Journal Home Online First Current Issue Archive For Authors Journal Information 中文版

Engineering >> 2019, Volume 5, Issue 2 doi: 10.1016/j.eng.2018.11.026

Steel Design by Advanced Analysis: Material Modeling and Strain Limits

Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK

Received:2018-07-31 Revised:2018-09-10 Accepted: 2018-11-12 Available online:2019-02-26

Next Previous


Structural analysis of steel frames is typically performed using beam elements. Since these elements are unable to explicitly capture the local buckling behavior of steel cross-sections, traditional steel design specifications use the concept of cross-section classification to determine the extent to which the strength and deformation capacity of a cross-section are affected by local buckling. The use of plastic design methods are restricted to Class 1 cross-sections, which possess sufficient rotation capacity for plastic hinges to develop and a collapse mechanism to form. Local buckling prevents the development of plastic hinges with such rotation capacity for cross-sections of higher classes and, unless computationally demanding shell elements are used, elastic analysis is required. However, this article demonstrates that local buckling can be mimicked effectively in beam elements by incorporating the continuous strength method (CSM) strain limits into the analysis. Furthermore, by performing an advanced analysis that accounts for both geometric and material nonlinearities, no additional design checks are required. The positive influence of the strain hardening observed in stocky cross-sections can also be harnessed, provided a suitably accurate stress–strain relationship is adopted; a quad-linear material model for hot-rolled steels is described for this purpose. The CSM strain limits allow cross-sections of all slenderness to be analyzed in a consistent advanced analysis framework and to benefit from the appropriate level of load redistribution. The proposed approach is applied herein to individual members, continuous beams, and frames, and is shown to bring significant benefits in terms of accuracy and consistency over current steel design specifications.


Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9


[ 1 ] EN 1993-1-1: Eurocode 3—design of steel structures—Part 1-1: general rules and rules for buildings. European standard. Brussels: European Committee for Standardization; 2005.

[ 2 ] AS 4100: Steel structures. Australian standard. Sydney: Standards Australia; 1998.

[ 3 ] AISC 360-16: Specification for structural steel buildings. American national standard. Chicago: American Institute of Steel Construction; 2016.

[ 4 ] Liew JYR, Chen WF, Chen H. Advanced inelastic analysis of frame structures. J Construct Steel Res 2000;55(1–3):245–65. link1

[ 5 ] Chen WF. Advanced analysis for structural steel building design. Front Archit Civ Eng China 2008;2(3):189–96. link1

[ 6 ] Kim SE, Chen WF. Design guide for steel frames using advanced analysis program. Eng Struct 1999;21(4):352–64. link1

[ 7 ] Trahair NS, Chan SL. Out-of-plane advanced analysis of steel structures. Eng Struct 2003;25(13):1627–37. link1

[ 8 ] Buonopane SG, Schafer BW. Reliability of steel frames designed with advanced analysis. J Struct Eng 2006;132(2):267–76. link1

[ 9 ] Rasmussen KJR, Zhang H, Cardoso F, Liu W. The direct design method for cold– formed steel structural frames. In: Proceedings of the 8th International Conference on Steel and Aluminium Structures; 2016 Dec 7–9; Hong Kong, China.

[10] Surovek AE. Advanced analysis in steel frame design: guidelines for direct second-order inelastic analysis. Reston: American Society of Civil Engineers; 2012. link1

[11] Gardner L. The continuous strength method. Proc Inst Civ Eng Struct Build 2008;161(3):127–33. link1

[12] Gardner L, Yun X, Macorini L, Kucukler M. Hot-rolled steel and steel-concrete composite design incorporating strain hardening. Structures 2017;9: 21–8. link1

[13] Yun X, Gardner L. Stress-strain curves for hot-rolled steels. J Construct Steel Res 2017;133:36–46. link1

[14] Yun X, Gardner L, Boissonnade N. The continuous strength method for the design of hot-rolled steel cross-sections. Eng Struct 2018;157:179–91. link1

[15] Yun X, Gardner L, Boissonnade N. Ultimate capacity of I-sections under combined loading—Part 2: parametric studies and CSM design. J Construct Steel Res 2018;148:265–74. link1

[16] Zhang H, Shayan S, Rasmussen KJR, Ellingwood BR. System-based design of planar steel frames, I: reliability framework. J Construct Steel Res 2016;123:135–43. link1

[17] Yun X, Gardner L, Boissonnade N. Ultimate capacity of I-sections under combined loading—Part 1: experiments and FE model validation. J Construct Steel Res 2018;147:408–21. link1

[18] Chan TM, Gardner L. Bending strength of hot-rolled elliptical hollow sections. J Construct Steel Res 2008;64(9):971–86. link1

[19] Wang J, Afshan S, Gkantou M, Theofanous M, Baniotopoulos C, Gardner L. Flexural behaviour of hot-finished high strength steel square and rectangular hollow sections. J Construct Steel Res 2016;121:97–109. link1

[20] EN 1993-1-5: Eurocode 3—design of steel structures—Part 1–5: plated structural elements. European standard. Brussels: European Committee for Standardization; 2006.

[21] Seif M, Schafer BW. Local buckling of structural steel shapes. J Construct Steel Res 2010;66(10):1232–47. link1

[22] Gardner L, Fieber A, Macorini L. Formulae for calculating elastic local buckling stresses of full structural cross-sections. Structures 2019;17:2–20. link1

[23] Li Z, Schafer BW. Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM: conventional and constrained finite strip methods. In: Proceedings of the 20th International Speciality Conference on Cold-Formed Steel Structures; 2010 Nov 3–4; Saint Louis, MO, USA. Rolla: Missouri University of Science and Technology; 2010. p. 1731.

[24] Lay MG. The experimental bases of plastic design—a survey of the literature. Fritz laboratory report. Bethlehem: Fritz Engineering Laboratory, Department of Civil Engineering, Lehigh University; 1964 Sep. Report No.: 297.3. Publication No.: 258.

[25] Gioncu V, Petcu D. Available rotation capacity of wide-flange beams and beam-columns. Part 2. Experimental and numerical tests. J Construct Steel Res 1997;43(1–3):219–44. link1

[26] Lay MG, Galambos TV. The inelastic behavior of beams under moment gradient. Fritz Engineering Laboratory Report. Bethlehem: Lehigh University; 1964. Report No.: 197.

[27] Dassault Systemes Simulia Corp. Abaqus analysis user’s manual, version 6.13. Providence: Dassault Systemes; 2013.

[28] Crisfield MA. A fast incremental/iterative solution procedure that handles ‘snap-through’. Comput Struct 1981;13(1–3):55–62. link1

[29] Greiner R, Lechner A, Kettler M. Background information to design guidelines for cross-section and member design according to Eurocode 3 with particular focus on semi-compact sections. Graz: Institute for Steel Structures and Shell Structures; 2012. link1

[30] Avery P, Mahendran M. Large-scale testing of steel frame structures comprising non-compact sections. Eng Struct 2000;22(8):920–36. link1

Related Research