A method for seismic design of RC frame buildings using fundamental mode and plastic rotation capacity


  • A. R. Vijayanarayanan
  • Rupen Goswami Indian Institute of Technology Madras
  • C. V. R. Murty




A seismic design method is proposed for RC frame buildings, with focus on two of the seven virtues of earthquake resistant buildings, namely deformation capacity and desirable collapse mechanism. Fundamental lateral translation mode of the building and plastic rotation capacity of beams are included as input to estimate lateral force demand. Guidelines are provided to proportion beam and column cross-sections through: (a) closed-form expressions of flexural rigidities to maximize participation of the fundamental mode, and (b) relative achievable plastic rotation capacity using current design and detailing practice. This method is seen to surpass two prominent displacement-based design methods reported in literature. Results of nonlinear static pushover and nonlinear time history analyses of buildings of three different heights designed by this and the said two methods are used to make a case for the proposed method; the proposed method is able to control plastic rotation demand in beams and provide at least 20% more lateral deformation capacity than the said methods.


Moehle JP (1992). “Displacement-based design of RC structures subjected to earthquakes”. Earthquake Spectra, 8(3): 403-428. https://doi.org/10.1193/1.1585688 DOI: https://doi.org/10.1193/1.1585688

Freeman SA (1998). “The capacity spectrum method as a tool for seismic design”. Proceedings of the Eleventh European Conference on Earthquake Engineering, Paris, France.

Aschheim MA and Black EF (2000). “Yield point spectra for seismic design and rehabilitation”. Earthquake Spectra, 16(2): 317-336. https://doi.org/10.1193/1.1586115 DOI: https://doi.org/10.1193/1.1586115

Browning JP (2001). “Proportioning of earthquake-resistant RC building structures”. Journal of Structural Division ASCE, 127(2): 145-151.

https://doi.org/10.1061/(ASCE)0733-9445(2001)127:2(145) DOI: https://doi.org/10.1061/(ASCE)0733-9445(2001)127:2(145)

Kappos AJ and Manafpour A (2001). “Seismic design of RC buildings with the aid of advanced analytical techniques”. Engineering Structures, 23(4): 319-332.

https://doi.org/10.1016/S0141-0296(00)00052-3 DOI: https://doi.org/10.1016/S0141-0296(00)00052-3

Chopra AK and Goel RK (2002). “A modal pushover analysis procedure for estimating seismic demands for buildings”. Earthquake Engineering and Structural Dynamics, 31(3): 561–582. https://doi.org/10.1002/eqe.144 DOI: https://doi.org/10.1002/eqe.144

Christopoulos C and Pampanin S (2004). “Towards performance-based seismic design of MDOF structures with explicit consideration of residual deformations”. ISET Journal, 41(1): 53-73.


Sullivan TJ, Priestley MJ and Calvi GM (2012). A Model Code for the Displacement-based Seismic Design of Structures. DBD12, ISBN 9788861980723, IUSS Press, Pavia, 105pp.

Vidot-Vega AL and Kowalsky MJ (2013). “Drift, strain limits and ductility demands for RC moment frames designed with displacement-based and force-based design methods”. Engineering Structures, 51: 128-140.

https://doi.org/10.1016/j.engstruct.2013.01.004 DOI: https://doi.org/10.1016/j.engstruct.2013.01.004

Bai J, Yang TY and Ou J (2018). “Improved performance-based plastic design of RC moment resisting frames: Development and a comparative study”. International Journal of Structural Stability and Dynamics, 18(4): 1-24.

https://doi.org/10.1142/S0219455418500505 DOI: https://doi.org/10.1142/S0219455418500505

Priestley MJN and Kowalsky MJ (2000). “Direct displacement based design of concrete buildings”. Bulletin of the New Zealand National Society for Earthquake Engineering, 33(4): 421-444.

https://doi.org/10.5459/bnzsee.33.4.421-444 DOI: https://doi.org/10.5459/bnzsee.33.4.421-444

Priestley MJN, Calvi GM and Kowalsky MJ (2007). “Direct displacement based seismic design of structures”. Proceedings of the NZSEE Conference on Earthquake Engineering, Palmerston North, New Zealand.


Pettinga JD and Priestley MJN (2005). “Dynamic behaviour of reinforced concrete frames designed with direct displacement-based design”. Journal of Earthquake Engineering, 9(2): 309-330.

https://doi.org/10.1142/S1363246905002419 DOI: https://doi.org/10.1142/S1363246905002419

Liao W-C (2010). “Performance-Based Plastic Design of Earthquake Resistant Reinforced Concrete Moment Frames”. PhD Dissertation, University of Michigan, USA, 184pp.

