Comparative study on the linear and nonlinear dynamic analysis of typical RC buildings
DOI:
https://doi.org/10.7764/RDLC.23.3.587Abstract
A careful evaluation has been carried out to reveal advantages and disadvantages of linear and nonlinear modelling in dynamic analysis. 4- and 7- story building models representing characteristics of about 500 existing buildings models in Turkey was used in analyses. In the study, displacement demand parameters such as roof drift ratio and interstory drift ratio obtained from linear and nonlinear analyses were compared using a total of 24 ground motion records including forward directivity effects (Set 2) as well as records (Set 1) recorded in type B and C soils. Although the seismic demands for Set 2 are obtained extremely high in the nonlinear models, the demand differences between Set 1 and Set 2 are not excessive for the linear models. In the region where the T/Tp ratio is close to one, the linear analysis predicts unrealistically high demands compared to the nonlinear analysis. Linear analysis results mostly show an increase or decrease depending on dynamic amplification effects. The effects of ground motion intensity and damage mechanism cannot be observed in linear analysis method. For all these reasons, it is recommended not to prefer linear modeling method when using time-history analysis.
Downloads
References
ACI, (2002). American Concrete Institute 2002. Building code requirements for structural concrete (ACI 318-02) and commentary (ACI 318R-02). Farm-ington Hills, Michigan.
Amadio, C., Fragiacomo, M., and Rajgelj, S. (2003). The effects of repeated earthquake ground motions on the non-linear response of SDOF systems. Earthq Eng Struct Dyn, 32(2), 291–308. https://doi.org/10.1002/eqe.225
Antoniou, K., Tsionis, G., and Fardis M.N. (2015). Inelastic shears in ductile RC walls of mid-rise wall-frame buildings and comparison to Eurocode 8. Bull Earthq Eng, 13, 841–869. https://doi.org/10.1007/s10518-014-9641-x
Aydemir, M.E. (2013a). Inelastic displacement ratios for evaluation of stiffness degrading structures with soil structure interaction built on soft soil sites. Struct Eng Mech, 45(6), 741–758. https://doi.org/10.12989/sem.2013.45.6.741
Aydemir, M.E. (2013b). Soil structure interaction effects on structural parameters for stiffness degrading systems built on soft soil sites. Struct Eng Mech, 45(5), 655–676. https://doi.org/10.12989/sem.2013.45.5.655
Aydinoǧlu, M.N. (2003). An incremental response spectrum analysis procedure based on inelastic spectral displacements for multi-mode seismic perfor-mance evaluation. Bull Earthq Eng, 1(1), 3–36. https://doi.org/10.1023/A:1024853326383
Bakir, P.G., De Roeck, G., Degrande, G., and Wong, K.K.F. (2007). Seismic risk assessment for the mega-city of Istanbul: Ductility, strength and maximum interstory drift demands. Soil Dyn Earthq Eng, 27(12), 1101–1117. https://doi.org/10.1016/j.soildyn.2006.12.006
Benaied, B., Hemsas, M., Benanane, A., & Hentri, M. (2023). Seismic analysis of RC building frames with vertical mass and stiffness irregularities using adaptive pushover analysis. Revista de la construcción, 22(3), 597-612. https://doi.org/10.7764/RDLC.22.3.597
Bikçe, M., and Çelik, T.B. (2016). Failure analysis of newly constructed RC buildings designed according to 2007 Turkish Seismic Code during the October 23, 2011 Van earthquake. Eng Fail Anal 64: 67–84. https://doi.org/10.1016/j.engfailanal.2016.03.008
Binici, B., Yakut, A., Ozcebe, G., and Erenler, A. (2015). Provisions for the seismic risk evaluation of existing reinforced concrete buildings in Turkey under the urban renewal law. Earthq Spectra, 31(3), 1353–1370. https://doi.org/10.1193/040513EQS093M
Borekci, M., and Kirçila, M.S. (2011). Fragility analysis of R/C frame buildings based on different types of hysteretic model. Struct Eng Mech, 39(6), 795–812. https://doi.org/10.12989/sem.2011.39.6.795
Borzi, B., and Elnashai, A.S. (2000). Assessment of inelastic response of buildings using force- and displacement-based approaches. Struct Des Tall Build, 9(4), 251–277. https://doi.org/10.1002/1099-1794(200009)9:4<251::AID-TAL151>3.0.CO;2-V
Bray, J.D., and Rodriguez-Marek, A. (2004). Characterization of forward-directivity ground motions in the near-fault region. Soil Dyn Earthq Eng, 24(11), 815–828. https://doi.org/10.1016/j.soildyn.2004.05.001
Cakir, F., Uckan, E., Shen, J., Seker, B.S., and Akbas, B. (2015). Seismic damage evaluation of historical structures during Van earthquake, October 23, 2011. Eng Fail Anal, 58, 249–266. https://doi.org/10.1016/j.engfailanal.2015.08.030
