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.

1. Comparison of Drift Control Criteria as Nominated by International
Seismic Design Standards
1
Luis Andrade
1
Senior Structural Engineer, Prisma Ingeniería, Peru
Synopsis: 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.
Keywords: inter-storey drift, seismic codes, lateral displacement, lateral drift limits,
acceleration response spectrum, displacement response spectrum, earthquake.
1. Introduction
The philosophy of aseismic design in most seismic standards is based on ensuring that a
building will not collapse when subject to the most severe earthquake likely to occur during
the economic life of a building (unless the structure is alternately fitted with base isolation or
passive dissipative systems). Whilst minimising collapse this philosophy deliberately allows
for major non-structural damage. Structural elements, specifically beam to column
connections and shear walls are permitted to undergo minor (reparable) damage to the extent
of developing plastic hinges.
Lateral displacements and inter-storey drift have three primary effects on a structure: damage
to structural elements (such as beams, columns and shear walls); damage to non structural
elements (such as windows, infill walls, partition walls, false ceiling, cladding, etc); and
displacements can also affect adjacent structures. Therefore without proper consideration
during the design process, large displacements and inter-storey drifts can have adverse
effects on structural elements, non-structural elements, and adjacent structures.
1.1 Inter-storey Drift vs Lateral Displacements
Lateral displacements are the predicted movement of a structure under lateral loads, with
reference to the original storey location in the horizontal plane.
Inter-storey drift however is defined as the difference of maximum elastic or elastoplastic
lateral displacements of any two adjacent floors under factored loads. While the ‘inter-storey
drift ratio’ is defined as the inter-storey drift divided by the respective storey height.

2. 1.2 Seismic Code Requirements for Inter-storey Drifts
Drift control requirements are nominated by the design provisions of most building codes.
However, design parameters and the analytical assumptions relating to lateral forces used to
calculate drifts vary from code to code.
The limiting inter-storey drift values recommended also vary widely, as can be seen in Table
1. It should be noted that most standards apply limiting values to the elastoplastic lateral
deflections, however some codes like the Chilean and Turkish, impose limits corresponding to
the elastic response of the structure. To enable direct comparison of elastoplastic lateral
deflections in Table 1, elastic inter-storey drift limits have been multiplied by their respective
lateral force reduction factor.
Table 1 includes the main design parameters required to calculate lateral forces for a
reinforced concrete building with dual system (a combination of ductile shear walls and
moment resisting frames, in which the frames alone are capable of resisting 25% of the lateral
shear 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 to
Country/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 ratio
For the same peak ground acceleration, soil conditions, and structural system, different
values for design base shear and lateral deflections are obtained depending on the code
adopted. 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.

3. 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).

4. 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 acceleration
spectra of various codes.
Australian, European, New Zealand and the American ASCE 7-05, all have a branch of
constant displacement for their response spectrum in the long period region, however, these
branches initiate at different fundamental periods varying from 1.5 sec to 8 sec.
For the Chilean, Colombian, Peruvian, Turkish and the American UBC 1997, the
displacements exponentially increase, as the fundamental period of the structure increases.
The displacement response spectrum as calculated using the Panamanian standard is unique
in 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 of
these codes, in the authors’ opinions, are too conservative because empirical data dictates
that displacement spectrums should increase linearly to a corner period, then remain

5. 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 from
increasing to constant spectral displacement levels depends on the type of fault that defines
the 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 excessively
low 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 periods
ranging from 4 to 16 sec, whereas the EC8 Type 1 spectrum (for the higher seismicity regions
of 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 Curves
2.1 Inter-storey Drift Ratio
For each separate mode of a structure, the maximum response can be obtained directly from
the displacement response spectrum (17). For example, the maximum displacement vector in
mode ‘n’ is given by:
L* (1)
d max = ⋅ SD (ξ N , Tn ) ⋅ φ n
M*
where
L* : participation factor of the system (representing the extent to which the
earthquake motion tends to excite the response)
M* : generalized mass of the system
L M :
* * modal mass participation ratio
th
SD (ξ N , Tn ) : spectral displacement corresponding to the damping, ξN, and period, TN, of the n
mode of vibration
φn : shape vector
A factor F (a ratio between the displacement amplification factor and force reduction factor) is
introduced to calculate elastoplastic displacements by amplifying elastic displacements. For
example, because elastoplastic displacements are calculated from elastic displacements
when using the American ASCE 7-05 / IBC 2009 and UBC 1997, these codes nominate an F
factor of Cd/IR and 0.7 respectively. For Eurocode 8 the F factor is 1, as its ratio for the
elastoplastic to elastic lateral displacements is q (see Table 1 showing a list of F factors for
other 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-storey
height, h:
d max 1 L* (3)
∆ max = = ⋅ * ⋅ SD (ξ N , Tn ) ⋅ φ n ⋅ F
h h M
From 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 a
magnitude (in lieu of a vector) as:
d max 1 L* (4)
∆ max = = ⋅ * ⋅ SD (ξ N , Tn ) ⋅ φ n ⋅ F
h h M

