Methods of analysis for buildings with uni-axial and bi-axial asymmetry in regions of lower seismicity

  • Lumantarna, Elisa (Department of Infrastructure Engineering, The University of Melbourne) ;
  • Lam, Nelson (Swinburne University of Technology, Sarawak Campus) ;
  • Wilson, John (Swinburne University of Technology, Sarawak Campus)
  • Received : 2017.12.11
  • Accepted : 2018.04.10
  • Published : 2018.07.25


Most buildings feature core walls (and shear walls) that are placed eccentrically within the building to fulfil architectural requirements. Contemporary earthquake design standards require three dimensional (3D) dynamic analysis to be undertaken to analyse the imposed seismic actions on this type of buildings. A static method of analysis is always appealing to design practitioners because results from the analysis can always be evaluated independently by manual calculation techniques for quality control purposes. However, the equivalent static analysis method (also known as the lateral load method) which involves application of an equivalent static load at a certain distance from the center of mass of the buildings can generate results that contradict with results from dynamic analysis. In this paper the Generalised Force Method of analysis has been introduced for multi-storey buildings. Algebraic expressions have been derived to provide estimates for the edge displacement ratio taking into account the effects of dynamic torsional actions. The Generalised Force Method which is based on static principles has been shown to be able to make accurate estimates of torsional actions in seismic conditions. The method is illustrated by examples of two multi-storey buildings. Importantly, the black box syndrome of a 3D dynamic analysis of the building can be circumvented.


  1. Anagnostopoulos, S.A., Kyrkos, M.T. and Stathopoulos, K.G. (2015), "Earthquake induced torsion in buildings: critical review and state of the art", Earthq. Struct., 8(2), 305-377.
  2. ASCE (2000), Prestandard and Commentary for the Seismic Rehabilitation of Buildings FEMA 356, Federal Emergency Management Agency, Washington, D.C., USA.
  3. Building Seismic Safety Council (2003), NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures Part I: Provisions (FEMA 450-1), Federal Emergency Management Agency; Washington, D.C., USA.
  4. Ceci, A.M., Contento, A., Fanale, L., Galeota, D., Gattulli, V., Lepidi, M. and Potenza, F. (2010), "Structural performance of the historic and modern buildings of the University of L'Aquila during the seismic events of April 2009", Eng. Struct., 32(7), 1899-1924.
  5. Chandler, A.M. and Duan, X.N. (1997), "Performance of asymmetric code-designed buildings for serviceability and ultimate limit states", Earthq. Eng. Struct. Dyn., 26, 717-735.<717::AID-EQE672>3.0.CO;2-X
  6. Chandler, A.M. and Hutchinson, G.L. (1986), "Torsional coupling effects in the earthquake response of asymmetric buildings", Eng. Struct., 8, 222-236.
  7. Cimellaro, G.P., Giovine, T. and Lopez-Garcia, D. (2014) "Bidirectional pushover analysis of irregular structures", J. Struct. Eng., 140(9), 04014059.
  8. D'Ambrisi, A., De Stefano, M. and Tanganelli, M. (2009), "Use of Pushover Analysis for Predicting Seismic Response of Irregular Buildings: A Case Study", J. Earthq. Eng., 13, 1089-1100.
  9. Dempsey, K.M. and Tso, W.K. (1982), "An alternative path to seismic torsional provisions", Soil Dyn. Earthq. Eng., 1, 3-10.
  10. Dimova, S.L. and Alashki, I. (2003), "Seismic design of symmetric structures for accidental torsion", Bull. Earthq. Eng., 1, 303-320.
  11. EN 1998-1 (2004), Eurocode 8: Design of Structures for Earthquake Resistance - Part 1: General Rules, Seismic Actions and Rrules for Buildings, European Committee for Standardization, Brussels, Belgium.
  12. Ferraioli, M. (2015), "Case study of seismic performance assessment of irregular RC buildings: hospital structure of Avezzano (L'Aquila, Italy)", Earthq. Eng. Eng. Vib., 14(1), 141-156.
  13. Habibullah, A. (1992), ETABS Users Manual, Computers and Structures, Inc., Berkeley, California, USA.
  14. Lam, N.T.K., Wilson, J.L. and Lumantarna, E. (2016), "Simplified elastic design checks for torsionally balanced and unbalanced low-medium rise buildings in lower seismicity regions", Earthq. Struct., 11(5), 741-777.
  15. Lumantarna, E., Lam, N. and Wilson, J. (2013), "Displacementcontrolled behavior of asymmetrical single-story building Models", J. Earthq. Eng., 17(6), 902-917.
  16. Lumantarna, E., Mehdipanah, A., Lam, N. and Wilson, J. (2017), "Methods of structural analysis of buildings in regions of low to moderate seismicity", The 2017 World Congress on Advances in Structural Engineering and Mechanics (ASEM17), Ilsan, Korea, August-September .
  17. Magliulo, G., Maddaloni, G. and Cosenza, E. (2012), "Extension of N2 method to plan irregular buildings considering accidental eccentricity", Soil Dyn. Earthq. Eng., 43, 69-84.
  18. Poursha, M., Khoshnoudian, F. and Moghadam, A.S. (2014), "The extended consecutive modal pushover procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings under influence of two horizontal components of ground motions", Soil Dyn. Earthq. Eng., 63, 162-173
  19. Sommer, A. and Bachmann, H. (2005), "Seismic behavior of asymmetric RC wall buildings: principles and new deformationbased design method", Earthq. Eng. Struct. Dyn., 34(2), 101-124.
  20. Standards Australia (2007), AS 1170.4-2007 Structural Design Actions-Part 4 Earthquake Actions, Standards Australia, Sydney, Australia.
  21. Stathopoulos, K.G. and Anagnostopoulos, S.A. (2010), "Accidental design eccentricity: Is it important for the inelastic response of buildings to strong earthquakes?", Soil Dyn. Earthq. Eng., 30, 782-797.
  22. Tscinias, T.G. and Hutchinson, G.L. (1981), "Evaluation of code requirements for the earthquake resistant design of torsionally coupled buildings", Proc. Inst. Civ. Eng., 71, 821-843.
  23. Westenek, B., de la Llera, J. C., Junemann, R., Hube, M. A., Besa, J. J., Luders, C., ... and Jordan, R. (2013), "Analysis and interpretation of the seismic response of RC buildings in Concepcion during the February 27, 2010, Chile earthquake", Bull. Earthq. Eng., 11(1), 69-91.
  24. Wilson, J. and Lam, N. (2006), "Earthquake design of buildings in Australia using velocity and displacement principles", Aust. J. Struct. Eng., 6(2), 103-118.