PBEE Class Full Report

ACE874
Performance-Based
Seismic Engineering
Report of Ground Motion Selection and Scaling
Name : Zulkarnaen, Gifari

ID No : 2018021329
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1. Introduction
1.1. Objectives
1. Designing and analyzing 40-storey building using performance-based design approach.
2. Selecting and scaling ground motions for basis of hazard analysis according to method
300 of PEER GMSM (Conditional Mean Spectrum by Baker, 2011).
3. Modelling the building and acquiring performance result of the building using
displacement-based design approach.
4. Analyzing the performance results using probabilistic approach according to prescriptive
code and PEER TBI guidelines.
1.2. Limitation
1. Does not considers soil stiffness, all base joints are considered to be fixed.
2. Does not considers vertical ground motions.
3. Does not analyzes damage and economic loss.
2. Study Case and Design Basis

2.1. Building Data
This performance based seismic design uses study case of a 40-storey tall reinforced
concrete building located in downtown Los Angeles. The case study structure is a 415-feet
tall reinforced concrete residential building with 118 × 96 feet plan area (Figure 1). Typical
storey height is 10 feet with a 20-feet high lobby level. Lateral load carrying system of the
building is bearing walls coupled with 32 to 60-inch deep spandrel beams. The gravity system
consists of 8-inch-thick post-tensioned concrete fl at slabs resting on reinforced concrete
gravity columns and bearing walls. The natural period shown in Table 1 is obtained using
ETABS modelling (figure 2). Materials used are 8 ksi and 6 ksi.
This building will be analyzed using Performance-Based Earthquake Engineering (PBEE)
approach to investigate the overall performance of the structural and non-structural parts of
the building under various hazard levels, including the damage and loss impacts. Building data
as follows:
 Building type : multistory building
 Building function : residential
 Building importance : III (Ie = 1.25)
 Structural system : special reinforced concrete shear wall (with beamless frame)
 Site location : Stanford University, Palo Alto
 Site class : B (soft rock)
 Building dimension :
• Building size : 118 x 96 ft2
• Building height : 400 ft
• Floors : 40 floors
• Floor height : 10 ft
Class : ACE874 – Performance-Based Earthquake Engineering

Subject : Study Case of PBEE in 40-story Building using PEER TBI Guidelines 2017
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Figure 1. Building Plan
Figure 2. ETABS Modelling

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Table 1. Natural Periods of Building Model

Mode Period (s)
1 3.88
2 3.18
3 1.14
4 0.79
5 0.66
6 0.43
7 0.32
8 0.29
9 0.25
10 0.18
2.2. Seismic Hazard

The location of this building is Stanford University, Palo Alto, California with coordinate
(37.43, -122.165). The hazard curve (Figure 3) and disaggregation data (Figure 4) of this
location is obtained using USGS (2014) interactive internet site based on USGS Dynamic
Conterminous US 2014 data sources. The site class is defined as B/C (VS30 = 760 m/s) and
return period is 50 years for SLE and 2,475 years for MCER. From disaggregation data, the
target magnitude, site-to-location distance, and epsilon value is obtained as 7.69, 8.26 km,
and 1.44σ respectively.
50 years (SLE)
2,475 years (MCER)
Figure 3. Hazard Curve.

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Figure 4. Disaggregation Data for SLE.
Mean:
r: 8.26 km
m: 7.69
ε0: 1.44σ
Figure 5. Disaggregation Data for MCER.

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Magnitude and Distance Disaggregation

of NGA West2 Ground Motion Database
1800
1600
1400
Number of Records
1200
1000
800
600
400 0
Distance (km)
200 150
0 300
3.0 3.5 4.0
4.5 5.0 450
5.5 6.0
6.5 7.0
Magnitude 7.5 8.0
8.5 9.0
>9.0
Magnitude and Soil Vs30 Disaggregation

of NGA West2 Ground Motion Database
1400
1200
Number of Records
1000
800
600
400
0
Soil Vs30 (m/s)
200
300
0 600
900
Magnitude
Figure 6. Disaggregation of NGA West2 Ground Motion Database.

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Magnitude and Distance Disaggregation of

Sorted Library based on Nearest Site Parameter
8
7
Number of Records
6
5
4
3
2
1
Distance (km)
0
0
6.7 6.8 6.9 7 20
7.1 7.2 7.3
7.4 7.5 7.6
7.7 7.8 7.9 40
8 8.1 8.2
Magnitude 8.3 8.4 8.5
8.6 8.7
Magnitude and Soil Vs30 Disaggregation of

Sorted Library based on Nearest Site Parameter
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12
Number of Records
10
8
6
4
2
Soil Vs30 (m/s)
0 560
6.7 6.9 810
7.1 7.3 7.5 7.7 7.9 8.1 8.3 8.5
Magnitude 8.7
Figure 7. Disaggregation of Sorted Library of Ground Motions with Nearest Range with Target
Earthquake Parameters.
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2.3. Database and Library

Database of ground motions that is used in this study is PEER West2 Berkeley which
contains more than 21,000 strong-motion records. The database is sorted by nearest range
with the target earthquake parameter to the library. Total 113 ground motions are
geophysically sorted to the library for initial phase of selection and scaling phase, before then
extended in optimization phase. The aggregation of the database and the sorted library is
respectively shown in Figure 5 and Figure 6. The search ranges are defined as follows:
 Magnitude: 6.7 – 8.7
 Distance: 0 – 50 km
 VS30: 560 – 960 m/s
3. Methodology
There are three steps used in this study. First, the building is modelled and designed
according to prescriptive code of ASCE 7-16 and ACI 318 using linear elastic response
spectrum analysis in ETABS 2016 software as preliminary design. The design result then
remodeled and designed according to PEER TBI Guidelines for PBD of Tall Building using
nonlinear time-history analysis in Perform-3D 7 software. The NLTHA analysis will be done in
50-years return period of Service Level Earthquake (SLE) and 2,475 years return period of
Risk-targeted Maximum Considered Earthquake (MCER).
Figure 8. Design Procedure

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4. Conditional Mean Target Spectrum

