the tbi case studies: rc core wall and rc dual...

PEER TBI SEAONC Seminar April 21, 2011

Tuna, Yang, Wallace 1

The TBI Case Studies:RC Core Wall and RC Dual Systemy

Zeynep Tuna, John WallaceUniversity of California, Los Angeles

Tony YangUniversity of British Columbia, Vancouver

PBEE and Its Application to Tall Building Design – San Francisco – April 19 & 21, 1011

Case Study Buildings

42-story RCCore Wall

42-story RCDual System

40-story Steel SM Frame

2



Today’s Discussion – Analysis

Overview, Ground Motions, DesignModeling

Detailed overview

Core wall/Dual System analysis resultsDrift ratiosCore wall shear stresses and axial strainsCoupling beam rotations

Dual System moment frame resultsBeam and Column plastic rotation demandsColumn axial load demands

Summary3

Overall Approach

Create 3D building models [Perform 3D]Uniform modeling approach

Subject models to 5 levels of ground shaking intensity [horizontal ground acceleration]:

SLE25 - Serviceability with a probability of 70%/30 yr

SLE43 - Serviceability with a probability of 50%/30 yr

DBE - Life-Safety with a probability of 10%/50 years

MCE - Maximum Considered Earthquake with a

probability of 2%/50 years

OVE - Higher intensity than MCE with a probability of

1%/50 years4



Overall Approach

Each building analyzed for each hazard level:

5 Levels @ 15 GMs

Engineering Demand Parameters (EDPs):

Drift, Rotation, Strain, ,

Fragility Relations

5

Modeling – Global Considerations

3-D nonlinear models

Perform 3D [practice oriented program]Perform 3D [practice oriented program]

Lateral force resisting system only

Soil-structure interaction is neglected

P-Delta effects are included

2.5% viscous Rayleigh damping0.2T1 & 1.5T1

6



Modeling – Uniform Approach

Core Wall modelingFlexure and axial loads

U i i l fib d l ( t i l l ti )Uniaxial fiber models (material relations)Flexural yielding, followed by shear failure

ShearBackbone relations (linear flexure, nonlinear shear)

Coupling beamsShear displacement hinges (backbone)p g ( )

Dual systemBeam and column plastic hinges

Linear elements (stiffness)Podium level slabs, basement walls

7

RC Core Wall/RC Dual SystemMODELING DETAILS

8



Modeling – Core Wall (Concrete)

Concrete stress-strain relationship (Mander et al., 1988)

A: (0.6fcc/Ec, 0.6fcc)

B: (0.75εcc, fcc)

C: (1.25εcc, fcc)8

12

16

oncr

ete

Stre

ss (k

si)

C

A

B

D

f’c,exp =1.3*f’c(NOWAK &

SZERSZEN)

D: (0.024, 0.6fcc)

0 0.005 0.01 0.015 0.02 0.025Concrete Strain (in/in)

0

4

Co

f’c = 10 ksi1.3f’c = 13 ksi

9

Modeling – Core Wall (Rebar)

Steel stress-strain relationshipA706 steel 100A706 steel

fy= 1.17(60) = 70 ksi

fu= 105 ksi

Post-yield stiffness

and cyclic degradation

b O akcal et al (2006)

-0.12 -0.08 -0.04 0 0.04 0.08 0.12

-50

0

50

100

Ste

el S

tress

(ksi

)

fy,exp=1.17*fy

(MIRZA et al.)

by Orakcal et al. (2006)

Steel Strain (in/in)

-100

10



Modeling – Core Wall Shear

Shear stress-strain relationship

( )1 5 1 5 ' ACI 318-08 §21 9 4 1v v f fα ρ= = +

0.5

1

1.5

Shea

r Stre

ss (V

ult/V

n)

( )exp

'

'

'

'

1.5 1.5 ACI 318 08 §21.9.4.1

6000 psi57,000 psi

> 6000 psi40 000 1 0 6 i

n c c t y

c

c c

c

v v f f

fE f

fE f E

α ρ+

≤

=

0 0.004 0.008 0.012 0.01

Shear Strain (in/in)

