Seismic collapse safety of reinforced concrete moment resisting frames with/without beam-column joint detailing
FEMA-P695 procedure was applied for seismic collapse safety evaluation of reinforced concrete moment resisting frames with/without beam-column joint detailing common in Pakistan. The deficient frame lacks shear reinforcement in joints and uses concrete of low compressive strength. Shake-table tests were performed on 1:3 reduced scale two-story models, to understand the progressive inelastic response of chosen frames and calibrate the inelastic finite-element based models. The seismic design factors i.e. response modification coefficient, overstrength, ductility, and displacement amplification factors (R, W0, Rμ, Cd) were quantified. Response modification factor R = 7.05 was obtained for the frame with beam-column joint detailing while R = 5.30 was obtained for the deficient frame. The corresponding deflection amplification factor Cd/R was found equal to 0.82 and 1.03, respectively. A suite of design spectrum compatible accelerograms was obtained from PEER strong ground motions for incremental dynamic analysis of numerical models. Collapse fragility functions were developed using a probabilistic nonlinear dynamic reliability-based method. The collapse margin ratio (CMR) was calculated as the ratio of seismic intensity corresponding to the 50th percentile collapse probability to the seismic intensity corresponding to the MCE level ground motions. It was critically compared with the acceptable CMR (i.e. the CMR computed with reference to a seismic intensity corresponding to the 10% collapse probability instead of MCE level ground motions). Frame with shear reinforcement in beam-column joints has achieved CMR 11% higher than the acceptable thus passing the criterion. However, the deficient frame achieved CMR 29% less than the conforming frame. This confirms the efficacy of beam-column joint detailing in reducing collapse risk.
ATC (1978). “Tentative Provisions for the Development of Seismic Regulations for Buildings”. Report No. ATC-3-06, Applied Technology Council (ATC), Redwood City, CA, USA, 505 pp.
ASCE 7-16 (2016). “Minimum Design Loads for Buildings and Other Structures”. American Society of Civil Engineers/Structural Engineering Institute, Reston, VA, USA, 822 pp.
EC8 (2004). “Design of Structures for Earthquake Resistance, Part 1: General Rules, Seismic Actions and Rules for Buildings. EN 1998-1”. European Committee for Standardization, Brussels, Belgium, 229 pp.
NBCC (2010). “National Building Code of Canada”. National Research Council of Canada, Ottawa, Ontario, 1203 pp.
ATC (1995). “Structural Response Modification Factors”. ATC-19, Applied Technology Council: Redwood City, CA, USA, 64 pp.
NEHRP (2000). “Part 2: Commentary – Recommended Provisions for Seismic Regulations for New Buildings and Other Structures”. Building Seismic Safety Council, Washington, DC, 460 pp.
Whittaker A, Hart G and Rojahn C (1999). “Seismic response modification factors”. ASCE Journal of Structural Engineering, 125 (4): 438-444. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:4(438) DOI: https://doi.org/10.1061/(ASCE)0733-9445(1999)125:4(438)
Kappos AJ (1999). “Evaluation of behaviour factors on the basis of ductility and overstrength studies”. Engineering Structures, 9(9): 823-835. https://doi.org/10.1016/S0141-0296(98)00050-9 DOI: https://doi.org/10.1016/S0141-0296(98)00050-9
Uang CM and Maarouf A (1993). “Safety and economy considerations of UBC seismic force reduction factors”. Proceedings of the 1993 National Earthquake Conference, Central United States Earthquake Consortium, May 2-5, Memphis, USA, 121-130.
Hwang H and Shinozuka M (1994). “Effect of large earthquakes on the design of buildings in eastern United States”. Proceedings of the 5th US National Conference on Earthquake Engineering, Earthquake Engineering Research Institute (EERI), July 10-14, Oakland, CA, USA, 223-231.
Mwafy AM and Elnashai AS (2002). “Calibration of force reduction factors of RC buildings”. Journal of Earthquake Engineering, 6(2): 239-273. https://doi.org/10.1080/13632460209350416 DOI: https://doi.org/10.1080/13632460209350416
Elnashai AS and Mwafy AM (2002). “Overstrength and force reduction factors of multistory reinforced-concrete buildings. The Structural Design of Tall and Special Buildings, 11(5): 329-351. https://doi.org/10.1002/tal.204 DOI: https://doi.org/10.1002/tal.204
Massumi A, Tasnimim AA and Saatcioglu M (2004). “Prediction of seismic overstrength in concrete moment resisting frames using incremental static and dynamic analysis”. Proceedings of the Thirteenth World Conference on Earthquake Engineering, August 1-6, Vancouver, BC, Canada, Paper No. 2826.