Target spectrum is then defined based on design earthquake parameters which will
be the target of ground motion selection and scaling. In this study, Conditional Mean Target
Spectrum is chosen, based on Ground Motion Prediction Equation (GMPE) provided by Baker
(2011).
Figure 9. Conditional Mean Spectrum.
The CMS conditions the entire spectrum on spectral acceleration at a single

userspecified period and then computes the mean values of spectral acceleration at all other
periods. This conditional calculation ensures that ground motions modified to match the
spectrum have properties of recorded ground motions. The CMS calculation requires hazard
disaggregation information, making it site-specific. The appropriate conditioning period may
not be immediately obvious and the CMS changes with conditioning period, unlike the UHS.
Further, the spectrum changes shape as the peak spectral value is changed, even when the
site and period are not changed. Multiple conditioning periods could be used to generate a
family of CMS for either design or performance assessment (NIST, 2011).
4.1. Computing the median and SD of log(Sa) at all periods
The first step of CMS analysis is computing the median and standard deviation of log
spectral acceleration at all periods. The median of ln Sa(T1) is computed using following
equation:
ln 𝑆𝑎(𝑇1 ) = 𝐹𝐸 (𝑀, 𝑚𝑒𝑐ℎ) + 𝐹𝑃 (𝑅𝐽𝐵 , 𝑀) + 𝐹𝑆 (𝑉𝑆30 , 𝑀, 𝑚𝑒𝑐ℎ, 𝑅𝐽𝐵 )
where FE, FP, and FS represent period-dependent functions for source (event), path, and site
effects, respectively. The predictor variables are M, mech, RJB, and VS30 which are moment
magnitude, distance (closest distance to the surface projection of the fault plane), site
parameter VS30, and fault type.

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 The source (event) function is given by:

𝑒0 𝑈 + 𝑒1 𝑆𝑆 + 𝑒2 𝑁𝑆 + 𝑒3 𝑅𝑆 + +𝑒4 (𝑀 − 𝑀ℎ ) + 𝑒5 (𝑀 − 𝑀ℎ )2 𝐌 ≤ M𝒉
𝐹𝐸 (𝑀, 𝑚𝑒𝑐ℎ) = {
𝑒0 𝑈 + 𝑒1 𝑆𝑆 + 𝑒2 𝑁𝑆 + 𝑒3 𝑅𝑆 + +𝑒6 (𝑀 − 𝑀ℎ )2 𝐌 > M𝒉
where U, SS, NS, and RS are dummy variables, with a value of 1 for unspecified, strike-slip,
normal-slip, and reverse-slip fault types, respectively, and 0 otherwise; the hinge magnitude
Mh is period dependent, and e0, e1, e2, e3, e4, e5, and e6 are model coefficients (see appendix).
 The path function is given by:

𝐹𝑃 (𝑅𝐽𝐵 , 𝑀) = [𝑐1 + 𝑐2 (𝑀 − 𝑀𝑟𝑒𝑓 )] ln(𝑅 ⁄𝑅𝑟𝑒𝑓 ) + (𝑐3 + ∆𝑐3 )(𝑅 − 𝑅𝑟𝑒𝑓 )
where
𝑅 = √𝑅𝐽𝐵 2 + ℎ2
and c1, c2, c3, Δc3, Mref, Rref and h are model coefficients (see appendix). Parameter Δc3 is
region-dependent.
 The site function is given by:
𝐹𝑆 (𝑉𝑆30 , 𝑀, 𝑚𝑒𝑐ℎ, 𝑅𝐽𝐵 ) = ln(𝐹𝑙𝑖𝑛 ) + ln(𝐹𝑛𝑙 )
where Flin represents the linear component of site amplification and Fnl represents the
nonlinear component of site amplification. The linear component of the site model (Flin)
describes the scaling of ground motion with VS30 for linear soil response conditions (i.e., small
strains) as follows:
𝑉𝑆30
𝑐 ln ( ) 𝑉𝑆30 ≤ 𝑉𝐶
𝑉𝑟𝑒𝑓
ln(𝐹𝑙𝑖𝑛 ) =
𝑉𝐶
𝑐 ln ( ) 𝑉𝑆30 > 𝑉𝐶
{ 𝑉𝑟𝑒𝑓
where Vref represents a reference velocity where the amplification is zero (in ln units), Vc is a
limiting velocity beyond which there is no further VS30 -scaling, and c represents the level of
VS30-scaling for VS30 < Vc (see appendix). The function for the Fnl term is as follows:
𝑃𝐺𝐴𝑟 + 𝑓3
ln(𝐹𝑛𝑙 ) = 𝑓1 + 𝑓2 ln ( )
𝑓3
where f1, f2, and f3 are model coefficients (see appendix) and PGAr is obtained by evaluating
ln Sa(T1) equation for the given M, mech, and RJB with VS30 = 760 m/s. Parameter f2 represents
the degree of nonlinearity for the vertical-component and is formulated as:
𝑓2 = 𝑓4 [exp{𝑓5 (min(𝑉𝑆30 , 760) − 360)} − exp{𝑓5 (760 − 360)}]
where f4 and f5 are model coefficients (see appendix).

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 The total standard deviation σ is partitioned into components that represent between-event
variability ( τ ) and within-event variability ( φ ) as follows:
𝜎(𝑀) = √𝜙 2 (𝑀) + 𝜏 2 (𝑀)
The M-dependent between-event standard deviation τ is given by

𝜏1 𝑀 ≤ 4.5
𝜏(𝑀) = { 𝜏1 + (𝜏2 − 𝜏1 )(𝑀 − 4.5) 4.5 < 𝑀 < 5.5
𝜏2 𝑀 ≥ 5.5
The M-dependent within-event standard deviation φ is given by
𝜙1 𝑀 ≤ 4.5
𝜙(𝑀) = {𝜙1 + (𝜙2 − 𝜙1 )(𝑀 − 4.5) 4.5 < 𝑀 < 5.5
𝜙2 𝑀 ≥ 5.5
 By using above equations, the median ln Sa(T1) and standard deviation σ for this study (for
MCER) is shown in Figure 8 below.
Median of Ground Motion Standard Deviation of Ground

Prediction Motion Prediction
10 0.8
0.7
0.6
1
0.5
Sa (g)
0.4
σ
0.3
0.1
0.2
Median 0.1 σ
0.01 0
0.01 0.1 1 10 0.01 0.1 1 10
Period (s) Period (s)
Figure 10. Median ln Sa(T1) and standard deviation σ, with target magnitude = 7.69, distance = 8.26 km,
soil VS30 = 760 m/s and unspecified rupture mechanism.

