Simulating the Seismic Response of Concentrically Braced Frames Using Physical Theory Brace Models


The aim of this paper is to assess the accuracy of brace models formulated in Drain 2DX and OpenSees by comparing the simulated results with those obtained from experimental tests. Both, Drain 2DX and OpenSees rely on the physical theory brace model. In this study, experimental tests conducted on the behaviour of structural hollow section braces subjected to symmetric and asymmetric quasi-static cyclic loading were selected for calibrating the numerical model. In addition, the predicted failure strain parameter resulted from a proposed empirical equation as a function of slenderness ratio, width-to-thickness ratio and steel properties was used to define the low-cycle fatigue material that was assigned to model braces in OpenSees. It is concluded that both Drain 2DX and OpenSees brace models give a good prediction in terms of maximum tensile and buckling force, as well as interstorey drift. However, in Drain 2DX, the brace model is not able to replicate the out-of-plan buckling and the braced frame model cannot provide an accurate response when the system experiences highly nonlinear demand. To emphasise the differences in performance between Drain 2DX and OpenSees, the behaviour of a 4-storey concentrically braced frame with zipper bracing configuration, located in Victoria, BC, was investigated.

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L. Chen and L. Tirca, "Simulating the Seismic Response of Concentrically Braced Frames Using Physical Theory Brace Models," Open Journal of Civil Engineering, Vol. 3 No. 2A, 2013, pp. 69-81. doi: 10.4236/ojce.2013.32A008.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] CAN/CSA-S16-09, “Limit States Design of Steel Structures,” Canadian Standard Association, Rexdale, 2009.
[2] V. Prakash, G. H. Powell and S. D. Campbell, “Drain 2DX Base Program Description and User Guide,” UCB/SEMM-1993, University of California, Berkeley, 1993.
[3] F. McKenna, “Object Oriented Finite Element Analysis: Frameworks for Analysis Algorithms and Parallel Computing,” Ph.D. Thesis, University of California, Berkeley, 1997.
[4] K. Ikeda and S. Mahin, “A Refined Physical Theory Model for Predicting the Seismic Behaviour of Braced Steel Frames,” Earthquake Engineering Research Center, University of California, Berkeley, 1984, Report No. UCB/EERC-84/12.
[5] P. Taddei, “Implementation of the Refined Theory Model of Braced Steel Frames in NONSPEC and Drain 2DX,” University of Ottawa, Canada, 1995.
[6] P. Uriz, “Towards Earthquake Resistant Design of Con centrically Braced Steel Buildings,” Ph.D. Dissertation, University of California, Berkeley, 2005.
[7] Y. Huang and S. Mahin, “Simulating the Inelastic Seismic Behaviour of Steel Braced Frames Including the Effects of Low-Cycle Fatigue,” Pacific Earthquake Eng. Research Center, Barkeley, 2010, Report No. 104.
[8] B. Fell, A. Kanvinde and G. Deierlein, “Large-Scale Testing and Simulation of Earthquake Induced Ultra Low Cycle Fatigue in Bracing Members Subjected to Cyclic Inelastic Buckling,” Stanford University, Stanford, 2010, Report No. 172.
[9] S. Pillai, “Beam-Columns of Hollow Structural Sections,” Canadian Journal of Civil Engineering, Vol. 1, No. 2, 1974, pp. 194-198. doi:10.1139/l74-018
[10] S. Mazzoni, F. McKenna, M. Scott, G. Fenves, et al., “OpenSees User Manual,” 2007.
[11] M. Menegotto and P. E. Pinto, “Method of Analysis for Cyclic Loaded R. C. Plane Frame Including Changes in Geometry and Non-Elastic Behaviour of Elements under Combined Normal Force and Bending,” Proceedings of IABSE Symposium on Resistance and Ultimate Deform ability of Structures Acted On by Well Defined Repeated Loads, Vol. 11, 1973, pp. 15-22.
[12] A. Aguero, C. Izvernari and R. Tremblay, “Modelling of the Seismic Response of Concentrically Braced Steel Frames Using the OpenSees Analysis Environment,” International Journal of Advanced Steel Construction, Vol. 2, No. 3, 2006, pp. 242-274.
