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Comparison of Drift Control Criteria as Nominated by International Seismic Design Standards
 

Comparison of Drift Control Criteria as Nominated by International Seismic Design Standards

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Major seismic events around the world have displayed the close relationship between lateral displacements, and structural and non-structural damage in buildings. Whilst most seismic design standards ...

Major seismic events around the world have displayed the close relationship between lateral displacements, and structural and non-structural damage in buildings. Whilst most seismic design standards are presently force-based, the majority have established limits on lateral drift.

This paper documents a study of the stiffness characteristics nominated in several seismic codes, focusing in particular on the requirement to control lateral drift. A method for evaluating and comparing the control of inter-storey displacements is proposed, and an evaluation of seismic codes is undertaken, including: Australia (1), Chile (2), Colombia (3), Europe (4), New Zealand (5), Panama (6), Peru (7), Turkey (8) and the USA (9, 10 & 11).

The results of this study show that the Chilean code is the most stringent in controlling lateral displacements. In the short period region (up to 0.13 sec) the Colombian, Peruvian and New Zealand codes are among the most stringent, while for periods in between 0.13 sec to 2.85 sec the Eurocode 8 is second only to the Chilean. For longer periods, the Colombian (2.85 sec), Peruvian (3.70 sec), Panamanian (4.00 sec), Turkish (4.75 sec), American (4.90 sec and 5.30 sec), New Zealand (7.70 sec), and Australian (9.65 sec) seismic standards, respectively, are all more stringent than the European normative. Among the least rigorous standards is the Panamanian for periods up to 2.65 sec, with the Australian standard the least stringent for periods up to 9.65 seconds. A direct comparison of the major seismic codes of the USA and Europe shows that the latter are more rigorous up to a period of 4.9 sec. The opposite applies thereafter, with American standards more stringent for longer period structures.

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    Comparison of Drift Control Criteria as Nominated by International Seismic Design Standards Comparison of Drift Control Criteria as Nominated by International Seismic Design Standards Document Transcript

    • Comparison of Drift Control Criteria as Nominated by International Seismic Design Standards 1 Luis Andrade 1 Senior Structural Engineer, Prisma Ingeniería, PeruSynopsis: Major seismic events around the world have displayed the close relationshipbetween lateral displacements, and structural and non-structural damage in buildings. Whilstmost seismic design standards are presently force-based, the majority have established limitson lateral drift.This paper documents a study of the stiffness characteristics nominated in several seismiccodes, focusing in particular on the requirement to control lateral drift. A method for evaluatingand comparing the control of inter-storey displacements is proposed, and an evaluation ofseismic codes is undertaken, including: Australia (1), Chile (2), Colombia (3), Europe (4), NewZealand (5), Panama (6), Peru (7), Turkey (8) and the USA (9, 10 & 11).The results of this study show that the Chilean code is the most stringent in controlling lateraldisplacements. In the short period region (up to 0.13 sec) the Colombian, Peruvian and NewZealand codes are among the most stringent, while for periods in between 0.13 sec to 2.85sec the Eurocode 8 is second only to the Chilean. For longer periods, the Colombian (2.85sec), Peruvian (3.70 sec), Panamanian (4.00 sec), Turkish (4.75 sec), American (4.90 secand 5.30 sec), New Zealand (7.70 sec), and Australian (9.65 sec) seismic standards,respectively, are all more stringent than the European normative. Among the least rigorousstandards is the Panamanian for periods up to 2.65 sec, with the Australian standard the leaststringent for periods up to 9.65 seconds. A direct comparison of the major seismic codes ofthe USA and Europe shows that the latter are more rigorous up to a period of 4.9 sec. Theopposite applies thereafter, with American standards more stringent for longer periodstructures.Keywords: inter-storey drift, seismic codes, lateral displacement, lateral drift limits,acceleration response spectrum, displacement response spectrum, earthquake.1. IntroductionThe philosophy of aseismic design in most seismic standards is based on ensuring that abuilding will not collapse when subject to the most severe earthquake likely to occur duringthe economic life of a building (unless the structure is alternately fitted with base isolation orpassive dissipative systems). Whilst minimising collapse this philosophy deliberately allowsfor major non-structural damage. Structural elements, specifically beam to columnconnections and shear walls are permitted to undergo minor (reparable) damage to the extentof developing plastic hinges.Lateral displacements and inter-storey drift have three primary effects on a structure: damageto structural elements (such as beams, columns and shear walls); damage to non structuralelements (such as windows, infill walls, partition walls, false ceiling, cladding, etc); anddisplacements can also affect adjacent structures. Therefore without proper considerationduring the design process, large displacements and inter-storey drifts can have adverseeffects on structural elements, non-structural elements, and adjacent structures.1.1 Inter-storey Drift vs Lateral DisplacementsLateral displacements are the predicted movement of a structure under lateral loads, withreference to the original storey location in the horizontal plane.Inter-storey drift however is defined as the difference of maximum elastic or elastoplasticlateral displacements of any two adjacent floors under factored loads. While the ‘inter-storeydrift ratio’ is defined as the inter-storey drift divided by the respective storey height.
