seismic code requirements

CE 243A Behavior & design of RC Elements Prof. J. W. Wallace

Fall 04 1

CE243A 1

Seismic Code RequirementsSeismic Code Requirements

John W. Wallace, Ph.D., P.E.John W. Wallace, Ph.D., P.E.Associate ProfessorAssociate Professor

University of California, Los AngelesUniversity of California, Los Angeles

CE243A 2

1971San Fernando, California

Earthquake


Fall 04 2

CE243A 31971 San Fernando Earthquake

Olive View Hospital Complex


Soft-story


Fall 04 3




Fall 04 4

CE243A 7

1971 San Fernando Earthquake

Ties @ 18” o.c. Spiral @ 3” o.c.

Confinement

CE243A 81994 Northridge Earthquake

Cal State Northridge


Fall 04 5


Cal State Northridge


Northridge Fashion Mall


Fall 04 6


Barrington Building


Barrington BuildingHoliday Inn – Van Nuys


Fall 04 7

CE243A 13

1994 Northridge Earthquake1994 Northridge Earthquake

Major failures:Major failures:–– Steel momentSteel moment--resisting framesresisting frames–– PrecastPrecast concrete parking structuresconcrete parking structures–– TiltupTiltup & masonry buildings with wood & masonry buildings with wood

roofsroofsMajor successesMajor successes–– retrofitted retrofitted unreinforcedunreinforced masonry masonry

structuresstructures–– retrofitted bridge structuresretrofitted bridge structures

CE243A 14

1994 Northridge Earthquake1994 Northridge Earthquake

1997 UBC & NEHRP 1997 UBC & NEHRP changes:changes:–– removal of preremoval of pre--

qualified steel qualified steel connection detailsconnection details

–– addition of nearaddition of near--fault factor to base fault factor to base shear equationshear equation

–– prohibition on prohibition on highly irregular highly irregular structures in nearstructures in near--fault regionsfault regions

–– stricter detailing for stricter detailing for nonnon--participating participating elementselements

–– deformation deformation compatibility compatibility requirementsrequirements

–– chords & collectors chords & collectors designed for “real” designed for “real” forcesforces

–– redundancy factor redundancy factor added to design added to design forcesforces


Fall 04 8

CE243A 15

SummarySummary

Observation of the behavior of real buildings in Observation of the behavior of real buildings in real earthquakes have been the single largest real earthquakes have been the single largest influence on the development of our building influence on the development of our building codescodesThe lull in earthquakes in populated areas The lull in earthquakes in populated areas between approximately 1940 and 1970 gave a between approximately 1940 and 1970 gave a false since of security at a time when the false since of security at a time when the population of California was expanding rapidlypopulation of California was expanding rapidlyPerformance of newer buildings and bridges has Performance of newer buildings and bridges has generally been good in recent earthquakes; generally been good in recent earthquakes; however, older buildings pose a substantial however, older buildings pose a substantial hazard. hazard.

CE243A 16

Seismic Codes and Source DocumentsSeismic Codes and Source Documents

SEAOC

ASCE 7

NEHRP

StandardStandardBuilding CodeBuilding Code

UniformUniformBuilding CodeBuilding Code

BOCA NationalBOCA NationalBuilding CodeBuilding CodeStandardStandard

Building CodeBuilding CodeUniformUniform

Building CodeBuilding Code

BOCA NationalBOCA NationalBuilding CodeBuilding Code

International Building CodeInternational Building Code


Fall 04 9

CE243A 17

IBC 2000, 2003IBC 2000, 2003

International Code International Code Council (ICC), Council (ICC), established in 1994established in 1994Seismic provisionsSeismic provisions–– ASCE 7ASCE 7--0202

ModelingModelingForcesForces

–– Material codesMaterial codesACI, ASCEACI, ASCE

IBC 2003 (ASCE 7IBC 2003 (ASCE 7--02, 02, ACI 318ACI 318--02)02)

CE243A 18

Material CodesMaterial CodesInternational Building CodeInternational Building Code

