Investigation on Deflection Amplification Factor for Special Moment Resisting Frames with Soft Story

Document Type : Research Article


1 Department of Civil Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 aDepartment of Civil Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran


One of the most common irregularities in structures is the irregularity in height and lateral stiffness. Due to the commonness of the use of irregular structures and also the different seismic responses of this type of structures, in comparison with regular structures, investigating the seismic response of irregular structures has always been the subject of several research studies. The structures designed for the reduced base shear, under the design earthquake, have inelastic response. To calculate the real (inelastic) displacements of structures under the design earthquake, the displacements obtained from the reduced base shear, are amplified by the deflection amplification factor (Cd). Seismic codes have dedicated a Cd for each structural system. But different studies have shown that the dedicated Cd by the codes cannot accurately estimate the real displacements. The main purpose of this research is to propose the Cd values for more accurately estimating the maximum inter-story drift ratio (MIDR) and maximum roof drift ratio (MRDR) in steel special moment resisting frames (SMRFs) with the soft story. The number of stories and the location of the soft story are the variables considered in this research. The results show that the use of Cd = 5.5, recommended by the 2800 standard and ASCE 7-16 for steel SMRFs, underestimates the real MIDR and also MRDR, under the design earthquake. It is shown that by increasing the number of stories, the mean Cd obtained from the analyses increases. The reason for this issue is the P-Δ effects that increase by increasing the number of stories. In addition, it is shown that a specified trend cannot be found between the location of the soft story and the mean Cd values in the stories of the structures. Thus, for more accurately estimating MIDR in the considered structures, under the design earthquake, Cd = 8.5 is proposed. Furthermore, for more accurately estimating MRDR, Cd roof = 8.0 is proposed.


