Bulletin of Earthquake Engineering

, Volume 17, Issue 2, pp 707–736 | Cite as

Simplified assessment of maximum interstory drift for RC buildings with irregular infills distribution along the height

  • M. Gaetani d’Aragona
  • M. PoleseEmail author
  • E. Cosenza
  • A. Prota
Original Research


This paper investigates on the effect of story lateral stiffness variation on the maximum elastic interstory drift ratio (IDRmax) for existing reinforced concrete (RC) buildings. Several classes of existing gravity load designed RC buildings are obtained via a simulated design approach. The presence of infills in the perimeter frames as well as different opening percentages along the height are considered. A simplified elastic analysis is performed, adopting an equivalent multistory cantilever system to represent the stiffness variation along the buildings height. IDRmax is significantly influenced by the ratio of the lateral stiffness at the second and upper stories over the lateral stiffness of the first story. Such a ratio has been found dependent on a number of geometric and configuration factors, including the variation of the opening percentage ratio. Two regression formulas are proposed to estimate, given the spectral displacement at the fundamental period T, the roof displacement and IDRmax as a function of the building height and the opening percentage at first and upper stories. Suitable modification of the formulas is also introduced to account for possible cracking of RC elements and infill panels even at very low levels of lateral drift. These expressions could be used for the simplified evaluation of the expected drift demands for buildings of existing RC typologies. Finally, the proposed formulations are applied to a number of permanently monitored buildings, comparing the calculated IDRmax with the one resulting from record processing, obtaining a fair good agreement.


Interstory drift ratio Reinforced concrete Existing building Infilled frame Lateral stiffness Openings Irregular frames Simplified method Spectral approach 



This study was performed within the framework of the joint program DPC-Reluis 2016 –special project RS4: Seismic observatory of structures and monitoring and of the joint program DPC-Reluis 2017–RC constructions - WP1: Vulnerability of RC constructions at the territorial scale. Detailed information on the studied monitored buildings in OSS and the RADOSS code were provided by Dr Daniele Spina of Department of Civil Protection, whose contribution is gratefully acknowledged.