ACI 318-02ACI 318R-02

Building Code Requirements forStructural Concrete (ACI 318-02)and Commentary (ACI 318R-02)

american concrete instituteP.O. BOX 9094

FARMINGTON HILLS, MI 48333aci

MANUALOF STEEL

CONSTRUCTION

LOAD &RESISTANCE

FACTORDESIGN

Volume I

Structural Members,Specifications,

& Codes

Second Edition

AISC

An ACI Standard

Reported by ACI Committee 318


Fall 04 10

CE243A 19

Shake Table Test Shake Table Test –– Flat PlateFlat Plate

CE243A 20

Earthquake Building ResponseEarthquake Building Response

TimeTimeShak

ing

Shak

ing

F4 = m4a4(t)

F3 = m3a3(t)

F2 = m2a2(t)

F1 = m1a1(t)

V(t) = ∑miai(t) i=1,4

Note: Forces generally Increase with height


Fall 04 11

CE243A 21

Building Response AnalysisBuilding Response Analysis

In general, three types of analyses are In general, three types of analyses are done to design buildings subjected to done to design buildings subjected to earthquakesearthquakes–– Response History AnalysisResponse History Analysis

Linear or nonlinear approach to Linear or nonlinear approach to calculate time varying responses calculate time varying responses (P, M, V, (P, M, V, δδ))

–– Response Spectrum AnalysisResponse Spectrum AnalysisLinear approach to calculate modal Linear approach to calculate modal responses (peak values) and responses (peak values) and combine modal responsescombine modal responses

–– Equivalent Lateral Force Equivalent Lateral Force Nonlinear approach used for Nonlinear approach used for rehabilitation (e.g., FEMA 356)rehabilitation (e.g., FEMA 356)Linear approach Linear approach –– assume assume response is dominated by first response is dominated by first mode response (very common)mode response (very common)

TimeTimeShak

ing

Shak

ing

SSdd

SSaa

Vbase

F4F3F2

F1

CE243A 22

Building Response AnalysisBuilding Response Analysis

Response History AnalysisResponse History Analysis–– Analyze structure by applying Analyze structure by applying

acceleration history at base of acceleration history at base of structurestructure

–– Typically requires use of several Typically requires use of several recordsrecords

–– Elastic or inelastic responseElastic or inelastic response–– Time consuming and results can vary Time consuming and results can vary

substantially between recordssubstantially between records

TimeTimeShak

ing

Shak

ing

SSaa

TT

Response Spectrum AnalysisResponse Spectrum Analysis–– Elastic responseElastic response–– Determine peak responses for each Determine peak responses for each

mode of responsemode of response–– Combine modal responses (SRSS, Combine modal responses (SRSS,

CQC)CQC)


Fall 04 12

CE243A 23

Acceleration Response SpectrumAcceleration Response Spectrum

KM

TimeTimeShakingShaking

MaximumAcceleration

Structural Period, T

Aground

KM2πT =

CE243A 24

Displacement Response SpectrumDisplacement Response Spectrum

KM

TimeTimeShakingShaking

MaximumDisplacement

Structural Period, T

KM2πT =


Fall 04 13

CE243A 25

Modal AnalysisModal Analysis

Sd,1

T3 T2 T1

nTn

nTn

φφφφ

KM2πTn =

Sd,2

Sd,3

ndnn S ,max, φδ =

CE243A 26

Dynamic Building ResponseDynamic Building Response

Base Shear

MDOF System SDOF Model

StoryForces

Sd,n

δx=4

Sd,n

δx=4

δx=1

δx=2

δx=1

δx=2


Fall 04 14

CE243A 27

ADRS SpectrumADRS Spectrum

Alternative format for Alternative format for response spectrumresponse spectrum

“Capacity Spectrum” “Capacity Spectrum” approach approach –– ATC 40ATC 40

Spectrum for a given Spectrum for a given earthquake versus earthquake versus smooth spectrumsmooth spectrum

Spectral Spectral AccelerationAcceleration

Spectral DisplacementSpectral Displacement

T = constant

CE243A 28

Code Analysis ProceduresCode Analysis Procedures

UBCUBC--97 and IBC97 and IBC--2000 2000 –– Equivalent static analysis approachEquivalent static analysis approach–– Response spectrum approachResponse spectrum approach–– Response (Time) history approachResponse (Time) history approach–– Other (Peer review)Other (Peer review)

