Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30127
Modal Approach for Decoupling Damage Cost Dependencies in Building Stories

Authors: Haj Najafi Leila, Tehranizadeh Mohsen


Dependencies between diverse factors involved in probabilistic seismic loss evaluation are recognized to be an imperative issue in acquiring accurate loss estimates. Dependencies among component damage costs could be taken into account considering two partial distinct states of independent or perfectly-dependent for component damage states; however, in our best knowledge, there is no available procedure to take account of loss dependencies in story level. This paper attempts to present a method called "modal cost superposition method" for decoupling story damage costs subjected to earthquake ground motions dealt with closed form differential equations between damage cost and engineering demand parameters which should be solved in complex system considering all stories' cost equations by the means of the introduced "substituted matrixes of mass and stiffness". Costs are treated as probabilistic variables with definite statistic factors of median and standard deviation amounts and a presumed probability distribution. To supplement the proposed procedure and also to display straightforwardness of its application, one benchmark study has been conducted. Acceptable compatibility has been proven for the estimated damage costs evaluated by the new proposed modal and also frequently used stochastic approaches for entire building; however, in story level, insufficiency of employing modification factor for incorporating occurrence probability dependencies between stories has been revealed due to discrepant amounts of dependency between damage costs of different stories. Also, more dependency contribution in occurrence probability of loss could be concluded regarding more compatibility of loss results in higher stories than the lower ones, whereas reduction in incorporation portion of cost modes provides acceptable level of accuracy and gets away from time consuming calculations including some limited number of cost modes in high mode situation.

Keywords: Dependency, story-cost, cost modes, engineering demand parameter.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 443


