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Nonlinear Analyses Nonlinear Analyses ImplementationImplementation
Alex Augustin, Assistant Civil Engineer, California State Lands Commission
and Marc Percher, P.E., Senior Engineer,
Halcrow, Inc.
October 19-20, 2010
Prevention First 2010
AgendaAgendaAgendaAgenda
Background Backgroundg Displacement vs. Force based design
Current Methodology in MOTEMS
g Displacement vs. Force based design
Current Methodology in MOTEMSgy Substitute Structure Substitute Structure Grey areas MOTEMS Improvements
gy Substitute Structure Substitute Structure Grey areas MOTEMS Improvements MOTEMS Improvements Critical Items
Future MOTEMS
MOTEMS Improvements Critical Items
Future MOTEMS Future MOTEMS Chopra-Goel method: Demand-Capacity Procedure Sensitivity Study
Future MOTEMS Chopra-Goel method: Demand-Capacity Procedure Sensitivity Study
Prevention First 2010
Recommendations Recommendations
BackgroundDisplacement vs. Force Based Design
BackgroundDisplacement vs. Force Based Designp gp g
Displacement Based Force BasedDisplacement Based Force BasedAcceptable damage:
Strain ductility
Force limits:Strengthstressductility
Displacement, rotationst ess
Directly capture “Seismic Performance”: OLE, CLE
Life Safety “No Structural Collapse”, p
Pushover or time history analysis
Simplified methods (ELF) or response spectrum analysis
I t i l t th t O t th (Ω) t t tIncrease material strength to protect against brittle response (shear)
Overstrength (Ω) to protect against brittle response (shear)
Demand displacement < Demand Force <
Prevention First 20103
Demand displacement < Displacement capacity
Demand Force < Factored strength
BackgroundDisplacement vs. Force Based Design
BackgroundDisplacement vs. Force Based Designp gp g
Displacement Based Force BasedpAnalytically challenging,Highly variable for small
parameter changes
Analytically simple, Prone to oversimplifying
complex responsegGood for existing Better for new
Cost savings in retrofit costs
Cost savings in Engineering Effortcosts
Supercool! …(but finicky)
Boring …(but reliable)
Prevention First 2010
Current Methodology in MOTEMSSubstitute Structure Analysis
Current Methodology in MOTEMSSubstitute Structure AnalysisSubstitute Structure AnalysisSubstitute Structure Analysis
Pushover Curve Pushover Curve Soil springs, nonlinear materials, etc. Simplify to Bilinear Soil springs, nonlinear materials, etc. Simplify to Bilinear
Substitute Structure Iterate displacement to determine
d tilit
Substitute Structure Iterate displacement to determine
d tilitductility Alter damping & acceleration based on
ductility
ductility Alter damping & acceleration based on
ductility
Used for almost all Audits Used for almost all Audits
Prevention First 2010
Substitute Structure – Demand DisplacementSubstitute Structure – Demand Displacement
Δ / Δ k / kμΔ = Δd / Δy r = kf / ki
0.60
0.20
0.30
0.40
0.50
Acc
eler
atio
n, S
a (g
)
0.00
0.10
0.0 1.0 2.0 3.0 4.0 5.0 6.0Period, sec.
A
Prevention First 2010
Substitute Structure Analysis Grey Areas
Substitute Structure Analysis Grey AreasGrey AreasGrey Areas
Bilinear Yield PointBilinear Yield PointBilinear Yield PointSecondary Stiffness
Wh f t
Bilinear Yield PointSecondary Stiffness
Wh f tWhere from, toPractical method
D i E ti
Where from, toPractical method
D i E tiDamping Equations ATC 40 has different
equations
Damping Equations ATC 40 has different
equationsq
Orthogonal Effectsq
Orthogonal Effects
Prevention First 2010
MOTEMS Future MOTEMS Future
Push d
ImprovementsImprovements
Plastic Hinge Length Plastic Hinge LengthDamaged
Plastic Hinge Length Steel piles Prestressed piles
Plastic Hinge Length Steel piles Prestressed piles
1/ΦθLpRegion
p Effective buckling length
“k” factors
p Effective buckling length
“k” factors For same θ as
Lp then must
Knowledge factor Soil Kinematic & Inertial Load
Combine? How?