6. 2.2 Drift Control Index
The 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 ratio
limit given by the standards, should thus be less than 100%. To this end, the author proposes
a Drift Control Index (i), given by:
∆ max (5)
i= (%)
∆ lim it
2.3 Code Stringency Index
To compare how stringent a code is in relation to another, the author proposes a factor
nominated as the Code Stringency Index, or CSI, defined as:
i CodeX (6)
CSI = (%)
i CodeY
Incorporating 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 CodeY
Subscripts Code X and Code Y, indicate that we are comparing Code X against Code Y in the
above formula. For example, if the CSI is lower than 100%, it means that Code Y is more
stringent than Code X, while if CSI is higher than 100% the opposite applies. Having a CSI
equal 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 the
structure’s lateral stiffness, K, as we know that (17):
K (8)
ω=
M
and
1 M (9)
SD (ξ N , TN ) = ⋅ SA (ξ N , TN ) = ⋅ SA (ξ N , TN )
ω2 K
where
ω: circular frequency of vibration of the equivalent SDOF (Hz)
M: mass of the building
K: lateral stiffness of the building
th
SA (ξ N , Tn ) : spectral acceleration corresponding to the damping, ξN, and period, TN, of the n
mode of vibration
As discussed in Section 1 of this paper, some standards require calculating lateral
displacements in concrete structures by considering cracked sections, while others allow
calculating displacements with gross sections. To account for this in our stringency
comparison we must introduce lateral stiffness into the equation for CSI. Introducing Eq. 9 in
Eq. 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 ]
where
K CodeX , K CodeY : type of lateral stiffness (cracked or uncracked) stipulated in Code X or Code Y,
respectively.

7. 3. Code Stringency Index Comparison from Spectral Curves
The CSI equation proposed in Eq. 10 enables comparison of the code’s stringency with
respect to limiting lateral displacements for a series of structures with different fundamental
periods.
Consider a set of buildings for which fundamental periods vary from close to 0 sec to up to 10
sec, 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 all
buildings are made of reinforced concrete, and consist of dual structural systems
incorporating both shear walls and moment resisting frames. For those codes which require
the modeling of buildings with cracked inertia, assume a lateral stiffness which is half the
lateral stiffness of the same structures with uncracked sections (as recommended in the
Eurocode 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 the
European 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 in
controlling 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 periods
between 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 least
rigorous for periods between 2.65 and 9.65 sec, after which Eurocode 8 becomes the least
stringent in requiring lateral displacement control.
Despite being the less stringent in the short fundamental periods range, the Panamanian
standard is the third more rigorous for periods larger than 4 sec after the Chilean and
Colombian standards.
A comparison among the American and the European design provisions (which are the codes
of choice in countries where there is a lack of seismic normative) indicates that Eurocode 8 is
more stringent for periods of up to 4.9 sec, after which the American ASCE 7-05/IBC 2009
and UBC 1997 take over.

8. 4. Conclusions & Recommendations
In studying and comparing seismic design provisions of various codes it is evident that lack of
uniformity exists regarding calculation of lateral displacements. Differences result from
varying factors including drift limit ratios, the use of cracked or uncracked sections, lateral
force reduction factors, upper limits to the fundamental period of vibration, minimum base
shear 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 displacement
response spectrum, and support the changing trend in seismic design philosophy from force-
based towards a displacement-based. Force-based codes of practice sometimes lead the
engineer towards expensive designs and unfeasible structures.
A code stringency index, CSI, is proposed to enable comparison of code stringency in
controlling lateral displacements obtained from spectral acceleration curves. The comparison
of several international standards shows that the Chilean code is the most stringent standard
over the whole range of periods (up to 10 sec). This probably explains why most structures
designed with the current Chilean seismic normative have had a good performance during the
8.8 magnitude earthquake that rocked the central and southern region of the South American
country on the 27th February 2010.
For short periods (up to 0.13 sec) the Colombian, Peruvian and New Zealand codes rank
among the most stringent, while, for periods in between 0.13 sec to 2.85 sec Eurocode 8 is
second 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 the
European normative.
Among the least rigorous standards is the Panamanian for periods up to 2.65 sec, after which
the Australian becomes the least stringent up to a period of 9.65 seconds. This makes the
Australian 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 are
more rigorous up to a period of 4.9 sec. The opposite applies thereafter, were for longer
period structures the American standards are more stringent. In view of the above, it seems
the American UBC is most applicable to regions such as Dubai, were high rises like the Burj
Dubai have reported fundamental periods up to 11.3 sec (18).
It is recommended that the displacement response spectrums nominated by Eurocode 8
should 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. Acknowledgments
The author expresses his sincere gratitude to Alejandro Muñoz, Professor of the Pontifical
Catholic University of Peru, for his constructive critique provided during the production of this
paper.

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