FEMA 273/356 & ATC 40FEMA 273/356 & ATC 40–– Linear Static & Dynamic Procedures (LSP, LDP)Linear Static & Dynamic Procedures (LSP, LDP)–– Nonlinear Static Analysis (NSP) “pushover”Nonlinear Static Analysis (NSP) “pushover”–– Nonlinear Dynamic Procedure (NDP)Nonlinear Dynamic Procedure (NDP)


Fall 04 15

CE243A 29

1997 UBC1997 UBC Design Response SpectrumDesign Response Spectrum

Period (Seconds)

V/W

(Acc

eler

atio

n)

CA

T0

CV/T

2.5CA

TS

Long-Period Limits

Control PeriodsTS = CV/2.5CA

T0 = 0.2TS

CE243A 30

UBCUBC--97: Response Spectrum Analysis97: Response Spectrum Analysis

6)-(30 Eq. 11.0

5)-(30 Eq. 5.2

4)-(30 Eq.

IWCV

WR

ICV

WRT

ICV

abase

abase

vbase

≥

≤

=

Ca = Seismic Coefficient (Acceleration)Cv = Seismic Coefficient (Velocity)


Fall 04 16

CE243A 31

Modal AnalysisModal AnalysisEigenEigen AnalysisAnalysis–– Requires mass (M) and stiffness (K) matricesRequires mass (M) and stiffness (K) matrices

M is often assumed to be diagonalM is often assumed to be diagonalK (e.g., from direct stiffness assembly)K (e.g., from direct stiffness assembly)

–– Frequencies (Frequencies (ωω, , T=2T=2ππ//ωω) ) and mode shapes (and mode shapes (ΦΦ))Mode shapes Mode shapes φφ are columns of are columns of ΦΦ matrix matrix (orthogonal property)(orthogonal property)

Modal Analysis Modal Analysis –– solve uncoupled equationssolve uncoupled equations

CQC) SRSS, (e.g., responses modal Combinefor solve )(

nm }]{[}{]][[][

}]{[}{ );}({}]{[}]{[}]{[

nTnnnnnnn

nT

mT

n

ytpyKyCyM

MMM

yvtpvKvCvM

φ

φφ

=++

==ΦΦ=

Φ==++

CE243A 32

UBCUBC--97 Approach: Response Spectrum97 Approach: Response Spectrum

Base Shear

MDOF System Model Equivalent SDOF

StoryForces

Sd,n

δx=4

Sd,n

δx=4

δx=1

δx=2

δx=1

δx=2


Fall 04 17

CE243A 33

UBCUBC--97 Approach: Response Spectrum97 Approach: Response SpectrumPeak modal responses Peak modal responses –– 11stst ModeMode

4/31

11

1

)(T

KM2πT

nt hC=

=

1,2

11,

1,11,

1,11

ad

abase

a

SS

SMVSMF

ω=

=

=

Sd,1

δx=4

δx=1

δx=2

Vbase,1

F1=M1Sa,1

K1

Period (Seconds)

V/W

(Acc

eler

atio

n)

T0 TST1Ac

cele

ratio

n, g

Period (sec)

δx=3

{ } 1,4131211114,1 ,,,}{ dT

x Sφφφφδ ==

CE243A 34

UBCUBC--97 Approach: Response Spectrum97 Approach: Response SpectrumPeak modal responses Peak modal responses –– 22ndnd to nto nthth ModeMode

{ }

i

i

KM

TTTT

π2T

,,,T

i

4321

=

=

)4/( 2222,2,

2,22,

2,22

πTSS

SMVSMF

ad

abase

a

=

=

=

Sd,2

δx=4

δx=1

δx=2

Vbase,2

K2

Period (Seconds)

V/W

(Acc

eler

atio

n)

T0 TST2

Acce

lera

tion,

g

Period (sec)

{ } 2,4232221224,1 ,,,}{ dT

x Sφφφφδ ==

δx=3F2=M2Sa,2


Fall 04 18

CE243A 35

UBCUBC--97 Approach: Response Spectrum97 Approach: Response SpectrumModal CombinationsModal Combinations