0

S40,000 1.0 6 psiACI Committee 363

0.2

c c

c c

E f E

G E

= +

=

11

Modeling – Core Wall (Flexure-shear)

Test results

12



Modeling – Core Wall (Flexure-shear)

PCA-Corley et al. (1981)

Cyclic loadingCyclic loading

Axial loads vary from 0.0 to 0.13Agf’c

2 types of cross-sections with different

aspect ratios: barbelled: h/l=3.5

and flanged: h/l 2 7and flanged: h/l=2.7

Load – deflection relation: Specimen B5 ( )'

,max 8.8u cv f=Load – deflection relation: Specimen B1 ( )'

,max 3.1u cv f=

13

Upcoming UCLA Tests

' 'c/ 1.5 to 2.0 P=0.05 to 0.15A f @ 5 to 9 fw w g u pr ch l v M= =

14



Modeling – Coupling BeamsElastic beam elements + Nonlinear displacement shear hinge

Relative Displacement [in]

Shear displacement hinge

θ

V/Vy

Beam Effective Stiffness

0

100

200

Lat

eral

Loa

d [

k]

-4.32 -2.16 0 2.16 4.32p

ln/h = 2.4TestShear hinge model

-0.12 -0.06 0 0.06 0.12Rotation [radians]

-200

-100

(Naish et al.)

EIeff=0.2*EIg

MElastic beam

θ

15

Modeling – Coupling BeamsElastic beam elements + Nonlinear displacement shear hinge

Relative Displacement [in]Vyexp=Expected yield shear strength (2*As*fyexp*sin(α)

Shear displacement hinge

θ

V/Vy


0

100

200

Lat

eral

Loa

d [

k]

-4.32 -2.16 0 2.16 4.32p

ln/h = 2.4TestShear hinge model

p p

Vuexp=Expected ultimate shear strength (1.33*Vyexp)

Vrexp= Expected residual strength (0.25*Vuexp)

-0.12 -0.06 0 0.06 0.12Rotation [radians]

-200

-100

(Naish et al.)

EIeff=0.2*EIg

MElastic beam

θ

16



Modeling – SMF Beam

n mnRigid

dRigid

d

Nonlinear Rotation Hinges

Col

umn

Col

um

M

EIeff=0.35*EIg

M

end zone end zone

θ


θ

Moment Strength

17

Modeling – SMF Beam

Myexp=Expected nominal moment capacity Muexp= Expected nominal ultimate capacity (1.18*Myexp )θy=Maximum elastic rotationθy=Maximum elastic rotationθu=Ultimate rotation observed in test (0.046 rad)

18



Modeling – SMF Column

P

BeamRigid end zone

EIeff=0.7*EIg

M

θ

MMoment Strength

Nonlinear Rotation Hinges

Column Effective Stiffness Axial

Force

BeamRigid end zone

19

Modeling – Basement Walls

Basement walls below grade were modeled using elastic shear wall elements (Eeff = 0.8Ec)

20



Modeling – Podium Level Slabs

Slabs below grade were modeled using elastic shear shell element (Eeff = 0.25Ec)

21

RESULTS

Core Wall: Core Wall & Dual SystemDrift ratios Wall shear force/stressWall Base tension/compressive strainsCoupling beam rotations

RC Moment Frame: Dual SystemB l ti t tiBeam plastic rotationsColumn axial loadColumn plastic rotations

22



RC Core WallRESULTS

23

Core Wall – Design Summary1A: Code 1B: PBEE 1C: PBEE+

Wall: Strong Stronger Strongest

Coupling beam:

Stronger Stronger Strong

24” 24” 28” 28” 32” 32”

bea

1st mode Period:

T1X = 5.2 sec

T1Y = 4.0 sec

T1X = 4.8 sec

T1Y = 3.6 sec

T1X = 4.6 sec

T1Y = 3.5 sec

24



Core Wall – Drift (%)