Mohammadi R, Massumi A and Mashkat-Dini A (2015). “Structural reliability index versus behavior factor in RC frames with equal lateral strength”. Earthquakes and Structures, 8(5): 995-1016. http://dx.doi.org/10.12989/eas.2015.8.5.995 DOI: https://doi.org/10.12989/eas.2015.8.5.995
Aydemir ME and Aydemir C (2016). “Overstrength factors for SDOF and MDOF systems with soil structure interaction”. Earthquake and Structures, 10(6): 1273-1289. http://dx.doi.org/10.12989/eas.2016.10.6.1273 DOI: https://doi.org/10.12989/eas.2016.10.6.1273
Standards New Zealand (2004). “NZS1170.5: Structural Design Actions. Part 5: Earthquake Actions ‐ New Zealand”. Standards New Zealand, Wellington, 76 pp. https://www.standards.govt.nz/sponsored-standards/building-standards/NZS1170-5
Newmark NM and Hall WJ (1982). “Earthquake Spectra and Design”. EERI Monograph Series, Earthquake Engineering Research Institute (EERI), Oakland, CA, USA, 103 pp.
Krawinkler H and Nassar AA (1992). “Seismic design based on ductility and cumulative damage demand and capacities”. In Fajfar P and Krawinkler H (Eds.) Nonlinear Seismic Analysis and Design of Reinforced Concrete Buildings. Elsevier Applied Science, New York, USA.
Miranda E and Bertero VV (1994). “Evaluation of strength reduction factors for earthquake resistant design”. Earthquake Spectra, 10(2): 357-379. https://doi.org/10.1193/1.1585778 DOI: https://doi.org/10.1193/1.1585778
Vidic T, Fajfar P and Fischinger M (1994). “Consistent inelastic design spectra: strength and displacement”. Earthquake Engineering and Structural Dynamics, 23(5): 507-521. https://doi.org/10.1002/eqe.4290230504 DOI: https://doi.org/10.1002/eqe.4290230504
Borzi B and Elnashai AS (2000). “Refined force reduction factors for seismic design”. Engineering Structures, 22(10): 1244-1260. https://doi.org/10.1016/S0141-0296(99)00075-9 DOI: https://doi.org/10.1016/S0141-0296(99)00075-9
Miranda E (2001). “Estimation of inelastic deformation demands of SDOF systems”. Journal of Structural Engineering, 127(9): 1005-1012. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:9(1005) DOI: https://doi.org/10.1061/(ASCE)0733-9445(2001)127:9(1005)
Veletsos AS and Newmark NM (1960). “Effect of inelastic behavior on the response of simple systems to earthquake motions”. Proceedings of the 2nd World Conference on Earthquake Engineering, Tokyo, Japan, 2: 895-912.
Krawinkler H (1996) “Pushover analysis: why, how, when, and when not to use it”. Proceedings of the 65th Annual Convention of the Structural Engineers Association of California, Maui, Hawaii, pp. 17-36.
Abou-Elfath H and Elhout E (2019). “Evaluating the code approaches for estimating the seismic drifts of steel frame buildings designed under variable levels of seismicity”. Bulletin of Earthquake Engineering, 17(7): 4169-4191. https://doi.org/10.1007/s10518-019-00634-z DOI: https://doi.org/10.1007/s10518-019-00634-z
Mollaioli F, Mura A and Decanini LD (2007). “Assessment of the deformation demand in multi-storey frames”. Journal of Seismology and Earthquake Engineering, 8(4): 203-219.
Rizwan M, Ahmad N and Khan AN (2018). “Seismic performance of compliant and noncompliant special moment-resisting reinforced concrete frames”. ACI Structural Journal, 115(4): 1063-1073. https://doi.org/10.14359/51702063 DOI: https://doi.org/10.14359/51702063
Ahmad N, Shahzad A, Rizwan M, Khan AN, Ali SM, Ashraf M, Naseer A, Ali Q, and Alam B (2019). “Seismic performance assessment of non-compliant SMRF reinforced concrete frame: shake-table test study”. Journal of Earthquake Engineering, 23(3): 444-462. https://doi.org/10.1080/13632469.2017.1326426 DOI: https://doi.org/10.1080/13632469.2017.1326426
Westenenk B, de la Llera JC, Jünemann R, Hube MA, Besa JJ, Lüders C, Inaudi JA, Riddell R and Jordán R (2013). “Analysis and interpretation of the seismic response of RC buildings in Concepcion during the February 27, 2010, Chile earthquake”. Bulletin of Earthquake Engineering, 11(1): 69-91. https://doi.org/10.1007/s10518-012-9404-5 DOI: https://doi.org/10.1007/s10518-012-9404-5
Kam WY, Pampanin S, Dhakal RP, Gavin H and Roeder CW (2010). “Seismic performance of reinforced concrete buildings in the September 2010 Darfield (Canterbury) earthquakes”. Bulletin of the New Zealand Society for Earthquake Engineering, 43(4): 340-350. https://doi.org/10.5459/bnzsee.43.4.340-350 DOI: https://doi.org/10.5459/bnzsee.43.4.340-350
Kam WY and Pampanin S (2011). “The seismic performance of RC buildings in the 22 February 2011 Christchurch earthquake”. Structural Concrete, 12(4): 223-233. http://hdl.handle.net/10092/9006 DOI: https://doi.org/10.1002/suco.201100044
FEMA (2009). “FEMA P695: Quantification of Building Seismic Performance Factors”. Federal Emergency Management Agency (FEMA), Washington, DC, USA, 378 pp.
