design of concrete shearwall

8/13/2019 Design of Concrete ShearWall

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Wall Terminology

(very confusing)

Wall Terminology

(very confusing)

In English: In English:Shear walls

Structural walls

Curtain walls (a glass facade in many instances)

Core walls

In Spanish:

Shear walls

Structural walls

Curtain walls (a glass facade in many instances)

Core walls

In Spanish:

Muros de cortante

Muros cortina

Pantallas

Paredes estructurales

Tabiques estructurales

Muros de cortante

Muros cortina

Pantallas

Paredes estructurales

Tabiques estructurales

Wall based structural systemsWall based structural systems

Bearing wallsBearing walls


Box systemBox system


Dual systemDual system


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Core systemsCore systems


Some core typesSome core types


Tube systemsTube systems

Shear-lag transferShear-lag transfer

Actual

stressesActual

Stresses without shear-lag

Lateral load

direction

stresses

Only lateral load

Stresses shown


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Use of structural systems for wind as the

dominant lateral load

Use of structural systems for wind as the

dominant lateral loadNo. stories

75

20

35

50

55

65

FRAME SHEAR WALLS DUAL EXTERNAL

TUBE

TUBE IN

TUBE

MODULAR

TUBE

Coupled wallsCoupled walls

Behavior of coupled wallsBehavior of coupled walls

(a) (b) (c)

Tunnel forms systemTunnel forms system

There is ample experimental evidence that the slab-walls joint reinforced

with welded wire reinforcement fails when subjected to cyclic moment

Demands In the nonlinear range. This means that this system requires

Walls in both direction in plan.

There is ample experimental evidence that the slab-walls joint reinforced

with welded wire reinforcement fails when subjected to cyclic moment

Demands In the nonlinear range. This means that this system requires

Walls in both direction in plan.


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General behavior of wall systemsGeneral behavior of wall systems

Building configuration in plan

Building configuration in height

Type of foundation

Building configuration in plan

Building configuration in height

Type of foundation

floor area

Wall section shape

floor area

Wall section shape

bhf

w

wf

bs

bh16

4

b

min.of

Effective flange

bw s

bhf

+ ++

w

wf

w

b2s

bh6

b12

b

min.of

bws

bw

hf

b

2

bh wf

f

w

b

b4b min.of

bf

Moment frame vs. wall system Fixed base vs. flexible foundationFixed base vs. flexible foundation

3 m

2 m

3 m

3 m

3 m

3 m

Wall

3 m

9 m9 m10 m

RockingStiffness


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Definition of stiffnessDefinition of stiffness1 m

P

1 m

P1 2

Infinitelly

rigid wall

Flexible

fixed-base

wall

Rocking

Stiffness

Wall

Stiffness

WALL BASE SHEAR1.0

0.7

0.8

.

Vwall/Vtotal

0.5

.

0 1 10 100 1 000 10 000 100 000

ROCKING STIFFNESS / WALL STIFFNESS

LATERAL DEFLECTION - TOP OF BUILDING

1.2%

t

0.4%

0.6%

0.8%

.

eflection/T

otalHeig

0.0%

0.2%

0 1 10 100 1 000 10 000 100 000

ROCKING STIFFNESS / WALL STIFFNESS

TopD

LATERAL DEFLECTION6

WALLROCKING

STIFFNESSRATIO

FIXED

2

3

4

STORY

FREE

1

10

100

1000

2000

5000

10000

50000

100000

1000000

FREE

0

1

0.00 0.05 0.10 0.15 0.20

Lateral Deflection (m)

FIXED


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STORY DRIFT6

WALL

ROCKING

STIFFNESS

RATIO

3

4

5

STORY

1

10

100

1000

2000

5000

10000

50000

100000

1000000

FREEFIXED

1

0.00% 0.05% 0.10% 0.15% 0.20% 0.25%

STORY DRIFT (%h)

FIXED

Structural system combinationStructural system combination

-

height of the building

Wall-frame combination when one system

is suspended in height

Frame in one direction and wall in other

-

height of the building

Wall-frame combination when one system

is suspended in height

Frame in one direction and wall in other

Combination of structural materials

Combination of structural materials

Reinforced concreteReinforced concreteReinforced concreteReinforced concrete

Reinforced masonryReinforced masonry

Structural steelStructural steel

Reinforced masonryReinforced masonry

Structural steelStructural steel

Structural materialsStructural materials

WoodWoodWoodWood

Bearing wall systemBearing wall system

Gravity loads Lateral forces

= +


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Frame systemFrame system(a)Non-moment resisting

frame for gravity loads

(a)