Causevic, M., and Mitrovic, S. (2011). Comparison between non-linear dynamic and static seismic analysis of structures according to European and US provisions. Bull Earthq Eng, 9, 467–489. https://doi.org/10.1007/s10518-010-9199-1
Çavdar, Ö, and Bayraktar, A. (2014). Pushover and nonlinear time history analysis evaluation of a RC building collapsed during the Van (Turkey) earth-quake on October 23, 2011. Nat Hazards, 70, 657–673. https://doi.org/10.1007/s11069-013-0835-3
Cayci, B.T., and Akpinar, M. (2021). Seismic pounding effects on typical building structures considering soil-structure interaction. Structures, 34, 1858–1871. https://doi.org/10.1016/j.istruc.2021.08.133
Cayci, B.T., Inel, M., and Ozer, E. (2021). Effect of soil–structure interaction on seismic behavior of mid- and low-rise buildings. Int J Geomech, 21(3), 04021009. https://doi.org/10.1061/(asce)gm.1943-5622.0001944
Çelik, S. (2011). Determination with non-linear time history analysis of displacement demands of low and mid-rise reinforced concrete buildings. MSc thesis, Pamukkale University, Denizli, Turkey.
Chaulagain, H., Rodrigue,s H., Jara, J., Spacone, E., and Varum, H. (2013). Seismic response of current RC buildings in Nepal: A comparative analysis of different design/construction. Eng Struct, 49, 284–294. https://doi.org/10.1016/j.engstruct.2012.10.036
Chopra, A.K. (1995). Dynamic of structure: Theory and applications to earthquake engineering. Prentice Hall.
Cirak Karakas, C., Palanci, M., and Senel, S. M. (2022). Fragility based evaluation of different code based assessment approaches for the performance estimation of existing buildings. Bulletin of Earthquake Engineering, 20(3), 1685-1716. https://doi.org/10.1007/s10518-021-01292-w
Das, A., Banerjee, A., Sahoo, D. R., & Matsagar, V. (2024). Performance comparison of linear and nonlinear compliant liquid dampers-inerter in control-ling across-wind response of benchmark tall building. Journal of Building Engineering, 90, 109400. https://doi.org/10.1016/j.jobe.2024.109400
Demir, A., Palanci, M., and Kayhan, A. H. (2020). Evaluation of supplementary constraints on dispersion of EDPs using real ground motion record sets. Arabian Journal for Science and Engineering, 45(10), 8379-8401. https://doi.org/10.1007/s13369-020-04719-9
Demir, A., Palanci, M., and Kayhan, A. H. (2021). Probabilistic assessment for spectrally matched real ground motion records on distinct soil profiles by simulation of SDOF systems. Earthquakes and Structures, 21(4), 395-411. https://doi.org/10.12989/eas.2021.21.4.395
Demir, A., Kayhan, A. H., and Palanci, M. (2023). Response-and probability-based evaluation of spectrally matched ground motion selection strategies for bi-directional dynamic analysis of low-to mid-rise RC buildings. Structures , 58, 105533. https://doi.org/10.1016/j.istruc.2023.105533
Demir, A., Palanci, M., and Kayhan, A. H. (2024). Evaluation the effect of amplitude scaling of real ground motions on seismic demands accounting different structural characteristics and soil classes. Bulletin of Earthquake Engineering, 22(2), 365-393. https://doi.org/10.1007/s10518-023-01780-1
Efraimiadou, S., Hatzigeorgiou, G.D., and Beskos, D.E. (2013). Structural pounding between adjacent buildings subjected to strong ground motions. Part I: The effect of different structures arrangement. Earthq Eng Struct Dyn, 42(10), 1509–1528. https://doi.org/10.1002/eqe.2285
El-Betar, S.A. (2017). Seismic performance of existing RC framed buildings. HBRC J, 13(2), 171–180. https://doi.org/10.1016/j.hbrcj.2015.06.001
Elnashai, A.S. (2000). Analysis of the damage potential of the Kocaeli (Turkey) earthquake of 17 August 1999. Eng Struct, 22(7), 746–754. https://doi.org/10.1016/S0141-0296(99)00104-2
Erduran, E. (2008). Assessment of current nonlinear static procedures on the estimation of torsional effects in low-rise frame buildings. Eng Struct, 30(9), 2548–2558. https://doi.org/10.1016/j.engstruct.2008.02.008
Eser, M., Aydemir, C., and Ekiz, I. (2012). Soil structure interaction effects on strength reduction factors. Struct Eng Mech, 41(3), 365–378. https://doi.org/10.12989/sem.2012.41.3.365
Eskandari, R., and Vafaei, D. (2015). Effects of near-fault records characteristics on seismic performance of eccentrically braced frames. Struct Eng Mech, 56(5), 855–870. https://doi.org/10.12989/sem.2015.56.5.855
Eurocode 8, (2005). Design of structures for earthquake resistance-Part 1. European Committee for Standardization.
