Fawad A. Najam A Modified Response Spectrum Analysis...
Transcript of Fawad A. Najam A Modified Response Spectrum Analysis...
A Modified Response Spectrum Analysis Procedure (MRSA) to Determine the Nonlinear Seismic Demands
of Tall Buildings
Fawad A. NajamPennung WarnitchaiAsian Institute of Technology (AIT), ThailandEmail: [email protected]
2Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
The Earthquake Problem
RockFault
Soil
Site
Site ResponseGround motion
can be amplified
by soil
AttenuationSeismic waves lengthen
and diminish in strength
as they travel away from
the ruptured fault.
Future ground shaking
Building
Linear/Nonlinear Analysis
Model
Characterization of Seismic
Ground Motions
Estimation of Linear/Nonlinear
Seismic Demands
• Global-level Responses
• Inter-story Responses
• Component-level Responses
… … … Simplified Estimation of
Seismic Demands
Simplified Structural Models
Simplified Loading
Any combination of
simplified approaches
Simplified Seismic Analysis
Procedures
Triangular
Modal Expansion
… … …
… … …
4Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Dynamic Response of Structures – The Concept of Vibration Mode Shapes
The Equivalent Lateral Force
Procedure (LSPs)
Seismic
Loading
Structural Models
Detailed 3D
Linear Model
Linear Elastic
MDF Model
Linear Elastic
SDF Model
Static Single Lateral
Load Vector
Static Multiple Lateral
Load Vectors
Ground Motions
The Linear Response
History Analysis (LRHA)
Procedure
(Direct Integration)
Modal Analysis, Spectral Analysis,
Standard Response Spectrum Analysis
(RSA) Procedure
Relative Uncertainty
Low
High
The World of Linear Elastic Seismic
Analysis of Structures
or
The NLRHA Procedure
using Simplified SDF
Model
The Nonlinear Static
Procedures (NSPs)
Seismic
Loading
Structural Models
Detailed 3D
Nonlinear Model
Equivalent
Nonlinear MDF
Model
Equivalent
Nonlinear SDF
Model
Static Single Lateral
Load Vector
Static Multiple Lateral
Load Vectors
Ground Acceleration
Records
The Detailed Nonlinear
Response History Analysis
(NLRHA) Procedure
The Multi-mode Pushover
Analysis Procedures
The NLRHA Procedure
using Simplified MDF
Model
Relative Uncertainty
Low
High
The World of Nonlinear Seismic
Analysis of Structures
7Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Linear Elastic Model
Determine Modal Properties
𝑇𝑖, 𝜙𝑖, 𝛤𝑖
𝑇1𝑇2𝑇3
𝑆𝐴1
𝑆𝐴2
𝑆𝐴3
Spe
ctr
al A
ccele
ratio
n (
SA
)
Time Period (sec)
𝑉𝑏𝑛 =
𝑖=1
𝑁
𝛤𝑛 . 𝑚𝑖 . 𝜙𝑖,𝑛 . 𝑆𝐴𝑛
Determine Spectral Acceleration
for each Significant Mode
𝑉𝑏1 𝑉𝑏2 𝑉𝑏3
𝑉𝑒𝑙 = (𝑉𝑏1 )2 + (𝑉𝑏2 )2 + (𝑉𝑏3 )2 + …
Determine Elastic Base Shears
Forc
e
Displacement
𝐹𝑒𝑙
𝐹𝑖𝑛
∆𝑒𝑙= ∆𝑖𝑛
𝑉𝑖𝑛 =𝑉𝑒𝑙𝑅
Reduce Elastic Base Shear to account for
inelasticity
𝜙1 𝜙2 𝜙3
𝑅 = Response Modification
Factor, ASCE 7 (or
Behavior Factor, EC 8)
For Initial
Viscous Damping…
N
Stories
Eigen-value Analysis
𝕂− 𝜔2𝕄 Φ = 𝕆
The Standard RSA Procedure (ASCE 7-10, IBS 2012, EC 8)
𝑉𝐷𝑒𝑠𝑖𝑔𝑛 =(𝑉𝑏1 )
2 + (𝑉𝑏2 )2 + (𝑉𝑏3 )
2 + …
𝑅
Problem
• Different modes undergoes different levels of
nonlinearity.