    • 1.2 Seismic Code Requirements for Inter-storey DriftsDrift control requirements are nominated by the design provisions of most building codes.However, design parameters and the analytical assumptions relating to lateral forces used tocalculate drifts vary from code to code.The limiting inter-storey drift values recommended also vary widely, as can be seen in Table1. It should be noted that most standards apply limiting values to the elastoplastic lateraldeflections, however some codes like the Chilean and Turkish, impose limits corresponding tothe elastic response of the structure. To enable direct comparison of elastoplastic lateraldeflections in Table 1, elastic inter-storey drift limits have been multiplied by their respectivelateral force reduction factor.Table 1 includes the main design parameters required to calculate lateral forces for areinforced concrete building with dual system (a combination of ductile shear walls andmoment resisting frames, in which the frames alone are capable of resisting 25% of the lateralshear forces). Table 1. Main parameters for calculating displacements in different Codes (for RC structures with Ductile Dual System) Inertia Required to Lateral Lateral Displacement Lateral Force Drift calculate Lateral Displacement Amplification Factor toCountry/Continent Code Reduction Ratio Stiffness in Reinforced Amplification Lateral Force Reduction Factor Limit Concrete Buildings Factor(1) Factor Ratio, F AS Australia Uncracked / Cracked µ / Sp = 5.97 µ / Sp = 5.97 (µ / Sp ) / (µ / Sp ) =1.00 0.0150 1170.4:2007 R* varies with Chile NCh433 Uncracked R* varies with T R* / R* = 1.00 0.002 R* T R varies with Colombia NSR-98 Uncracked R varies with T R / R = 1.00 0.010 T EC 8 - EN Europe Cracked q = 5.85 q = 5.85 q / q = 1.00 0.010 1998-1:2004 NZ µ kdm varies from (µ kdm ) / (µ / Sp ) varies New Zealand Cracked µ / Sp = 8.57 0.025 1170.5:200 7.20 to 9.00 from 0.84 to 1.05 Panama REP2004 Uncracked R = 8.00 Cd = 6.50 Cd / R = 0.81 0.020 Peru NTE E-030 Uncracked R = 7.00 0.75 R = 5.25 0.75 R / R = 0.75 0.007 R varies with 0.020 or Turkey 1997 Uncracked R varies with T R / R = 1.00 T 0.0035 R UBC 1997 Cracked R = 8.50 0.70 R = 5.95 0.70 R / R = 0.70 0.020 USA ASCE 7-05 Cracked R = 7.00 Cd / I = 5.50 (Cd / I ) / R = 0.79 0.020 IBC 2009(1) elastoplastic to elastic displacement ratioFor the same peak ground acceleration, soil conditions, and structural system, differentvalues for design base shear and lateral deflections are obtained depending on the codeadopted. The differences are a combination of the following aspects:• Cracked or Uncracked Inertia: For reinforced concrete structures, some standards require the adoption of cracked sections in the modelling of a building, while some others allow the use of gross sections (see Table 1). This affects the stiffness of the building, and consequently its fundamental period. A building modelled with uncracked sections has a lower fundamental period and could have a different base shear value than its pair modelled with cracked sections, depending on the shape of the acceleration response spectrum given by the design provisions (usually a larger fundamental period is related to a lower base shear if the building is located in rock or stiff soil). The stiffness of the building not only affects the calculation of inertial forces but also the lateral displacements. The stiffer the building, the lesser are the values of its lateral deflections. There is also disagreement among the standards on the level of cracking that should be adopted for modelling as can be extracted from Table 2.
