improving seismic performance of asymmetric … seismic performance of asymmetric buildings with ......

March 27, 2002 1 R. K. Goel

Improving Seismic Performance of Improving Seismic Performance of Asymmetric Buildings With Asymmetric Buildings With

Viscous DampersViscous Dampers

Rakesh K. GoelRakesh K. GoelAssociate ProfessorAssociate Professor

Cal Poly State University, Cal Poly State University, San Luis ObispoSan Luis Obispo


OutlineOutline

! Seismic behavior of asymmetric buildings! Background on viscous damper and current

applications! Research on dampers in asymmetric

buildings! Conclusions and recommendations! Future research


AcknowledgementAcknowledgement

! The National Science Foundation, Grant # CMS-9812414

! Graduate Students"Linda Tam, Elastic behavior"Cecilia Booker, Inelastic behavior"Kelly Thomas, Bi-direction ground motion

! Undergraduate Students"Cori McDaniel, Jodi Collins"Marty Downs"Adam Fredericks, Maria Koenig, John Leventini


Torsion in Asymmetric BuildingsTorsion in Asymmetric Buildings

Simulation of a commercial building at street corner


Adverse Effects of TorsionAdverse Effects of Torsion

! Excessive deformation leads to increased potential for"Failure of brittle, non-

ductile structural elements

"Pounding between closely spaced buildings

"Increased second-order (P-∆) effects


Failure Due to Torsion: Failure Due to Torsion: 1995 Kobe Japan1995 Kobe Japan

! Open storefront! Irregular distribution of

columns and shear walls

! Torsion during earthquake

! Failure in first story from excessive deformation due to torsion


Damage Due to Torsion: Damage Due to Torsion: 2001 India2001 India

! T-shaped building! Damage occurred on

the flexible side due to torsion


Reduction in Demand:Reduction in Demand:Traditional ApproachesTraditional Approaches

! Redistribute stiffness/mass to minimize eccentricity"Limitations for new construction

!Needs intervention of structural engineer at early design stage

!Not possible sometimes due to architectural/functional constraints

"Limitations for existing structures!Requires significant downtime!Requires expensive foundation work

! Provide additional strength to vulnerable elements"This code approach reduces ductility but not deformations


Reduction in Demand:Reduction in Demand:Viscous DampersViscous Dampers

! Reduce deformation, ductility, and hysteretic energy demand without increasing foundation forces"Damper forces are nearly 90° out-of-phase with

the beam-column action forces"Avoid expensive foundation work

! Viscous dampers work for small as well as large earthquakes"Friction dampers/ base isolation may not engage

in small/medium earthquakes

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Viscous DampersViscous Dampers! Capacity range from 2 kips to 2000 kips! Permit thermal movement without inducing

stresses! Very compact/ maintenance free/ economical! No external power source needed

50 kip Damper 1500 kip Damper

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Viscous DamperViscous Damper

! Piston head (with orifices) moves inside a cylinder

! Fluid is a stable, noncombustible, inert silicone polymer

! Force FD = CVα

"C = damper constant"V = velocity"α = damper exponent (=1

for linear damper)

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Damper InstallationsDamper Installations

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Money Store HeadquartersMoney Store Headquarters

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Example ApplicationsExample Applications

Money Store Headquarter, SacramentoHotel Woodland,

Woodland

Science Building, CSU Sacramento

Hundreds of other buildings

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Money MattersMoney Matters

! Building damper "$6000 each"Capacity of 200 to 300 kips

! Retrofit"Traditional: $10/sq-ft"With dampers: $5 to $8/sq-ft (saving of 20 to 50%)

! New construction"Additional cost of 1% to 2%"Much better performance"May even be able to design system as elastic

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ApplicationsApplications

! Most applications for symmetric systems"Symmetric damper distribution in the system plan

! Question for asymmetric systems "Is symmetric distribution still the most effective?"If not, what is the most effective distribution?

