Seismic Code Requirements

CE 243A Behavior & design of RC Elements

Prof. J. W. Wallace

Seismic Code Requirements John W. Wallace, Ph.D., P.E. Associate Professor

University of California, Los Angeles

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1971 San Fernando, California Earthquake

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Prof. J. W. Wallace

Olive View Hospital Complex

1971 San Fernando Earthquake CE243A

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Soft-story


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Prof. J. W. Wallace


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Prof. J. W. Wallace

Confinement

Ties @ 18” o.c.

Spiral @ 3” o.c.


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Cal State Northridge

1994 Northridge Earthquake CE243A

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Cal State Northridge


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Northridge Fashion Mall


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Barrington Building


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Barrington Building

Holiday Holiday Inn Inn – Van Nuys Nuys


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Prof. J. W. Wallace

1994 Northridge Earthquake 

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Major failures: – Steel moment-resisting frames – Precast concrete parking structures – Tiltup & masonry buildings with wood roofs Major successes – retrofitted unreinforced masonry structures – retrofitted bridge structures

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1994 Northridge Earthquake 

1997 UBC & NEHRP changes: – removal of pre qualified steel connection details – addition of near near fault factor to base shear equation – prohibition on highly irregular structures in near near fault regions

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– stricter detailing for non--participating non elements – deformation compatibility requirements – chords & collectors designed for “real” forces – redundancy factor added to design forces 14

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Prof. J. W. Wallace

Summary 

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

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Seismic Codes and Source Documents SEAOC

NEHRP ASCE 7

Standard Building Code

BOCA National National Building Code

Uniform Building Code

International Building Code CE243A

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Prof. J. W. Wallace

IBC 2000, 2003 

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International Code Council (ICC), established in 1994 Seismic provisions 7-02 – ASCE 7 Modeling  Forces – Material codes  ACI, ASCE IBC 2003 (ASCE 77-02, ACI 318318-02)

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Material Codes International Building Code

MANUAL OF STEEL CONSTRUCTION

ACI 318-02 ACI 318R-02

LOAD & RESISTANCE FACTOR DESIGN

Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02) An ACI Standard

Volume I

Reported by ACI Committee 318

Structural Members, Specifications, & Codes AISC

aci

american concrete institute P.O. BOX 9094 FARMINGTON HILLS, MI 48333

Second Edition

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Prof. J. W. Wallace

Shake Table Test – Flat Plate

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Earthquake Building Response F4 = m4a4(t) F3 = m3a3(t) F2 = m2a2(t) F1 = m1a1(t) Note: Forces generally Increase with height g n i k a h S

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V(t) = ∑miai(t) i=1,4 Time 20

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Prof. J. W. Wallace

Building Response Analysis 

In general, three types of analyses are done to design buildings subjected to earthquakes

g n i k a h S

– Response History Analysis  Linear or nonlinear approach to calculate time varying responses (P, M, V, )

Sa

– Response Spectrum Analysis  Linear approach to calculate modal responses (peak values) and combine modal responses – Equivalent Lateral Force  Nonlinear approach used for rehabilitation (e.g., FEMA 356) approach – assume  Linear approach – assume response is dominated by first mode response (very common)

Time

Sd F4 F3 F2 F1

Vbase

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Building Response Analysis 

Response History Analysis – Analyze structure by applying acceleration history at base of structure – Typically requires use of several records – Elastic or inelastic response – Time consuming and results can vary substantially between records



Response Spectrum Analysis

g n i k a h S

Time

Sa

– Elastic response – Determine peak responses for each mode of response – Combine modal responses (SRSS, CQC) CE243A

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Prof. J. W. Wallace

Acceleration Response Spectrum Maximum Acceleration Aground Structural Period, T T

2π M

M K

K

Shaking CE243A

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Time

Displacement Response Spectrum Maximum Displacement

Structural Period, T T

2π M

M K

K

Shaking CE243A

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Time

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Prof. J. W. Wallace

Modal Analysis Sd,1 Sd,2 Sd,3 T3

Tn = 2π

φ nT Mφ n

φ nT K φ n

T2

T1

δ max,n = φ n S d ,n

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Dynamic Building Response MDOF System

SDOF Model x=4

Sd,n

Story Forces

x=4

Sd,n

x=2

x=2

x=1

x=1

Base Shear CE243A

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ADRS Spectrum 

Alternative format for response spectrum

Spectral Acceleration

T = constant 



“Capacity Spectrum” approach – ATC 40 Spectrum for a given earthquake versus smooth spectrum Spectral Displacement

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Code Analysis Procedures 

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UBC-97 and IBC-2000 – Equivalent static analysis approach – Response spectrum approach