    • Table 2. Criteria for adoption of cracked inertias for modelling seismic design Country/Continent Code Inertia Required to calculate Lateral Stiffness in Reinforced Concrete Buildings (2) In the calculation of deformations and action effects in a structure, for both the serviceability and strength limit states, an estimate of the stiffness of each member shall be based on either AS Australia (a) the dimensions of the uncracked (gross) cross-sections; or 1170.4:2007 (b) other reasonable assumptions, which better represent conditions at the limit state being considered, provided they are applied consistently throughout the analysis. EC 8 - EN Europe All structural elements 0.50 Igross(3) 1998-1:2004 The stiffness to be used in the analysis for seismic actions in the ultimate limit state, should be based on the member stiffness determined from the load and deflection that is sustained by the member when either: NZ New Zealand 1170.5:200 (a) the material sustains first yield; or (b) the material sustains significant inelastic deformation. (4) UBC 1997 Columns 0.70 Igross Walls cracked (4) 0.35 Igross (4) USA Walls uncracked 0.70 Igross ASCE 7-05 IBC 2009 Beams (4) 0.35 Igross (4) Flat Plates 0.25 Igross(2) extracted from AS-3600:2009 (12)(3) Igross refers to the uncracked first moment of area of the section of a reinforced concrete element.(4) extracted from ACI 318-08 (13)• Lateral Force Reduction Factor: Lateral displacements, are also closely related to the amount of lateral force introduced in a structure during an earthquake. Unfortunately, codes are not in agreement when introducing lateral force reduction factors for calculating design base shears (see Table 1). In the codes of different countries, we can find that for a given material and type of structural system, the amount of elastic force reduction varies considerably from standard to standard. This is indeed another direct cause of the differences in the values of the lateral displacements.• Fundamental Period Limits: Some standards, like the Americans ASCE 7-05 and IBC 2009, and the Panamanian REP 2004, apply an upper limit for the fundamental period of a structure in order to establish the minimum base shear to be adopted in the design. This greatly influences the amount of lateral force introduced in the design of long fundamental period structures. For a structure with long fundamental period and located in a site on rock or stiff soil, limiting the value of its fundamental period to a lower value means that the building will be designed for a higher base shear, and consequently, higher values for its inter-storey drifts can be expected. Nevertheless, ASCE 7-05 and IBC 2009 permit the calculation of lateral displacements using seismic design forces based on computed fundamental period without considering the upper limit (Cl. 12.8.6.2 from ASCE 7-05). On the other hand, the Panamanian standard does not provide such concession.• Base Shear Limits: Most standards specify a minimum level of base shear to be applied in the design of buildings; however, the majority of codes permit the calculation of drifts without taking into account this requirement. An exception to the rule are the codes of Colombia, Chile, Panama and Turkey.• Shape of the Acceleration and Displacement Response Spectrum: The difference in shape of the acceleration response spectrum (Figure 1) and intrinsically, the displacement response spectrum (Figure 2) amongst codes, also has a significant influence in the resulting lateral displacements. Figure 2 shows the displacement response spectrums, as gained from the acceleration response spectrums using Eq. 9 (see Section 2. Code Stringency Index (CSI) Method for Comparing Inter-storey Drift obtained from Spectral Curves). Acceleration spectra as nominated by the various codes tend to be inaccurate (and often excessively conservative) in the long-period range. A more representative alternative to using acceleration spectra to generate displacement spectra, is to use source mechanics, and recent digital records (e.g. Bommer, 2001, Faccioli et al, 2002) (14).
