Advanced Steel Construction

Vol. 15, No. 2, pp. 137-144 (2019)




Jeriniaina Sitraka Tantely 1 and Zheng He 1, 2, *

1 Department of Civil Engineering, Dalian University of Technology, Dalian, Liaoning, China

2 State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, Liaoning, China

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

Received: 27 August 2017; Revised: 27 July 2018; Accepted: 01 August 2018




View Article   Export Citation: Plain Text | RIS | Endnote


Finding an optimum design based on collapse safety assessment for bracing systems in steel structures can result in a safer and economical design, and therefore is highly desirable. Several works in the literature have successfully applied various design methodologies for braced frames. The occurrence of unforeseen events outside the scope of these designs might jeopardize their structural integrity. Therefore, tools such as incremental dynamic analysis and modal pushover analysis have been developed to assess the probability of structural collapse. However, their implementation in the design process is challenging because their procedures are onerous and time-consuming. To overcome this issue, a straightforward method utilizing empirical equation to estimate the collapse margin of the structure is used. The proposed methodology uses the brace locations and sections as variables. A probabilistic analysis using multi-element removal identifies the bracing layouts, and explicit equations determine their optimal discrete sections. The methodology creates all the possible schemes, then identifies the optimal one that has the highest safety index based on a targeted collapse margin ratio. Through solving four typical examples of steel framed structures, the practicality, and accuracy of the proposed approach are proved.



Steel structures, Brace frames, Collapse safety, Probabilistic analysis, Multi-element removal, Safety index


[1] Stromberg L.L., Beghini A., Baker W.F. and Paulino G.H., "Topology optimization for braced frames: Combining continuum and beam/column elements", Engineering Structures, 37, April, 106-124, 2012.

[2] Vamvatsikos D. and Cornell C.A., "Incremental dynamic analysis", Earthquake Engineering & Structural Dynamics, 31(3), 491-514, 2002.

[3] Han S.W. and Chopra A.K., "Approximate incremental dynamic analysis using the modal pushover analysis procedure", Earthquake Engineering and Structural Dynamics, 35(15), 1853-1873, 2006.

[4] Hamidia M., Filiatrault A. and Aref A., "Simplified seismic sidesway collapse analysis of frame buildings", Earthquake Engineering & Structural Dynamics, 43(3), 429-448, 2014.

[5] Hardyniec A. and Charney F., "A new efficient method for determining the collapse margin ratio using parallel computing", Computers and Structures, 148, February, 14-25, 2015.

[6] Liu S.W., Bai R. and Chan S.L., Dynamic Time-history Elastic Analysis of Steel Frames Using One Element per Member, presented at the Structures, 2016.

[7] Liu S.W., Liu Y.P. and Chan S.L., "Pushover analysis by one element per member for performance-based seismic design", International Journal of Structural Stability and Dynamics, 10(01), 111-126, 2010.

[8] Chopra A.K. and Goel R.K., "A modal pushover analysis procedure for estimating seismic demands for buildings", Earthquake Engineering & Structural Dynamics, 31(3), 561-582, 2002.

[9] Han S.W., Moon K.H. and Chopra A.K., "Application of MPA to estimate probability of collapse of structures", Earthquake Engineering and Structural Dynamics, 39(11), 1259-1278, 2010.

[10] Moon K.H., Han S.W., Lee T.S. and Seok S.W., "Approximate MPA-based method for performing incremental dynamic analysis", Nonlinear Dynamic, 67(4), 2865-2888, 2012.

[11] FEMA, Quantification of Building Seismic Performance Factors, Federal Emergency Management Agency, Washington, DC, 2009.

[12] Ou X., He Z. and Ou J., "Parametric study on collapse margin ratio of structure", Journal of Central South University, 21(6), 2477-2486, 2014.

[13] Farsangi E.N., Yang T.Y. and Tasnimi A.A., "Influence of concurrent horizontal and vertical ground excitations on the collapse margins of non-ductiles RC frame buildings", Structural Engineering and Mechanics, 59(4), 653-669, 2016.

[14] Xian L., He Z. and Ou X., "Incorporation of collapse safety margin into direct earthquake loss estimate", Earthquakes and Structures, 10(2), 429-450, 2016.