– Response (Time) history approach – Other (Peer review) FEMA 273/356 & ATC 40 – Linear Static & Dynamic Procedures (LSP, LDP) – Nonlinear Static Static Analysis (NSP) “pushover” – Nonlinear Dynamic Procedure (NDP)

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1997 UBC Design Response Spectrum Control Periods

2.5CA

TS = CV /2.5CA

) n o i t a r e l e c c A ( CA

T0 = 0.2TS

CV /T Long-Period Limits

W / V

T0

TS Period (Seconds)

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UBC-97: Response Spectrum Analysis

V base = V base ≤ V base

C v I

Eq. (30 - 4)

W

RT 2.5C a I

W

R ≥ 0.11C a IW

Eq. (30 - 5) Eq. (30 - 6)

Ca = Seismic Coefficient (Acceleration) Cv = Seismic Coefficient (Velocity) CE243A

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Modal Analysis 

Eigen Analysis – Requires mass (M) and stiffness (K) matrices M is often assumed to be diagonal  K (e.g., from direct stiffness assembly) 

– Frequencies ( , T=2 / ) and mode shapes ( ) Mode shapes are columns of matrix (orthogonal property) Modal Analysis – Analysis – solve uncoupled equations 



[ M ]{v} + [C ]{v} + [ K ]{v} = { p}(t ); T

T

M n = [Φ ] [ M ][Φ ] = {φ m } [ M ]{φ n } T

n + C n y n + K n yn = φ n p(t ) M n y

{v} = [Φ ]{ y} m=n

solve for yn

Combine modal responses (e.g., SRSS, CQC) CE243A

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UBC-97 Approach: Response Spectrum MDOF System Model

Equivalent SDOF x=4

Sd,n

Story Forces

x=4

Sd,n

x=2

x=2

x=1

x=1

Base Shear CE243A

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UBC-97 Approach: Response Spectrum Peak modal responses – 1st Mode T

{δ x=1, 4}1 = {φ 11,φ 21,φ 31 ,φ 41} S d ,1 x=4

F1=M1Sa,1

x=3

M1

T1 = 2π

T1 = C t ( hn )

F 1 = M 1S a ,1

K 1

3/ 4

V base,1 = M 1S a,1 2

S d ,1 = ω 1 S a ,1

Sd,1

x=2

K1

x=1

g ,

) n n o o i i t t a r a e r l e e c l c e A (

c

W c / V

A

T0 T1 TSPeriodPeriod (Seconds)(sec)

Vbase,1 CE243A

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UBC-97 Approach: Response Spectrum Peak modal responses – 2nd to nth Mode T

{δ x=1, 4 }2 = {φ 12 ,φ 22 ,φ 32 ,φ 42 } Sd , 2 x=4

F2=M2Sa,2

Ti = 2π

M i K i

F 2 = M 2 Sa , 2 V base, 2 = M 2 Sa , 2 2 2 S d , 2 = Sa , 2 (T 2 / 4π )

x=3

Sd,2 x=2

K2

T = {T 1 , T 2 , T 3 , T 4 }

x=1

g ,

) n n o o i i t t a r a e r l e e c l c e A ( c W c / V

A

Vbase,2 CE243A

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T2 T0

TSPeriodPeriod (Seconds)(sec) 34

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Prof. J. W. Wallace

UBC-97 Approach: Response Spectrum Modal Combinations 



Peak modal responses do not occur at the same time, that is, the peak roof displacement displacement for for mode mode one occurs at t 1 , whereas the peak displacement for mode two occurs at t 2, and so on. Therefore, peak modal responses must be combined based on the correlation between modes. Modal Combination Approaches

– SRSS: Square -root-sum-squares, works well for systems with well -separated modes (2D models) Complete-Quadratic Quadratic--Combination (3D) – CQC: CompleteCE243A

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UBC-97 Approach: Response Spectrum Mass Participation 

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

PF m ,n = 

{φ n }T [ M ]{φ n }

Typical mass participation factors: PF m – Frame buildings: 1 st Mode Mode – – 80 to 85% – Shear wall buildings: 1 st Mode – 60 to 70% – To achieve 100% mass participation, all modes must be included in the modal analysis

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{φ n }T [ M ]{r = 1}

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UBC-97 Approach: Response Spectrum Specific Requirements 

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

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UBC-97 Approach: Response Spectrum Dead & Live Loads

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Combine response spectrum analysis results with analysis results for gravity forces Load combinations (1612)

– Same as new ACI load combinations Drift limits (1630.10) – h s = Story height – s = = Displ Displ . for code level forces ∆ m = 0.7 R∆ s

T < 0.7 sec : ∆ m < 0.025hs T ≥ 0.7 sec : ∆ m < 0.025hs CE243A

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Prof. J. W. Wallace

1997 UBC – – Equivalent Static Control Periods

2.5CA

TS = CV /2.5CA

) n o i t a r e l e c c A ( CA

T0 = 0.2TS

CV /T Long-Period Limits

W / V

T0

T1

TS Period (Seconds)