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3.2. Compute Target ε(T1), from Hazard Disaggregation.

This can be determined from direct back-calculation in the case where a
deterministic magnitude and distance scenario was used, or from probabilistic seismic
hazard analysis disaggregation. The ε(1.14) value obtained from USGS for this study is 1.44.
Then the median + εσ of log(Sa) at all periods (Figure 9) which equal with Uniform
Hazard Spectrum is calculated using following equation.
𝜇ln(𝑆𝑎+𝜀𝜎) (M, 𝑅𝐽𝐵 , 𝑉𝑆30 , 𝑚𝑒𝑐ℎ) = 𝐹𝐸 (M, 𝑚𝑒𝑐ℎ) + 𝐹𝑃 (𝑅𝐽𝐵 ,M) + 𝐹𝑆 (𝑉𝑆30 ,M, 𝑚𝑒𝑐ℎ, 𝑅𝐽𝐵 ) + 𝜀𝑛 𝜎(M)
Median+εσ of Ground Motion Prediction

(M = 7.69, Rjp = 8.26 km, Vs = 760 km)
10
1
Sa (g)
0.1
Median
Median+εσ
0.01
0.01 0.1 1 10
Period (s)
Figure 11. Median + εσ of log(Sa) at all periods.
3.3. Compute Conditional Mean ε(T1) at All Other Periods, Using Correlation Coefficient ρ
This calculation based on study of Baker & Jayaram (2008) “Correlation of spectral
acceleration values from NGA ground motion models”. The predicted correlation
coefficient for conditional mean ε(T1) at all other periods is given by
𝐶2 𝑇𝑚𝑎𝑥 < 0.109

𝐶 𝑇𝑚𝑖𝑛 > 0.109
𝜌𝜀(𝑇1 ),𝜀(𝑇2 ) ={ 1
min(𝐶1 , 𝐶4 ) 𝑇𝑚𝑎𝑥 < 0.2
𝐶4 otherwise

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where
𝜋 𝑇𝑚𝑎𝑥
𝐶1 = 1 − cos ( − 0.366 ln ( ))
2 max(𝑇𝑚𝑖𝑛 , 0.109)
1 𝑇𝑚𝑎𝑥 − 𝑇𝑚𝑖𝑛
1 − 0.105 (1 − ) ( ) if 𝑇𝑚𝑎𝑥 < 0.2
𝐶2 = { 1 + 𝑒 100𝑇𝑚𝑎𝑥 −5 𝑇𝑚𝑎𝑥 − 0.0099
0 otherwise
𝐶 if 𝑇𝑚𝑎𝑥 < 0.109
𝐶3 = { 2
𝐶1 otherwise
𝜋𝑇𝑚𝑖𝑛
𝐶4 = 𝐶1 + 0.5(√𝐶3 − 𝐶3 ) (1 + cos ( ))
0.109
3.4. Compute CMS Sa at all other periods

Then the CMS anchored at 3.88 s as first mode of the building can be computed
using following equation:
𝜇ln(𝑆𝑎 (𝑇1 )|ln(𝑆𝑎(𝑇 ∗)) = 𝜇ln 𝑆𝑎 (𝑀, 𝑅, 𝑚𝑒𝑐ℎ, 𝑇𝑖 ) + 𝜌(𝑇𝑖 , 𝑇 ∗ )𝜀(𝑇𝑖 , 𝑇 ∗ )𝜎ln 𝑆𝑎(𝑇𝑖 )
Conditional Mean Target Spectrum at T1 = 3.88 s

10
1
Sa(g)
0.1
CMS Mode 1 (T=3.88s)
Median
Median+εσ
0.01
0.01 0.1 1 10
Period (s)
Figure 12. CMS Anchored at 3.88 s (Mode 1).

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Repeating step 3 for other building natural period, the comparison of CMS anchored
at period of mode 1 (3.88 s), mode 2 (3.18 s), mode 3 (1.14 s), and mode 4 (0.79 s) is shown
in Figure 11. Period of mode 3 is chosen as target of CMS (Figure 12) for this study.
Figure 13. Comparison of CMS Anchored at Various Mode of The Building

in Logarithmic Scale (Upper) and Linear Scale (Below).
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Conditional Mean Target Spectrum

at T1 = 1.14 s (Mode 3)
10
1
Sa(g)
0.1 CMS Mode 3 (T=1.14s)

Median
Median+εσ
0.01
0.01 0.1 1 10
Period (s)
Figure 14. CMS Used in This Study which is Anchored at Mode 3 for MCER.
5. Ground Motion Selection

In this study, the ground motion selection uses method and algorithm provided by
Baker & Lee (2016) using MATLAB software. The procedure of the software (Figure 13) is as
follows:
1) Specifying target spectra.
2) Statistically simulating realizations of response spectra from the target distribution.
The simulation is done by sampling from multivariate normal distribution with the
target mean and covariance matrices. The simulation is performed multiple times, and
select a set of simulation best matching the target spectrum.
3) Specifying candidate ground motions library (sorted based on range of Magnitude,
distance, Vs30, or other properties).
4) Selecting (optionally scaled) ground motion with error defined as:
5) Evaluating whether it is sufficiently close to the target distribution. If errors are too
large, greedy optimization is performed by replacing individual GM and seeing
whether the set is improved, until meets the target.