Ahmad N, Ali Q, Crowley H and Pinho R (2014). “Earthquake loss estimation of residential buildings in Pakistan”. Natural Hazards, 73(3): 1889-1955. https://doi.org/10.1007/s11069-014-1174-8 DOI: https://doi.org/10.1007/s11069-014-1174-8
IBC (2019). “The 2018 International Building Code”. International Code Council, ICC Publications, IL, USA, 728 pp.
Haselton CB, Liel AB, Deierlein GG, Dean BS and Chou JH (2011). “Seismic collapse safety of reinforced concrete buildings. Part I: Assessment of ductile moment frames”. Journal of Structural Engineering, 137(4): 481-491. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000318 DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0000318
Haselton CB, Liel AB and Deierlein GG (2008). “Example evaluation of the ATC-63 methodology for reinforced concrete special moment frame buildings”. Proceedings of the ASCE SEI Structures Congress, Vancouver, Canada.
Liel AB, Haselton CB and Deierlein GG (2011). “Seismic collapse safety of reinforced concrete buildings. ii: comparative assessment of nonductile and ductile moment frames”. Journal of Structural Engineering, 137(4): 492-502. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000275 DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0000275
ACI (2005). “ACI 318: Building Code Requirements for Structural Concrete”. American Concrete Institute (ACI), Farmington Hills, MI, USA, 430 pp.
Quintana-Gallo P, Pampanin S, Carr AJ and Bonelli P (2010). “Shake table tests of under designed RC frames for the seismic retrofit of buildings – design and similitude requirements of the benchmark specimen”. Proceedings of the Annual Conference of the New Zealand Society of Earthquake Engineering, March 26-28, Wellington, NZ, Paper No. 39.
Morcarz P and Krawinkler H (1981). “Theory and Application of Experimental Model Analysis in Earthquake Engineering”. Technical Report, Report No. 50, John Blume Earthquake Engineering Center, Department of Civil and Environmental Engineering, Stanford University, USA, 263 pp.
Ahmad N, Masoudi M and Salawdeh S (2020). “Cyclic response and modelling of special moment resisting beams exhibiting fixed-end rotation”. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-020-00987-w DOI: https://doi.org/10.1007/s10518-020-00987-w
Pampanin S, Calvi GM and Moratti M (2002). “Seismic behavior of R.C. beam-column joints designed for gravity only”. Proceedings of the 12th European Conference on Earthquake Engineering, September 9-13, London, UK, Paper No. 726.
Priestley MJN (1997). “Displacement-based seismic assessment of reinforced concrete buildings”. Journal of Earthquake Engineering, 1(1): 157-192. https://doi.org/10.1080/13632469708962365 DOI: https://doi.org/10.1080/13632469708962365
Ahmad ME, Ahmad N, Pervez S, Iqbal A, Khan AZ, Rahim ME, Hassan W, Umer K and Khan K (2019). “Seismic performance evaluation of modern bare and masonry-infilled RC SMRF structures”. Advances in Civil Engineering, 2019(Article ID 6572465): 15 pp. https://doi.org/10.1155/2019/6572465 DOI: https://doi.org/10.1155/2019/6572465
Crowley H and Pinho R (2004). “Period-height relationship for existing European reinforced concrete buildings”. Journal of Earthquake Engineering, 8(1): 93-119. https://doi.org/10.1080/13632460409350522 DOI: https://doi.org/10.1080/13632460409350522
Masi A and Vona M (2010). “Experimental and numerical evaluation of the fundamental period of undamaged and damaged RC framed buildings”. Bulletin of Earthquake Engineering, 8(3): 643-656. https://doi.org/10.1007/s10518-009-9136-3 DOI: https://doi.org/10.1007/s10518-009-9136-3
Pinho R (2007). “Nonlinear dynamic analysis of structures subjected to seismic actions” Page 63-89 in Advanced Earthquake Engineering Analysis. Editor: Pecker A, Springer.