• Reducing elastic responses of every mode by the
same R factor is not correct.
• Several ‘modified’ RSA procedures have been
proposed—using different R factor for different mode.
𝑀𝐷𝑒𝑠𝑖𝑔𝑛 =(𝑀𝑏1 )
2 + (𝑀𝑏2 )2 + (𝑀𝑏3 )
2 + …
𝑅
∆ =𝐶𝑑 (∆𝑒𝑙1)
2 + (∆𝑒𝑙2)2 + (∆𝑒𝑙3)
2 + …
𝑅
8Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50 60
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50 60
The Original Intent of R
• Basic Idea:• A structure can be economically designed for a “fraction”
of the estimated elastic seismic design forces, while maintaining the basic life safety performance objective.
• The intent of R is to simplify the structural design forces such that only linearly elastic static analysis is needed for most building design.
• “R” factor can be traced back to a “K” factor which appeared in the first edition of the Blue Book (SEAOC Recommended Lateral Force Requirements and Commentary) in 1959.
The elastic forces obtained from the
standard RSA procedure
The RSA elastic forces reduced by 𝑅
The inelastic forces obtained from the
NLRHA procedure
The “reward” of making
a nonlinear model
The underestimation causing a “false
sense of safety” due to directly reducing
the RSA elastic forces by 𝑅 factor
Story Shear (x106 N)
Sto
ry L
eve
l
9Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
What “R” to use?
Structural Type and MaterialUS West
CoastJapan
New Zealand**
Europe
Concrete Frame 8 1.8 – 3.3 9 5.85
Concrete Structural Wall 5 1.8 – 3.3 7.5 4.4
Steel Frame 8 2.0 – 4.0 9 6.3
Steel Eccentrically Braced Frame 8 2.0 – 4.0 9 6.0
Masonry Walls 3.5 - 6 3.0
Timber Structural Walls - 2.0 – 4.0 6 5.0
Pre-stressed Wall 1.5 - - -
Dual Wall/Frame 8 1.8 – 3.3 6 5.85
Bridges 3 – 4 3.0 6 3.5
**Sp factor of 0.67 incorporated
Source: “Direct Displacement-based Design” by Priestley MJN et al., 2007
10Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Is it justified to “equally” modify the response of each vibration mode?
Lets separate them and check one-by-one
R ???
What “R” to use?
What actually happens to the structure during the time history analysis?
Our Approach
11Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
The Concept of Modal Decomposition
12Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Modal Decomposition of Nonlinear Seismic Responses
≅+ +…
Mode 1Mode 2
Mode 3
+
A Detailed 3D Elastic
Structural Model
Classical Modal Analysis
The Uncoupled Modal Response History Analysis (UMRHA)
F
D
F
D
F
D
NLNL NL
A Detailed 3D Inelastic
Structural Model
≅
+ + …
Mode 1Mode 2
Mode 3
+
13Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
The Uncoupled Modal Response History Analysis (UMRHA) Procedure
≅+ + + + + + …
14Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Full 3D Nonlinear MDF Model
𝐹𝑛
𝐹1
.
.
.
Monotonic Pushover Analysis
𝑥1𝑟
𝑉𝑏1
Determination of Pushover Curve
𝑉𝑏1
𝑥1𝑟
Idealization of Pushover Curve
𝐹1
𝐷1
Equivalent SDF System
The Equivalent Single-degree-of-freedom (SDF) System
15Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Monotonic Pushover Analysis
3D View
A 44-story Case Study Building
Elevation View
Pushover Curve (Strong Direction)
Base Shear vs. Roof Drift Ratio
No Crack
Cracked
Cyclic Pushover Analysis
Base Shear (V)
Roof Drift (Δ)
V
Δ
17Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
-0.05
-0.03
-0.01
0.01
0.03
0.05
-0.0075 -0.005 -0.0025 0 0.0025 0.005 0.0075
No
rmaliz
ed
Base S
he
ar
()
Roof Drift ( )
Reversed-cyclic Pushover Analysis (Solid Line)Response of an equivalent SDF system under a ground motion
Mapping the Cyclic Response to an Equivalent SDF System
18Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
-0.006 -0.004 -0.002 0 0.002 0.004 0.006
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
-0.003 -0.002 -0.001 0 0.001 0.002 0.003
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
-0.015 -0.01 -0.005 0 0.005 0.01 0.015
The CONCLUSION – Each Mode is Different …
Mode 1Mode 2
Mode 3
Normalized Base Shear (𝑽𝒃𝟏/𝑾) 𝑽𝒃𝟐/𝑾 𝑽𝒃𝟑/𝑾
Roof Drift (𝒙𝟏𝒓/𝑯) Roof Drift (𝒙𝟐
𝒓/𝑯) Roof Drift (𝒙𝟑𝒓/𝑯)
Cyclic pushover curve
Idealized SDF system
19Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
The CONCLUSION – Each Lollipop is Different …
≅+ + + + + + …
20Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
From UMRHA to The Modified Response Spectrum Analysis (MRSA)
21Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
What Happens when a System Starts Experiencing Nonlinearity?