Inter-story Drifts – Building I40

Building 1A - MCE

40

Building 1B - MCE

40

Building 1C - MCE

15

20

25

30

35

loor

num

ber [

-]

15

20

25

30

35

15

20

25

30

35

0 1 2 3 4 5

0

5

10

Fl

Drift (%)0 1 2 3 4

0

5

10

Drift (%)0 1 2 3 4

0

5

10

Drift (%)

meanmean + stdindividual record

μ = 2.5%μ+σ=3.33%

μ = 2.4%μ+σ= 3.0%

μ = 2.25%μ+σ= 2.75%

Core Wall - Wall Shear Stress

40

Building 1A - MCE

40

Building 1B - MCE

40

Building 1C - MCE

meanmean + std

1A: Code 1B: PBEE PBEE+

15

20

25

30

35

Floo

r num

ber [

-]

15

20

25

30

35

Floo

r num

ber [

-]

15

20

25

30

35

Floo

r num

ber [

-]

mean std8sqrt(fc)individual record

0 0.5 1

0

5

10

F

Stress (ksi)0 0.5 1

0

5

10

F

Stress (ksi)0 0.5 1

0

5

10

F

Stress (ksi)



Core Wall – Wall Strains εc

L38 L38 L38

1A: Code 1B: PBEE 1C: PBEE+

L3L8

L13L18L23L28L33L38

Floo

r num

ber [

-]

L3L8

L13L18L23L28L33L38

Floo

r num

ber [

-]

L3L8

L13L18L23L28L33L38

Floo

r num

ber [

-]

-2.5 -2 -1.5 -1 -0.5 0x 10

-3

B3L3

Wall edge strain - South west corner [in./in.]

-2.5 -2 -1.5 -1 -0.5 0x 10

-3

B3L3


-2.5 -2 -1.5 -1 -0.5 0x 10

-3

B3L3


Wall concrete compressive strain x 2; Wallace, SDTB (2007)PEER/ATC -72 Report: Modeling & Acceptance Criteria

εc = 0.0014/0.002 εc = 0.0013/0.0016 εc = 0.0012/0.0014

27

L38

L43

PEERTBI-1AM

MCE

L38

L43

PEERTBI-1BM

MCE

L38

L43

PEERTBI-1CM

MCE

Core Wall – Wall Strains εt1A: Code 1B: PBEE 1C: PBEE+

Yield Yield Yield

L13

L18

L23

L28

L33

L38

Flo

or n

umbe

r [-]

L13

L18

L23

L28

L33

L38

Flo

or n

umbe

r [-]

L13

L18

L23

L28

L33

L38

Flo

or n

umbe

r [-]

28

0 0.5 1 1.5 2B3

L3

L8

WallStrain01 [%]

0 0.5 1 1.5 2B3

L3

L8

WallStrain01 [%]

0 0.5 1 1.5 2B3

L3

L8

WallStrain01 [%]

εt,max = 0.02 εt,max = 0.01 εt,max = 0.004



Core Wall – Wall Reinforcement

29

Core Wall – CB Rotations θcb

L37L42

Building 1A - MCE

meanmean + std L37

L42

Building 1B - MCE

L37L42

Building 1C - MCE1A: Code 1B: PBEE 1C: PBEE+

0 0.02 0.04 0.06 0.08L2L7

L12L17L22L27L32L37

Floo

r num

ber [

-]

individual record

0 0.02 0.04 0.06 0.08L2L7

L12L17L22L27L32L37

Floo

r num

ber [

-]

0 0.02 0.04 0.06 0.08L2L7

L12L17L22L27L32L37

Floo

r num

ber [

-]

Coupling beam plastic rotation - South wall [radian] Coupling beam plastic rotation - South wall [radian] Coupling beam plastic rotation - South wall [radian]