Knowledge factor Soil Kinematic & Inertial Load
Combine? How? Combine? How? Simplified Structural Analysis Methodology
Combine? How? Simplified Structural Analysis Methodology
Prevention First 2010
Critical ItemsCritical Items
Existing Poorly Existing PoorlyPoorlyConfined
Existing Poorly Confined Concrete εcu < L2 strain
Existing Poorly Confined Concrete εcu < L2 strain εcu
εL2
Balance Stiffnessand Ductility
Balance Stiffnessand Ductility
cu
Coronel, Chile
and Ductility
Pipe Stress forS i i
and Ductility
Pipe Stress forS i iSeismic displacementSeismic displacement
Prevention First 2010
Chopra-Goel PEER 1999 MethodChopra-Goel PEER 1999 Method(spectra iteration equivalent linearization)(spectra iteration equivalent linearization)
SystemM ( )
Find YieldΔ V K0 = Vy/ Δy2000
3000
4000
5000
6000
7000
Forc
e (k
ip)
StartMass (m)Δy, Vy
K0 Vy/ Δy
Acceleration
0
1000
2000
0.0 10.0 20.0 30.0 40.0Displacement (in)
F F-D 00
Assume D tilit ( *) 0 15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
lera
tion,
Sa
(g)
5%
5%
Tb, Tc, Tc’
Find Ry RSAccelerationSaj* = Saj / Ry
Ductility (μ*)0.00
0.05
0.10
0.15
0.0 1.0 2.0 3.0 4.0 5.0 6.0Period, sec.
Acc
el RSy
(from μ, Tb, Tc, Tc’)
Displacement
For all Periods
(Tj)
RS
Ductilityμ* = Δ / Δ
If μ* – μ*-1
< T l
noSdj* = μ * Saj* * (Tj / 2π)2
μ = Δ1 / Δy Tolerance
yesOverlay Saj*
Prevention First 2010
FinishedΔd = Δ1Δ1
& F-Dand Find Intersection Note: Similar to ATC 40
Chopra-Goel Methodology Grey Areas
Chopra-Goel Methodology Grey AreasGrey AreasGrey Areas
Bilinear YieldBilinear Yield 450
500
Bilinear Yield Point
Hinge Length
Bilinear Yield Point
Hinge Length
2.69 4.38
350
400
DESHL1 MI Lng DyE Pushover CurveFirst Yield of Structure or SoilHinge Length
“R” EquationsO th l
Hinge Length “R” EquationsO th l 1.41
2.88
250
300
Acc
eler
atio
n (in
/sec
^2) First Yield of Structure or Soil
L1 50% in 50yr UnfactoredL2 10% in 50yr UnfactoredL1 50% in 50yr μ= 0.89L1 50% in 50yr μ= 0.89 DemandDESHL1 MI Lng DyE L1 Strain CapacityL2 10% in 50yr μ= 1.49L2 10% in 50yr μ= 1.49 DemandDESHL1 MI Lng DyE L2 Strain Capacity
Orthogonal Effects
Iteration
Orthogonal Effects
Iteration150
200
Spe
ctra
l DESHL1 MI Lng DyE L2 Strain Capacity
Iteration Sensitivity
Iteration Sensitivity
0
50
100
Prevention First 2010
00.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00
Displacement Demand ∆(in)
Sensitivity StudySensitivity Study
Pushover Curve
4000 Effective Bilinear Curve Effective Bilinear Curve
3000
3500
4000 Effective Bilinear Curve First Yield or
EffectiveL t D t L2
Effective Bilinear Curve First Yield or
EffectiveL t D t L2
2000
2500
3000
e (k
ip)
Effective Dy
Locate Du at L2 strain for practicality
Damping Equations
Locate Du at L2 strain for practicality
Damping Equations
1000
1500
2000
Forc
Effective Dy
First Yield
L1
L2
MOTEMS FEMA 440 (eq. only)
Method Comparison
MOTEMS FEMA 440 (eq. only)
Method Comparison
0
500
1000 L2 Method Comparison Spectra iteration vs
displacement
Method Comparison Spectra iteration vs
displacement
Prevention First 2010