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Figure 15. Procedure of Ground Motion Selection Algorithm by Baker & Lee (2016).
4.1. Algorithm Input

The following parameters are inputted to the software:
GM Parameter Input
Cond : conditional selection
Arb : average component sigma
RotD : SaRotD100
isScaled : scaled
maxScale :5
optType : SSE
Weight :0
Target Rupture Input

Magnitude M : 7.69
Distance to fault RJB : 8.26 km
Epsilon value ε : 1.44σ
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Fault type : unspecified fault

Region : global
Basin depth zl : unknown
Shear wave velocity VS30 : 259 km/s
GM number and time of interest

GM number : 14
T conditional : 1.14 s
Period of interest : 0.1 – 10 s
Sa(Tcond) :-
GM properties from database

Database : NGA_West2
Vs30 bound : 560 – 960 m/s
Magnitude bound : 6.7 – 8.7
Distance bound : 0 – 50 km
4.2. Selected Ground Motions

The result of selected ground motions’ list is shown in Table 2. From these 14
selected ground motions, records can be manually sorted further to eliminate records
which have parameters too far from requirement. Here record 38, 54 and 67 are eliminated
because the distances are above 100 km, and record 111 is eliminated because the
magnitude is below 5. The accelerogram of remaining ground motions are shown in Figure
14.
Table 2. List of Selected Ground Motions from Software.
Rec. Scale Station RJB VS30
Earthquake Name Year Station Name Mag Rup
ID Factor Number (km) (m/s)
9 4.45 'Borrego' 1942 'El Centro Array #9' 75 6.50 56.9 213.4 U
38 3.60 'Borrego Mtn' 1968 'LB - Terminal Island' 81 6.63 199.8 217.9 U
45 2.65 'Lytle Creek' 1970 'Devil''s Canyon' 106 5.33 20.2 667.1 RS
47 0.59 'Lytle Creek' 1970 'Lake Hughes #1' 320 5.33 90.4 425.3 RS
50 2.33 'Lytle Creek' 1970 'Wrightwood - 6074 Park Dr' 99 5.33 12.1 486.0 RS
54 1.79 'San Fernando' 1971 'Borrego Springs Fire Sta' 69 6.61 214.3 338.5 NS
64 1.89 'San Fernando' 1971 'Fort Tejon' 122 6.61 61.6 394.2 NS
65 1.45 'San Fernando' 1971 'Gormon - Oso Pump Plant' 121 6.61 46.8 308.4 NS
67 1.76 'San Fernando' 1971 'Isabella Dam (Aux Abut)' 137 6.61 131.0 591.0 NS
73 2.84 'San Fernando' 1971 'Lake Hughes #9' 79 6.61 22.6 670.8 NS
81 1.67 'San Fernando' 1971 'Pearblossom Pump' 84 6.61 39.0 529.1 NS
87 3.86 'San Fernando' 1971 'Santa Anita Dam' 68 6.61 30.7 667.1 NS
101 4.40 'Northern Calif-07' 1975 'Cape Mendocino' 501 5.20 34.7 567.8 U
111 4.12 'Oroville-04' 1975 'Up & Down Cafe (OR1)' 169 4.37 12.2 377.3 RS

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0.2
Lytle Creek 1970 - Devils Canyon
0.1
Sa (g)
0
-0.1
-0.2
0.02
0.01
Lytle Creek 1970 - Lake Hughes #1
Sa (g)
0
-0.01
-0.02
0.2
Lytle Creek 1970 - Wrightwood
0.1
Sa (g)
0
-0.1
-0.2
0.05
San Fernando 1971 - Fort Tejon
0.025
Sa (g)
0
-0.025
-0.05
0.2
San Fernando 1971 - Gormon Oso Pump Plant
0.1
Sa (g)
0
-0.1
-0.2
0.2
California 07 1975 - Cape Mendocino
0.1
Sa (g)
0
-0.1
-0.2
0 3 6 9 12 15
Period (s)
Figure 14 (a). Accelerogram of Selected Ground Motions

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0.2
San Fernando 1971 - Lake Hughes #9
0.1
Sa (g)
0
-0.1
-0.2
0.2
0.1
San Fernando 1971 - Perblossom Pump Plant
Sa (g)
0
-0.1
-0.2
0.2
San Fernando 1971 - Santa Anita Dam
0.1
Sa (g)
0
-0.1
-0.2
0.2
0.1 Borrego 1942 - El Centro Array #9
Sa (g)
0
-0.1
-0.2
0 5 10 15 20 25 30 35 40 45 50
Period (s)
Figure 16 (b). Accelerogram of Selected Ground Motions
From accelerograms above, none of those has duration more than 100 seconds. But
some (no. 47 and 64) have peak ground acceleration less than 0.1g which very small and need
to be eliminated before go to the next step.
6. Ground Motion Matching
In this study, the method for ground motion scaling uses selective manipulation of
accelerogram approach developed by Abrahamson (1993, 2006, 2010). The method adds
wave packages to those parts of the time-series for those frequencies for which there is a
mismatch between the record and target spectrum. The original wavelet function developed
by Lilhanand and Tseng (1987, 1988)is:

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Tapered cosine wavelet is then introduced to the scaling method by Hancock (2006):
The tapered cosine wavelet which has flaw on the endless function in the end of period is
then improved further by Atik and Abrahamson (2010):
Pseudospectral acceleration adjustment is also added to the method for better scaling result:
The original software developed for this method is RspMatch, and then adopted by
many other softwares including SeismoMatch (2018) and ETABS (2016). SeismoMatch is used
in this study for ground motion scaling. Step by step procedure of scaling the selected ground
motions using SeismoMatch software is as follows:
1) Input the original accelerograms
Figure 17. Accelerograms Input in Seismo Match.

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2) Input the computed CMS as target spectrum
Figure 18. CMS as Target Spectrum Input in Seismo Match.
3) Define the range of period in which the matching will be performed. In this study, the
period range of spectral matching is defined in between 0.2T 1 – 3T1 where T1 is 1.14 s.
Figure 19. Defining Range of Period of Spectral Matching, 0.2T1 – 3T1, in Seismo Match.
4) Do the matching and export the result of matched accelerograms.
Figure 20. Matched Accelerograms Output in Seismo Match.

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The saved output file can then be used for non-linear time-history structural analysis.
The comparison between original and matched accelerograms is shown in Figure 18, and the
comparison between mean of matched response spectrums and CMS is shown in Figure 19.
It can be seen that although the response spectra is matched very well to the target CMS
along the defined matching period, the remaining period of some matched accelerograms
(no. 47 and 65) are distorted too much and not well neutralized to zero acceleration, thus
one of them can be eliminated to achieve 7 ground motions. Since using too many same
earthquake should be avoided, record 65 (San Fernando 1971 – Gormon Oso Pump Plant) is
eliminated.
0.5
Lytle Creek 1970 - Devils Canyon
0.25
Sa (g)
0
-0.25
-0.5
0.5
0.25 Lytle Creek 1970 - Wrightwood
Sa (g)
0
-0.25
-0.5
0.5
0.25
San Fernando 1971 - Gormon Oso Pump Plant
Sa (g)
0 (eliminated)
-0.25
-0.5
0.5
0.25 California 07 1975 - Cape Mendocino
Sa (g)
0
-0.25
-0.5
0 3 6 9 12 15
Period (s)
Figure 21 (a). Comparison of Original (Red) and Matched (Black) Accelerograms.