Faisal, A., Majid, T.A., and Hatzigeorgiou, G.D. (2013). Investigation of story ductility demands of inelastic concrete frames subjected to repeated earth-quakes. Soil Dyn Earthq Eng, 44, 42–53. https://doi.org/10.1016/j.soildyn.2012.08.012
FEMA-356, (2000). Federal Emergency Management Agency 2000. Prestandard and Commentary for the Seismic Rehabilitation of Buildings. American Society of Civil Engineers (ASCE), Washington, USA.
Fontara, I.K.M., Kostinakis, K.G., Manoukas, G.E., and Athanatopoulou, A.M. (2015). Parameters affecting the seismic response of buildings under bi-directional excitation. Struct Eng Mech, 53(5), 957–979. https://doi.org/10.12989/sem.2015.53.5.957
Gallegos, M. F., Araya-Letelier, G., Lopez-Garcia, D., & Parra, P. F. (2023). Collapse Assessment of Mid-Rise RC Dual Wall-Frame Buildings Subjected to Subduction Earthquakes. Buildings, 13(4), 880. https://doi.org/10.3390/buildings13040880
Goel, R.K., and Chopra, A.K. (2005). Extension of modal pushover analysis to compute member forces. Earthq Spectra, 21(1), 125–139. https://doi.org/10.1193/1.1851545
Gonzales, H., and López-Almansa, F. (2012). Seismic performance of buildings with thin RC bearing walls. Eng Struct, 34, 244–258. https://doi.org/10.1016/j.engstruct.2011.10.007
Gunes, O. (2015). Turkey’s grand challenge: Disaster-proof building inventory within 20 years. Case Stud Constr Mater, 2, 18–34. https://doi.org/10.1016/j.cscm.2014.12.003
Hancilar, U., Çaktö, E., Erdik, M., Franco, G., and Deodatis, E.G. (2014). Earthquake vulnerability of school buildings: Probabilistic structural fragility analyses. Soil Dyn Earthq Eng, 67, 169–178. https://doi.org/10.1016/j.soildyn.2014.09.005
Hatzigeorgiou, G.D. (2010a). Behavior factors for nonlinear structures subjected to multiple near-fault earthquakes. Comput Struct, 88, 309–321. https://doi.org/10.1016/j.compstruc.2009.11.006
Hatzigeorgiou, G.D. (2010b). Ductility demand spectra for multiple near- and far-fault earthquakes. Soil Dyn Earthq Eng, 30(4), 170–183. https://doi.org/10.1016/j.soildyn.2009.10.003
Hatzigeorgiou, G.D., and Beskos, D.E. (2009). Inelastic displacement ratios for SDOF structures subjected to repeated earthquakes. Eng Struct, 31(11), 2744–2755. https://doi.org/10.1016/j.engstruct.2009.07.002
Hatzigeorgiou, G.D., and Liolios, A.A. (2010). Nonlinear behaviour of RC frames under repeated strong ground motions. Soil Dyn Earthq Eng, 30(10), 1010–1025. https://doi.org/10.1016/j.soildyn.2010.04.013
Hatzigeorgiou, G.D., Papagiannopoulos, G.A., and Beskos, D.E. (2011). Evaluation of maximum seismic displacements of SDOF systems from their residual deformation. Eng Struct, 33(12), 3422–3431. https://doi.org/10.1016/j.engstruct.2011.07.006
Hatzivassiliou, M., and Hatzigeorgiou, G.D. (2015). Seismic sequence effects on three-dimensional reinforced concrete buildings. Soil Dyn Earthq Eng, 72, 77–88. https://doi.org/10.1016/j.soildyn.2015.02.005
Inel, M., Cayci, B.T., and Meral, E. (2018). Nonlinear static and dynamic analyses of RC buildings. Int J Civ Eng, 16, 1241–1259. https://doi.org/10.1007/s40999-018-0285-0
Inel, M., Çelik, S., Ozmen, H.B., and Önür, Ö. (2010). Evaluation of seismic displacement demands of existing reinforced concrete buildings using nonline-ar time history analysis subjected to forward directivity ground motions. Seventh Natl Conf Earthq Eng, Istanbul, Turkey.