    • 1.40 Australia - AS 1170.4:2007 Chile - NCh433 Colombia - NSR-98 1.20 Eurocode 8 - EN 1998-1:2004 New Zealand - NZ 1170.5:2004 Panama - REP2004 Peru - NTE E-030 Elastic Spectral Acceleration, Sa (g) 1.00 Turkey - 1997 USA - UBC 1997 USA - ASCE 7-05/IBC 2009 0.80 0.60 0.40 0.20 0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Period, T (sec) Figure 1. Elastic Acceleration response spectrum for different codes. 2000 1900 Australia - AS 1170.4:2007 Chile - NCh433 1800 Colombia - NSR-98 1700 Eurocode 8 - EN 1998-1:2004 1600 New Zealand - NZ 1170.5:2004 Panama - REP2004 1500 Peru - NTE E-030 Spectral Displacement, Sd (mm) . 1400 Turkey - 1997 1300 USA - UBC 1997 USA - ASCE 7-05/IBC 2009 1200 1100 1000 900 800 700 600 500 400 300 200 100 0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Period, T (sec) Figure 2. Displacement response spectrum for different codes.Figure 2 displays the variation of displacement spectra as obtained by using the accelerationspectra of various codes.Australian, European, New Zealand and the American ASCE 7-05, all have a branch ofconstant displacement for their response spectrum in the long period region, however, thesebranches initiate at different fundamental periods varying from 1.5 sec to 8 sec.For the Chilean, Colombian, Peruvian, Turkish and the American UBC 1997, thedisplacements exponentially increase, as the fundamental period of the structure increases.The displacement response spectrum as calculated using the Panamanian standard is uniquein having an abrupt increase at the fundamental period of 4 sec.All of the above-mentioned standards violate the most basic principle of structural dynamics,as they nominate infinite maximum ground displacements for very long periods (14). All ofthese codes, in the authors’ opinions, are too conservative because empirical data dictatesthat displacement spectrums should increase linearly to a corner period, then remain
    • constant, for large earthquakes, or decrease for moderate earthquakes. At very large periods(eg T>10sec) the response spectrum must decrease to match the peak ground displacement(15). It should also be noted that the fundamental period that defines the transition fromincreasing to constant spectral displacement levels depends on the type of fault that definesthe seismicity of the site, the magnitude and the distance to the fault (16).Concern has been expressed recently that the EC8 spectral ordinates may be excessivelylow at longer periods (16), particularly if compared with those defined for the USA in ASCE 7-05 and IBC 2009. In the latter codes, the constant displacement plateau begins at periodsranging from 4 to 16 sec, whereas the EC8 Type 1 spectrum (for the higher seismicity regionsof Europe) has a constant displacement plateau commencing at just 2 sec.2. Code Stringency Index (CSI) Method for Comparing Inter-storey Drift obtained from Spectral Curves2.1 Inter-storey Drift RatioFor each separate mode of a structure, the maximum response can be obtained directly fromthe displacement response spectrum (17). For example, the maximum displacement vector inmode ‘n’ is given by: L* (1) d max = ⋅ SD (ξ N , Tn ) ⋅ φ n M*whereL* : participation factor of the system (representing the extent to which the earthquake motion tends to excite the response)M* : generalized mass of the systemL M : * * modal mass participation ratio thSD (ξ N , Tn ) : spectral displacement corresponding to the damping, ξN, and