00.0 2.0 4.0 6.0 8.0
Displacement (in)iterationiteration
Sensitivity StudySensitivity Study
Examined 12 REAL structures Examined 12 REAL structures
Prevention First 2010
Yield PointYield Point
Effective Yield Larger Demand Di l t S ll D tilit
Effective Yield Larger Demand Di l t S ll D tilitDisplacement Smaller DuctilityDisplacement Smaller Ductility
Demand Displacement
14
Perfect Correllation+- 10%+ 30%
Ductility (μ=Δd/Δy) 4
10
12
Firs
t Yie
ld
+-30%B-P Method w/ MOTEMS ξB-P Method w/ FEMA440 ξC-G Method
2 5
3
3.5
Yiel
d6
8
Dis
p. (i
n) w
/
1.5
2
2.5
ctili
ty w
/ Firs
t
2
4
Dem
and
0.5
1Duc
Prevention First 2010
00 2 4 6 8 10 12 14
Demand Displ. (in) w/ Effective Yield
00 0.5 1 1.5 2 2.5 3 3.5 4
Ductility w/ Effective Yield
MethodologyMethodology
Damping vary +10%, Methods vary +30% Damping vary +10%, Methods vary +30% All converge at ductility = 1.0 More ductility more variation All converge at ductility = 1.0 More ductility more variation
Ductility (μ=Δd/Δy) B-P method w/ MOTEMS ξ OR C-G Method vs B-PDuctility (μ=Δd/Δy) B-P method w/ MOTEMS ξ OR C-G Method vs B-P Method w/ FEMA 440 ξ (All with Effective Yield Displacement)
3.5
4
G
Perfect Correllation+-10%+-30%Effective Yield, B-P Method w/ MOTEMS ξEff ti Yi ld C G M th d
2
2.5
3
MO
TEM
S ξ
OR
C-G Effective Yield, C-G Method
1ELASTIC
1
1.5
2
Duc
tility
B-P
w/ M
Prevention First 2010Prevention First 2010
0
0.5
0 0.5 1 1.5 2 2.5 3 3.5 4
Demand Displacement (in) B-P Method w/ FEMA 440 ξ
D
00 1
RecommendationsSignificant Parameters
RecommendationsSignificant ParametersSignificant ParametersSignificant Parameters
Effective Yield at Effective Yield at Pushover Curve Effective Yield at
secondary stiffness to L2 capacity
Effective Yield at secondary stiffness to L2 capacity
3500
4000
FEMA 440 method OK Hinge Lengths Steel
1 di t i d
FEMA 440 method OK Hinge Lengths Steel
1 di t i d 2000
2500
3000
ce (k
ip)
Effective Dy
1 diameter in ground ½ diameter at deck NEEDS more research
1 diameter in ground ½ diameter at deck NEEDS more research 1000
1500
Forc First Yield
L1
L2
Keep “r” in MOTEMS damping reasonable (< 0 3)
Keep “r” in MOTEMS damping reasonable (< 0 3)
0
500
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Prevention First 2010
(< 0.3)(< 0.3) Displacement (in)
Lessons LearnedLessons Learned
Methods vary significantly Methods vary significantly Coronel Chile Methods vary significantly Consider answer PASS/FAIL Brittle will NOT pass
Methods vary significantly Consider answer PASS/FAIL Brittle will NOT pass
Coronel, Chile
NEED additional research, comparison with real world Orthogonal loading
NEED additional research, comparison with real world Orthogonal loadingg g Kinematic loading Instrumented structures
Ramps / piping / other must
g g Kinematic loading Instrumented structures
Ramps / piping / other must Ramps / piping / other must satisfy displacements
Some Existing structures C f O S
Ramps / piping / other must satisfy displacements
Some Existing structures C f O S
Prevention First 2010
CAN satisfy MOTEMSCAN satisfy MOTEMS