Kalkan, E., and Kunnath, S.K. (2007). Assessment of current nonlinear static procedures for seismic evaluation of buildings. Eng Struct, 29(3), 305–316. https://doi.org/10.1016/j.engstruct.2006.04.012
Kamal, M. (2022). Code-based new approaches for determining the minimum required separation gap. Structures, 46, 750-764. https://doi.org/10.1016/j.istruc.2022.10.075
Kamal, M., and Inel, M. (2022a). Simplified approaches for estimation of required seismic separation distance between adjacent reinforced concrete buildings. Eng Struct, 252, 113610. https://doi.org/10.1016/j.engstruct.2021.113610
Kamal, M., and Inel, M. (2022b). A new equation for prediction of seismic gap between adjacent buildings located on different soil types. J Build Eng, 57, 104784. https://doi.org/10.1016/j.jobe.2022.104784
Kamal, M., and Inel, M. (2021). Correlation between ground motion parameters and displacement demands of mid-rise rc buildings on soft soils consider-ing soil-structure-interaction. Buildings, 11(3), 125. https://doi.org/10.3390/buildings11030125
Kamal, M., Inel, M., and Cayci, B.T. (2022). Seismic behavior of mid-rise reinforced concrete adjacent buildings considering soil-structure interaction. J Build Eng, 51, 104296. https://doi.org/10.1016/j.jobe.2022.104296
Kappos, A.J., and Panagopoulos, G. (2004). Performance-based seismic design of 3D R/C buildings using inelastic analysis procedures. ISET Journal of Earthquake Technology, 41(1), 141–158.
Kayhan, A. H., Demir, A., and Palanci, M. (2018). Statistical evaluation of maximum displacement demands of SDOF systems by code-compatible nonlinear time history analysis. Soil Dynamics and Earthquake Engineering, 115, 513-530. https://doi.org/10.1016/j.soildyn.2018.09.008
Koçak, A. (2015). Earthquake performance of FRP retrofitting of short columns around band-type windows. Struct Eng Mech, 53(1), 1–16. https://doi.org/10.12989/sem.2015.53.1.001
Koçak, A., Zengin, B., and Kadioğlu, F. (2015). Performance assessment of irregular RC buildings with shear walls after Earthquake. Eng Fail Anal, 55, 157–168. https://doi.org/10.1016/j.engfailanal.2015.05.016
Kokot, S., Anthoine, A., Negro, P., and Solomos, G. (2012). Static and dynamic analysis of a reinforced concrete flat slab frame building for progressive collapse. Eng Struct, 40, 205–217. https://doi.org/10.1016/j.engstruct.2012.02.026
Korkmaz, K.A., Kayhan, A.H., and Ucar, T. (2013). Seismic assessment of R/C residential buildings with infill walls in Turkey. Comput Concr, 12(5), 681–695. https://doi.org/10.12989/cac.2013.12.5.681
Krawinkler, H. (1996). Pushover analysis why when and not to use it. Proc 1996 Conv Struct Eng Assoc Calif, 17–36.