[15] Tirca L., Chen L. and Tremblay R., "Assessing collapse safety of CBF buildings subjected to crustal and subduction earthquakes", Journal of Constructional Steel Research, 115, December, 47-61, 2015.

[16] Kicinger R., Arciszewski T. and De Jong K., "Evolutionary computation and structural design: A survey of the state-of-the-art", Computers and Structures, 83(23-24), 1943-1978, 2005.

[17] Pezeshk S. and Camp C.V., State of the Art on the Use of Genetic Algorithms in Design of Steel Structures, American Society of Civil Engineers, Reston, VA, 2002.

[18] Schafer B.W. and Bajpai P., "Stability degradation and redundancy in damaged structures", Engineering Structures, 27(11), 1642-1651, 2005.

[19] Gholizadeh S. and Poorhoseini H., "Seismic layout optimization of steel braced frames by an improved dolphin echolocation algorithm", Structural and Multidisciplinary Optimization, 54(4), October 01, 1011-1029, 2016.

[20] Liu M., "Progressive collapse design of seismic steel frames using structural optimization", Journal of Constructional Steel Research, 67(3), 322-332, 2011.

[21] Moghaddam H., Hajirasouliha I. and Doostan A., "Optimum seismic design of concentrically braced steel frames: concepts and design procedures", Journal of Constructional Steel Research, 61(2), 151-166, 2005.

[22] ASCE-360, "Specification for Structural Steel Buildings," American Society of Civil Engineers, Reston, VA, 2010.

[23] Coeto G. and Teran-Gilmore A., Stiffness-Based Sizing of Bracing Systems for Tall and Slender Buildings, Proceeding of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal, 10, 2012.

[24] Baker J.W., "Efficient analytical fragility function fitting using dynamic structural analysis", Earthquake Spectra, 31(1), 579-599, 2015.

[25] Bradley B.A. and Dhakal R.P., "Error estimation of closed-form solution for annual rate of structural collapse", Earthquake Engineering and Structural Dynamics, 37(15), 1721-1737, 2008.

[26] Porter K., Kennedy R. and Bachman R., "Creating fragility functions for performance-based earthquake engineering", Earthquake Spectra, 23(2), 471-489, 2007.

[27] ASCE-7, Minimum Design Loads for Buildings and Others Structures, American Society of Civil Engineers, Reston, VA, 2010.

[28] Ibarra L.F., Medina R.A. and Krawinkler H., "Hysteric models that incorporate strength and stiffness deterioration", Earthquake Engineering & Structural Dynamics, 34(12), 1489-1511, 2005.

[29] Nobahar E., Farahi M. and Mofid M., "Quantification of seismic performance factors of the buildings consisting of disposable knee bracing frames", Journal of Constructional Steel Research, 124, September, 132-141, 2016.

[30] Shin D.H. and Kim H.J., "Influential properties of hysteretic energy dissipating devices on collapse capacities of frames", Journal of Constructional Steel Research, 123, August, 93- 105, 2016.

[31] Hamidia M., Filiatrault A. and Aref A., "Seismic collapse capacity–based evaluation and design of frame buildings with viscous dampers using pushover analysis", Journal of Structural Engineering, 141(6), 04014153, 2015.

[32] Elhami Khorasani N., Garlock M.E.M. and Quiel S.E., "Modeling steel structures in OpenSees: Enhancements for fire and multi-hazard probabilistic analyses", Computers and Structures, 157, September, 218-231, 2015.

[33] Lu X., Xie L., Guan H., Huang Y. and Lu X., "A shear wall element for nonlinear seismic analysis of super-tall buildings using OpenSees", Finite Elements in Analysis and Design, 98, 14-25, 2015.

[34] Terzic V., Modeling SCB Frames Using Beam-Column Elements, Berkeley, CA, 2013.

[35] Uriz P. and Mahin S.A., Toward Earthquake-Resistance Design of Concentrically Braced Steel-Frame Structures, Pacific Earthquake Engineering Research Center, Berkeley, CA, 2008.

[36] Hsiao P.C., Lehman D.E. and Roeder C.W., "Improved analytical model for special concentrically braced frames", Journal of Constructional Steel Research, 73, June, 80-94, 2012.

[37] Mazzoni S., McKenna F., Scott M.H. and Fenves G.L., Open System for Earthquake Engineering Simulation (OpenSees): Command Language Manual, Available at, 2007.