[13] M. H. Scot and G. L. Fenves, “Plastic Hinge Integration methods for Force-Based Beam-Column Elements,” Journal of Structural Engineering, Vol. 132, No. 2, 2006, pp. 244-252. doi:10.1061/(ASCE)0733-9445(2006)132:2(244)
[14] R. Tremblay, “Influence of Brace Slenderness on the Fracture Life of Rectangular Tubular Steel Bracing Members Subjected to Seismic Inelastic Loading,” Proceeings of ASCE Structures Congress, Vancouver, 2008.
[15] S. Salawdeh and J. Goggins, “Numerical Simulation for Steel Brace Members Incorporating a Fatigue Model,” Engineering Structures, Vol. 46, 2013, pp. 332-349. doi:10.1016/j.engstruct.2012.07.036
[16] P. Uriz, F. C. Filippou and S. Mahin, “Model for Cyclic Inelastic Buckling of Steel Braces,” ASCE Journal of Structural Engineering, Vol. 134, No. 4, 2008, pp. 619-628. doi:10.1061/(ASCE)0733-9445(2008)134:4(619)
[17] R. Ziemian, “Guide to Stability Design Criteria for Metal Structures,” John Wiley & Sons, Hoboken, 2010. doi:10.1002/9780470549087
[18] P. C. Hsiao, D. Lehman and C. Roeder, “Improved Analytical Model for Special Concentrically Braced Frames,” Journal of Constructional Steel Research, Vol. 73, 2012, pp. 80-94. doi:10.1016/j.jcsr.2012.01.010
[19] L. Xue, “A Unified Expression for Low Cycle Fatigue and Extremely Low Cycle Fatigue and its Implication for Monotonic Loading,” International Journal of Fatigue, Vol. 30, No. 10-11, 2008, pp. 1691-1698. doi:10.1016/j.ijfatigue.2008.03.004
[20] P. Uriz and S. Mahin, “Toward Earthquake Resistant Design of Concentrically Braced Steel Frame Structures,” PEER Report 2008/08.
[21] S. S. Manson and M. H. Hirschberg, “Fatigue Behavior in Strain Cycling in the Low and Intermediate-Cycle Range,” The 10th Sagamore Army Research Conference: Fatigue—An Interdisciplinary Approach, New York, 1963, pp. 13-16.
[22] L. F. Coffin Jr., “Low Cycle Fatigue—A Review,” Applied Material Research, Vol. 1, No. 3, 1962, pp. 129-141.
[23] S. Santagati, D. Bolognini and R. Nascimbene, “Strain Life Analysis at Low-Cycle Fatigue on Concentrically Braced Steel Structures with RHS Shape Braces,” Journal of Earthquake Enineering, Vol. 16, No. S1, 2012, pp. 107-137. doi:10.1080/13632469.2012.675840
[24] D. Lignos and E. Karamanci, “Predictive Equations for Modelling Cyclic Buckling and Fracture of Steel Braces,” The 10th International Conference on Urban Earthquake Engineering, Tokyo, 1-2 March 2013, 2013, pp. 5-107.
[25] L. Tirca and L. Chen, “Numerical Simulation of Hollow Structural Steel Braces Upon Fracture,” Journal of Advanced Steel Construction (under review).
[26] M. H. Archambault, “Etude du Comportement Seismique des Contreventements Ductile en X Avec Profiles Tubulaires en Acier,” Ecole Polytechnique, Montreal, 1995, Rapport No. EPM/GCS-1995-09.
[27] B. Shaback, “Behaviour of Square HSS Braces with End Connections under Reversed Cyclic Axial Loading,” Master’s Thesis, University of Calgary, Calgary, 2001.
[28] R. Tremblay, “Inelastic Seismic Response of Steel Bracing Members,” Journal of Constructional Steel Research, Vol. 58, No. 5-8, 2002, pp. 665-701. doi:10.1016/S0143-974X(01)00104-3
[29] B. Shaback and T. Brown, “Behaviour of Square Hollow Structural Steel Braces with end Connections under Re versed Cyclic Axial Loading,” Canadian Journal of Civil Engineering, Vol. 30, No. 4, 2003, pp. 745-753. doi:10.1139/l03-028
[30] K. Lee and M. Bruneau, “Energy Dissipation of Compression Members in Concentrically Braced Frames: Re view of Experimental Data,” Journal of Structural Engineering, ASCE, Vol. 131, No. 4, 2005, pp. 552-559. doi:10.1061/(ASCE)0733-9445(2005)131:4(552)
[31] L. Tirca and L. Chen, “The Influence of Lateral Load Patterns on the Seismic Design of Zipper Braced Frames,” Engineering Structures Journal. Vol. 40, 2012, pp. 536-555. doi:10.1016/j.engstruct.2012.
[32] National Research Council of Canada, “National Building Code of Canada—Part 4,” NBCC 2010, Ottawa, 2010.
[33] American Society of Civil Engineers (ASCE), “Minimum Design Loads for Buildings and Other Structures,” ASCE/SEI 7-05, Reston.

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