period, TN, of the n mode of vibrationφn : shape vectorA factor F (a ratio between the displacement amplification factor and force reduction factor) isintroduced to calculate elastoplastic displacements by amplifying elastic displacements. Forexample, because elastoplastic displacements are calculated from elastic displacementswhen using the American ASCE 7-05 / IBC 2009 and UBC 1997, these codes nominate an Ffactor of Cd/IR and 0.7 respectively. For Eurocode 8 the F factor is 1, as its ratio for theelastoplastic to elastic lateral displacements is q (see Table 1 showing a list of F factors forother codes). Introducing F in Eq. 1, the maximum displacement vector is given by: L* (2) d max = ⋅ SD (ξ N , Tn ) ⋅ φ n ⋅ F M*The inter-storey drift ratio, ∆ max , can now be obtained dividing Equation 2 by the inter-storeyheight, h: d max 1 L* (3) ∆ max = = ⋅ * ⋅ SD (ξ N , Tn ) ⋅ φ n ⋅ F h h MFrom Equation 3 we can easily obtain the maximum inter-storey drift ratio of a given level,∆ max , directly from the displacement response spectrum, and express its value in terms of amagnitude (in lieu of a vector) as: d max 1 L* (4) ∆ max = = ⋅ * ⋅ SD (ξ N , Tn ) ⋅ φ n ⋅ F h h M
    • 2.2 Drift Control IndexThe maximum drift ratio obtained in the analysis ( ∆ max ) must be less than the upper limit ( ∆ lim it) stipulated by the code/s to ensure the structure under interrogation satisfies code drift limits.The relationship between the maximum drift ratio obtained from analysis, and the drift ratiolimit given by the standards, should thus be less than 100%. To this end, the author proposesa Drift Control Index (i), given by: ∆ max (5) i= (%) ∆ lim it2.3 Code Stringency IndexTo compare how stringent a code is in relation to another, the author proposes a factornominated as the Code Stringency Index, or CSI, defined as: i CodeX (6) CSI = (%) i CodeYIncorporating Eq. 5 in Eq. 6 we obtain the following expression for the CSI: SD (ξ n , Tn ) CodeX ⋅ FCodeX / ∆ lim it CodeX (7) CSI = (%) SD (ξ n , Tn ) CodeY ⋅ FCodeY / ∆ lim it CodeYSubscripts Code X and Code Y, indicate that we are comparing Code X against Code Y in theabove formula. For example, if the CSI is lower than 100%, it means that Code Y is morestringent than Code X, while if CSI is higher than 100% the opposite applies. Having a CSIequal to 100% means that both Codes X and Y are equally stringent.The CSI can also be expressed in terms of the spectral acceleration, SA (ξ N , Tn ) , and thestructure’s lateral stiffness, K, as we know that (17): K (8) ω= Mand 1 M (9) SD (ξ N , TN ) = ⋅ SA (ξ N , TN ) = ⋅ SA (ξ N , TN ) ω2 Kwhereω: circular frequency of vibration of the equivalent SDOF (Hz)M: mass of the buildingK: lateral stiffness of the building thSA (ξ N , Tn ) : spectral acceleration corresponding to the damping, ξN, and period, TN, of the n mode of vibrationAs discussed in Section 1 of this paper, some standards require calculating lateraldisplacements in concrete structures by considering cracked sections, while others allowcalculating displacements with gross sections. To account for this in our stringencycomparison we must introduce lateral stiffness into the equation for CSI. Introducing Eq. 9 inEq. 7, we obtain: [SA (ξ n , Tn ) CodeX ⋅ FCodeX ]/[∆ lim it CodeX ⋅ K CodeX ] (10) CSI = (%) [SA (ξ n , Tn ) CodeY ⋅ FCodeY ]/[∆ lim it CodeY ⋅ K CodeY ]whereK CodeX , K CodeY : type of lateral stiffness (cracked or uncracked) stipulated in Code X or Code Y, respectively.