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Research ObjectivesResearch Objectives

! Identify system parameters for asymmetric buildings with viscous dampers

! Investigate the effects of system parameters"Elastic systems"Inelastic systems

! Experimentally verify analytical results! Develop simplified design procedure

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System ConsideredSystem Considered

CMCR

CSD

a

d X

Y

e

esd

Flexible-Edge Stiff-Edge

Damper

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Damping ParametersDamping Parameters

! Supplemental Damping Ratio, ζsd

! Normalized Supplemental Damping Eccentricity, esd

! Normalized Supplemental Damping Radius of Gyration, ρsd

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Response of Elastic SystemsResponse of Elastic Systems

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Damping EccentricityDamping Eccentricity

! Supplemental damping reduces deformation of flexible edge

! Reduction strongly depends on damping eccentricity"Asymmetric distribution

(esd = -0.2 ) leads to larger reduction

"If not selected carefully, asymmetric distribution (esd = 0.2 ) may give smaller reduction

March 27, 2002 22 R. K. Goel

Damping Radius of GyrationDamping Radius of Gyration

! Larger radius of gyration leads to larger reduction

! Reduction is not significant unless radius of gyration is very large

! Radius of gyration is not as important as damping eccentricity

March 27, 2002 23 R. K. Goel

Supplemental Damping Ratio Supplemental Damping Ratio

! Larger damping leads to larger reduction

! Asymmetric damping (esd = -0.2) is twice as effective as symmetric damping (esd = 0)"Only 20% damping

needed for esd = -0.2 where as about 40% needed for symmetric distribution to achieve same response level

March 27, 2002 24 R. K. Goel

Response of Inelastic SystemsResponse of Inelastic Systems

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ForceForce--Deformation HysteresisDeformation Hysteresis

! Area under the force-deformation curve represents hysteretic energy demand"Larger the demand,

larger the expected damage

! Supplemental damping significantly reduces"Hysteretic energy

demand "Deformation demand

March 27, 2002 26 R. K. Goel

Deformation and Ductility DemandDeformation and Ductility Demand

! Demands reduce with supplemental damping

! Reduction strongly depends on damping eccentricity"esd = -0.2 gives lowest

demand"Demands can be

reduced to below symmetric level

March 27, 2002 27 R. K. Goel

Hysteretic Energy DemandHysteretic Energy Demand

! Asymmetric damping reduces hysteretic energy demand"esd = -0.2 gives lowest

demand! Asymmetric damping

may be used to design systems with smaller damage expected at flexible side

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Experimental VerificationExperimental Verification

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Experimental ModelExperimental Model

! 18” × 18” × 18” model! 1/2” & 3/8” sq. steel

hollow tube columns ! 0.5” steel plate deck! Added mass = 39 lbs on

flexible side and 13 lbs on stiff side

! 15% system eccentricity

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Damper SpecificationDamper Specification

! Taylor fluid viscous damper

! 450 lbs capacity! 2” stroke length! C = 1.2 lb-sec/in! One damper

March 27, 2002 31 R. K. Goel

Shaking Table TestShaking Table Test! Tested on a 3’ by 3’ shaking table with 2500

lbs payload capacity! Sine-sweep test from 4 Hz to 12 Hz! Table acceleration maintained at 0.25g! Acceleration measured at deck level! Three configuration tested

"Damping eccentricity = 34% (damper at stiff edge)"Damping eccentricity = 0% (damper in middle)"Damping eccentricity = -34% (damper at flexible

edge)

March 27, 2002 32 R. K. Goel

Experimental ResultsExperimental Results

! Small scale experiments support analytical results"Damper on flexible side

gives lowest response"Improvement is by a factor of

nearly two compared to damper on center

! Need further studies with"Large-scale testing"Earthquake input

March 27, 2002 33 R. K. Goel

Development of Simplified Design Development of Simplified Design ProcedureProcedure

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Requirements of Simplified Requirements of Simplified ProcedureProcedure

! Should be based on sound theory! Should be simple enough to be used by

practicing engineers! Should be able to utilize existing analytical

tools

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Theoretical BackgroundTheoretical Background

! Systems with supplemental damping are in general non-proportional (or non-classical)

"Traditional modal analysis methods are not applicable

! Modal analysis requires solution of damped eigen-value problem

0Tn r ≠Φ CΦ

March 27, 2002 36 R. K. Goel

Damped EigenDamped Eigen--Value Problem:Value Problem:StateState--Space FormulationSpace Formulation

(B + λ A) ΦΦΦΦ = 0

−=M00K

A

−=CKK0

B

ζ−ωωζ=λ 21 nnnnn j∓

DampingodalApparent M =ζ n

FrequencyodalApparent M =ωn

March 27, 2002 37 R. K. Goel

Modal AnalysisModal Analysis

! Modal analysis is in complex-domain"Modal parameters are complex-valued

!Eigen values!Eigen vectors (or mode shapes)!Modal participation factors

! Eigen values can be expressed as a function of"Apparent modal frequency (or period)"Apparent modal damping ratio