Peak modal responses do not occur at the same Peak modal responses do not occur at the same time, that is, the peak roof displacement for mode time, that is, the peak roof displacement for mode one occurs at tone occurs at t11 , whereas the peak displacement , whereas the peak displacement for mode two occurs at tfor mode two occurs at t22, and so on. Therefore, , and so on. Therefore, peak modal responses must be combined based peak modal responses must be combined based on the correlation between modes. on the correlation between modes. Modal Combination ApproachesModal Combination Approaches–– SRSS: SquareSRSS: Square--rootroot--sumsum--squares, works well squares, works well

for systems with wellfor systems with well--separated modes (2D separated modes (2D models)models)

–– CQC: CompleteCQC: Complete--QuadraticQuadratic--Combination (3D)Combination (3D)

CE243A 36

UBCUBC--97 Approach: Response Spectrum97 Approach: Response SpectrumMass ParticipationMass Participation

The (force) participation of each mode can be The (force) participation of each mode can be gauged by the mass participation factor. gauged by the mass participation factor.

Typical mass participation factors: Typical mass participation factors: PFPFmm–– Frame buildings: 1Frame buildings: 1stst Mode Mode –– 80 to 85%80 to 85%–– Shear wall buildings: 1Shear wall buildings: 1stst Mode Mode –– 60 to 70%60 to 70%–– To achieve 100% mass participation, all modes To achieve 100% mass participation, all modes

must be included in the modal analysismust be included in the modal analysis

}]{[}{}1]{[}{

,n

Tn

Tn

nm MrMPFφφ

φ ==


Fall 04 19

CE243A 37

UBCUBC--97 Approach: Response Spectrum97 Approach: Response SpectrumSpecific RequirementsSpecific Requirements

1631.5.2 1631.5.2 -- For regular buildings, include sufficient For regular buildings, include sufficient modes to capture 90% of participating mass. In modes to capture 90% of participating mass. In general, this is relatively few modesgeneral, this is relatively few modes1631.5.3 1631.5.3 -- Modal combinations Modal combinations –– Use appropriate Use appropriate methods (SRSS, CQC). For 3D models with methods (SRSS, CQC). For 3D models with closely spaced modes closely spaced modes –– need CQC. need CQC. 1630.5.4 1630.5.4 –– R factors and limits on reducing base R factors and limits on reducing base shear where response spectrum analysis is usedshear where response spectrum analysis is used1630.5.5 1630.5.5 –– Directional effects: consider seismic Directional effects: consider seismic forces in any horizontal direction (1630.1)forces in any horizontal direction (1630.1)1630.5.6 1630.5.6 –– Account for torsionAccount for torsion

CE243A 38

UBCUBC--97 Approach: Response Spectrum97 Approach: Response Spectrum

Combine response Combine response spectrum analysis results spectrum analysis results with analysis results for with analysis results for gravity forcesgravity forcesLoad combinations (1612)Load combinations (1612)–– Same as new ACI load Same as new ACI load

combinationscombinationsDrift limits (1630.10)Drift limits (1630.10)–– hhss = Story height= Story height–– ∆∆ss = = DisplDispl. for code . for code

level forceslevel forces

Dead & Live Loads

sm

sm

sm

hh

R

025.0 :sec 0.7T025.0 :sec 0.7 T

7.0

<∆≥<∆<

∆=∆


Fall 04 20

CE243A 39

1997 UBC1997 UBC –– Equivalent StaticEquivalent Static

Period (Seconds)

V/W

(Acc

eler

atio

n)

CA

T0

CV/T

2.5CA

TS

Long-Period Limits

Control PeriodsTS = CV/2.5CA

T0 = 0.2TS

T1

CE243A 40

UBCUBC--97 Base Shear Equations97 Base Shear EquationsEquivalent Static AnalysisEquivalent Static Analysis

6)-(30 Eq. 11.0

5)-(30 Eq. 5.2

4)-(30 Eq.