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UBC-97 Base Shear Equations Equivalent Static Analysis

V base = V base ≤ V base

C v I

Eq. (30 - 4)

W

RT 2.5C a I

W

R ≥ 0.11C a IW

Eq. (30 - 5) Eq. (30 - 6)

Ca = Seismic Coefficient (Acceleration) Cv = Seismic Coefficient (Velocity) CE243A

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UBC-97 Approach: Equivalent Static

C v = 0.40

v

For Z = 0.4, SB (Table 16 - R)

C a = 0.40 N a

For Z = 0.4, SB (Table 16 - Q)

Z = Seismic Zone Factor (0.075 to 0.4) S = Soil Profile Type Nv = 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

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UBC-97 Equivalent Static Analysis V base = I = W= R = T =

C v I RT

W

Eq. (30 - 4)

Importance Factor (1.0 to 1.25; Table 16-K) Building Seismic Dead Load Force Reduction Coefficient (Table 16-N) Fundamental Structural Period

T = C t ( hn ) 3 / 4 = 0.02(48 ft ) 3 / 4 = 0.37 sec Ct = Coefficient Coefficient (e.g., 0.02 for rc walls) hn = Building height (feet) CE243A

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Prof. J. W. Wallace

Equivalent Static Lateral Forces Dead & Live Loads

Ft

F 4

F x =

F 3

(V base − F t ) w x h x n

∑ wi hi i =1

F 2

F t = 0.07TV T > 0.7 sec F t = 0.0

F 1

T < 0.7 sec

Vbase CE243A

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Lateral Force Resisting System LFR S

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“Gravity” System

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Details of a building in Emeryville CE243A

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“Non-Participating” System  

Also referred to as: “Gravity” System Flat plate floor systems (Gravity loads)

– Efficient and economical – Easy to form, low story heights – Strong column – weak beam concept

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Prof. J. W. Wallace

Perimeter LFRS and Interior “GFRS”

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UBC-97: LFRS Design Equivalent Static or Response Spectrum 12 ft

LFRS Model

12 ft

100 ft 12 ft 12 ft

50 ft Floor Plan

Elevation View LFRS

Note: Neglecting torsion CE243A

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Prof. J. W. Wallace

UBC-97 Equivalent Static Analysis C v I 0.4(1.6)(1.0) V base = W = W 3/ 4 RT R (T = C t hn ) W 4 = (100' x 50' )(100 psf) = 500 kips W 3 = (100' x 50' )(100 psf) = 500 kips W 2 = (100' x 50' )(100 psf) = 500 kips W 1 = (100' x 50' )(100 psf) = 500 kips W = 500 kips (4 floors) = 2000 kips CE243A

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UBC-97 Equivalent Static Analysis V base =

C v I RT

W =

0.4(1.6)(1.0) R (T =

3/ 4 C t hn )

(W = 2000 kips)

R = Force Reduction Coefficient (Table 16-N) Accounts for nonlinear response of building (Building strength, ductility, damping) R = 1 is associated with elastic response Typical Values: R = 8.5 for a rc special moment frame R = 5.5 for a rc wall build building ing CE243A

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Prof. J. W. Wallace

UBC-97 Equivalent Static Analysis C v I 0.4(1.6)(1.0) W = W RT R (0.63)

V base = V base =

0.64 R (0.37)

W =

1.73 R

W =

1.73g R

M

2.5C a I 2.5(0.4)(1.2) 1.2 g W = W = M R R R = 1.2( 2000) / R = 1 = 2400 kips (elastic)

V base ≤ V base

V base = 2400 /( R = 5.5) = 435 kips (design) R > 1.0 requires inelastic response Structure must be specially detailed to control inelastic behavior CE243A

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1997 UBC Seismic Criteria

(Seismic Zone 4, Soil Type S B, Na =Nv =1) 1.5 Response Spectrum Design Spectrum (CN) Design Force F orce - R/I = 4.5 Design Force F orce - R/I = 8.5

1.25 ) n 1 o i t a r e 0.75 l e c c 0.5 A ( W / 0.25 V 0 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Period (Seconds) CE243A

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Confinement

Ties @ 18” o.c.

Spiral @ 3” o.c.