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1
Sa (g) 0.5 San Fernando 1971 - Lake Hughes #9
0
-0.5
-1
0.5
0.25
San Fernando 1971 - Perblossom Pump Plant
Sa (g)
0
-0.25
-0.5
1
0.5 San Fernando 1971 - Santa Anita Dam
Sa (g)
0
-0.5
-1
0.5
0.25 Borrego 1942 - El Centro Array #9
Sa (g)
0
-0.25
-0.5
0 5 10 15 20 25 30 35 40 45 50
Period (s)
Figure 22 (b). Comparison of Original (Red) and Matched (Black) Accelerograms.
Comparison of Mean Matched Ground Motions and

Conditional Mean Target Spectrum (CMS) for MCER
1.6
1.4
1.2
1 Individual GM
Sa (g)
0.8 Mean of GMs

0.6 CMS
0.4
0.2
0
0 0.5 1 1.5 2 2.5 3 3.5 4
Period (s)
Figure 23. Comparison of Mean Matched Ground Motions and

Conditional Mean Target Spectrum (CMS) for MCER.
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ID No. : 2018021329
Similarly, the result of ground motion selection and matching for SLE is shown in
Figure 24-25.
Figure 24a. Original (orange) and matched (blue) accelerograms for SLE.

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ID No. : 2018021329
Figure 24b. Original (orange) and matched (blue) accelerograms for SLE.
Figure 25. Comparison of Mean Matched Ground Motions and

Conditional Mean Target Spectrum (CMS) for SLE.

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ID No. : 2018021329
7. Design Based Earthquake

7.1. Modelling
In this study, linear elastic response spectrum analysis is used in DBE level using ETABS 2016
following requirements mentioned in ASCE 7-18 and ACI 318. The earthquake parameters
according to building type, use, and location are as follows:
 Occupancy : residential
 Risk category : III
 Importance factor ( Ie ) : 1.25
 Seismice-resisting system : special reinforced concrete shear walls
 Response modification coef. (R) :6
 Overstrength factor ( Ω0 ) : 2.5
 Deflection amplification factor ( Cd ) : 5
 Seismic design category :D
 USGS-provided spectra parameter SS : 1.663 g
S1 : 0.761 g
 Soil type : B (soft rock)
 Site class coefficient Fa :1
Fv :1
The response spectrum (RS) for the earthquake load (damping 5%) shown in Figure 26 is
calculated using these formulas:
Figure 26. Response spectrum used for linear analysis in DBE.

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ID No. : 2018021329
Other inputs in the building model in ETABS are as follows:

 Dead load D : self-weight & 28 psf
 Live load L : 28 psf
 Effective seismic weight : D + 0.25L
 Modal analysis : Ritz
 Number of modes : 40
 Modal combination method : CQC
 Directional combination type : SRSS
 Element stiffness, moment of inertia (ACI 318 Table 6.6.3.1)
o Columns : 0.70 Ig
o Walls : 0.70 Ig
o Beams : 0.35 Ig
o Slabs : 0.25 Ig
The scaling factor for earthquake load is defined following these equations:
 Approximate fundamental period (ASCE 7-16 12.8.2.1):
Ct : 0.0488
x : 0.75
building height hn : 125 m
upper limit Cd : 1.4
approximate fund. period Ta = Cthnx = 1.791 s
max approx fund. period T = CdTa = 2.507 s
 Seismic response coefficient (ASCE 7-16 12.1.1):
CS = SDS / (R / Ie) = 0.2310
CS max = SD1 / (T x (R / Ie)) = 0.0950
CS min1 = 0.044SDSIe = 0.0610 ≥ 0.01
CS min2 = 0.5S1/(R/Ie) = 0.0793 (for S1 ≥ 0.6 g)
So, CS used is : 0.0793
 Scaling factor = CS x g = 777.33
7.2. Results Check

7.2.1. Modal Check
It is required in ASCE 7-16 12.19.1 that the modal mass participation of at least 90% is
obtained using inputted number of modes. The analysis shows the requirement is fulfilled in the
mode 12 above, shown in Figure 27.

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ID No. : 2018021329
Figure 27. Modal participating mass ratios.
7.2.2. Weight Check

The weight check confirms the modelling input. The difference of weight between
calculation and model output is less than 1%, shown in Table below.
Table 3. Modelling Weight Check
Load Calculation (kN) Result (kN) Error
Dead 305,510 308,360 0.93%
Super Dead 52,401 52,670 0.51%
Live 74,858 75,253 0.53%
7.2.3. Lateral Seismic Load Check

It is required in ASCE 7-16 12.9.1.4 that the scaling factor shall fulfill the targeted
seismic response base shear according to ASCE 7-16 12.8. From the The model scaling
factor needs to be re-scaled as follows:
W = D + 0.25L = 379,475 kN
V = CSW = 30,081 kN
Vt = 21,238 kN
V/Vt = 1.53
Figure 28. Lateral seismic load check

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ID No. : 2018021329
7.2.4. Drift Check

According to the code, the drift in each story shall not exceed the maximum
allowed drift determined in ASCE 7-16 Table 12.12-1, which is 1.5%. The amplified drift is
equal to Cd/Ie = 4. The story drift result shown in Figure 29 meets the requirement.
Story Drift (DBE)
40
35
30
25
Story
20
15
10 X Y
5
0
0.00% 0.50% 1.00% 1.50% 2.00%
Drift
Figure 29. Story drift of DBE using response spectrum analysis.
7.3. Concrete Design

After checking all the requirements, the elements are designed following ACI 318-14
provisions. The response spectrum results are shown in Figure 30 and Table 4, while design
results are shown in Table 5 and Figure 31-32 below.
Figure 30. Story shear and moment of DBE using response spectrum analysis.

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ID No. : 2018021329
Table 4. DBE response spectrum analysis results of element forces.