Non-moment resisting

frame for gravity loads= +

Lateral forces carried

by walls or bracing

(b)

Moment resisting frame

for gravity loads and

lateral forces

Lateral forces carried

by walls or bracing

(b)

Moment resisting frame

for gravity loads and

lateral forces


Walls resist tributarygravity loads and help

resist lateral forces

Not enough walls to

meet Dual requirements

Walls resist tributarygravity loads and help

resist lateral forces

Not enough walls to

meet Dual requirements

+=

Moment frame systemMoment frame systemMoment resisting frame supports gravity loads andMoment resisting frame supports gravity loads and

CARGASVERTICALES

FUERZASHORIZONTALES


+

Dual systemDual systemCombination of moment resisting frame plus walls

such that:

(a) Frame supports majority of gravity loads.

Combination of moment resisting frame plus walls

such that:

(a) Frame supports majority of gravity loads.

(b) Both frame and walls resist lateral loads.

(c) Frame must resist at least 25% of base shear.

(d) Wall must resist at least 75% of base shear.

(b) Both frame and walls resist lateral loads.

(c) Frame must resist at least 25% of base shear.

(d) Wall must resist at least 75% of base shear.

Gravity loads

Lateral forces

=+

Dual systemDual system

Lateralforces

Floor

diaphragmStructural wall

Lateral force resistance:

75 % walls

25 % frame

Lateral force resistance:

75 % walls

25 % frame


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Inertial forces are transmitted to the vertical

lateral force resisting element through thediaphragm

Inertial forces are transmitted to the vertical

lateral force resisting element through thediaphragm

Column shear forceColumn shear force

FxFx==

from upper storiesfrom upper stories

Accumulate column

shear force (upperstories plus this story

Accumulate column

shear force (upperstories plus this story

The diaphragm transmit s

floor inertial forces tovertical elements and

distributes shear from

upper stories

The diaphragm transmit s

floor inertial forces tovertical elements and

distributes shear from

upper stories

When vertical elements stiffness contribution to lateral

stiffness is not uniformly distributed in plan torsion ofthe whole structure arises

When vertical elements stiffness contribution to lateral

stiffness is not uniformly distributed in plan torsion ofthe whole structure arises

Story lateral forces are

distributed by diaphragm to

Story lateral forces are

distributed by diaphragm to

FxFx==

a era oa res s ng

elements in proportion to their

stiffness

a era oa res s ng

elements in proportion to their

stiffness

Accumulate columnshear force (upper stories

plus this story

Accumulate columnshear force (upper stories

plus this story

If the diaphragm is considered rigid in its own plane

inertial floor lateral forces can be considered to act

at the center of mass of the diaphragm.

The structure rotates with respect to the stiffness

centroid

If the diaphragm is considered rigid in its own plane

inertial floor lateral forces can be considered to act

at the center of mass of the diaphragm.

The structure rotates with respect to the stiffness

centroid

FxFx

Stiffness

centroid

Stiffness

centroid

Mass

centroid

Mass

centroid

Torsion of

the structure

Torsion of

the structure

as a wholeas a whole


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The soft story problem Two casesThe soft story problem Two cases

Abrupt change

in stiffness

Olive View HospitalOlive View Hospital


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Imperial County Services BuildingImperial County Services Building


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Planta Primer Piso

Fachada Oeste Fachada Este

Street level planWest facade East facade

Planta Piso Tpico

Fachada Norte

Typical floor planNorth facade


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Wall Area Ratio (p) DefinitionWall Area Ratio (p) Definition

HH

hh

tt

DD

x

sectionareaof walls acting in x directionp

floor area=

The Chilean formulaThe Chilean formula

Defining parametersDefining parameters

w ih w g = Where:

= Story drift as % ofhpAa = PGA(Peak Ground Acceleration) as a fraction ofg

hw = Wall height from base to top, m

w = Horizontal wall length, m

Where:

= Story drift as % ofhpAa = PGA(Peak Ground Acceleration) as a fraction ofg

hw = Wall height from base to top, m

w = Horizontal wall length, m

a

w pE p h =

wi = Average building dead load per unit area, kN/m2

g = Acceleration of gravity, m/s2

E = Modulus of elasticity of wall concrete, kN/m2

p = Wall area ratio

hp = Story height (typical), m

wi = Average building dead load per unit area, kN/m2

g = Acceleration of gravity, m/s2

E = Modulus of elasticity of wall concrete, kN/m2

p = Wall area ratio

hp = Story height (typical), m

Theoretical relationship between p and story drift(Moderate seismic risk)

Theoretical relationship between p and story drift(Moderate seismic risk)

1.8

2.0

0.6

0.8

1.0

1.2

1.4

1.6

deriva(%h)

H/D = 7H/D = 6H/D = 5H/D = 4

H/D = 3H/D = 2H/D = 1

Story

Drift

(%hp)

0.0

0.2

0.4

0 1 2 3 4 5 6 7

= rea total de muros / rea del piso (%)pp = total wall area in dir. x or y / story area (%)


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W ll d i


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Some cases of wallSome cases of wall

structures designed

using the Bogota

structures designed

using the Bogota

Bogota Seismic Microzonation spectraBogota Seismic Microzonation spectra

0.7

0.8

Zona 2 - Piedemonte

Zona 3 - Lacustre A

aS

0.3

0.4

0.5

.

(g)

Zona 1 - Cerros

Zona 4 - Lacustre B

Zona 5 - Terrazas y Conos

0.0

0.1

0.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

T (s)

W ll d i


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The casesThe cases 26 buildings with a total area of 243 000 m2 26 buildings with a total area of 243 000 m2

19 apartment buildings

5 office buildings

2 educational buildings

Height from 7 to 20 stories

12 stories in average

19 apartment buildings

5 office buildings

2 educational buildings

Height from 7 to 20 stories

12 stories in average

Building area from 1 200 to 50 000 m2

9 400 m2in average

Building area from 1 200 to 50 000 m2

9 400 m2in average

Building locationBuilding location 6 buildings in 6 buildings in

Zona 4N

Zone 1

4 buildings inthe transition

from Zone 1

to 2

2 buildings inZone 2

Zone 1

4 buildings inthe transition

from Zone 1

to 2

2 buildings inZone 2

Zona 1

Zona 2

Zona 3

Zona 5B

20 4 6 8 10 kmEscala

Zona 1 - Cerros

Zona 2 - Piedemonte

Zona 4 - Lacustre B

Zona 5A - Terrazas y Conos

-

Zona 3 - Lacustre A

12 buildingsin Zone 3

2 buildings in

Zone 4

12 buildingsin Zone 3

2 buildings in

Zone 4

Zona 5A - rr

Potencialmente Licuables

Lets look at the following parameterLets look at the following parameter

Fundamental building vibration period computed

Fundamental building vibration period computed

Relationship between building period and number

of stories

Roof lateral deflection as a % of building height Structural wall area as a function of floor area

Base shear strength from collapse mechanisms

Relationship between building period and number

of stories

Roof lateral deflection as a % of building height Structural wall area as a function of floor area

Base shear strength from collapse mechanisms

Capacity/demand ratio for horizontal seismic

forces

Capacity/demand ratio for horizontal seismic

forces

Vibration period T (s)Vibration period T (s)

1.25

1.50

1.25

1.50

0.50

0.75

1.00

PerodoDirecciny(s)

Zona 1

Trans 1-2

Zona 2

Zona 3

Zona 40.50

0.75

1.00

PerodoDirecciny(s)

Zona 1

Trans 1-2

Zona 2

Zona 3

Zona 4

0.00

0.25

0.00 0.25 0.50 0.75 1.00 1.25 1.50

Perodo Direccin x (s)

0.00

0.25

0.00 0.25 0.50 0.75 1.00 1.25 1.50

Perodo Direccin x (s)


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7

8

7

8 Capacity/DemandCapacity/Demand

3

4

5

6

Vny/(SayW) Zona 1

Trans 1-2

Zona 2

Zona 3

Zona 43

4

5

6

Vny/(SayW) Zona 1

Trans 1-2

Zona 2

Zona 3

Zona 4

Mean = 2.2Mean = 2.2

Mean = 2.0Mean = 2.0

0

1

0 1 2 3 4 5 6 7 8

Vnx/(SaxW)

0

1

0 1 2 3 4 5 6 7 8

Vnx/(SaxW)

Effect of the wall sectionEffect of the wall sectiont = 0.01t = 0.01 ==CompressionCompression

TensionTensionent

ent . .

