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Abdelghani Meslem & Dominik LangDepartment of Earthquakes and the Environment
NORSAR, Kjeller, Norway
Seismic Vulnerability AssessmentPPT07
Clarifications
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Content
o Set Mass Source for Modal Analysis
o How to determine if higher modes are significant
o Gound motion selection and scaling for for nonlinear time history
o Second-order effects (P-Delta effects)
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
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A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Define
Mass Source...
From Element and Additional Masses and Loads
G + 0.3 ∙ Q G = 1
Q = 0.3
Set Mass Source for Modal Analysis
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A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
in new version of SAP2000 in old version of SAP2000
Set Mass Source for Modal Analysis
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A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Nonlinear static analysis: Criteria
shall be permitted for structures in which higher mode effects are not
significant.
To determine if higher modes are significant:
• Step 1: Perform modal analysis to identify number of modes required to
obtain 90% mass participation;
• Step 2: a modal response spectrum analysis shall be performed for thestructure using sufficient modes to capture 90% mass participation;
• Step 3: a second modal response spectrum analysis shall also be
performed, considering only the first mode participation;
• Higher mode effects shall be considered significant if the shear in any
story resulting from the modal analysis considering modes required to
obtain 90% mass participation exceeds 130% of the corresponding story
shear considering only the first mode response.
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Nonlinear static analysis: Criteria
Step 1: Modal analysis
select the number of
modes to be considered
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Nonlinear static analysis: Criteria
Step 1: Modal analysis
first torsional
mode is 3rd
Σ = 0,90 0,98
n
j
i j j
n
ji j j
i
m
m
1
2
,
1,
Modal participation factor of mode k:
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Nonlinear static analysis: Criteria
4 modes to be
considered
Step 1: Modal analysis
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Nonlinear static analysis: Criteria
Design spectral accelerations Sa(T i )/g for each mode i :
Mode shape i: 1 2
3 n,1
j+1,1
j,1
n,2
j+1,2
j,2
n,3
j+1,3
j,3
Period T [sec]
S p e c t r a l a c c e l e r a
t i o n S a
T 2T 1 T 3
Sa,d (T 1 )
Sa,d (T 2 )
Sa.d (T 3 )
tep 2: a modal response spectrum analysis shall be performed for the structure
using sufficient modes to capture 90% mass participation
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Nonlinear static analysis: Criteria
)T(SmF id,aii, j ji, j
F n,1
F j+1,1
F j,1
F n,2
F j+1,2
F j,2
F n,3
F j+1,3
F j,3
Mode shape i: 1 2
3 n,1
j+1,1
j,1
n,2
j+1,2
j,2
n,3
j+1,3
j,3
resulting shear forces F b,m : 2
i,m,b
n
1im,b FF
EN 1998-1:2004, 4.3.3.3
tep 2: a modal response spectrum analysis shall be performed for the structure
using sufficient modes to capture 90% mass participation
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Nonlinear static analysis: Criteria
tep 2: a modal response spectrum analysis shall be performed for the structure
using sufficient modes to capture 90% mass participation
F 1,1
= 100 0.30 1.426 0.846 = 36.2 kN
F 2,1
= 75 0.644 1.426 0.846 = 58.3 kN
F 3,1
= 50 1.00 1.426 0.846 = 60.3 kN
F 1,2
= 100 ( –0.676) ( –0.511) 1.813 = 62.6 kN
F 2,2
= 75 ( –0.601) ( –0.511) 1.813 = 41.8 kN
F 3,2
= 50 1.00 ( –0.511) 1.813 = –46.3 kN
F 1,3 = 100 2.47 0.090 2.115 = 47.0 kN
F 2,3
= 75 ( –2.57) 0.090 2.115 = –36.7 kN
F 3,3
= 50 1.00 0.090 2.115 = 9.5 kN
)T(SmF id,aii, j ji, j F 3,1= 60.3
F 2,1 = 58.3
F 1,1 = 36.2
F 3,2 = –46.3
F 2,2 = 41.8
F 1,2 = 62.6
F 3,3 = 9.5
F 2,3 = –36.7
F 1,3 = 47.0
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Nonlinear static analysis: Criteria
tep 2: a modal response spectrum analysis shall be performed for the structure
using sufficient modes to capture 90% mass participation
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Nonlinear static analysis: Criteria
tep 2: a modal response spectrum analysis shall be performed for the structure
using sufficient modes to capture 90% mass participation
A number of ways to combine modes given direction including CQC, SRSS,..and others...
Response spectrum will be applied as an acceleration in U1 (UX) direction using the
previously defined curve EC-8-B
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Nonlinear static analysis: Criteria
tep 2: a modal response spectrum analysis shall be performed for the structure
using sufficient modes to capture 90% mass participation
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Nonlinear static analysis: Criteria
tep 2: a modal response spectrum analysis shall be performed for the structure
using sufficient modes to capture 90% mass participation
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Nonlinear static analysis: Criteria
tep 2: a modal response spectrum analysis shall be performed for the structure
using sufficient modes to capture 90% mass participation
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Nonlinear static analysis: Criteria
tep 2: a modal response spectrum analysis shall be performed for the structure
using sufficient modes to capture 90% mass participation
li i l i i i
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Nonlinear static analysis: Criteria
1 mode to be
considered
Step 3: a second modal response spectrum analysis shall also be performed,
considering only the first mode participation
li i l i C i i
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Nonlinear static analysis: Criteria
If higher mode effects are significant, the nonlinear static method shall
be permitted if a linear dynamic analysis is also performed tosupplement the NSP (i.e. to verify the adequacy of the design).