Frame P V2 V3 T M2 M3
kN kN kN kNm kNm kNm
Col 1-10 -23514.5 151.99 196.32 25.09 615.39 462.35
Col 11-20 -17116.2 123.96 69.82 15.21 75.49 204.85
Col 21-30 -11106.7 126.14 67.25 8.58 75.93 198.91
Col 31-40 -5431.2 169.28 57.87 4.35 111.10 315.86
CB 1-20 0 3025.48 0 38.42 0 1380.21
CB 21-40 0 1819.11 0 41.30 0 824.17
Table 5. Element design results.

Column Coupling Beam
C1 C2 C3 C4 CB1 CB2
Section
Floor 1-10 11-20 21-30 31-40 1-20 21-40

Dim. (mm) 914 x 914 813 x 813 711 x 711 609 x 609 813 x 762 813 x 609
Long. rebar 12D32 12D29 12D25 08D25 6D32 6D29
Trans. rebar 4D19-150 4D19-150 4D19-150 3D19-150 6D19-150 6D16-150
Figure 31. Auto post-tension slab design by gravity load using ETABS 2016.

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ID No. : 2018021329
Figure 32. Wall reinforcement design with confined concrete only in first story.
8. Service Level Earthquake (SLE)

8.1. Modelling
Nonlinear time-history analysis is used in SLE and MCER earthquake level. Perform-3D
7 is used in for modelling and analyze the building. Nonlinear materials and elements are
used in the building model. Unconfined and confined concrete (8 ksi for slab, and 6 ksi for
other elements) materials follow Mandel (1984) concrete model, shown in Figure 32. The
rebar material follows regular ductile steel material properties of A615 60 ksi.

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ID No. : 2018021329
(a)
(b)
Figure 33. (a) Concrete stress-strain curve and (b) its equations.
The slab is modelled with equivalent width slab-beam following ATC-72 provision. The
effective width, shown in Figure 34 and Table 6 of the slab-beam is calculated using following
formula:
𝑏𝑒𝑓𝑓 = 𝛽 ∙ (5 ∙ 𝑐1 + 0.25 ∙ 𝑙1 )
β = 1 for post-tensioned floor
c1 = column width
l1 = span length
Figure 34. Equivalent width slab-beam model layout.

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ID No. : 2018021329
Table 6. Slab-beam dimension calculation.

Col Beam c1 l2 β beff h
mm mm mm mm
C36 BX-1 914.4 9144.0 1 6858.0 203.2
BY1-1 914.4 8839.2 1 6781.8 203.2
BY2-1 914.4 7315.2 1 6400.8 203.2
C32 BX-2 812.8 9144.0 1 6350.0 203.2
BY1-2 812.8 8839.2 1 6273.8 203.2
BY2-2 812.8 7315.2 1 5892.8 203.2
C28 BX-3 711.2 9144.0 1 5842.0 203.2
BY1-3 711.2 8839.2 1 5765.8 203.2
BY2-3 711.2 7315.2 1 5384.8 203.2
C24 BX-4 609.6 9144.0 1 5334.0 203.2
BY1-4 609.6 8839.2 1 5257.8 203.2
BY2-4 609.6 7315.2 1 4876.8 203.2
Coupling beam and slab-beam is modelled using moment-curvature relation obtained

from Response-2000 section analysis software. FEMA beam section is used in this model
with limit states following FEMA 356 provision. Fiber section with non-linear materials is
used for shear wall in first floor and elastic shear wall in other floors. Rigid link member is
used in wall between floors to connect the members. Axial strain gauges are inputted in the
extreme wall fibers. Eleven pairs of 50 years return period for earthquake load are applied.
Layout summary of the model is shown in Figure 35 below.
Figure 35. Layout summary of modelling in Perform-3D.

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ID No. : 2018021329
8.2. Global Acceptance Evaluation

According to TBI guidelines, calculated story drift shall not exceed 0.5% of story height
in any story, computed at extreme points for each floor plan in each of two orthogonal plan
directions. The NLTHA analysis result shows that the building design meets the global
acceptance requirement, with story drift result is shown in Figure 36. The maximum story
drift in any story of all earthquakes is 0.39%.
Story Drift (SLE)

X-direction Y-direction
Figure 36. Peak story drift (SLE) of every earthquake (grey) with its mean (solid blue) and maximum
(dashed blue) value.
8.3. Component Acceptance Evaluation

According to TBI guidelines, calculated deformations shall be less than those that
result in damage that (a) exceeds minor cracking of concrete or yielding of steel in a limited
number of structural elements, (b) impairs the ability of the structure to survive MCER
shaking, (c) results in unacceptable permanent deformation, or (d) requires repairs beyond
that which is necessary to restore appearance or protection from water intrusion, fire, or
corrosion. Repair, if required, should not require removal and replacement of structural
concrete other than cover, nor should it require replacement of reinforcing steel or
structural steel. Acceptance criteria shall be demonstrated by appropriate laboratory testing.

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ID No. : 2018021329
In lieu of the use of laboratory test data, it shall be permissible to use the acceptance criteria
for Immediate Occupancy performance as contained in ASCE 41.
However, in this study, building has been designed according to elastic response
spectrum analysis in DBE level which is stronger load than SLE level, and the elements has
been designed to accommodate all loads within elastic capacity which is lower than
Immediate Occupancy performance requirement. Thus, component acceptance evaluation
in SLE level is not critical and not considered in this study.
9. Risk-targeted Maximum Considered Earthquake (MCER)

9.1. Modelling
Using the same modelling with SLE, eleven pairs of 2,475 years return period time
histories are applied for MCER analysis.
9.2. Global Acceptance Evaluation

According to PEER TBI guidelines, for MCER level, the building needs to be evaluated
to meet following global acceptance:
1. Analytical solution fails to converge;
2. Demands on deformation-controlled elements exceed the valid range of modeling;
3. Demands on critical or ordinary force-controlled elements exceed the element
capacity;
4. Deformation demands on elements not explicitly modeled exceed the deformation
limits
5. at which the members are no longer able to carry their gravity loads;
6. Peak transient story drift ratio in any story exceeds 0.045;
7. Residual story drift ratio in any story exceeds 0.015;
8. In each story, the mean of the absolute values of the peak transient story drift ratios
from each suite or set of analyses shall not exceed 0.03; and
9. In each story, the mean of the absolute values of residual drift ratios from the suite
of analyses shall not exceed 0.01.
The NLTHA analysis shows that the building design meets all the requirements, with story
drift results showed in Figure 37 and Table 7.

