Advanced Steel Construction

Vol. 16, No. 3, pp. 246-254 (2020)




Anh Q Vu 1, *, Nghia H Hoang 2, and Hien M Nghiem 1

Department of Civil Engineering, Hanoi Architectural University, Hanoi Vietnam

Department of Civil Engineering, Haiphong University, Haiphong Vietnam

*(Corresponding author: E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.)

Received: 4 October 2019; Revised: 30 April 2020; Accepted: 30 May 2020




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The paper presents a new method to generate efficiently yield and failure surfaces of the doubly symmetrical wide flange I-section under axial force combined with biaxial bending moments in nonlinear analysis of the steel frame. The I-section is divided into several rectangular areas, and the axial force is integrated from uniform stress on each area to form the equilibrium equations of the failure surface. Hyperbolic equations are proposed to approximate the biaxial bending moments of gradually yielding cross-section that represent the yield surfaces lie between limit elastic and failure surfaces. A computer code SPH developed with the implementation of the proposed method aims to perform analyses for numerous cross-sections. The proposed method may help to improve the effectiveness of the finite element analysis of the steel frame in comparison to the fiber method. Several computational examples are conducted to validate the accuracy and efficiency of the proposed method by comparing the results predicted by SPH with those retrieved from other methods.



yield surface, failure surface, biaxial bending, steel I-section


[1] Duan, L., and Chen, W.F., (1990), “A yield surface equation for doubly symmetrical sections”, Eng. Struc., 12; 114-119.

[2] Orbison, J. G., McGuire, M., and Abel, J.F. (1982), “Yield surface application in nonlinear steel frame analysis”, Computer methods in applied mechanics and engineering, 33; 557-573.

[3] Taucer, F., Spacone, E., and Filippou, F.C. (1991). A Fiber Beam-Column Element for Seismic Response Analysis of Reinforced Concrete Structures. Berkekey, California: Earthquake Engineering Research Center, College of Engineering, University of California, 91(17).

[4] Ngo Huu, C. (2006), “Practical advanced analysis of steel-concrete composite structures using fiber–hinge method”, Ph.D. dissertation, Department of Civil and Environmental Engineering, the Graduate school of Sejong University.

[5] Ngo, H.C., and Kim, S.E. (2009), “Practical advanced analysis of space steel frames using fiber hinge method”, Thin-Walled Structures, 47(4), 421-430.

[6] Nguyen, P.C., and Kim, S.E., (2015), “Second-order spread-of-plasticity approach for nonlinear time-history analysis of space semi-rigid steel frames”, Finite Elements in Analysis and Design, 105:1–15.

[7] Chiorean, C.G. (2010), “Computerised interaction diagrams and moment capacity contours for composite steel-concrete cross-sections”, Eng. Struc., 32; 3734-3757.

[8] Liew, J. R., Chen, H., and Shanmugam, N. E. (2001), “Inelastic analysis of steel frames with composite beams”, Journal of Structural Engineering, 127(2), 194-202.

[9] Iu, C. K., Bradford, M.A., & Chen, W.F. (2009), “Second-order inelastic analysis of composite framed structures based on the refined plastic hinge method”, Eng. Struc., 31(3), 799-813.

[10] Chiorean, C.G. (2013), “A computer method for nonlinear inelastic analysis of 3D composite steel–concrete frame structures”, Eng. Struc., 57, 125-152.

[11] Liew, J.R., Chen, H., Shanmugam, N.E. and Chen, W.F. (2000), “Improved nonlinear plastic hinge analysis of space frame structures”, Eng. Struc., 22(10), pp.1324-1338.

[12] Kim, S.E., Kim, Y. and Choi, S.H. (2001a), “Nonlinear analysis of 3-D steel frames”, Thin-walled structures, 39(6), pp.445-461.

[13] Kim, S.E., Park, M.H. and Choi, S.H., (2001b), “Direct design of three-dimensional frames using practical advanced analysis”, Eng. Struc., 23(11), pp.1491-1502.

[14] Kim, S.E. and Choi, S.H., (2001), “Practical advanced analysis for semi-rigid space frames”, International journal of solids and structures, 38(50-51), pp.9111-9131.

[15] Skordeli, M.A. and Bisbos, C.D., (2010), “Limit and shakedown analysis of 3D steel frames via approximate ellipsoidal yield surfaces”, Eng. Struc., 32(6), pp.1556-1567.