CompressionCompression

TensionTension


TensionTension

MoMo


TensionTensionCompressionCompression

TensionTension


TensionTension

CurvatureCurvature

Typical wall failure modesTypical wall failure modes

Flexure Flexure

Steel fails in tension

Concrete spalls in the compression zone

Lateral buckling in the compression zone

Shear

Diagonal tension

Steel fails in tension

Concrete spalls in the compression zone

Lateral buckling in the compression zone

Shear

Diagonal tension

Sliding

Web buckling

General buckling

Sliding

Web buckling

General buckling

Experimental behavior of low

walls under horizontal load

Experimental behavior of low

walls under horizontal load

Based on 143 low wall tests

All loaded statically

All failed in shear Distributed horizontal and vertical

reinforcement (no boundary elements)

Based on 143 low wall tests

All loaded statically

All failed in shear Distributed horizontal and vertical

reinforcement (no boundary elements)

Vertical steel ratio between 0.0007 and 0.0290

Horizontal steel ratio between 0.007 and 0.0190

Vertical steel ratio between 0.0007 and 0.0290

Horizontal steel ratio between 0.007 and 0.0190


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Experimental behavior of slender walls

under horizontal load

Experimental behavior of slender walls

under horizontal load Boundary elements improve the energy

dissipation capacity in the nonlinear range of Boundary elements improve the energy

dissipation capacity in the nonlinear range of

walls failing in flexure.

Boundary elements do not improve behavior for

walls failing in shear.

walls failing in flexure.

Boundary elements do not improve behavior for

walls failing in shear.

horizontal steel ratio is lower.

The strength for horizontal loads decreases as

more cycles in the nonlinear range are performed.

horizontal steel ratio is lower.

The strength for horizontal loads decreases as

more cycles in the nonlinear range are performed.

Structural analysis of wall systemsStructural analysis of wall systems

Diaphragm effect Diaphragm effect

ox e ec

Effective flange of T or C shaped sections

Rigid zone effect for coupling beams

Shear deformations

Warping of section due to general torsion

-

ox e ec

Effective flange of T or C shaped sections

Rigid zone effect for coupling beams

Shear deformations

Warping of section due to general torsion

-

Global slenderness effects

Effect of the nonlinear response

Global slenderness effects

Effect of the nonlinear response

Finite elementsFinite elementsy

Py

a a

b4 3

v3v4u 3

u4

x

P

x

b1 2

v1 v2

u1u 2

(a)(b)

1 2M1 M1 M2 M2

(c) (d)

Finite elementsFinite elements

y

a a vv

u34

4 3

y

a a

b

vv

u

u

34

3

4

(a)

x

4

1 2

3 b

b

v v

u

u

u

1

2

1

2

3

4

x

1 2 b

v v

u

u1 2

1

2

(c) (b)

Wall design


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ACI 318-08ACI 318-08

Wall requirements in ACI 318-08Wall requirements in ACI 318-08

Chapter 10 Flexure and axial loadChapter 10 Flexure and axial load

Chapter 11 - Shear

Chapter 14 - Walls

Chapter 11 - Shear

Chapter 14 - Walls

Chapter 21 Seismic requirementsChapter 21 Seismic requirements

General requirementsGeneral requirements

Cover Cover20 mm

Maximum bar spacing Maximum bar spacing h

ss

ss

s 3hs 450 mm

s

s

Minimum steel ratioMinimum steel ratio

14.3.2 Minimum steel ratio of vertical reinforcement computed over gross section is:

14.3.2 Minimum steel ratio of vertical reinforcement computed over gross section is:

0.0012 or deformed bars not larger than N 5 (5/8) 16M (16mm), withfy not less than 420 MPa.

0.0015 for other deformed bars.

0.0012 for welded wire reinforcement with diameter not larger

than16 mm.

14.3.3 - Minimum ratio of horizontal reinforcement area to

gross concrete area,t:

0.0012 or deformed bars not larger than N 5 (5/8) 16M (16mm), withfy not less than 420 MPa.


0.0012 for welded wire reinforcement with diameter not larger

than16 mm.

14.3.3 - Minimum ratio of horizontal reinforcement area to

gross concrete area,t:

0.0020 for deformed bars not larger than N 5 (5/8) 16M (16mm), withfy not less than 420 MPa.


0.0020 for welded wire reinforcement with diameter not largerthan16 mm.