Chopra AK, Bertero VV and Mahin SA (1974). “Response of the Olive View Medical Center main building during the San Francisco earthquake”. Proceedings of the Fifth World Conference on Earthquake Engineering, Rome, 1:26-35.


Structural Engineers Association of California (SEAOC) Seismology Committee (1999). “Recommended Lateral Force Requirements and Commentary”. SEAOC, Sacramento, California, USA, 472pp.

Ambrose J and Vergun D (1995). Simplified Design for Wind and Earthquake Forces. ISBN 0471192112, John Wiley and Sons, New York, 376pp.

Arnold C (2001). Architectural Considerations, Seismic Design Handbook. ISBN 978-1-4615-1693-4, Edited by Naeim F, 2nd Edition, Kluvier Academic Publishers, Netherland, 277-328pp.

Moehle JP and Mahin SA (1991). “Observations on the behaviour of reinforced concrete buildings during earthquakes”. Earthquake Resistant Concrete Structures – Inelastic Response and Design, SP 127, ACI, Farmington Hill, MI, USA, 67-90pp.

Villaverde R (1997). Discussion of “A more rational approach to capacity design of seismic moment frame columns”. by Bondy KD, Earthquake Spectra, 13(2): 321–322. https://doi.org/10.1193/1.1585949 DOI: https://doi.org/10.1193/1.1585949

Dooley KL and Bracci JM (2001). “Seismic evaluation of column-to-beam strength ratios in reinforced concrete frames”. Structural Journal ACI, 98(6): 843-851.

Jan TS, Liu MW and Kao YC (2004). “An upper-bound pushover analysis procedure for estimating the seismic demands of high-rise buildings”. Engineering Structures, 26(1): 117-128.

https://doi.org/10.1016/j.engstruct.2003.09.003 DOI: https://doi.org/10.1016/j.engstruct.2003.09.003

Mamun A and Saatcioglu M (2017). “Seismic performance evaluation of moderately ductile RC frame structures using Perform-3D”. Proceedings of 16th World Conference on Earthquake Engineering, Santiago, Chile.


Priestley MJN (2003). Myths and Fallacies in Earthquake Engineering, Revisited. The Mallet Milne Lecture, 2003, ISBN 978-8873580096, IUSS Press, Pavia, 120pp.

Shanmugasundaram D (2012). “Improved Procedure for Design of Beams in Earthquake-Resistant RC Moment Frame Buildings”. Masters Thesis, Indian Institute of Technology Madras, India, 81pp.

ACI (2014). “Building Code Requirements for Structural Concrete (ACI 318-14)”. American Concrete Institute, Farmington Hills, MI, USA, 520pp.

CEN (2004). Design of Structures for Earthquake Resistance – Part 1: General Rules, Seismic Actions and Rules for Buildings (EN-1998-1:2004 - Eurocode 8)”. European Committee for Standardization, Brussels.

Lee HS (1996). “Revised rule for concept of strong-column weak-girder design”. Journal of Structural Engineering ASCE, 122(4): 359-364.

https://doi.org/10.1061/(ASCE)0733-9445(1996)122:4(359) DOI: https://doi.org/10.1061/(ASCE)0733-9445(1996)122:4(359)

Paulay T (2001). Comments on “Seismic evaluation of column-to-beam strength ratios in reinforced concrete frames”. by Dooley KL and Bracci JM. ACI Structural Journal, 98(6): 843-843. DOI: https://doi.org/10.14359/10751

Chao S-H and Goel SC (2008). “Performance-Based Plastic Design of Earthquake Resistant Steel Structures”. ISBN 9781580017145, International Code Council, 261pp.

ASCE (2017). “Seismic Evaluation and Retrofit of Existing Buildings (ASCE/SEI 41-17)”. American Society of Civil Engineers, Virginia, USA, 550pp.

NIST (2017). “Guidelines for Non-linear Structural Analysis for Design of Buildings, Part II b: Reinforced Concrete Moment Frames, NIST GCR17-917-46v3”. National Institute of Standards and Technology, NEHRP, USA, 135pp.