  1. Akkar S, Yazgan U, Gülkan P (2005) Drift estimates in frame buildings subjected to near-fault ground motions. J Struct Eng 131(7):1014–1024CrossRefGoogle Scholar
  2. Al-Chaar G (2002) Evaluating strength and stiffness of unreinforced masonry infill structures. Rep. No. ERDC/CERL TR-02-1, U.S. Army Corps of Engineers, Champaign, ILGoogle Scholar
  3. Alonso-Rodríguez A, Miranda E (2016) Dynamic behavior of buildings with non-uniform stiffness along their height assessed through coupled flexural and shear beams. Bull Earthq Eng 14(12):3463–3483CrossRefGoogle Scholar
  4. ASCE/SEI 41-13 (2014) American Society of Civil Engineers. Seismic rehabilitation of existing buildings: ASCE standard ASCE/SEI 41-13. American Society of Civil Engineers, RestonGoogle Scholar
  5. Aslani H, Miranda E (2005) Probabilistic earthquake loss estimation and loss disaggregation in buildings. Report No. 157, John A. Blume Earthquake Engineering Center 2005/06, Stanford University, StanfordGoogle Scholar
  6. Asteris PG (2003) Lateral stiffness of brick masonry infilled plane frames. J Struct Eng 129(8):1071–1079CrossRefGoogle Scholar
  7. Asteris PG, Repapis CC, Tsaris AK, Di Trapani F, Cavaleri L (2015) Parameters affecting the fundamental period of infilled RC frame structures. Earthq Struct 9(5):999–1028CrossRefGoogle Scholar
  8. Asteris PG, Cavaleri L, Di Trapani F, Sarhosis V (2016) A macro-modelling approach for the analysis of infilled frame structures considering the effects of openings and vertical loads. Struct Infrastruct Eng 12(5):551–566CrossRefGoogle Scholar
  9. ATC-63 (2008) Quantification of building seismic performance factors. Rep. No. ATC 63. Redwood city, CaliforniaGoogle Scholar
  10. Bal IE, Crowley H, Pinho R, Gulay FG (2007) Structural characteristics of Turkish RC building stock in Northern Marmara region for loss assessment applications. ROSE research report no. 2007/03. IUSS Press; Pavia, ItalyGoogle Scholar
  11. Blume JA (1968) Dynamic characteristics of multi-story buildings. J Struct Div ASCE 94(2):377–402Google Scholar
  12. Browning J, Warden B, Matamoros A, Lepage A (2008) Global and local seismic drift estimate for RC frames. Eng Struct 30:71–1262CrossRefGoogle Scholar
  13. Caterino N, Cosenza E, Azmoodeh BM (2013) Approximate methods to evaluate storey stiffness and interstory drift of RC buildings in seismic area. Struct Eng Mech 46(2):245–267CrossRefGoogle Scholar
  14. CEN (2004) European Standard ENV 1998-1-1/2/3. Eurocode 8: design provisions for earthquake resistance of structures – part I: general rules. Technical Committee 250/SC8, Comité Européen de Normalisation, BrusselsGoogle Scholar
  15. Chintanapakdee C, Chopra AK (2004) Seismic response of vertically irregular frames: response history and modal pushover analyses. J Struct Eng 130(8):1177–1185CrossRefGoogle Scholar
  16. De Marco R, Martini MG, Di Pasquale G, Fralleone A, Pizza AG (2000) La classificazione e la normativa sismica italiana dal 1909 al 1984. Servizio sismico nazionale, 2000 (in Italian)Google Scholar
  17. Di Trapani F, Macaluso G, Cavaleri L, Papia M (2015) Masonry infills and RC frames interaction: literature overview and state of the art of macromodeling approach. Eur J Environ Civ Eng 19(9):1059–1095CrossRefGoogle Scholar
  18. DM 20.02.2018 Updating of technical standards for construction (In Italian)Google Scholar
  19. Dolce M, Nicoletti M, De Sortis A, Marchesini S, Spina D, Talanas F (2017) Osservatorio sismico delle strutture: the Italian structural seismic monitoring network. Bull Earthq Eng 15(2):621–641CrossRefGoogle Scholar
  20. Elwood KJ, Matamoros AB, Wallace JW, Lehman DE, Heintz JA, Mitchell AD, Moehle JP (2007) Update to ASCE/SEI 41 concrete provisions. Earthq Spectra 23(3):493–523CrossRefGoogle Scholar
  21. Fardis M, Carvalho EC, Fajfar P, Pecker A (2015) Seismic design of concrete buildings to Eurocode 8. CRC Press, Boca RatonCrossRefGoogle Scholar
  22. FEMA (2012) FEMA P58-1: Seismic Performance Assessment of Buildings. Volume 1–Methodology. Prepared by the Applied Technology Council for the Federal Emergency Management Agency, Washington, D.C, 2012Google Scholar
  23. Gaetani d’Aragona M, Polese M, Elwood K, Baradaran Shoraka M, Prota A (2017a) Aftershock collapse fragility curves for non-ductile rc buildings: a scenario-based assessment. Earthq Eng Struct Dynam 46:2083–2102. CrossRefGoogle Scholar