0.0020 for deformed bars not larger than N 5 (5/8) 16M (16mm), withfy not less than 420 MPa.


0.0020 for welded wire reinforcement with diameter not largerthan16 mm.


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21.9 - Special structural walls and

coupling beams


coupling beams

eas wo cur a ns o re n orcemen

must be used in a wall if Vu exceeds

(MPa) =

eas wo cur a ns o re n orcemen

must be used in a wall if Vu exceeds

(MPa) =cv c0.17 A f cv c0.53 A f (kgf/cm2)(kgf/cm2)


coupling beams


coupling beams

performed, effective flange widths of

flanged sections ( I, L, Cor T) may be

supposed to extend from the face of the

web a distance equal to the smaller of:

performed, effective flange widths of

flanged sections ( I, L, Cor T) may be

supposed to extend from the face of the

web a distance equal to the smaller of:

(a) 1/2 the distance to an adjacent wall web,

and

(b) 25 percent of the total wall height.

(a) 1/2 the distance to an adjacent wall web,

and

(b) 25 percent of the total wall height.


coupling beams


coupling beams

V of structural walls shall not exceedV of structural walls shall not exceedn

(21-7)

n

(21-7)n cv c c t yV A f f + c.

0.17

1.5 2.0

w

w

h

Recommendation for pre-dimensioningRecommendation for pre-dimensioning

Minimum amount of walls

Shear strength

Minimum amount of walls

Shear strength

SlendernessSlenderness

iuw wc

Vb (MPa)

0.25 f

h h

bw

w

w

4

Vu

wthis slenderness ratio willlead to a maximum story

drift 1% hpthis slenderness ratio will

lead to a maximum story

drift 1% hp

Wall design

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Recommendation for pre-dimensioningRecommendation for pre-dimensioning

boundary elements boundary elements

300 mm 300 mm300 mm300 mm

bw bw

w w

n

w n

w

mm

b h 20

25

Coupling beamsCoupling beams

Wall boundary elementsWall boundary elements

Boundary elements must be placed at edges and

around openings when inelastic response is Boundary elements must be placed at edges and

around openings when inelastic response is

expec e . - g ves wo a erna ves o

define if boundary elements are needed:

1) Section 21.9.6.2 presents a displacement-based

procedure. Boundary elements are needed ornot depending on the compressive strain at the

edge of wall caused by the seismic lateral

expec e . - g ves wo a erna ves o

define if boundary elements are needed:

1) Section 21.9.6.2 presents a displacement-based

procedure. Boundary elements are needed ornot depending on the compressive strain at the

edge of wall caused by the seismic lateral

e ec on, or

2) Section 21.9.6.3 requires boundary elements

when the compressive stress at the edge of wall

caused by the seismic forces exceeds a

threshold value.

e ec on, or

2) Section 21.9.6.3 requires boundary elements

when the compressive stress at the edge of wall

caused by the seismic forces exceeds a

threshold value.


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Nonlinear wall deflectionNonlinear wall deflection

wwCurvature

at yieldDeflection

at yieldNonlineardeflection

Nonlinearcurvatureyy uy)uy)

hwhw

) )pp pp

The total deflection is:

We can solve for the ultimate curvature

demand and obtain:

The total deflection is:

We can solve for the ultimate curvature

demand and obtain:

yy u y)u y)

Moment-curvature diagram for wall sectionMoment-curvature diagram for wall section

MM

MnMn

Ultimate curvaturedemandUltimate curvaturedemand

McrMcr

00 crcr yy uunn

What happens at section?What happens at section?

cucuAt level ofdisplacementAt level ofdisplacement

ccs > ys > yAt level ofAt level of

At level of

nominal

strength

At level of

nominal

strength

demanddemandStrainStrain

c= 0.003c= 0.003s = s = c< 0.003c< 0.003

uu

nn

wwhh

yield in

tension of

extreme

reinforcement

yield in

tension of

extreme

reinforcement

cycy

Equation (21-8) deductionEquation (21-8) deduction

The rotation at the plastic hinge when the displacement

demand (u) takes place is:The rotation at the plastic hinge when the displacementdemand (u) takes place is:

With a plastic hinge length equal to half the wall horizontal

length:

With a plastic hinge length equal to half the wall horizontal

length:

Then the curvature at the wall base when the displacement

demand occurs is:

Then the curvature at the wall base when the displacement

demand occurs is:


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The EndThe End

design of concrete shearwall

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