k
Natural Period Elongation
Additional Hysteretic Damping
Natural Period Elongation
The Basic Concept of Modified Response Spectrum Analysis (MRSA)
Nonlinear Structure
Detailed 3D Nonlinear Response History Analysis (NLRHA)
𝑇𝑒𝑞1, 𝜉𝑒𝑞1
≅
+ + +…
F
DF
D
F
D
Mode 1Mode 2
Mode 3
Uncoupled Modal Response History Analysis (UMRHA)
+ + +…
Mode 1Mode 2
Mode 3
Modified Response Spectrum Analysis (MRSA)
F
D
F
D
F
D
NLNL NL
ELEL
EL
𝑇𝑒𝑞2, 𝜉𝑒𝑞2 𝑇𝑒𝑞3, 𝜉𝑒𝑞3
≅
NLRHA
UMRHA
MRSA
24Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
𝑇2
𝑆𝐴2
Spectr
al A
ccele
ratio
n (
SA
)
Time Period (sec)
𝑇1
𝑆𝐴1
Spectr
al A
ccele
ratio
n (
SA
)
Time Period (sec)
The Basic Concept of Modified Response Spectrum Analysis (MRSA)
Linear Elastic Structure
≅ + + + …
Mode 1Mode 2
Mode 3
F
D
F
D
F
D
𝑇3
𝑆𝐴3
Spectr
al A
ccele
ratio
n (
SA
)
Time Period (sec)
Spectr
al A
ccele
ratio
n (
SA
)
Time Period (sec)
For Initial
Viscous Damping
25Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
≅
𝑥𝑜
K𝑒𝑞
Total 𝜉𝑒𝑞 = Sum of Equivalent
Inherent Damping and
Equivalent Hysteretic Damping
Equivalent Viscous
Damping (𝜉𝑒𝑞)
An Equivalent Linear System with Elongated Period and Additional Damping
Force
𝐸𝑠𝑜(𝑥)
𝐸𝐷(𝑥)
𝜉ℎ =1
4𝜋
)𝐸𝐷(𝑥
)𝐸𝑠𝑜(𝑥=
)𝐸𝐷(𝑥
2𝜋 K𝑒𝑥𝑜2
K𝑒𝑞
Energy dissipated by total
damping in a Nonlinear
System
Energy dissipated by
equivalent viscous damping in
an equivalent linear system
=
K𝑖
𝑥𝑜
Hysteretic
Damping (𝜉ℎ)
A Nonlinear SystemConverted to
Equal-Energy Assumption
Displacement
Force
Displacement
Conversion of a Nonlinear System in to an “Equivalent Linear” System
Evaluation of the MRSA Procedure - 3 Case study Buildings
44 StoryB1
33 StoryB2
20 StoryB3
• Located in Bangkok, Thailand
• Heights vary from 20 to 44 stories
• RC slab-column frames carry gravity loads
• RC walls & cores resist lateral loads
• Masonry infill walls extensively used
• Designed for wind loads, but not for seismic effects
• Possess configuration irregular features commonly found in typical tall buildings, such as podium and non-symmetrical arrangement of RC walls, etc.
27Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Ground Motions
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.5 1 1.5 2 2.5 3 3.5 4
Spectr
al A
ccele
ration
(g)
Time Period (sec)
Short-Period Target Spectrum and
Matched Ground Motions – Set 2
UHS Target Spectrum and Matched
Ground Motions – Set 1
Long-Period Target Spectrum
and Matched Ground Motions
– Set 3
Target
Mean of Matched
Individual Ground Motions
0
0.1
0.2
0.3
0.4
0 0.5 1 1.5 2 2.5 3 3.5 4
Sp
ectr
al A
cce
lera
tio
n (
g)
Period (sec)
7.5%-damped
Mean Spectrum
0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4
Sp
ectr
al A
cce
lera
tio
n (
g)
Period (sec)
0
0.1
0.2
0.3
0 0.5 1 1.5 2 2.5 3 3.5 4
Sp
ectr
al A
cce
lera
tio
n (
g)
Period (sec)
2.5%-damped
Mean Spectrum
5%-damped
Mean Spectrum
Target
Mean of Matched GMs
Individual Ground Motions
7.5%-damped
Mean Spectrum
5%-damped
Mean Spectrum
2.5%-damped
Mean Spectrum
7.5%-damped
Mean Spectrum
5%-damped
Mean Spectrum2.5%-damped
Mean Spectrum
Set 2
Set 3
Set 1
29Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Ground Motions
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2 2.5 3 3.5 4
Sp
ectr
al A
cce
lera
tio
n (
g)
Period (sec)
5%-damped Target Response Spectrum
Mean of Matched Ground Motions
Individual Ground Motions
𝜉 = 2.5%
𝜉 = 10%
𝜉 = 5%
Typical Code Target Spectrum
and Matched Ground Motions
– Set 4
Set 4
30Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
MVLEM for RC WallsLumped Fibers for RC ColumnsMasonry Infill Wall Model (FEMA 356)
Nonlinear Modeling of Case Study Buildings
Level m
Level m-1
Rigid Link
Concrete and Steel fibers
Linear shear springLinear-elastic frame
element (shear deformation excluded)
Fiber section element (concrete and steel fibers)
Linear shear spring
-0.09
-0.07
-0.05
-0.03
-0.01
0.01
0.03
0.05
0.07
0.09
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
Cyclic Pushover
Monotonic Pushover in Positive Direction
Monotonic Pushover in Negative Direction
Brick walls begin to crack
Shear walls begin to crack
Columns
begin to
Crack
Shear wall’s steel reinforcement
bars begin to yield in tension
Shear wall’s steel bars begin
to yield in compression
Concrete crushing in
shear wall
Column’s bars begin to
yield in compression
Column’s steel bars
begin to yield in tensionN
orm
aliz
ed B
ase S
hear
(𝑉𝑏1/𝑊
)
Roof Drift (𝑥𝑖𝑟/𝐻)
Strong (𝑥) Direction
32Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Cyclic Pushover Analysis – Strong Direction
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-0.06
-0.04
-0.02
0
0.02
0.04
0.06
-0.025 -0.015 -0.005 0.005 0.015 0.025
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
-0.03 -0.02 -0.01 0 0.01 0.02 0.03
19-story Building
Mode 133-story Building
Mode 1
44-story Building
Mode 1
Normalized Base Shear (𝑉𝑏/𝑊) 𝑉𝑏/𝑊 𝑉𝑏/𝑊
Roof Drift (∆/𝐻) Roof Drift (∆/𝐻) Roof Drift (∆/𝐻)
20-story 33-story 44-story
33Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
UMRHA vs. NLRHA
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50
Story Shear (x106 N)
Story Shear Envelope
0
5
10
15
20
25
30
35
40
45
0 0.5 1 1.5 2
Moment (x106 KN m)
Overturning Moment
0
5
10
15
20
25
30
35
40
45
0 200 400 600
No.
of S
tories
Displacement (mm)
Displacement Envelope
UMRHA (Combined3 Modes)
NLRHA
0
5
10
15
20
25
30
35
40
45
0 0.25 0.5 0.75 1
IDR (%)
Inter-story Drift Ratio
UMRHA(Combined 3 Modes)
NLRHA
44-story case study building in Strong Direction
34Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Modal Decomposition of Nonlinear Response
0
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500 600
Level N
o.