IWCV

WR

ICV

WRT

ICV

abase

abase

vbase

≥

≤

=

Ca = Seismic Coefficient (Acceleration)Cv = Seismic Coefficient (Velocity)


Fall 04 21

CE243A 41

UBCUBC--97 Approach: Equivalent Static97 Approach: Equivalent Static

Q)-16 (Table S 0.4,For Z 40.0R)-16(Table S0.4,For Z 40.0

B

B

====

aa

vv

NCNC

Z = Seismic Zone Factor (0.075 to 0.4)S = Soil Profile TypeNv = Near Source Coefficient (velocity)

Seismic Source A (M > 7.0, SR > 5 mm/yr)Distance = 5 km Nv = 1.6 (Table 16-T)

Na = Near Source Coefficient (acceleration)Seismic Source A (M > 7.0, SR > 5 mm/yr)Distance = 5 km Na = 1.2 (Table 16-S)

CE243A 42

UBCUBC--97 Equivalent Static Analysis97 Equivalent Static Analysis

4)-(30 Eq. WRT

ICV vbase =

I = Importance Factor (1.0 to 1.25; Table 16-K)W = Building Seismic Dead LoadR = Force Reduction Coefficient (Table 16-N)T = Fundamental Structural Period

sec37.0)48(02.0)( 4/34/3 === fthCT nt

Ct = Coefficient (e.g., 0.02 for rc walls)hn = Building height (feet)


Fall 04 22

CE243A 43

Equivalent Static Lateral ForcesEquivalent Static Lateral Forces

sec 0.7 T 0.0sec 0.7T 07.0

)(

1

<=>=

−=

∑=

t

t

n

iii

xxtbasex

FTVF

hw

hwFVF

Vbase

4F

3F

2F

1F

Dead & Live Loads

Ft

CE243A 44

Lateral Force Resisting SystemLateral Force Resisting SystemLFRS “Gravity” System


Fall 04 23

CE243A 45

Details of a Details of a building in building in EmeryvilleEmeryville

CE243A 46

““NonNon--Participating” SystemParticipating” SystemAlso referred to as: “Gravity” SystemAlso referred to as: “Gravity” SystemFlat plate floor systems (Gravity loads)Flat plate floor systems (Gravity loads)–– Efficient and economicalEfficient and economical–– Easy to form, low story heightsEasy to form, low story heights–– Strong column Strong column –– weak beam concept weak beam concept


Fall 04 24

CE243A 47

Perimeter LFRS and Interior “GFRS”Perimeter LFRS and Interior “GFRS”

CE243A 48

UBCUBC--97: LFRS Design97: LFRS DesignEquivalent Static or Response SpectrumEquivalent Static or Response Spectrum

50 ft

100 ft

Floor Plan Elevation View LFRS

12 ft

12 ft

12 ft

12 ft

LFRSModel

Note: Neglecting torsion


Fall 04 25

CE243A 49


WhCTR

WRT

ICVnt

vbase )(

)0.1)(6.1(4.04/3=

==

kips 500psf))(10050'x '100(4 ==W

kips 500psf))(10050'x '100(3 ==W

kips 500psf))(10050'x '100(2 ==W

kips 500psf))(10050'x '100(1 ==W

kips 2000floors)(4kips500 ==W

CE243A 50


R = Force Reduction Coefficient (Table 16-N)Accounts for nonlinear response of building(Building strength, ductility, damping)R = 1 is associated with elastic responseTypical Values: R = 8.5 for a rc special moment frameR = 5.5 for a rc wall building

)kips 2000()(

)0.1)(6.1(4.04/3 =

=== W

hCTRW

RTICV

nt

vbase


Fall 04 26

CE243A 51


R > 1.0 requires inelastic responseStructure must be specially detailed to control inelastic behavior

(design) kips 435)5.5/(2400(elastic) 24001/)2000(2.1

2.1)2.1)(4.0(5.25.2

73.173.1)37.0(

64.0)63.0(

)0.1)(6.1(4.0

======

==≤

===

==

RVkipsRV

MR

gWR

WR

ICV

MR

gWR

WR

V

WR

WRT

ICV

base

base

abase

base

vbase

CE243A 52

1997 UBC1997 UBC Seismic CriteriaSeismic Criteria(Seismic Zone 4, Soil Type S(Seismic Zone 4, Soil Type SBB, N, Naa ==NNvv =1)=1)

0

0.25

0.5

0.75

1

1.25

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2Period (Seconds)

V/W

(Acc

eler

atio

n)

Response SpectrumDesign Spectrum (CN)Design Force - R/I = 4.5Design Force - R/I = 8.5


Fall 04 27


Ties @ 18” o.c. Spiral @ 3” o.c.