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ID No. : 2018021329
Transient Story Drift (MCER)

X-direction Y-direction
Figure 37. Transient drift (MCER) of every earthquake (grey) with its mean (solid blue) and maximum
(dashed blue) value.
Table 7. Story drift (MCER) result and acceptance.

Story drift Result TBI limit
Peak transient 3.26% 4.5%
Peak residual 0.79% 1.5%
Mean of transient 2.76% 3.0%
Mean of residual 0.31% 1.0%
9.3. Component Acceptance Evaluation

Each element is evaluated using deformation-controlled evaluation. If the ultimate
deformation capacity (δu) associated with any mode of deformation in a component is
exceeded in any of the response history analyses, according to TBI guidelines, it is permitted
either to:
1. Assume the strength associated with this mode of deformation is negligible for the
remainder of that analysis and evaluate the stability of the structure and the effects
on related strength quantities, or,
2. Consider the analysis to have unacceptable response.

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ID No. : 2018021329
Coupling Beam Rotation (MCER)
Figure 38. Peak coupling beam rotation(MCER) of every earthquake (grey) with its mean (solid blue) and
maximum (dashed blue) value.
Table 8. Coupling beam result and acceptance.

Coupling beam end rotation (rad) FEMA 356 collapse
Maximum Minimum prevention limit (rad)
Average rotation 0.0135 -0.0149 0.020
Maximum rotation 0.0195 -0.0203 0.020
Table 9. Shear wall measured strain result.

Core wall measured strain at extreme location
Maximum (tension) Minimum (compression)
Average strain 0.00527 -0.00258
Maximum strain 0.00915 -0.00372
The coupling beam rotation can be seen in Figure 38 and Table 8-9. The coupling beam
rotation enters plastic deformation (above 0.005 radians) but meets FEMA 356 collapse
prevention limit of 0.020 rad almost in all earthquake, except one that exceed the limit with
rotation of 0.0203 rad. This can be reminder that the design should be improved, but can be
exception since the average rotation value of 0.0149 is far from the limit.

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ID No. : 2018021329
The deformation of shear wall is measured only in first floor since plastic behavior is
expected to be occurred only in there, the strain result is shown in Table 9. Minimum strain
(compression) result shows that there is concrete in certain earthquake with strain value up
to -0.00372, while the average compression strain is -0.00258. Because deformation is
measured in extreme point of confined concrete, although this maximum value exceed the -
0.003 ultimate strain of normal (unconfined) concrete, this maximum value still lies within
confined concrete capacity which the ultimate strain is up to -0.008. On the other hand, the
average and maximum tension strain of core wall is 0.00527 and 0.00915 respectively. These
value shows that rebar has exceed steel yield strain (0.002) but still far from still ultimate
strain value which is up to 0.1.
10. Conclusion
This study shows step by step of Performance Based Design procedures on 40-story
building example using PEER TBI Guidelines for PBD of Tall Buildings 2017, including
conditional mean target spectrum calculation, ground motion selection and matching,
prescriptive code based design on 495 years return period Design Based Earthquake (DBE)
level using linear response spectrum analysis for preliminary design, and nonlinear time
history analysis on 50 years return period Service Level Earthquake (SLE) and 2,475 years
return period Risk-targeted Maximum Considered Earthquake (MCER) level.
For this 40-story wall-slab-column frame structure study case, the results show that
the building design meets all requirements in both prescriptive code as well as PBD provisions.
The analysis shows that all calculated story drifts in all earthquake levels lie within limits. In
MCER level, coupling beams and 1st story core wall’s rebar have enter plastic deformation but
still inside acceptance level, while 1st story core wall’s compression strain are still within
confined concrete ultimate capacity.

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ID No. : 2018021329
References
ACI Committee. (2014). 318, Building Code Requirements for Structural Concrete (ACI 318–14)
and Commentary (ACI 318R–14). American Concrete Institute, Farmington Hills, MI, 519.
ASCE/SEI 7-16: Minimum Design Loads and Associated Criteria for Buildings and Other Structures.
ACSCE 41-17: Seismic Evaluation and Retrofit of Existing Buildings.
Al Atik, L., & Abrahamson, N. (2010). An improved method for nonstationary spectral
matching. Earthquake Spectra, 26(3), 601-617.
Baker, J.W. and Jayaram, N., (2008). Correlation of spectral acceleration values from NGA ground
motion models. Earthquake Spectra, 24(1), 299-317.
Baker, J. W., & Lee, C. (2018). An improved algorithm for selecting ground motions to match a
conditional spectrum. Journal of Earthquake Engineering, 22(4), 708-723.
Bommer, J. J., & Acevedo, A. B. (2004). The use of real earthquake accelerograms as input to
dynamic analysis. Journal of Earthquake Engineering, 8(spec01), 43-91.
Bommer, J. J. and Ruggeri, C. [2002]. The specication of acceleration time-histories in seismic
design codes," European Earthquake Engineering 16(1), 3{17.
Boore, D. M., & Atkinson, G. M. (2008). Ground-motion prediction equations for the average
horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between
0.01 s and 10.0 s. Earthquake Spectra, 24(1), 99-138.
Boore, D. M., Stewart, J. P., Seyhan, E., and Atkinson, G. M. (2014). NGA-West2 Equations for
Predicting PGA, PGV, and Damped PSA for Shallow Crustal Earthquakes. Earthquake
Spectra, 30(3), 1057-1085.
FEMA, P. (2000). Commentary for the seismic rehabilitation of buildings. FEMA-356, Federal
Emergency Management Agency, Washington, DC.
FEMA P-1050-1 / 2015: NEHRP Recommended Seismic Provisions for New Buildings and Other
Structures.
Ha, S. J., & Han, S. W. (2016). An efficient method for selecting and scaling ground motions
matching target response spectrum mean and variance. Earthquake Engineering &
Structural Dynamics, 45(8), 1381-1387.
Hancock, J., Bommer, J. J., & Stafford, P. J. (2008). Numbers of scaled and matched accelerograms
required for inelastic dynamic analyses. Earthquake Engineering & Structural
Dynamics, 37(14), 1585-1607.
Hancock, J., Watson-Lamprey, J., Abrahamson, N. A., Bommer, J. J., Markatis, A., McCOY, E. M.
M. A., & Mendis, R. (2006). An improved method of matching response spectra of
recorded earthquake ground motion using wavelets. Journal of earthquake
engineering, 10(spec01), 67-89.
Haselton, C. B., Whittaker, A. S., Hortacsu, A., Baker, J. W., Bray, J., & Grant, D. N. (2012,
September). Selecting and scaling earthquake ground motions for performing response-
history analyses. In Proceedings of the 15th World Conference on Earthquake
Engineering (pp. 4207-4217). Earthquake Engineering Research Institute.