Li, S., Zuo, Z., Zhai, C., and Xie, L. (2017). Comparison of static pushover and dynamic analyses using RC building shaking table experiment. Eng Struct, 136, 430–440. https://doi.org/10.1016/j.engstruct.2017.01.033
Liao, W.I., Loh, C.H., and Wan, S. (2001). Earthquake responses of RC moment frames subjected to near‐fault ground motions. Struct Des Tall Build, 10(3), 219–229. https://doi.org/10.1002/tal.178
López-López, A., Tomás, A., and Sánchez-Olivares, G. (2016). Influence of adjusted models of plastic hinges in nonlinear behaviour of reinforced con-crete buildings. Eng Struct, 124, 245–257. https://doi.org/10.1016/j.engstruct.2016.06.021
Massumi, A., and Gholami, F. (2016). The influence of seismic intensity parameters on structural damage of RC buildings using principal components analysis. Appl Math Model, 40(3), 2161–2176. https://doi.org/10.1016/j.apm.2015.09.043
Memari, A.M., Motlagh, A.Y., and Scanlon, A. (2000). Seismic evaluation of an existing reinforced concrete framed tube building based on inelastic dynamic analysis. Eng Struct, 22(6), 621–637. https://doi.org/10.1016/S0141-0296(99)00020-6
Meral, E. (2021). Determination of seismic isolation effects on irregular RC buildings using friction pendulums. Structures, 34, 3436–3452. https://doi.org/10.1016/j.istruc.2021.09.062
Meral, E. (2024). Relationships between ground motion parameters and energy demands for regular low-rise RC frame buildings. Bulletin of Earthquake Engineering, 22(6), 2829-2865. https://doi.org/10.1007/s10518-024-01885-1
Miranda, E. (1993). Site-dependent strength reduction factors. J Struct Eng ASCE, 119(12), 3503–3519.
Moon, K.H., Han, S.W., and Lee, C.S. (2017). Seismic retrofit design method using friction damping systems for old low- and mid-rise regular reinforced concrete buildings. Eng Struct, 146, 105–117. https://doi.org/10.1016/j.engstruct.2017.05.031
Mosleh, A., Rodrigues, H., Varum, H., Costa, A., and Arêde, A. (2016). Seismic behavior of rc building structures designed according to current codes. Structures, 7, 1–13. https://doi.org/10.1016/j.istruc.2016.04.001
Moustafa, A., and Takewaki, I. (2011). Response of nonlinear single-degree-of-freedom structures to random acceleration sequences. Eng Struct, 33(4), 1251–1258. https://doi.org/10.1016/j.engstruct.2011.01.002
Mwafy, A.M., and Elnashai, A.S. (2001). Static pushover versus dynamic collapse analysis of RC buildings. Eng Struct, 23, 407–424. https://doi.org/10.1016/S0141-0296(00)00068-7
Naserkhaki, S., Aziz, F.N.A.A., and Pourmohammad, H. (2012). Parametric study on earthquake induced pounding between adjacent buildings. Struct Eng Mech, 43(4), 503–526. https://doi.org/10.12989/sem.2012.43.4.503
Ni, P. (2014). Seismic assessment and retrofitting of existing structure based on nonlinear static analysis. Struct Eng Mech, 49(5), 631–644.
Önür, Ö, (2011). Determination with linear time history analysis of displacement demands of low and mid-rise reinforced concrete buildings. MSc thesis, Pamukkale University, Denizli, Turkey.
Oz, I., Senel, S. M., Palanci, M., and Kalkan, A. (2020). Effect of soil-structure interaction on the seismic response of existing low and mid-rise RC build-ings. Applied Sciences, 10(23), 8357. https://doi.org/10.3390/app10238357
Ozer, E., Inel, M., and Cayci, B.T. (2022a). Seismic behavior of LRB and FPS type isolators considering torsional effects. Structures, 37, 267–283. https://doi.org/10.1016/j.istruc.2022.01.011
Ozer, E., Inel, M., and Cayci B.T. (2022b). Seismic performance comparison of fixed and base-isolated models. Iran J Sci Technol - Trans Civ Eng, 47, 1007-1023. https://doi.org/10.1007/s40996-022-00936-4
Ozmen, H.B. (2011). Evaluation of factors that affects seismic performance of low and mid-rise reinforced concrete buildings. PhD thesis, Pamukkale University, Denizli, Turkey.
Ozmen, H.B., Inel, M., Senel, S.M., and Kayhan, A.H. (2015). Load carrying system characteristics of existing Turkish RC building stock. Int J Civ Eng, 13(1), 76–91.