Neuenhofer A and Filippou FC (1997). “Evaluation of nonlinear frame finite-element models”. Journal of Structural Engineering - ASCE, 123(7): 958-966. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:7(958) DOI: https://doi.org/10.1061/(ASCE)0733-9445(1997)123:7(958)
Spacone E, Ciampi V and Filippou FC (1996). “Mixed formulation of nonlinear beam finite element”, Computers and Structures, 58(1): 71-83. https://doi.org/10.1016/0045-7949(95)00103-N DOI: https://doi.org/10.1016/0045-7949(95)00103-N
Koopaee ME, Dhakal RP and MacRae G (2015). “Analytical simulation of seismic collapse of RC frame buildings”. Bulletin of the New Zealand Society for Earthquake Engineering, 48(3): 157-169. https://doi.org/10.5459/bnzsee.48.3.157-169 DOI: https://doi.org/10.5459/bnzsee.48.3.157-169
Calabrese A, Almeida JP and Pinho R (2010). “Numerical issues in distributed inelasticity modelling of RC frame elements for seismic analysis”. Journal of Earthquake Engineering, 14(S1): 38-68. https://doi.org/10.1080/13632461003651869 DOI: https://doi.org/10.1080/13632461003651869
Celik OC and Ellingwood BR (2008). “Modelling beam-column joints in fragility assessment of gravity load designed reinforced concrete frames”. Journal of Earthquake Engineering, 12(3): 357-381. https://doi.org/10.1080/13632460701457215 DOI: https://doi.org/10.1080/13632460701457215
Alath S and Kunnath SK (1995). “Modeling inelastic shear deformations in RC beam-column joints”. Proceedings of the 10th Conference on Engineering Mechanics, University of Colorado at Boulder, Boulder, Colorado.
Sivaselvan M and Reinhorn AM (2001). “Hysteretic models for deteriorating inelastic structures”. ASCE Journal of Engineering Mechanics, 126(6): 633-640. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:6(633) DOI: https://doi.org/10.1061/(ASCE)0733-9399(2000)126:6(633)
Kim J and LaFave M (2012). “A simplified approach to joint shear behavior prediction of RC beam-column connections”. Earthquake Spectra, 28(3): 1071-1096. https://doi.org/10.1193/1.4000064 DOI: https://doi.org/10.1193/1.4000064
Ahmad N, Shahzad A, Ali Q, Rizwan M and Khan AN (2018). “Seismic fragility functions for code compliant and non-compliant RC SMRF structures in Pakistan”. Bulletin of Earthquake Engineering, 16(10): 4675-4703. https://doi.org/10.1007/s10518-018-0377-x DOI: https://doi.org/10.1007/s10518-018-0377-x
Vamvatsikos D and Cornell C (2002). “Incremental dynamic analysis”. Earthquake Engineering and Structural Dynamics, 31(3): 491-514. https://doi.org/10.1002/eqe.141 DOI: https://doi.org/10.1002/eqe.141
Der Kiureghian A (2005). “First- and second-order reliability methods” Chapter 14 in Engineering Design Reliability Handbook. Editors: Nikolaidis E, Ghiocel DM and Singhal S, CRC Press LLC.
Baker JW (2015). “Efficient analytical fragility function fitting using dynamic structural analysis”. Earthquake Spectra, 31(1): 579-599. https://doi.org/10.1193/021113EQS025M DOI: https://doi.org/10.1193/021113EQS025M
Koopaee ME, Dhakal RP and MacRae G (2017). “Effect of ground motion selection methods on seismic collapse fragility of RC frame buildings”. Earthquake Engineering and Structural Dynamics, 46(11): 1875-1892. https://doi.org/10.1002/eqe.2891 DOI: https://doi.org/10.1002/eqe.2891
Baker JW and Cornel CA (2006). “Spectral shape, epsilon, and record selection”. Earthquake Engineering and Structural Dynamics, 35(9): 1077-1095. https://doi.org/10.1002/eqe.571 DOI: https://doi.org/10.1002/eqe.571
Tena-Colunga A and Cortes-Benitez JA (2015). “Assessment of redundancy factor for the seismic design of special moment resisting reinforced concrete frames”. Latin American Journal of Solids and Structures, 12(12): 2330-2350. http://dx.doi.org/10.1590/1679-78251800 DOI: https://doi.org/10.1590/1679-78251800