  24. Gaetani d’Aragona M, Polese M, Prota M (2017b) Influence factors for the assessment of maximum lateral seismic deformations in Italian multistorey RC buildings. In: Proceedings of COMPDYN 2017 6th ECCOMAS thematic conference on computational methods in structural dynamics and earthquake engineering, Rhodes Island, 15–17 JuneGoogle Scholar
  25. Gallipoli MR, Mucciarelli M, Sket-Motnikar B, Zupancic P, Gosar A, Prevolnik S et al (2010) Empirical estimates of dynamic parameters on a large set of European buildings. Bull Earthq Eng 8(3):593–697CrossRefGoogle Scholar
  26. Guler K, Yuksel E, Kocak A (2008) Estimation of the fundamental vibration period of existing RC buildings in Turkey utilizing ambient vibration records. J Earthq Eng 12(S2):140–150CrossRefGoogle Scholar
  27. Gülkan P, Akkar S (2002) A simple replacement for the drift spectrum. J Eng Struct 24(11):1477–1484CrossRefGoogle Scholar
  28. Günay MS, Sucuoglu H (2009) Predicting the seismic response of capacity-designed structures by equivalent linearization. J Earthq Eng 13(5):623–649CrossRefGoogle Scholar
  29. Günay MS, Sucuoglu H (2010) An improvement to linear elastic procedures for seismic performance assessment. Earthq Eng Struct Dyn 39(8):907–931Google Scholar
  30. HAZUS (1999) SR2: earthquake loss estimation methodology. Advanced engineering building module. Technical and user’s manual. Federal Emergency Management Agency, WashingtonGoogle Scholar
  31. Heidebrecht AC, Stafford Smith B (1973) Approximate analysis of tall wall-frame structures. J Struct Div ASCE 99(2):199–221Google Scholar
  32. Hong LL, Hwang WL (2000) Empirical formula for fundamental vibration periods of reinforced concrete buildings in Taiwan. Earthq Eng Struct Dyn 29(3):326–333CrossRefGoogle Scholar
  33. Hosseini M, Imagh-e-Naiini MR (1999) A quick method for estimating the lateral stiffness of building systems. Struct Des Tall Build 8(3):247–260CrossRefGoogle Scholar
  34. Iwan WD (1997) Drift spectrum: measure of demand for earthquake ground motions. J Struct Eng ASCE 123(4):397–404CrossRefGoogle Scholar
  35. Kakaletsis DJ, Karayannis CG (2007) Experimental investigation of infilled R/C frames with eccentric openings. Struct Eng Mech 26(3):231–250CrossRefGoogle Scholar
  36. Kakaletsis DJ, Karayannis CG (2008) Influence of masonry strength and openings on infilled R/C frames under cycling loading. J Earthq Eng 12(2):197–221CrossRefGoogle Scholar
  37. Kakaletsis DJ, Karayannis CG (2009) Experimental investigation of infilled reinforced concrete frames with openings. ACI Struct J 106(2):132–141Google Scholar
  38. Lin YY, Miranda E (2009) Evaluation of equivalent linear methods for estimating target displacements of existing structures. Eng Struct 31(12):3080–3089CrossRefGoogle Scholar
  39. Mainstone RJ (1971) On the stiffnesses and strengths of infilled frames. In: Proceedings of the institution of civil engineering, Supplement IV, 57–90Google Scholar
  40. Medina RA, Krawinkler H (2005) Evaluation of drift demands for the seismic performance assessment of frames. J Struct Eng 131(7):1003–1013CrossRefGoogle Scholar
  41. Miranda E (1999) Approximate seismic lateral deformation demands in multistory buildings. J Struct Eng 125:417–425CrossRefGoogle Scholar
  42. Miranda E (2005) Simplified analysis tools for rapid seismic evaluation of existing buildings in urban areas. In Proceedings of the Simposio Luis Esteva, organized by UNAM, Mexico, Mexico City, downloadable at
  43. Miranda E, Akkar SD (2006) Generalized interstory drift spectrum. J Struct Eng 132(6):840–852CrossRefGoogle Scholar
  44. Miranda E, Reyes CJ (2002) Approximate lateral drift demands in multistory buildings with nonuniform stiffness. J Struct Eng 128(7):840–849CrossRefGoogle Scholar
  45. Miranda E, Ruiz-García J (2002) Evaluation of approximate methods to estimate maximum inelastic displacement demands. Earthq Eng Struct Dyn 31(3):539–560CrossRefGoogle Scholar
  46. Mohammadi M, Nikfar F (2012) Strength and stiffness of masonry-infilled frames with central openings based on experimental results. J Struct Eng 139(6):974–984CrossRefGoogle Scholar
  47. Mondal G, Jain SK (2008) Lateral stiffness of masonry infilled reinforced concrete (RC) frames with central opening. Earthq Spectra 24(3):701–723CrossRefGoogle Scholar