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UBC-97 Equivalent Static Analysis F 4

F x =

F 3

(V base − F t ) w x h x n

∑ wi hi

F 2 F 1

i =1

F t = 0.07TV T > 0.7 sec F t = 0.0

T < 0.7 sec

Base Shear Vbase = 435 kips CE243A

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Prof. J. W. Wallace

UBC-97 Equivalent Static Analysis n

F 4

∑ wi hi

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

i =1

= 60,000 kip - ft

F 3 F x =4

F 2

=

F x =3 =

F 1

F x =2 = F x =1 =

( 435 − 0)(500 k )(48' ) 60,000

ft −k

(435 − 0)(500 k )(36' ) 60,000 ft −k ( 435 − 0)(500 k )(24' ) 60,000

ft − k

( 435 − 0)(500 k )(12' ) 60,000 ft −k

= 0.4V = 174

k

k

= 0.3V = 131 = 0.2V = 87

k

k

= 0.1V = 43

4

∑ F x = 174 + 131 + 87 + 43 = 435 kips

Base Shear Vbase = 435 kips

x =1

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UBC-97 Equivalent Static Analysis Dead & Live Loads



F 4

– U = 1.2D + 0.5L + 1.0E – U = 0.9D +/- 1.0E – Where: E = Eh+ Ev Ev=0.5CaID = 0.24D

F 3 F 2 

F 1



Base Shear = Eh CE243A

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Load Combinations UBC--97 - S16.12.2.1 UBC

U = 0.9D +/+/- 1.0( Eh+ Ev) U = (0.9+/(0.9+/-0.24)D +/+/- Eh = redundancy factor 1.0 Conduct static analysis e.g., use SAP2000 56

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Prof. J. W. Wallace

UBC-97 Equivalent Static Analysis Dead & Live Loads

F4



F3 F2 F1





Vbase

Load Combinations UBCUBC-97 - S16.12.2.1

– U = 1.2D + 0.5L + 1.0E – U = 0.9D +/- 1.0E – Where: E = Eh+ Ev Ev=0.5CaID = 0.24D U = 0.9D +/- 1.0( Eh+ Ev) U = (0.9+/(0.9+/-0.24)D +/+/- Eh = redundancy factor 1.0 Conduct static analysis e.g., use SAP2000

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UBC-97: 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

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Code level Design forces: Story Displ.: (e.g., R=8.5)

s

s,x=4 s,x=3 s,x=2 s,x=1

Elevation View

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Prof. J. W. Wallace

UBC-97 Requirements  

1633 – Detailed systems design requirements 1633.1 General:

– Only the elements of the designated LFRS shall be used to resist design forces – Consider both seismic and gravity (D, L, S) – For some structures (irregular), must consider orthogonal effects: 100% of seismic forces in one direction, 30% in the perpendicular direction

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UBC-97 Requirements  

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16333.2 Structural Framing Systems 1633.2.1 General: – Defined by the types of vertical elements elements used used 1633.2.2 For structures with multiple systems, must use requirements for more restrictive system 1633.2.3 Connections – if resisting seismic forces, then must be on drawings 1633.2.4 Deformation compatibility

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LFRS and Deformation Compatibility LFR S

“Gravity” System

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LFRS and Deformation Compatibility Code level Design forces: (e.g., R=8.5)

s,x=4

Story Displ.:

s

s,x=4 s,x=3 s,x=2 s,x=1 diaphragm

Elevation View

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Plan View: Roof Rigid diaphragm Flexible diaphragm 62

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Prof. J. W. Wallace

UBC-97 Requirements 

1633.2.4 – Deformation compatibility – Requires that non -participating structural elements be designed to ensure compatibility of deformations with lateral force resisting system – Non-participating elements must be capable of maintaining support for gravity loads at deformations expected due to seismic forces – Design of LFRS:  

Model LFRS and apply design seismic forces Neglect lateral stiffness and strength of non participating elements

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1633.2.4 – Deformation 1633.2.4 – compatibility – For LFRS M = 0.7R S for lateral frame at each story

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

Story Displ.:

s

s,x=4





s,x=3

That is, compute story displacements for design seismic forces applied to the LFRS, then multiple by them by 0.7R

s,x=2 s,x=1

Elevation View

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Prof. J. W. Wallace


1633.2.4 – Deformation compatibility

– Non-participating frame Model the system system (linear - element stiffness) stiffness) – Shear and flexural flexural stiffness limited to ½ gross section values – Must consider flexibility of diaphragm and foundation Impose story displacements on the model of nonparticipating 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 



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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 resistanc e to these forces

– Diaphragms (1633.2.9) 



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Deflection of diaphragm limited by the permissible deflection of the attached elements Design forces specified in (33-1)

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Reinforced Concrete: ACI 318-02 Chapter 21 – Seismic Provisions 







CE243A

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Provide transverse steel - Confinement, buckling - Maintain gravity loads Strong -column, weak -beam - Beam flexural yielding Capacity design - Beam & column shear - Joint regions Prescriptive requirements - Little flexibility - Quick, easy, and usually conservative 67

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Seismic Code Requirements

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