Peak Displacement (mm)
Mode 2
Mode 3
0
5
10
15
20
25
30
35
40
45
0 0.2 0.4 0.6 0.8
Peak Inter-story Drift Ratio (%)
Mode 1
Mode 2
Mode 3
Envelope of
Combined History
Mode 1
Envelope of
Combined History
44-story case study building in Strong Direction
35Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Modal Decomposition of Nonlinear Response
0
5
10
15
20
25
30
35
40
45
0 15 30 45
Peak Story Shear (x 106 N)
0
5
10
15
20
25
30
35
40
45
0 0.5 1 1.5 2 2.5
Peak Moment (x 106 KN m)
Mode 2
Mode 1
Mode 3
Envelope of
Combined History
Mode 2
Mode 1
Mode 3
Envelope of
Combined History
44-story case study building in Strong Direction
Shear Wall Cracking
UHS-Matched Ground Motion 0.2 sec CMS-Matched Ground Motion 3 sec CMS-Matched Ground Motion
25% of Cracking Strain
50% of Cracking Strain
80% of Cracking Strain
Already Cracked
Set 1 Set 2 Set 3
37Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.5 1 1.5 2 2.5
33-story (Mode 1)
Roof Drift ratio, 𝑥𝑖𝑟/𝐻 (%)
𝑇𝑠𝑒𝑐,𝑖/𝑇𝑖
20-story
(Mode 1)
44-story (Mode 1)
33 Story (Mode 2)
Secant Periods from Envelope of Cyclic Pushover Curves
44 Story (Mode 2)
20 Story (Mode 2)
33 Story (Mode 3)
44 Story
(Mode 3)
20 Story (Mode 3)
(a) 𝑇𝑠𝑒𝑐,𝑖/𝑇𝑖 vs. Roof Drift Ratio (𝑥𝑖𝑟/𝐻)
“Equivalent Linear” Properties
38Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
5
10
15
20
25
30
0 0.5 1 1.5 2 2.5 3
𝜉ℎ,𝑖 (%)
33-story
(Mode 1)
20-story
(Mode 1)
44-story
(Mode 1)
20-story (Mode 1) - Each
loop start from initial
unloaded condition
Hysteretic Damping from Area Enclosed by Cyclic Pushover Curves
Roof Drift ratio, 𝑥𝑖𝑟/𝐻 (%)
(b) 𝜉ℎ,𝑖 vs. Roof Drift Ratio (𝑥𝑖𝑟/𝐻)
“Equivalent Linear” Properties
39Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20
Story Shear (x106 N)
Mode 1
UMRHAMRSAStandard RSA (R = 4.5)
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40
Story Shear (x106 N)
Mode 2
0
5
10
15
20
25
30
35
40
45
0 5 10 15
Story Shear (x106 N)
Mode 3
No
. o
f S
torie
s
Modal Story Shears of a 44-story case study building in Strong Direction
Performance of MRSA at Individual Mode Level – EQ 1
40Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
5
10
15
20
25
30
35
40
45
0 2 4 6 8 10
Story Shear (x106 N)
Mode 1
UMRHA
MRSA
Standard RSA (R = 4.5)
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30
Story Shear (x106 N)
Mode 2
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20
Story Shear (x106 N)
Mode 3
No. of S
tories
Performance of MRSA at Individual Mode Level – EQ 2
Modal Story Shears of a 44-story case study building in Strong Direction
41Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20
Story Shear (x106 N)
Mode 2
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4
Story Shear (x106 N)
Mode 3
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25
Story Shear (x106 N)
Mode 1
UMRHA
MRSA
Standard RSA (R = 4.5)
No. of S
tories
Performance of MRSA at Individual Mode Level – EQ 3
Modal Story Shears of a 44-story case study building in Strong Direction
42Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
5
10
15
20
25
30
35
40
45
0 200 400 600 800
No
. o
f S
torie
s
Displacement (mm)
Displacement Envelope
0
5
10
15
20
25
30
35
40
45
0 0.25 0.5 0.75 1
IDR (%)
Inter-story Drift Ratio
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40
Story Shear (x106 N)
Story Shear Envelope
0
5
10
15
20
25
30
35
40
45
0 0.5 1 1.5 2
