is proposed. This method can analyze the frame member applied with laterally-distributed loads only using one element even that a plastic hinge appears within the member. By dividing the member into two segments at the location of the maximum moment, the incremental stiffness matrix of the two segments from time t to t + dt are derived, then the beam element stiffness equation with internal plastic hinge after the static condensation can be obtained. What’s more, this method also considers the influences of some geometrical and material nonlinear factors including second-order effect of axial forces, shear deformation, cross-sectional plastification, residual stress and initial imperfection. This method not only overcomes the time-consuming disadvantages of plastic zone method of frame members because of the fine mesh discretization but also makes up for the problem of the traditional plastic hinge element that plastic hinges must form at the elemental ends. Analysis results show that the proposed method is satisfactory.



Steel frames; nonlinear analysis; internal plastic hinge; plastic zone method; cross-section plastification


[1] Kim, Seung-Eock, Kim, Moon-Kyum and Chen, Wai-Fah, “Improved Refined Plastic Hinge Analysis Accounting for Strain Reversal”, Engineering Structures, 2000, Vol. 22, pp. 15-25.

[2] Kim, S.E. and Chen, W.F., “Practical Advanced Analysis for Unbraced Steel Frames Design”, Journal of Structural Engineering, ASCE, 1996, Vol. 122, No. 11, pp. 1259-1265.

[3] King, W.S., White, D.W. and Chen, W.F., “A Modified Plastic Hinge Method for Second-order Inelastic Analysis of Rigid Frames”. Structural Engineering Review, 1992, Vol. 4, No. 1, pp. 31-41.

[4] Liew, J.Y.R., “Second-order Refined Plastic Hinge Analysis of Frame Design Part 1”, Journal of Structural Engineering, 1993, Vol. 119, pp. 3196-3216.

[5] Liew, J.Y.R., “Second-order Refined Plastic Hinge Analysis of Frame Design Part 2”, Journal of Structural Engineering, 1993, Vol. 119, pp. 3217-3237.

[6] Li, Guo-qiang, Shen, Zu-yan. “Elastic and Elasto-plastic Analysis and Computational Theory for Steel Frame Systems”, Shanghai, Shanghai Science and Technology Press, 1998. (in Chinese)

[7] Duan, L. and Chen, W.F., “Design Interaction Equation for Steel Beam-columns”. Journal of Structural Engineering, 1989, Vol. 115, No. 5, pp. 1225-1243.

[8] Chen, W.F. “Analysis and Design of Beam-column, Volume (I), Planar Problem Characteristic and Design”. Beijing, China Communications Press, 1997. (in Chinese)

[9] Chan, S.L. and Chui, P.P.T., “Non-linear Static and Cyclic Analysis of Steel Frames with Semi-rigid Connections”, Oxford, Elesvier, 2000.