    • 3. Code Stringency Index Comparison from Spectral CurvesThe CSI equation proposed in Eq. 10 enables comparison of the code’s stringency withrespect to limiting lateral displacements for a series of structures with different fundamentalperiods.Consider a set of buildings for which fundamental periods vary from close to 0 sec to up to 10sec, and which are situated on very stiff soil with 0.4g peak ground acceleration (10%probability of being exceeded in 50 years, or 475 years mean return period). Assume that allbuildings are made of reinforced concrete, and consist of dual structural systemsincorporating both shear walls and moment resisting frames. For those codes which requirethe modeling of buildings with cracked inertia, assume a lateral stiffness which is half thelateral stiffness of the same structures with uncracked sections (as recommended in theEurocode 8). Some other parameters of importance are taken as per Table 1.Figure 4 shows the results of this comparison against the Eurocode 8 (i.e. parameters of theEuropean standard are used as the denominator in Eq. 10): 10000 Australia - AS 1170.4:2007 Chile - NCh433 Colombia - NSR-98 Eurocode 8 - EN 1998-1:2004 New Zealand - NZ 1170.5:2004 Panama - REP2004 Peru - NTE E-030 Turkey - 1997 1000 USA - UBC 1997 USA - ASCE 7-05/IBC 2009 CSI (%) 100 10 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Period, T (sec) Figure 4. CSI values for various codes.The results displayed by Figure 4 show that the Chilean standard is the most stringent incontrolling lateral displacements for the whole spectrum of fundamental periods.For very short periods, up to 0.13 sec, Eurocode 8 is less stringent than the Colombian,Peruvian and New Zealand design provisions, but is the second most stringent for periodsbetween 0.13 sec to 2.85 sec.The Panamanian code is the least stringent up to a period of 2.65, the Australian code is leastrigorous for periods between 2.65 and 9.65 sec, after which Eurocode 8 becomes the leaststringent in requiring lateral displacement control.Despite being the less stringent in the short fundamental periods range, the Panamanianstandard is the third more rigorous for periods larger than 4 sec after the Chilean andColombian standards.A comparison among the American and the European design provisions (which are the codesof choice in countries where there is a lack of seismic normative) indicates that Eurocode 8 ismore stringent for periods of up to 4.9 sec, after which the American ASCE 7-05/IBC 2009and UBC 1997 take over.
    • 4. Conclusions & RecommendationsIn studying and comparing seismic design provisions of various codes it is evident that lack ofuniformity exists regarding calculation of lateral displacements. Differences result fromvarying factors including drift limit ratios, the use of cracked or uncracked sections, lateralforce reduction factors, upper limits to the fundamental period of vibration, minimum baseshear to be considered, and the shape of acceleration and displacement response spectrums.The author’s proposes that further consideration should be given in defining the displacementresponse spectrum, and support the changing trend in seismic design philosophy from force-based towards a displacement-based. Force-based codes of practice sometimes lead theengineer towards expensive designs and unfeasible structures.A code stringency index, CSI, is proposed to enable comparison of code stringency incontrolling lateral displacements obtained from spectral acceleration curves. The comparisonof several international standards shows that the Chilean code is the most stringent standardover the whole range of periods (up to 10 sec). This probably explains why most structuresdesigned with the current Chilean seismic normative have had a good performance during the8.8 magnitude earthquake that rocked the central and southern region of the South Americancountry on the 27th February 2010.For short periods (up to 0.13 sec) the Colombian, Peruvian and New Zealand codes rankamong the most stringent, while, for periods in between 0.13 sec to 2.85 sec Eurocode 8 issecond to the Chilean. For longer periods the Colombian (2.85 sec), Peruvian (3.70 sec),Panamanian (4.00 sec), Turkish (4.75 sec), American (4.90 sec and 5.30 sec), New Zealand(7.70 sec) and Australian (9.65 sec) seismic standards, are all more stringent than theEuropean normative.Among the least rigorous standards is the Panamanian for periods up to 2.65 sec, after whichthe Australian becomes the least stringent up to a period of 9.65 seconds. This makes theAustralian standard one of the least conservative for the design of long period structures(particularly high-rise buildings).A direct comparison of the seismic codes of the USA and Europe showed that the latter aremore rigorous up to a period of 4.9 sec. The opposite applies thereafter, were for longerperiod structures the American standards are more stringent. In view of the above, it seemsthe American UBC is most applicable to regions such as Dubai, were high rises like the BurjDubai have reported fundamental periods up to 11.3 sec (18).It is recommended that the displacement response spectrums nominated by Eurocode 8should be revised, as it is found that its ordinates are exceedingly low for longer periods,especially in comparison to ASCE 7-05 and IBC 2009.5. AcknowledgmentsThe author expresses his sincere gratitude to Alejandro Muñoz, Professor of the PontificalCatholic University of Peru, for his constructive critique provided during the production of thispaper.