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Jayaram, N., & Baker, J. W. (2008). Statistical tests of the joint distribution of spectral acceleration
values. Bulletin of the Seismological Society of America, 98(5), 2231-2243.
PEER/ATC. (2010). Modeling and acceptance criteria for seismic design and analysis of tall
buildings, in PEER/ATC 72-1.
PEER TBI Guidelines for Performance-Based Seismic Design of Tall Buildings 2017.
Zekioglu, Atila, et al. "Case study using the Los Angeles tall buildings structural design council
guidelines: 40-storey concrete core wall building." The Structural Design of Tall and
Special Buildings 16.5 (2007): 583-597.

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APPENDIX
A. Model Coefficients for Conditional Mean Spectrum (CMS) Equations

3 0.004
0.003
2
0.002
1
Coefficient Value
0.001
Coefficient Value
0 0
-1 -0.001
-0.002
-2
e1 e2 e3 -0.003 Δc3 California
-3 Δc3 Global
e4 e5 e6 -0.004
Δc3 China, Turkey, Italy
-4 -0.005
0.01 0.1 1 10 0.01 0.1 1 10
-1 0.2
c1 0.18 c2
Coefficient Value
Coefficient Value
-1.1
0.16
-1.2 0.14
0.12
-1.3
0.1
-1.4 0.08
0.01 0.1 1 10 0.01 0.1 1 10
0 10
c3 h
Coefficient Value
Coefficient Value
8
-0.005
6
-0.01
4
-0.015 2
0.01 0.1 1 10 0.01 0.1 1 10

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ID No. : 2018021329
6.4 0
Mh c
Coefficient Value
6.2 -0.2
Coefficient Value
-0.4
6
-0.6
5.8
-0.8
5.6 -1
5.4 -1.2
0.01 0.1 1 10 0.01 0.1 1 10
0.1 0
f4 f5
Coefficient Value
Coefficient Value
0 -0.002
-0.004
-0.1
-0.006
-0.2 -0.008
-0.3 -0.01
0.01 0.1 1 10 0.01 0.1 1 10
0.8
0.7
0.6
Coefficient Value
0.5
0.4
0.3
0.2 τ1 τ2
0.1 φ1 φ2
0
0.01 0.1 1 10
Period (s)

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ACE874

Name : Zulkarnaen, Gifari

2. Study Case and Design Basis

Class : ACE874 – Performance-Based Earthquake Engineering

Figure 1. Building Plan

Figure 2. ETABS Modelling

Class : ACE874 – Performance-Based Earthquake Engineering

Table 1. Natural Periods of Building Model

2.2. Seismic Hazard

2,475 years (MCER)

Figure 3. Hazard Curve.

Class : ACE874 – Performance-Based Earthquake Engineering

Figure 4. Disaggregation Data for SLE.

Figure 5. Disaggregation Data for MCER.

Class : ACE874 – Performance-Based Earthquake Engineering

Magnitude and Distance Disaggregation

Magnitude and Soil Vs30 Disaggregation

Figure 6. Disaggregation of NGA West2 Ground Motion Database.

Class : ACE874 – Performance-Based Earthquake Engineering

Magnitude and Distance Disaggregation of

Magnitude and Soil Vs30 Disaggregation of

2.3. Database and Library

Figure 8. Design Procedure

Class : ACE874 – Performance-Based Earthquake Engineering

4. Conditional Mean Target Spectrum

Figure 9. Conditional Mean Spectrum.

The CMS conditions the entire spectrum on spectral acceleration at a single

ln 𝑆𝑎(𝑇1 ) = 𝐹𝐸 (𝑀, 𝑚𝑒𝑐ℎ) + 𝐹𝑃 (𝑅𝐽𝐵 , 𝑀) + 𝐹𝑆 (𝑉𝑆30 , 𝑀, 𝑚𝑒𝑐ℎ, 𝑅𝐽𝐵 )

Class : ACE874 – Performance-Based Earthquake Engineering

 The source (event) function is given by:

 The path function is given by:

Class : ACE874 – Performance-Based Earthquake Engineering

𝜎(𝑀) = √𝜙 2 (𝑀) + 𝜏 2 (𝑀)

The M-dependent between-event standard deviation τ is given by

Median of Ground Motion Standard Deviation of Ground

Class : ACE874 – Performance-Based Earthquake Engineering

3.2. Compute Target ε(T1), from Hazard Disaggregation.

Median+εσ of Ground Motion Prediction

Figure 11. Median + εσ of log(Sa) at all periods.

𝐶2 𝑇𝑚𝑎𝑥 < 0.109

Class : ACE874 – Performance-Based Earthquake Engineering

3.4. Compute CMS Sa at all other periods

Conditional Mean Target Spectrum at T1 = 3.88 s

Figure 12. CMS Anchored at 3.88 s (Mode 1).

Class : ACE874 – Performance-Based Earthquake Engineering

Figure 13. Comparison of CMS Anchored at Various Mode of The Building

Conditional Mean Target Spectrum

0.1 CMS Mode 3 (T=1.14s)

5. Ground Motion Selection

Class : ACE874 – Performance-Based Earthquake Engineering

4.1. Algorithm Input

Target Rupture Input

Fault type : unspecified fault

GM number and time of interest

GM properties from database

4.2. Selected Ground Motions

Class : ACE874 – Performance-Based Earthquake Engineering

Figure 14 (a). Accelerogram of Selected Ground Motions

Class : ACE874 – Performance-Based Earthquake Engineering

Figure 16 (b). Accelerogram of Selected Ground Motions