Coupling beam plastic rotations

θcb = 0.008/0.013 θcb = 0.009/0.017 θcb = 0.028/0.043

30



RC Dual SystemCORE WALL RESULTS

31

Core Wall Building Design2A: Code 2B/2C: PBEE/PBEE+

Columns Walls Columns Walls

Wall: Strong Stronger

24” 24” 28” 28”

Column: Strong Stronger

36”x36” 46”x46”

Coupling beam:

Stronger Strong

1st mode Period:

T1X = 4.28 secT1Y = 3.88 sec

T1X = 4.46 secT1Y = 4.03 sec

Column: Strong Stronger

32



Dual System – Drift (%)

Inter-story Drifts – Building II

35

40

Building 2A - MCE

35

40

Building 2B - MCE2A: Code 2B/2C: PBEE

15

20

25

30

35

Floo

r num

ber [

-]

15

20

25

30

35

0 0.5 1 1.5 2 2.5

0

5

10

F

Drift (%)0 0.5 1 1.5 2 2.5

0

5

10

Drift (%)

μ = 1.6%μ+σ= 2.0%

μ = 1.55%μ+σ= 2.05%

Dual System - Wall Shear vn

35

40

Building 2A - MCE

35

40

Building 2B - MCE

meanmean + std8sqrt(fc)

'1.5 8 cVn f≈

15

20

25

30

35

Floo

r num

ber [

-]

15

20

25

30

35

Floo

r num

ber [

-]

individual record

0 0.2 0.4 0.6 0.8 1

0

5

10

Stress (ksi)0 0.2 0.4 0.6 0.8 1

0

5

10

Stress (ksi)



Dual System - Wall Shear vn

40

MCE40

OVE

2A: Code

10

20

30

10

20

30

'1 5 8Vn f≈

2A: Code

2B/2C: PBEE

0 0.4 0.8Stress (ksi)

0

10

0 0.4 0.8Stress (ksi)

0

10 1.5 8 cVn f≈

2A/CodeShear FailureOVE (1%/50yr)

Dual System – Wall Shear vn

Building 2A –Failure modes

Δz3

Elevation view

1.5South Long Walls

0.5

1

1.5

Shea

r Stre

ss (V

ult/V

n)

z1 z3(1-3)

( - )=Hw

ε Δ Δ

z2 z4(2-4)

( - )=Hw

ε Δ ΔHw

Lw

Δz4

Δz2Δz1

0 0025

0.5

1

hear

stre

ss ra

tio V

/Vn,

AC

I

Failure Envelope1st floor2nd floor3rd floor4th floor5th floor6th floor

(OVE#10)Calculations

0 0.004 0.008 0.012 0.016

Shear Strain (in/in)

0 (1-3) (2-4)-curvature =

Lwε ε

φ0.0025yield curvature

Lwφ ≈y

curvature ductility =y

φφ

0 1 2 3 4 5 6 7 8 9 100

Curvature Ductility

Sh



Dual System – Shear Failure

Building 2A

South Long Walls South Long Walls

0.5

1

1.5g

ear s

tress

ratio

V/V

n,A

CI


0.5

1

1.5

ear s

tress

ratio

V/V

n,A

CI


(OVE#15) (OVE#4)

0 1 2 3 4 5 6 7 8 9 100

Curvature Ductility

She

0 1 2 3 4 5 6 7 8 9 100

Curvature DuctilityS

he

Dual System – Shear Failure

Building 2B

South Long Walls South Long Walls

0.5

1

1.5g

ar s

tress

ratio

V/V

n,A

CI


0.5

1

1.5South Long Walls

ar s

tress

ratio

V/V

n,A

CI


(OVE#15) (OVE#4)

0 1 2 3 4 5 6 7 8 9 100

Curvature Ductility

She

a

0 1 2 3 4 5 6 7 8 9 100

Curvature Ductility

She

a



Dual System – Wall Strains εc

Core Wall Strains – Building II

35

40

Building 2A - MCE

35

40


20

25

30

35

Floo

r num

ber

20

25

30

35

Floo

r num

ber

εc = 0.0008/0.0011εc = 0.0012/0.0016

x2

39

-2.5 -2 -1.5 -1 -0.5 0x 10-3

5

10

15

South west corner [in./in.]-2 -1.5 -1 -0.5 0

x 10-3

5

10

15

South west corner [in./in.]