RegularityAllowed simplification in model
Plan Elevation
● ● Planar (2D)● ○
○ ● Spatial (3D)
○ ○
Regularity vs. allowed simplification model in nonlinear static analysis
EN 1998-1:2004, 4.3.3.4.2
N li i hi l i
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Nonlinear time history analysis
This approach is the most rigorous, and is required by some building
codes for buildings of unusual configuration or of special importance .
N li ti hi t l i
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A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Nonlinear time history analysis
the calculated response can be very sensitive to the characteristics of
the individual ground motion used as seismic input; therefore, severalanalyses are required using different ground motion records to achieve
a reliable estimation of the probabilistic distribution of structural
response.
Since the properties of the seismic response depend on the intensity,or severity, of the seismic shaking, a comprehensive assessment calls
for numerous nonlinear dynamic analyses at various levels of intensity
to represent different possible earthquake scenarios.
N li ti hi t l i
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• Accelerograms to be used in non-linear time history analysis shallbe selected according to EN 1998-1, 3.2.3.1 ( Session III)
Determination of Response Parameters:
N - number of accelerograms used in non-linear time history analysis
N ≥ 7 Response Computation
yes no
● ○ Use average of the response quantities
○ ● Use the most unfavorable value of the
response quantity amongst all motions
EN 1998-1:2004, 4.3.3.4.3
Nonlinear time history analysis
Ground motion selection and scaling
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N li ti hi t l i
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Nonlinear time history analysis
Ground motion selection and scaling
The parameters (that have the most influence on ground motion spectral shape)that need to be considered in selecting records :
• Magnitude range of anticipated significant event;
• Distance range of the site from the causative fault;
• Site Condition (i.e. looking at the average shear velocity);
• Basin effect (if basin exists)
N li ti hi t l i
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Nonlinear time history analysis
Ground motion selection and scaling
Select pairs of ground motion records to perform dynamic response history analysis.
The use of 11 pairs of motions (i.e. 22 motions set) is recommended;
For each ground motion pair, run analysis: the amplitude should be incremented, and
nonlinear response history analysis performed until the occurrence
N li ti hi t l i
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Nonlinear time history analysis
Ground motion selection and scaling
Step 1: Run nonlinear static analysis (pushover) and identify the different damagestates.
S l i g h t D a m a g e
M o d e r a t e D
a m a g e
E x t e n s i v e D a m a g e
C o m p l e t e D a m a g e
Nonlinear time history analysis
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Nonlinear time history analysis
Ground motion selection and scaling
Step 2: For each selected ground motion, run nonlinear time history analysis
Use scaling to increase the IM level of the ground motion records, until all the limit
states are reached as defined above. Details on scaling procedures that the analyst
may implement are beyond the scope of these guidelines. Reference on this matter
can be made to ATC-58 (FEMA P-58, 2012)
1, 1.5, 2, ….3.1, 3.2, 3.3, …4, 4.5, 5.0….6.1, 6.2, 6.3, ….7, 7.5, 8, …….9.1, 9.2, 9.3, …..10, 10.5, 11.0…….12.1, 12.2, 12.3
Slight
Damage
Moderate
Damage
Extensive
DamageComplete
Damage
Nonlinear time history analysis
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A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Nonlinear time history analysis
Ground motion selection and scaling
Use scaling to increase the IMlevel of the ground motion
records
Nonlinear time history analysis
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Nonlinear time history analysis
Ground motion selection and scaling
Mean Curve
Second order Effects (P Δ effects)
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Structures in real life are flexible and can exhibit largelateral displacements in unusual circumstances. The lateral
displacements can be caused by wind or seismically
induced inertial forces.
Gravity loading will influence structural response undersignificant lateral displacement.
P-Δ may contribute to loss of lateral resistance, ratcheting
of residual deformations, and dynamic instability.
Second-order Effects (P- Δ effects)
Second order Effects (P Δ effects)
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Second-order effects (P-∆ effects) need not be taken into account if the following
condition is fulfilled in all storeys:
EN 1998-1:2004, 4.4.2.2
10,0
hV
d P
tot
r tot
h
V
d
P
tot
r
tot
= is the interstorey drift sensitivity coefficient;
= is the total gravity load at and above the storey considered in the seismic design
situation;
= is the design interstorey drift, evaluated as the difference of the average lateral
displacements ds at the top and bottom of the storey under consideration and
calculated in accordance with Chapter 4.3.4;
= is the total seismic storey shear; and
= is the interstorey height.
Second-order Effects (P- Δ effects)
Second order Effects (P Δ effects)
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If 0,1 < θ≤0,2, the second-order effects may approximately be taken into account bymultiplying the relevant seismic action effects by a factor equal to 1/(1 - θ).
value of the coefficient θ shall not exceed 0,3
Second-order Effects (P- Δ effects)
Second order Effects (P Δ effects)
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Use P-Delta in SAP2000
Second-order Effects (P- Δ effects)
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Contact details
Abdelghani Meslem, Dominik Lang
Department of Earthquakes and the Environment
NORSAR, 2027 Kjeller, Norway
Phone: (+47) 974 10 740 (Dr. Meslem)
(+47) 988 42 924 (Dr. Lang)
E-mail: [email protected]
Web: http://www.norsar.no