Main Subjects

[1] ASCE/SEI-7-16 Minimum Design Loads for Buildings and Other Structures. Structural Engineering Institute of the American Society of Civil Engineers: Reston, Virginia, 2016.
[2] Standard No.  2800. Iranian code of practice for seismic resistant design of building. 4th Edition. Road, Housing and Urban Development Research Center, Tehran, Iran, 2014. (in Persian)
[3] M. Amiri, M. Yakhchalian, Performance of intensity measures for seismic collapse assessment of structures with vertical mass irregularity. Structures, 24 (2020) 728-741.
[4] B.J. Choi, Hysteretic energy response of steel moment-resisting frames with vertical mass irregularities, The Structural Design of Tall and Special Buildings, 13(2) (2004) 123-144.
[5] T.L. Karavasilis, N. Bazeos, D.E. Beskos, Estimation of seismic inelastic deformation demands in plane steel MRF with vertical mass irregularities, Engineering structures, 30(11) (2008) 3265-75.
[6] E.V. Valmundsson and J.M. Nau, Seismic response of building frames with vertical structural irregularities, Journal of Structural Engineering, 123(1) (1997) 30-41.
[7] A.A. Al-Ali, Effects of vertical irregularities on seismic behavior of building structures, John A. Blume Earthquake Engineering Center, Stanford University, 1999.
[8] S. Das, J.M. Nau, Seismic design aspects of vertically irregular reinforced concrete buildings, Earthquake Spectra, 19(3) (2003) 455-477.
[9] C. Chintanapakdee, A.K. Chopra, Seismic response of vertically irregular frames: response history and modal pushover analyses, Journal of Structural Engineering, 130(8) (2004) 1177-1185.
[10] M. Ouazir, A. Kassoul, A. Ouazir, B. Achour, Inelastic seismic response of torsionally unbalanced structures with soft first story, Asian Journal of Civil Engineering, 19(5) (2018) 571-581.
[11] R.M. Oinam, D.R. Sahoo, Numerical evaluation of seismic response of soft-story RC frames retrofitted with passive devices, Bulletin of Earthquake Engineering, 16(2) (2018) 983-1006.
[12] M. Pirizadeh, H. Shakib, Probabilistic seismic performance evaluation of non-geometric vertically irregular steel buildings, Journal of Constructional Steel Research, 82 (2013) 88-98.
[13] R. Tremblay, L. Poncet, Seismic performance of concentrically braced steel frames in multistory buildings with mass irregularity, Journal of Structural Engineering, 131(9) (2005) 1363-75.
[14] M. Dolšek, P. Fajfar, Soft storey effects in uniformly infilled reinforced concrete frames, Journal of Earthquake Engineering 5(1) (2001) 1-12.
[15] M. De Stefano, B. Pintucchi, A review of research on seismic behaviour of irregular building structures since 2002, Bulletin of Earthquake Engineering, 6(2) (2008) 285-308.
[16] Z. Bohlouli, M. Poursha, Seismic evaluation of geometrically irregular steel moment resisting frames with setbacks considering their dynamic characteristics, Bulletin of Earthquake Engineering, 14(10) (2016) 2757-2777.
[17] T. Choudhury, H.B. Kaushik, Component level fragility estimation for vertically irregular reinforced concrete frames. Journal of Earthquake Engineering, 24(6) 2018 947-971.
[18] A. Tena-Colunga, D.A. Hernández-García, Peak seismic demands on soft and weak stories models designed for required code nominal strength, Soil Dynamics and Earthquake Engineering, 129 (2019) 105698.
[19] R. Soleimani, H Hamidi, Improved Substitute-Frame (ISF) model for seismic response of steel-MRF with vertical irregularities, Journal of Constructional Steel Research, 186 (2021) 106918.
[20] C.M. Uang, A. Maarouf, Deflection amplification factor for seismic design provisions, Journal of Structural Engineering, 120(8) 1994 2423-2436.
[21] R.K. Mohammadi, Approximate evaluation of deflection amplification factor, Journal of Structural Engineering, 128(2) (2002) 179-87.
[22] M. Zaker Salehi, A.A. Tasnimi, Amplification factor for estimation of maximum inelastic lateral displacement of reinforced concrete moment resisting frames, Modares Civil Engineering journal, 13(2) (2013) 67-78. (in Persian)
[23] O. Şeker, B. Akbas, J. Shen, A. Zafer Ozturk, Evaluation of deflection amplification factor in steel moment‐resisting frames, The Structural Design of Tall and Special Buildings, 23(12) (2014) 897-928.
[24] M. Samimifar, A. Vatani Oskouei, F. Rahimzadeh Rofooei, Deflection amplification factor for estimating seismic lateral deformations of RC frames, Earthquake Engineering and Engineering Vibration, 14(2) (2015): 373-384.
[25] A. Kuşy𝚤lmaz, C. Topkaya, Displacement amplification factors for steel eccentrically braced frames, Earthquake Engineering and Structural Dynamics, 44(2) (2015) 167-184.
[26] A. Kuşyılmaz, C. Topkaya, Evaluation of seismic response factors for eccentrically braced frames using FEMA P695 methodology, Earthquake Spectra, 32(1) (2016) 303-321.
[27] M. Yakhchalian, N. Asgarkhani, M. Yakhchalian, Evaluation of deflection amplification factor for steel buckling restrained braced frames, Journal of Building Engineering, 30 (2020) 101228.