Confinement

CE243A 54


Base Shear Vbase = 435 kips

sec 0.7 T 0.0sec 0.7T 07.0

)(

1

<=>=

−=

∑=

t

t

n

iii

xxtbasex

FTVF

hw

hwFVF4F

3F

2F

1F


Fall 04 28

CE243A 55


Base ShearVbase = 435 kips

kips 4354387131174

431.0000,60

)'12)(500)(0435(

872.0000,60

)'24)(500)(0435(

1313.0000,60

)'36)(500)(0435(

1744.0000,60

)'48)(500)(0435(

ft-kip 60,000

)48'36'24'kips)(12' (500

4

1

1

2

3

4

1

=+++=

==−=

==−

=

==−

=

==−=

=

+++=

∑

∑

=

−=

−=

−=

−=

=

xx

kkft

k

x

kkft

k

x

kkft

k

x

kkft

k

x

n

iii

F

VF

VF

VF

VF

hw4F

3F

2F

1F

CE243A 56


Base Shear = ρρEEhh

4F

3F

2F

1F

Load Combinations Load Combinations UBCUBC--97 97 -- S16.12.2.1S16.12.2.1–– U = 1.2D + 0.5L + 1.0E U = 1.2D + 0.5L + 1.0E –– U = 0.9D +/U = 0.9D +/-- 1.0E1.0E–– Where: E = Where: E = ρρEEhh+ + EEvv

EEvv=0.5C=0.5CaaID = 0.24DID = 0.24DU = 0.9D +/U = 0.9D +/-- 1.0(1.0(ρρEEhh+ + EEvv))U = (0.9+/U = (0.9+/--0.24)D +/0.24)D +/-- ρρEEhh

ρρ = redundancy factor = redundancy factor ≥≥1.01.0Conduct static analysise.g., use SAP2000

Dead & Live Loads


Fall 04 29

CE243A 57

UBCUBC--97 Equivalent Static Analysis97 Equivalent Static AnalysisLoad Combinations Load Combinations UBCUBC--97 97 -- S16.12.2.1S16.12.2.1–– U = 1.2D + 0.5L + 1.0E U = 1.2D + 0.5L + 1.0E –– U = 0.9D +/U = 0.9D +/-- 1.0E1.0E–– Where: E = Where: E = ρρEEhh+ + EEvv

EEvv=0.5C=0.5CaaID = 0.24DID = 0.24DU = 0.9D +/U = 0.9D +/-- 1.0(1.0(ρρEEhh+ + EEvv))U = (0.9+/U = (0.9+/--0.24)D +/0.24)D +/-- ρρEEhh

ρρ = redundancy factor = redundancy factor ≥≥1.01.0Conduct static analysise.g., use SAP2000Vbase

Dead & Live LoadsF4

F3

F2

F1

CE243A 58

UBCUBC--97: Drift & Drift Limits97: Drift & Drift Limits

1630.9 – Drift for all analysis is defined– Defines drift for

Maximum Inelastic Response Displacement (∆M ) and for Design Seismic Forces (∆S ): ∆M= 0.7R∆S

1630.10 – Drift limits defined– Drift < 0.025 times story

height if T < 0.7 sec– Drift < 0.02 times story

height if T ≥ 0.7 sec

Code levelDesign forces: (e.g., R=8.5)

∆ s,x=4

∆ s,x=1

∆ s,x=2

∆ s,x=3

Story Displ.: ∆s

Elevation View


Fall 04 30

CE243A 59

UBCUBC--97 Requirements97 Requirements

1633 1633 –– Detailed systems design requirementsDetailed systems design requirements1633.1 General: 1633.1 General: –– Only the elements of the designated LFRS Only the elements of the designated LFRS

shall be used to resist design forcesshall be used to resist design forces–– Consider both seismic and gravity (D, L, S)Consider both seismic and gravity (D, L, S)–– For some structures (irregular), must consider For some structures (irregular), must consider

orthogonal effects: 100% of seismic forces in orthogonal effects: 100% of seismic forces in one direction, 30% in the perpendicular one direction, 30% in the perpendicular directiondirection