Priestley MJN (1995). “Displacement-based seismic assessment of existing reinforced concrete buildings”. Bulletin of the New Zealand National Society for Earthquake Engineering, 29(4): 256-272.

https://doi.org/10.5459/bnzsee.29.4.256-272 DOI: https://doi.org/10.5459/bnzsee.29.4.256-272

Fenwick R, Dely R and Davidson B (1999). “Ductility demand for uni-directional and reversing plastic hinges in ductile moment resisting frames”. Bulletin of the New Zealand National Society for Earthquake Engineering, 32(1):1-12. https://doi.org/10.5459/bnzsee.32.1.1-12 DOI: https://doi.org/10.5459/bnzsee.32.1.1-12

Vijayanarayan AR (2019). “Fundamental Lateral Mode Guided Plastic Rotation Capacity Based Seismic Design of RC Moment Frame Buildings”. PhD Dissertation, Indian Institute of Technology Madras, India, 238pp.

Vijayanarayanan AR, Goswami R and Murty CVR (2017). “Identifying stiffness irregularity in buildings using fundamental lateral mode shape”. Earthquakes and Structures, 12(4): 437-448.

https://doi.org/10.12989/eas.2017.12.4.437 DOI: https://doi.org/10.12989/eas.2017.12.4.437

BIS (2016). “Indian Standard Criteria for Earthquake Resistant Design of Structures (IS:1893; 2016-Part 1)”. Bureau of Indian Standards, New Delhi, India.

ASCE (2016). “Minimum Design Loads for Buildings and Other Structures (ASCE 7-16)”. American Society of Civil Engineers, Virginia, USA, 800pp.

Newmark NM and Hall WJ (1982). Earthquake Spectra and Design. ISBN 943198224, EERI, Berkley, California, 103pp.

Priestley MJN (1998). “Brief comments on elastic flexibility of reinforced concrete frames and significance to seismic design”. Bulletin of the New Zealand National Society for Earthquake Engineering, 31(4): 246-259.

https://doi.org/10.5459/bnzsee.31.4.246-259 DOI: https://doi.org/10.5459/bnzsee.31.4.246-259

FEMA (2009). “Quantification of Building Seismic Performance Factors (FEMA 695)”. Federal Emergency Management Agency, Washington DC, 421pp.

CSI (2015). Nonlinear Analysis and Performance Assessment for 3D Structures (PERFORM-3D). Computers and Structures Inc., USA.

FEMA (2009). “Effects of Strength and Stiffness Degradation on Seismic Response (FEMA P440A)”. Federal Emergency Management Agency, Washington DC, 312pp.

Sivaselvan MV and Reinhorn AM (1999). “Hysteretic Models for Cyclic Behavior of Deteriorating Inelastic Structures”. MCEER-99-0018, 136pp.

FEMA (2005). “Improvement of Nonlinear Static Seismic Analysis Procedures (FEMA 440)”. Federal Emergency Management Agency, Washington DC, USA, 392pp.

Huang Y-N, Whittaker AS, Luco N and Hamburger RO (2009). “Scaling ground motions for performance-based assessment of buildings”. Journal of Structural Engineering, ASCE, 137(3): 311-321.

https://doi.org/10.1061/(ASCE)ST.1943-541X.0000155 DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0000155

Reyes JC and Kalkan E (2012). “How many records should be used in an ASCE/SEI-7 ground motion scaling procedure?”. Earthquake Spectra, 28 (3): 1223-1242.

https://doi.org/10.1193/1.4000066 DOI: https://doi.org/10.1193/1.4000066

Sunitha P (2017). “Seismic Design of Low-Rise RC Moment Frame Buildings Rationalised with Earthquake Resistant Design Philosophy”. PhD Dissertation, Indian Institute of Technology Madras, India, 168pp.

Schultz AE (1992). “Approximating lateral stiffness of storeys in elastic frames”. Journal of Structural Engineering, ASCE, 118(1): 243-263. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1992)118:1(243)


Medina RA and Krawinkler H (2003). “Seismic Demands for Nondeteriorating Frame Structures and their Dependence on Ground motion”. Report No: 144, The John Blume Earthquake Engineering Center, USA.

Massena B, Bento R, Degee H and Candeias P (2018). “Direct displacement-based design for RC structures: Procedure, advantages and shortcomings”. Revista Portuguesa de Engenharia de Estruturas, 6: 67-88.




How to Cite

A.R., V., Goswami, R., & C. V. R., M. (2022). A method for seismic design of RC frame buildings using fundamental mode and plastic rotation capacity. Bulletin of the New Zealand Society for Earthquake Engineering, 55(2), 112–128. https://doi.org/10.5459/bnzsee.55.2.112-128