  48. Muto K (1965) Seismic analysis of reinforced concrete buildings. Shokokusha Publishing Co., Inc., TokyoGoogle Scholar
  49. Naeim F, Hagie S, Alimoradi A, Miranda E (2006) Automated post-earthquake damage assessment of instrumented buildings. Advances in earthquake engineering for urban risk reduction. Springer, Dordrecht, pp 117–134CrossRefGoogle Scholar
  50. Nicoletti M, Palka P, Spina D, Valente C (2001) An automatic procedure to create in real time reports on the post-earthquake state of structures monitored within the seismic observatory of structures. In: Proceedings X Convegno Nazionale ANIDIS “L’Ingegneria Sismica in Italia”, Potenza, Italy, 9–13 September (in Italian)Google Scholar
  51. Oliveira CS, Navarro M (2010) Fundamental periods of vibration of RC buildings on Portugal from in situ experimental and numerical techniques. Bull Earthq Eng 8(3):42–609CrossRefGoogle Scholar
  52. Panagiotakos TB, Fardis M (1996) Seismic response of infilled RC frames structures. In: Proceedings of the 11th world conference on earthquake engineering, Acapulco, Mexico. paper n. 225Google Scholar
  53. Paulay T, Priestley MJ (1992) Seismic design of reinforced concrete and masonry buildings. Wiley, New YorkCrossRefGoogle Scholar
  54. Polese M, Verderame GM, Manfredi G (2011) Static vulnerability of existing RC buildings in Italy: a case study. Struct Eng Mech 39(4):599–620CrossRefGoogle Scholar
  55. Polese M, Di Ludovico M, Marcolini M, Prota A, Manfredi G (2015a) Assessing reparability: simple tools for estimation of costs and performance loss of earthquake damaged reinforced concrete buildings. Earthq Eng Struct Dyn 44(1):1539–1557. CrossRefGoogle Scholar
  56. Polese M, Marcolini M, Zuccaro G, Cacace F (2015b) Mechanism based assessment of damaged- dependent fragility curves for RC building classes. Bull Earthq Eng 13(5):1323–1345. CrossRefGoogle Scholar
  57. Polese M, Marcolini M, Gaetani d’Aragona M, Cosenza E (2017) Reconstruction policies: explicitating the link of decisions thresholds to safety level and costs for RC buildings. Bull Earthq Eng 15(2):759–785. CrossRefGoogle Scholar
  58. Polese M, Gaetani d’Aragona M, Di Ludovico M, Prota A (2018) Sustainable selective mitigation interventions towards effective earthquake risk reduction at the community scale. Sustainability 10(8):2894. CrossRefGoogle Scholar
  59. Ramasco R (2000) Lecture notes of the course on buildings in seismic areas. University of Naples Federico II (in Italian)Google Scholar
  60. RDL 2229 (1939) Regio Decreto Legge n. 2229 del 16/11/1939. Norme per la esecuzione delle opere in conglomerate cementizio semplice od armato. GU n. 92 del 18/04/1940 (in Italian)Google Scholar
  61. Ricci P, Verderame GM, Manfredi G (2011a) Simplified analytical approach to seismic vulnerability assessment of reinforced concrete buildings. In Proceedings XIV Convegno ANIDIS “L’ingegneria sismica in Italia”, Bari, Italy, 18-22 SeptemberGoogle Scholar
  62. Ricci P, Verderame GM, Manfredi G (2011b) Analytical investigation of elastic period of infilled RC MRF buildings. Eng Struct 33(2):308–319CrossRefGoogle Scholar
  63. Ricci P, De Risi MT, Verderame GM, Manfredi G (2016) Procedures for calibration of linear models for damage limitation in design of masonry-infilled RC frames. Earthq Eng Struct Dyn 45(8):1315–1335CrossRefGoogle Scholar
  64. Spina D, Lamonaca BG, Nicoletti M, Dolce M (2011) Structural monitoring by the Italian Department of Civil Protection and the case of 2009 Abruzzo seismic sequence. Bull Earthq Eng 9(1):325–346CrossRefGoogle Scholar
  65. Verderame GM, Polese M, Mariniello C, Manfredi G (2010) A simulated design procedure for the assessment of seismic capacity of existing reinforced concrete buildings, Advances in Engineering Software; 41(2): 323-335. ISSN 0965-9978Google Scholar
  66. Zuccaro G, Dolce M, De Gregorio D, Speranza E, Moroni C (2015) La scheda CARTIS per la caratterizzazione tipologico- strutturale dei comparti urbani costituiti da edifici ordinari. Valutazione dell’esposizione in analisi di rischio sismico. In: Proceedings of GNGTS 2015 (in italian)Google Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Structures for Engineering and ArchitectureUniversity of Naples Federico IINaplesItaly

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