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Effects of Damping DistributionEffects of Damping Distribution

! Most modal properties are affected very little"Apparent vibration frequencies (or periods)"Mode shapes"Modal participation factors

! Apparent damping ratios are affected significantly"Apparent damping influences the system

response

March 27, 2002 39 R. K. Goel

Apparent Modal Damping RatioApparent Modal Damping Ratio

! ζ1 increases significantly as"CSD moves from right to

left"Damping radius of

gyration increases! Small supplemental

damping (10%) gives large ζ1 (more than 60%) with careful plan-wise distribution

March 27, 2002 40 R. K. Goel

Limitations of Complex Modal Limitations of Complex Modal AnalysisAnalysis

! Need to calculate complex eigen values and eigen vectors

! Problem size is doubled compared to real-valued eigen problem

! Implementation in complex domain is difficult! Unlikely to find acceptance among practicing

engineers

March 27, 2002 41 R. K. Goel

Simplified MethodSimplified Method

! Calculate apparent damping ratio approximately

! Use mode shapes and frequencies of undamped system

! Utilize traditional modal analysis method

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Calculation of Damping RatioCalculation of Damping Ratio

! Make the damping matrix proportional by neglecting the off-diagonal terms

12 1

21 2

1

1

22

2

1 N

T

N

N

N NN

c cc c

c cc

cc

=

Φ CΦ

""

# #$$#

March 27, 2002 43 R. K. Goel

Calculation of Damping RatioCalculation of Damping Ratio

! Calculate nth mode damping ratio from the nth diagonal term" Use frequencies and mode shapes of the

undamped system

2

Tn n

n Tn n n

ζω

= CM

φ φφ φφ φφ φφ φφ φφ φφ φ

March 27, 2002 44 R. K. Goel

Damping Ratio: Simplified MethodDamping Ratio: Simplified Method

! Exact damping from complex-valued eigen analysis

! Approximate damping from simplified method

! Simplified procedure gives damping ratio either"Identical to exact value,

or"Slightly smaller than

exact value

March 27, 2002 45 R. K. Goel

Response: Simplified MethodResponse: Simplified Method

! Exact response from THA

! Simplified response from modal analysis using approximate modal damping ratios

! Simplified procedure gives response"Same as exact for short-

period systems"Slightly larger for longer

period systems

March 27, 2002 46 R. K. Goel

Error: Simplified MethodError: Simplified Method

! Error is less than 15%"Well within acceptable

engineering errors! Error are positive

"Estimated deformation is more than exact deformation

"Simplified procedure gives conservative estimate

March 27, 2002 47 R. K. Goel

ConclusionsConclusions

! Asymmetric distribution of supplemental damping gives larger response reduction for asymmetric-plan buildings"Further improvement by a factor of two possible

! Most important parameters are the damping ratio and damping eccentricity"Response is less sensitive to damping radius of

gyration

March 27, 2002 48 R. K. Goel

ConclusionsConclusions

! Largest reduction is obtained by concentrating all damping on the flexible edge (esd = -0.5)"No redundancy in the damping system

! Near optimal reduction if damping eccentricity = −−−− structural eccentricity

! Small scale experiments verify analytical findings

March 27, 2002 49 R. K. Goel

RecommendationsRecommendations

! Distribute damping in the system plan such that damping eccentricity = −−−− structural eccentricity"Use two or more dampers"Spread dampers as far from the CSD as possible"Keep redundancy in the system

March 27, 2002 50 R. K. Goel

RecommendationsRecommendations

! Use simplified method for analysis of asymmetric systems with supplemental dampers"Gives conservative response within 15% of exact

value"Can be implemented using traditional modal

analysis method

March 27, 2002 51 R. K. Goel

Future ResearchFuture Research

! Nonlinear viscous dampers"Damping and stiffness

! Friction and yielding dampers! Application to multi-story buildings! Large scale testing

March 27, 2002 52 R. K. Goel

Other ResearchOther Research

! Performance based design"Modal Pushover Analysis (MPA) for symmetric

structures"MPA for asymmetric structures"Correlation between damage and drift

! Soil-structure interaction"Bridge abutments

improving seismic performance of asymmetric … seismic performance of asymmetric buildings with ......

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