Palanci, M., Senel, S. M., and Kalkan, A. (2017). Assessment of one story existing precast industrial buildings in Turkey based on fragility curves. Bulletin of Earthquake Engineering, 15, 271-289. https://doi.org/10.1007/s10518-016-9956-x
Palanci, M., Kayhan, A. H., and Demir, A. (2018). A statistical assessment on global drift ratio demands of mid-rise RC buildings using code-compatible real ground motion records. Bulletin of earthquake engineering, 16(11), 5453-5488. https://doi.org/10.1007/s10518-018-0384-y
Palanci, M., and Senel, S. M. (2019). Correlation of earthquake intensity measures and spectral displacement demands in building type structures. Soil Dynamics and Earthquake Engineering, 121, 306-326. https://doi.org/10.1016/j.soildyn.2019.03.023
Palanci, M., Demir, A., and Kayhan, A. H. (2023). Quantifying the effect of amplitude scaling of real ground motions based on structural responses of vertically irregular and regular RC frames. Structures, 51, 105-123. https://doi.org/10.1016/j.istruc.2023.03.040
Priestley, N. (1995). Myths and fallacies in earthquake engineering - conflicts between design and reality. ACI Spec Publ, 157, 231–254. https://doi.org/10.14359/983
RezaTabatabaiefar, S.H., Fatahia, B., and Samali, B. (2013). Lateral seismic response of building frames considering dynamic soil-structure interaction effects. Struct Eng Mech, 45, 307–317. https://doi.org/10.12989/sem.2013.45.3.311
Ruiz-García, J., and Miranda, E. (2006). Residual displacement ratios for assessment of existing structures. Earthq Eng Struct Dyn, 35(3), 315–336. https://doi.org/10.1002/eqe.523
SAP2000, (2018). Integrated finite element analysis and design of structures basic analysis reference manual.
Somerville, P.G. (2003). Magnitude scaling of the near fault rupture directivity pulse. Phys Earth Planet Inter, 137, 201–212. https://doi.org/10.1016/S0031-9201(03)00015-3
Somerville, P.G. (1997). Engineering characteristics of near fault ground motion. in: SMIP Semin Proc, California.
Somerville P.G. (1989). Development of an improved representation of near-fault ground motions. in: SMIP89 Semin Proc, California.
Subramanian, K., and Velayutham, M. (2014). Seismic performance of lateral load resisting systems. Struct Eng Mech, 51(3), 487–502. https://doi.org/10.12989/sem.2014.51.3.487
Tabatabaiefar, H.R., Fatahi, B., Ghabraie, K., and Zhou, W.H. (2015). Evaluation of numerical procedures to determine seismic response of structures under influence of soil-structure interaction. Struct Eng Mech, 56(1), 27–47. https://doi.org/10.12989/sem.2015.56.1.027
Turkish Earthquake Code (TEC) (1975). Specifications for buildings to be built in seismic areas. Ministry of Public Works and Settlement, Ankara, Turkey.
Turkish Earthquake Code (TEC) (1998). Specifications for buildings to be built in seismic areas. Ministry of Public Works and Settlement, Ankara, Turkey.
Turkish Earthquake Code (TEC) (2007). Specifications for buildings to be built in seismic areas. Ministry of Public Works and Settlement, Ankara, Turkey.
Tedesco, J.W., McDougal, W.G., and Ross, C.A. (1998). Structural dynamics: Theory and application. Addison Wesley Longman Inc.
Tremayne, B., and Kelly, T.E. (2005). Time history analysis as a method of implementing performance based design. 2005 NZSEE Conf.
USGS, (2016). United States Geological Survey. Earthquake Hazards Program. http://earthquake.usgs.gov/. Accessed 04 May 2023.
Van Nguyen, D., Kim, D., and Choo, Y. (2024). Nonlinear seismic performance of buildings considering deep excavation-soil-structure interaction. Bulletin of Earthquake Engineering, 22(10), 5119-5145. https://doi.org/10.1007/s10518-024-01966-1
Wilkinson, S.M., and Hiley, R.A. (2006). A non-linear response history model for the seismic analysis of high-rise framed buildings. Comput Struct, 84, 318–329. https://doi.org/10.1016/j.compstruc.2005.09.021
Zhou, J., He, F., and Liu, T. (2014). Curvature ductility of columns and structural displacement ductility in RC frame structures subjected to ground mo-tions. Soil Dyn Earthq Eng, 63, 174–183. https://doi.org/10.1016/j.soildyn.2014.03.009
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Emrah Meral, Bayram Tanik Cayci , Mehmet Inel
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