CE243A 60


16333.216333.2 Structural Framing SystemsStructural Framing Systems1633.2.11633.2.1 General: General: –– Defined by the types of vertical elements usedDefined by the types of vertical elements used

1633.2.2 1633.2.2 For structures with multiple systems, For structures with multiple systems, must use requirements for more restrictive must use requirements for more restrictive systemsystem1633.2.31633.2.3 Connections Connections –– if resisting seismic if resisting seismic forces, then must be on drawingsforces, then must be on drawings1633.2.41633.2.4 Deformation compatibilityDeformation compatibility


Fall 04 31

CE243A 61

LFRS and Deformation CompatibilityLFRS and Deformation CompatibilityLFRS “Gravity” System

CE243A 62

LFRS and Deformation CompatibilityLFRS and Deformation Compatibility

Plan View: RoofRigid diaphragmFlexible diaphragm

diaphragm

∆s,x=4Code levelDesign forces:(e.g., R=8.5)

∆ s,x=4

∆ s,x=1

∆ s,x=2

∆ s,x=3

Story Displ.: ∆s

Elevation View


Fall 04 32

CE243A 63


1633.2.4 1633.2.4 –– Deformation compatibilityDeformation compatibility–– Requires that nonRequires that non--participating structural participating structural

elements be designed to ensure compatibility elements be designed to ensure compatibility of deformations with lateral force resisting of deformations with lateral force resisting systemsystem

–– NonNon--participating elements must be capable of participating elements must be capable of maintaining support for gravity loads at maintaining support for gravity loads at deformations expected due to seismic forcesdeformations expected due to seismic forces

–– Design of LFRS: Design of LFRS: Model LFRS and apply design seismic forcesModel LFRS and apply design seismic forcesNeglect lateral stiffness and strength of nonNeglect lateral stiffness and strength of non--participating elementsparticipating elements

CE243A 64


1633.2.4 1633.2.4 –– Deformation Deformation compatibilitycompatibility–– For LFRSFor LFRS

∆∆MM = 0.7R= 0.7R∆∆S S for for lateral frame at each lateral frame at each storystoryThat is, compute That is, compute story displacements story displacements for design seismic for design seismic forces applied to the forces applied to the LFRS, then multiple LFRS, then multiple by them by by them by 0.7R0.7R

Code levelDesign forces:(e.g., R=8.5)

∆ s,x=4

∆ s,x=1

∆ s,x=2

∆ s,x=3

Story Displ.: ∆s

Elevation View


Fall 04 33

CE243A 65


1633.2.4 – Deformation compatibility– Non-participating frame

Model the system (linear - element stiffness)– Shear and flexural stiffness limited to ½ gross

section values– Must consider flexibility of diaphragm and

foundationImpose story displacements on the model of non-participating frame

– The imposed displacements produce element forces, consider these to be ultimate

– check stability (support for gravity loads)– Detailing requirements: 21.11 in ACI 318-02

CE243A 66


Other items of interest– Collectors (1633.2.6)

Must provide collectors to transfer seismic forces originating in other portions of the structure to the element providing the resistance to these forces

– Diaphragms (1633.2.9)Deflection of diaphragm limited by the permissible deflection of the attached elementsDesign forces specified in (33-1)


Fall 04 34

CE243A 67

Reinforced Concrete: ACI 318Reinforced Concrete: ACI 318--0202Chapter 21 Chapter 21 –– Seismic ProvisionsSeismic Provisions

Provide transverse steelProvide transverse steel-- Confinement, bucklingConfinement, buckling-- Maintain gravity loadsMaintain gravity loads

StrongStrong--column, weakcolumn, weak--beambeam-- Beam flexural yieldingBeam flexural yielding

Capacity designCapacity design-- Beam & column shearBeam & column shear-- Joint regionsJoint regions

Prescriptive requirementsPrescriptive requirements-- Little flexibilityLittle flexibility-- Quick, easy, and usually Quick, easy, and usually

conservativeconservative