εc = 0.0012/0.0015εc = 0.0018/0.0023

40

45Building 2A - MCE

40

45Building 2B - MCE

Dual System – Wall Strains εt

Yield

2A: Code 2B/2C: PBEE

Yield

20

25

30

35

Floo

r num

ber [

-]

20

25

30

35

Floo

r num

ber [

-]

40

0 0.005 0.01 0.015 0.020

5

10

15

South west corner [in./in.]0 0.005 0.01 0.015 0.02

0

5

10

15

South west corner [in./in.]



Dual System – CB Rotations θcb

Coupling Beam Rotations – Building II40

Building 2A - MCE

meanmean + stdindividual record

40


20

25

30

35

Floo

r num

ber [

-]

20

25

30

35

Floo

r num

ber [

-]

θcb = 0.007/0.013θcb = 0.03/0.042

0 0.02 0.04 0.06 0.08

5

10

15

South wall [rad]

F

0 0.02 0.04 0.06 0.08

5

10

15

South wall [rad]

F

Dual System – Fragility Curves Damage State Definition of damage Repair procedures

Yield -Substantial change in stiffness of load-deformation plot none

DS1-Minor damage -Residual cracks greater than 1/16”Epoxy injection of cracks(200”-240” in length)

DS2-Major damage (I) -Residual cracks greater than 1/8”-Minor spalling of concrete

-Epoxy injection of cracks in beam(600”-720”) and slab (300”)-Replacement of spalled concrete

-Chip away damaged concreteA h h i l l

DS3-Major damage (II)-Significant strength degradation

(<0.8Vn)-Buckling/fracture of reinforcement-Crushing of concrete

-Attach mechanical couplers to remaining bars

-Replace damaged/fractured reinforcement

-Replace damaged concrete

Consistent with ATC-5842



Coupling Beams – Fragility Curves

0 8

1oc

curr

ing

0.4

0.6

0.8

y of

dam

age

stat

e o

Yield

0 2 4 6 8 10Beam Chord Rotation [%]

0

0.2

Prob

abili

ty DS1-Minor repairDS2-Major repair 1DS3-Major repair 2

43

RC Core Wall and RC Dual System

COMPARE RESULTS

44



Core Wall (I) vs Dual System (II)Story (mean) DriftEdit as you wish

40

OVE

40

MCE

40

DBE

40

SLE43

40

SLE25

1A CCore…

20

25

30

35

40

20

25

30

35

40

20

25

30

35

40

20

25

30

35

40

20

25

30

35

40

oor n

umbe

r

1A1B1C2A2B

CoreDual

Dual

45

0 2 4

0

5

10

15

Mean Drift (%)0 2 4

0

5

10

15

Mean Drift (%)0 2

0

5

10

15

Mean Drift (%)0 2

0

5

10

15

Mean Drift (%)0 2

0

5

10

15

Mean Drift (%)

Flo

Core Wall (1) vs Dual System (2)Coupling beam rotation demands

40

MCE

40

DBE

40

SLE43

40

SLE25

40

OVE

1A1B CoreCore

20

25

30

35

20

25

30

35

20

25

30

35

20

25

30

35

Floo

r num

ber

20

25

30

35

1B1C2A2B

DualDual

θcb = 0.028

460 0.03 0.06

0

5

10

15

Mean (rad)0 0.03 0.06

0

5

10

15

Mean (rad)0 0.03 0.06

0

5

10

15

Mean (rad)0 0.03 0.06

0

5

10

15

Mean (rad)

F

0 0.03 0.06

0

5

10

15

Mean (rad)

