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

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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 <

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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)

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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

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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

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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

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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

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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

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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*

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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

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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

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00.0 2.0 4.0 6.0 8.0

Displacement (in)iterationiteration

Sensitivity StudySensitivity Study

Examined 12 REAL structures Examined 12 REAL structures

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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

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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

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(< 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

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CAN satisfy MOTEMSCAN satisfy MOTEMS

Questions?Questions?

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