    • 6. References1. Standards Association of Australia, “Structural Design Actions – Part 4: Earthquake Actions in Australia – AS 1170.4”. Sydney, NSW, 2007.2. Instituto Nacional de Normalización, “Diseño Sísmico de Edificios, Norma NCh 433 Of.96”, Santiago, Chile, 1996.3. Asociación Colombiana de Ingeniería Sísmica, “Normas Colombianas de Diseño y Construcción Sismo Resistente, NSR-98. Título A – Requisitos Generales de Diseño y Construccion Sismorresistente, Ley 400 de 1997, Decreto 33”, Santafé de Bogotá D. C. Colombia, 1998.4. NS EN 1998-1:2004 CEN, “Eurocode 8: Design of Structures for Earthquake Resistance - Part 1: General Rules, Seismic Actions and Rules for Buildings”, Brussels, 2004.5. Standards New Zealand, “NZS 1170.5, 2004, Structural Design Actions, Part 5 Earthquake Actions”, Wellington, 2004.6. Ministerio de Obras Públicas, Junta Técnica de Ingeniería y Arquitectura, “Reglamento de Diseño Estructural de la República de Panamá, REP 2004”. Panamá, 2004.7. Ministerio de Transportes y Comunicaciones, “Norma Técnica de Edificación E-0.30, Diseño Sismorresistente”, Lima, Perú, 2003.8. Ministry of Public Works and Settlement Government of the Republic of Turkey, “Specification for Structures to be Build in Disaster Areas, Part III, Earthquake Disaster Prevention”, Istanbul, Turkey, 1998.9. International Conference of Building Officials (ICBO), “Uniform Building Code, 1997 Edition, Volume 2”, Whittier, California, 1997.10. ASCE/SEI, “ASCE 7-05, Minimum Design Loads for Buildings and Other Structures”, American Society of Civil Engineers, Reston, Virginia, 2005.11. International Code Council (ICC), “2009 International Building Code”, Country Club Hills, Illinois, 2009.12. Standards Association of Australia, “AS 3600-2009 Concrete Structures”. Sydney, NSW, 2009.13. American Concrete Institute, “Building Code Requirements for Structural Concrete ACI 318-08 and Commentary”, Farmington Hills, Michigan.14. Jaramillo, J., “Modelo Para la Rama Descendente de Espectros de Diseño Sísmico y Aplicaciones al Caso de la Ciudad de Medellín”, Revista de Ingeniería Sísmica No. 68 1- 20 (2003), Mexico D.F. 2003.15. Priestley, N. “Seismological Information for Displacement-Based Seismic Design - A Structural Engineer’s Wish List” Proceedings of the First European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland, 2006.16. Akkar, S., Bommer, J., “Prediction of Elastic Displacement Response Spectra in Europe and the Middle East”, Earthquake Engineering and Structural Dynamics, Vol. 36 No. 10, pp. 1275-1301, 2007.17. Clough, R., Penzien, J., “Dynamics of Structures” Third Edition, Computers & Structures, Inc., Berkeley, California, 1995.18. Baker, W., Korista, D., Novak, L., “Burj Dubai: Engineering the Worlds Tallest Building”, The Structural Design of Tall and Special Buildings, Vol 16, pp. 361-375, 2007.19. Andrade, L., “Control de la Deriva en las Normas de Diseño Sismorresistente”, Pontificia Universidad Católica del Perú, January 2004.20. Sindel, Z., Akbas, R. & Tezcan, S.S., “Drift Control and Damage in Tall Buildings”, Engineering Structures, Vol. 18, No. 12, pp. 957-966, Elsevier Science Ltd 1996.