[28] M. Yakhchalian, S. Abdollahzadeh, Investigation on deflection amplification factor for special moment resisting frames with vertical mass irregularity, Modares Civil Engineering journal 20(6) (2020) 163-173. (in Persian)
[29] M. Mohammadi, B. Kordbagh, Quantifying panel zone effect on deflection amplification factor, The Structural Design of Tall and Special Buildings, 27(5) (2018) e1446.
[30] Y.O. Özkılıç, M.B. Bozkurt, C. Topkaya, Evaluation of seismic response factors for BRBFs using FEMA P695 methodology, Journal of Constructional Steel Research, 151 (2018) 41-57.
[31] H. Abou-Elfath, Evaluating the inelastic displacement ratios of moment-resisting steel frames designed according to the Egyptian code, Earthquake Engineering and Engineering Vibration, 18(1) (2019) 159-170.
[32] E. Kizilarslan, M. Broberg, S. Shafaei, A.H. Varma, M. Bruneau, Seismic design coefficients and factors for coupled composite plate shear walls/concrete filled (CC-PSW/CF), Engineering Structures, 244 (2021) 112766.
[33] R. Soleimani, H. Hamidi, General Substitute Frame Model (GSF) for efficient estimation of seismic demands of steel and RC moment frames. Engineering Structures, 246, (2021) 113031.
[34] M. Mahmoudi, M. Jalili Sadr Abad, Assessment on the deflection amplification factor of steel buckling-restrained bracing frames, Advances in Structural Engineering, 25(2) (2022) 231-246.
[35] UBC, Uniform Building Codes, International Conference of Building Officials, Whittier, California, USA, 1991.
[36] NEHRP, Recommended provisions for the development of seismic regulations for new buildings, FEMA Report 223, Federal Emergency Management Agency, Washington, DC, USA, 1992.
[37] J. Kennedy, R.C. Eberhart, Particle Swarm Optimization, Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, IEEE Service Center, Piscataway, (1995) 1942-1948.
[38] SAC Joint Venture, State of the art report on systems performance of steel moment resisting frames subject to earthquake ground shaking, Report No. FEMA 355C, Washington DC, 2000.
[39] NIST GCR 10–917-8, Evaluation of the FEMA P695 methodology for quantification of building seismic performance factors. Gaithersburg, MD, 2010.
[40] ETABS, Computers and Structures Inc., User's Guide: Integrated Building Design Soft-ware. Computers and Structures, Inc, Berkeley, California, USA, 2017.
[41] AISC Committee. "Specification for Structural Steel Buildings (ANSI/AISC 360-16). " American Institute of Steel Construction, Chicago-Illinois, 2016.
[42] AISC, ANSI. "AISC 341-16, Seismic Provisions for Structural Steel Buildings." Chicago, IL: American Institute of Steel Construction, 2016.
[43] Open System for Earthquake Engineering Simulation (OpenSees). Pacific Earthquake Engineering Research Center, University of California, Berkeley,, 2015.
[44] H.R. Jamshidiaha, M. yakhchalian, New vector-valued intensity measure for predicting the collapse capacity of steel moment resisting frames with viscose dampers, Soil Dynamics and Earthquake Engineering, 125 (2019) 105625.
[45] R.A. Medina, H. Krawinkler, Evaluation of drift demands for the seismic performance assessment of frames, Journal of Structure Engineering, 131(7) (2005) 1003-1013.
[46] D.G. Lignos, H. Krawinkler, Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading, Journal of Structural Engineering, 137(11) (2011) 1291-1302.
[47] S. Mazzoni, F. McKenna, M.H. Scott, G.L. Fenves, OpenSees command language manual. Pacific Earthquake Engineering Research (PEER) Center, 2006.
[48] SAC Joint Venture. Proceedings of the invitational workshop on steel seismic issues. Report No. SAC 94-01, Los Angeles, CA, 1994.
[49] H.R. Jamshidiha, M. Yakhchalian, B. Mohebi, Advanced scalar intensity measures for collapse capacity prediction of steel moment resisting frames with fluid viscous dampers, Soil Dynamics and Earthquake Engineering, 109 (2018) 102-118.
[50] C.B. Haselton, G.G. Deierlein, Assessing Seismic Collapse Safety of Modern Reinforced Concrete Moment-Frame Building, Peer Report 2007/08, Pacific Engineering Research Center, University of California, California, 2008.
[51] PEER NGA, Database. The pacific earthquake engineering research center, University of California at Berkeley, 2018.
[52] F.A. Charney, Seismic loads: Guide to the seismic load provisions of ASCE 7-10, American Society of Civil Engineers, 2015.
[53] M.H. Soleimani-Babakamali, K. Nasrollahzadeh, A. Moghadam, Iterative-R: A reliability-based calibration framework of response modification factor for steel frames, Steel and Composite Structures, 42(1) (2022) 59-74.
[54] L. Shen, L. Rong-Rong, W. De-Fa, P. Xiu-Zhen, G. Hong-Chao, Response Modification Factor and Displacement Amplification Factor of Y-Shaped Eccentrically Braced High-Strength Steel Frames, International Journal of Steel Structures, 21(5) (2021) 1823-1844.