θcb 0.028θcb = 0.030



Core Wall (1) vs Dual System (2)Core Wall Shear Stress Demands

35

40

OVE

35

40

MCE

35

40

DBE

35

40

SLE43

40

SLE25

1A1B1C2A

CoreDual

CoreDual

15

20

25

30

35

15

20

25

30

35

15

20

25

30

35

15

20

25

30

35

15

20

25

30

35

Floo

r num

ber

2A2B

47

0 1 2x 104

0

5

10

0 1 2x 104

0

5

10

0 1 2x 104

0

5

10

0 1 2x 104

0

5

10

0 1 2x 104

0

5

10

Shear Force (k)

RC Dual System

SMF RESULTS

48



40

Building 2A2A Mean±StDev

Dual System – SMF Beams θp

10

20

30

Floo

r Lev

el

Building 2B2B Mean±StDevAcceptance Limit

ASCE 41-06

49

-0.06 -0.04 -0.02 0 0.02 0.04 0.06Rotation (rad)

0

Dual System – SMF Columns

40 NE

Building 2A40 NE

Building 2B

At OVE level (similar at MCE)2A: Code 2B/2C: PBEE

10

20

30

Floo

r Lev

el

NWSESWSouthNorthWestEast

10

20

30

Floo

r Lev

el

NWSESWSouthNorthWestEast

~Pbal ~Pbal

50

0 0.2 0.4 0.6 0.8 1P/Agf'c

0

10

0 0.2 0.4 0.6 0.8 1P/Agf'c

0

10




At OVE level40 Building 2A-interior

Building 2A-exteriorP

20

30

Floo

r Lev

el

Building 2B-interiorBuilding 2B-exterior

~Pbal

51

0 0.2 0.4 0.6 0.8 1P/Agf'

c

0

10

P/Agf’c


Building 2A Code (OVE)

SW column (Ground floor) 14000SW column (15th floor)SW Column (ground Floor) SW Column (15th Floor)

4000

6000

8000

10000

12000

14000

xial

For

ce (k

ips)

P-MOVE#1OVE#11OVE#13

SW column (Ground floor)

4000

6000

8000

10000

12000

14000

Axi

al F

orce

(kip

s)

P-MOVE#1OVE#11OVE#13

52

0 1000 2000 3000 4000 5000 6000

Moment (k-ft)-4000

-2000

0

2000Ax

0 1000 2000 3000 4000 5000 6000

Moment (k-ft)-4000

-2000

0

2000A



Dual System – Columns Column Plastic Rotations θp

2A Code 2B/2C: PBEE

53

ASCE 41-06CP-values

Summary – Systematic Study

RC Core Wall and RC Dual System1A (code), 1B (PBEE), and 1C (PBEE+)2A ( d ) 2B/2C (PBEE )2A (code), 2B/2C (PBEE+)

PERFORM 3D nonlinear modelsConsistent modeling approachesExpected values, best-available information

Subjected to 5 Hazard levels, 15 GMSLE25, SLE43, DBE, MCE, OVE

Engineering Demand ParametersDrift, normal strain, shear stress, rotations

Information for loss studies54



Challenges

Shear wall modeling – Influence of shearModerate shear stress – Influence on maximum concrete compressive strainmaximum concrete compressive strainHigh shear stress – Influence on deformation capacity [shear failure]; lack of test data

Fragility relationsWalls: strain-based relations

Yielding, spalling, buckling, strength lossg, p g, g, g

Coupling beams: Rotation-based relationsLimited data [10 tests] from aspect ratios and reinforcement commonly used in modern tall buildings

55

Analysis Results Overall

Code & PBEE – Good expected performanceRelatively low design wall shear stress: '5 cf

Code > PBEE > PBEE+Lower drift, wall shear stress, core wall compressive/tensile strainsHigher coupling beam plastic rotation demands (stronger wall)

PBEE+ [Core wall]

cf

Wall strain: εc=0.0012(x2); εt=0.004Coupling beam rotations: θcb = 0.028/0.043

CodeWall tensile strains: more yielding over wall heightDual System SMF: High column axial loads

56

the tbi case studies: rc core wall and rc dual...

Documents