[1] Building Seismic Safety Council (BSSC), “NEHRP recommended provisions for seismic regulations for new buildings and other structures,” FEMA 450, Federal Emergency Management Agency, Washington D.C, 2003.
[2] C. Ramirez and E. Miranda, “Building-specific loss estimation methods & tools for simplified performance-based earthquake engineering,” Report No. 171, (Ph.D. dissertation), John A. Blume Earthquake Engineering Center: Stanford University; 2009.
[3] C. A. Goulet, C. B. Haselton, J. Mitrani-Reiser, J. L. Beck, G. G. Deierlein, K. A. Porter, J. P. Stewart, “Evaluation of the Seismic Performance of a Code-Conforming Reinforced Concrete Frame Building - from Seismic Hazard to Collapse Safety and Economic Losses,” Earth. Eng. Struc. Dyn., vol. 36, no.13, pp.1973-1997, 2007.
[4] C. B. Haselton, C. A. Goulet, J. Mitrani-Reiser, J. L. Beck, G. G. Deierlein, K. A. Porter, J. P. Stewart, E. Taciroglu, “An Assessment to Benchmark the Seismic Performance of a Code-Conforming Reinforced Concrete Moment-Frame Building,” PEER Report No. 2007/12, Pacific Earthquake Engineering Research Center, College of Engineering: University of California, 2008.
[5] E. Miranda, H. Aslani and S. Taghavi, “Assessment of Seismic Performance in Terms of Economic Losses,” PEER 2004/05, P. Fajfar and H. Krawinkler, editors. International Workshop on Performance-Based Seismic Design Concepts and Implementation, Bled, Slovenia: 2004. pp. 149-160.
[6] H. Aslani and E. Miranda, “Probabilistic Earthquake Loss Estimation and Loss Deaggregation in Buildings,” Report No. 154, (Ph.D. dissertation), John A. Blume Earthquake Engineering Center: Stanford, CA; 2006.
[7] J. W. Baker and C. A. Cornell, “Uncertainty Propagation in Probabilistic Seismic Loss Estimation,” Struct. Saf., vol. 30, no. 3, pp. 236-252, 2008.
[8] J. W. Baker and C. A. Cornell, Uncertainty Specification and Propagation for Loss Estimation Using FOSM Method,” PEER 2003-07. Pacific Earthquake Engineering Research Center, University of California at Berkeley: Berkeley, California, 2003.
[9] R. Lee and A. S. Kiremidjian, “Uncertainty and Correlation for Loss Assessment of Spatially Distributed Systems. Earth Spec. 2007; 23(4): 753-770.
[10] C. B. Haselton and G. G. Deierlein, “Assessing Seismic Collapse Safety of Modern Reinforced Concrete Frame Buildings,” Technical Report No. 156. Stanford, CA: John A. Blume Earthquake Engineering Center, Stanford University; 2007.
[11] J. W. Backer, “Introducing correlation among fragility functions for multiple components,” The 14th World Conference on Earthquake Engineering, October 12-17, Beijing, China: 2008.
[12] FEMA P-58-1. “Seismic Performance Assessment of Buildings, Applied Technology Council and Federal Emergency Management Agency,” Report No. P-58-1, Washington D.C; 2012.
[13] Balaboni, B. RSMeans Square Foot Costs 2014, RSMeans Engineering Department, 35th ed. New York, United States; 2014.
[14] M. A. Touran and L. Suphot, “Rank Correlations in Simulating Construction Costs,” J. Constr. Eng. Manag., vol. 123, no. 3, pp. 297-301, 1997.
[15] J. W. Baker, “Measuring Bias in Structural Response Caused by Grand Motion Scaling,” 8th Pacific Conference on Earthquake Engineering: Final program and book of abstracts, 5-7 December 2007, Technological University, School of Civil and Environmental Engineering: 2007, pp. 82–91.
[16] C. B. Haselton, A.S. Whittaker, J. W. Baker, J. Bray and D. N. Gray, “Selecting and Scaling Earthquake Ground Motion for Performing Response-History Analyses,” In: Proceedings of the 15th world conference on Earthquake Engineering, Earthquake Engineering Research Institute; 2012, pp. 4207–4217.
[17] ASCE, “Minimum Design Loads for Buildings and Other Structures,” ASCE/SEI 7-10. American Society of Civil Engineers, Reston, Virginia; 2010.
[18] Applied Technology Council, “Guidelines for Seismic Performance Assessment of Buildings,” ATC-58-1 50% Draft, Washington D.C. (cited 2011 May 1). Available from:
[19] L. Haj Najafi and M. Tehranizadeh, “Ground motion selection and scaling in practice,” Period. Polytech. Civ. Eng., vol. 59, no. 2, pp. 233-248, 2015. DOI:10.3311/PPci.7808.
[20] PEER Strong Ground Motion Database. (cited 2016 May 05). Available from:
[21] NIST, “Soil-Structure Interaction for Building Structures, NIST/GCR 11-917-14. NEHRP Consultants Joint Venture for the National Institute of Standards and Technology, Gaithersburg, Maryl; 2011.
[22] OpenSees, Open system for earthquake engineering simulation, Pacific Earthquake Engineering Research Center, Berkeley, CA; 2009.
[23] AISC2005, “Specification for Structural Steel Buildings, American Institute of Steel Construction,” One East Wacker Drive, Suite 700, Chicago, Illinois 60601-1802, Third Printing: April 2007.
[24] L. F. Ibarra, R. A. Medina and H. Krawinkler, “Hysteretic models that incorporate strength and stiffness deterioration, Earth. Eng. Struct. Dyn., vol. 34, no. 12, pp.1489–1511, 2005.
[25] D. G. Lignos and H. Krawinkler, “Sideway collapse of deteriorating structural system under seismic excitations,” Report No. 177, (Ph.D. Dissertation), John A. Blume Earthquake Engineering Center, Stanford University, United State; 2012.
[26] D. G. Lignos, H. Krawinkler and A. S. Whittaker, “Prediction and validation of sideway collapse of two scale models of a 4-story steel moment frame,” Earthq. Eng. Struct. Dyn., 2011; DOI: 10.1002/eqe.1061.
[27] F. Zareian and R.A. Medina, “A practical method for proper modeling of structural damping in inelastic plane Structural systems,” Computers Struct. Vol. 88, no. 12, pp.45-53, 2010.
[28] Lignos D. G., “Modeling Steel Moment Resisting Frames with OpenSees,” OpenSees Workshop, University of California, Berkeley, United States; 2014.
[29] A. Gupta and H. Krawinkler, “Seismic Demand for Performance Evaluation of Steel Moment Resisting Frames Structures,” Report No. 132. Stanford, CA: John A. Blume Earthquake Engineering Center, Stanford University, 1999.
[30] FEMA P 695, “Quantification of Building Seismic Performance Factors,” Building seismic safety council for the Federal Emergency Management Agency, Report No. FEMA P695,” Federal Emergency Management Agencies, Washington DC; 2009.