Moment (x106 KN m)
Overturning Moment
44-story case study building in Strong Direction
NLRHA
MRSA
Standard RSA
(Cd = 4, R = 4.5)
Overall Performance of MRSA – EQ Set 1
43Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
5
10
15
20
25
30
35
40
45
0 50 100 150 200
No
. o
f S
tori
es
Displacement (mm)
Displacement Envelope
0
5
10
15
20
25
30
35
40
45
0 0.05 0.1 0.15 0.2 0.25
IDR (%)
Inter-story Drift Ratio
0
5
10
15
20
25
30
35
40
45
0 0.25 0.5 0.75 1 1.25
Moment (x106 KN m)
Overturning Moment
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40
Story Shear (x106 KN)
Story Shear Envelope
NLRHA
MRSA
Standard RSA
(Cd = 4, R = 4.5)
Overall Performance of MRSA – EQ Set 2
44-story case study building in Strong Direction
44Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
5
10
15
20
25
30
35
40
45
0 250 500 750
No
. o
f S
torie
s
Displacement (mm)
Displacement Envelope
0
5
10
15
20
25
30
35
40
45
0 0.15 0.3 0.45 0.6 0.75
IDR (%)
Inter-story Drift Ratio
0
5
10
15
20
25
30
35
40
45
0 10 20 30
Story Shear (x106 KN)
Story Shear Envelope
0
5
10
15
20
25
30
35
40
45
0 0.5 1 1.5 2
Moment (x106 KN m)
Overturning Moment
NLRHA
MRSA
Standard RSA
(Cd = 4, R = 4.5)
Overall Performance of MRSA – EQ Set 3
44-story case study building in Strong Direction
45Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Local Response - Bending Moment in Columns (EQ Set 4)
0
5
10
15
20
25
30
35
40
45
-3000 -2000 -1000 0 1000 2000 3000
Moment (x106 N mm)
0
5
10
15
20
25
30
35
40
45
-3000 -2000 -1000 0 1000 2000 3000
Moment (x106 N mm)
NLRHA Mean
MRSA
Standard RSA
Standard RSA × ΩNo
. o
f S
torie
s MM
44-story case study building (Strong Direction)
46Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Local Response – Shear Walls (EQ Set 4)
0
5
10
15
20
25
30
35
40
45
-50000 -25000 0 25000 50000
Moment (x106 N mm)
0
5
10
15
20
25
30
35
40
45
-15 -10 -5 0 5 10 15
Shear (x106 N)
No
. o
f S
torie
s V M
NLRHA Mean
MRSA
Standard RSA
Standard RSA × Ω
44-story case study building (Strong Direction)
47Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Local Response – Axial Strain in Shear Walls (EQ Set 4)
0
5
10
15
20
25
30
35
40
45
-400 -300 -200 -100 0 100 200 300 400
Axial Strain (x106 mm/mm)
0
5
10
15
20
25
30
35
40
45
-1000-750 -500 -250 0 250 500 750 1000
Axial Strain (x106 mm/mm)
Tensile
Cracking
Tensile
Cracking
No
. o
f S
torie
s
NLRHA Mean
MRSA
Standard RSA
Standard RSA × Ω
44-story case study building (Strong Direction)
48Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
Seismic Analysis Practice for Structural Design - The Case of Pakistan
Source: Zaman and Warnitchai (2016)
50Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
How Safe are Our Buildings Against Earthquakes?
Peak Ground Acceleration (g)
Source: Durrani et al.,
Abbottabad, 8th October 2005
54Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3 3.5 4
Period (sec)
SD
SC
SB
SA
Elastic Spectrum of EW
Component
Abbottabad, 8th October 2005
How much we understand?
Peak Ground Acceleration
Source: Zaman and Warnitchai (2016)
Source: Zaman and Warnitchai (2016)
Spectral Acceleration at 0.2 sec
Source: Zaman and Warnitchai (2016)
Spectral Acceleration at 1 sec
59Design of Tall Buildings: Trends and Advancements for Structural Performance (24 – 25 April 2017, NUST, Islamabad)
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