Design of Concrete ShearWall

Wall design Luis E. Garcia

Wall Terminology (very confusing)

Wall based structural systems Bearing walls



In English: 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

Wall based structural systems Box system

Wall based structural systems Dual system

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Wall design Luis E. Garcia

Wall Terminology (very confusing)

Wall based structural systems Bearing walls



In English: 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

Wall based structural systems Box system

Wall based structural systems Dual system

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Wall design Luis E. Garcia

Wall based structural systems Core systems

Wall based structural systems Some core types

Shear-lag transfer 

Wall based structural systems Tube systems

 Actual  stresses

Stresses without shear-lag  Actual  stresses

Lateral load  direction

Only lateral load Stresses shown

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Wall design Luis E. Garcia

Use of structural systems for wind as the dominant lateral load

Coupled walls

No. stories 75  65  55  50 

35  20 

FRAME

SHEAR WALLS

DUAL

EXTERNAL TUBE 

TUBE IN  TUBE 

MODULAR  TUBE 

Behavior of coupled walls

(a)

(b)

(c)

Tunnel 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.

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Wall design Luis E. Garcia

Effective flange

General behavior of wall systems

 4

b

min.of  16 h f 

b

hf 

s

bw

bw

Building configuration in plan



Building configuration in height 



bw

Type of foundation



s

b

hf 



b

12

s 2

s

floor area Wall section shape



bw 2

bw bw

bw bf  b

h f 

bw

min.of  6 h f 

b

hf 

min.of 

4 bw b f 

bw

Moment frame vs. wall system

Fixed base vs. flexible foundation 2m 3m 3m Wall

3m 3m 3m 3m

Rocking Stiffness 10 m

9m

9m

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Wall design Luis E. Garcia

WALL BASE SHEAR 

Definition of stiffness 1m

1.0

1m P1

P2

.    l   a0.8    t   o    t

Infinitelly rigid wall

   V    /

   l 0.7    l   a   w

   V

.

Flexible fixed-base wall

0.5

0

10

100

1 000

10 000

100 000

ROCKING STIFFNESS / WALL STIFFNESS

Wall Stiffness

Rocking Stiffness

1

LATERAL DEFLECTION - TOP OF BUILDING 

LATERAL DEFLECTION  WALL ROCKING STIFFNESS RATIO

6

1.2%

FIXED

   t   g .    i   e    H    l 0.8%   a    t   o    T    / 0.6%   n   o    i    t   c   e 0.4%    l    f   e    D   p 0.2%   o    T

FREE

FREE

1

4

10

   Y    R    O 3    T    S

100 1000 2000 5000 10000 50000

2

100000 1000000 FIXED

1 0

0.0% 0

1

10

100

1 000

10 000

ROCKING STIFFNESS / WALL STIFFNESS

100 000

0.00

0.05

0.10

0.15

0.20

Lateral Deflection (m)

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Wall design Luis E. Garcia

STORY DRIFT 

WALL ROCKING STIFFNESS RATIO

6 5

1

Structural system combination 

10 100

4    Y    R    O    T 3    S

1000

FIXED

2000

FREE



5000 10000 50000 100000

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

1000000 FIXED

1

0.00%

0.05%

0.10% 0.15% STORY DRIFT (%h)

Reinforced concrete

0.20%

0.25%

Bearing wall system

Reinforced masonry Lateral forces

Gravity loads

Structural steel

Wood

=

+

Structural materials

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Wall design Luis E. Garcia

Frame system (a) Non-moment resisting frame for gravity loads

Moment frame system Moment resisting frame supports gravity loads and

=

Lateral forces carried by walls or bracing  

(b) Moment resisting frame for gravity loads and lateral forces

+

Gravity loads

Lateral forces CARGAS 

Walls resist tributary gravity loads and help resist lateral forces 

FUERZAS  Lateral forces

Gravity loads VERTICALES 



HORIZONTALES 

+ +

=

Not enough walls to meet Dual requirements 

Dual system

Dual system

Combination of moment resisting frame plus walls such that:

Lateral forces

(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.

Floor diaphragm Structural wall 

(d) Wall must resist at least 75% of base shear. Lateral forces Gravity loads

=

+

Lateral force resistance: 75 % walls 25 % frame

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Wall design Luis E. Garcia

Inertial forces are transmitted to the vertical lateral force resisting element through the diaphragm

When vertical elements stiffness contribution to lateral stiffness is not uniformly distributed in plan torsion of the whole structure arises Story lateral forces are distributed by diaphragm to a era oa res s ng elements in proportion to their  stiffness

Column shear force from upper stories

=  Accumulate column shear force (upper stories plus this story 

Fx The diaphragm transmit transmit s floor inertial forces to vertical elements and distributes shear from upper stories

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  Stiffness centroid 

=

Fx

 Accumulate column shear force (upper stories  plus this story 

Torsion of the structure as a whole

Fx Mass centroid 

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Wall design Luis E. Garcia

The soft story problem – Two cases

Olive View Hospital

Abrupt change in stiffness

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Wall design Luis E. Garcia

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Wall design Luis E. Garcia

Imperial County Services Building

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Wall design Luis E. Garcia

Fachada Oeste

Planta Primer Piso

Street level plan

West facade

Fachada Este East facade

Fachada Norte

Planta Piso Típico

Typical floor plan

North facade

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Wall design Luis E. Garcia

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Wall design Luis E. Garcia

Wall Area Ratio (p) Definition

The Chilean formula

H h t

D

px

section area of walls acting in x direction floor area

Defining parameters hw a w

wi g E p hp

Where: =

Story drift as % of   hp

Aa

=

PGA(Peak Ground Acceleration) as a fraction of  g

hw

=

=

Wall height from base to top, m Horizontal wall length, 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

w

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

Story deriva Drift (%h) (%hp)

2.0  1.8  1.6  1.4 1.2  1.0  0.8  0.6  0.4 0.2  0.0  0

H/D = 7 H/D = 6 H/D = 5 H/D = 4 H/D = 3 H/D = 2 H/D = 1

1

2

3

4

5

6

7

 

p = área área del piso (%)(%) p = total walltotal areadeinmuros dir. x /or y / story area

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Wall design Luis E. Garcia

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Wall design Luis E. Garcia

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Wall design Luis E. Garcia

Some cases of wall structures designed using the Bogota

Bogota Seismic Microzonation spectra 0.8  Zona 2 - Piedemonte 0.7  Zona 3 - Lacustre A . Zona 4 - Lacustre B 0.5  Zona 5 - Terrazas y Conos

Sa 0.4 (g) 0.3 Zona 1 - Cerros 0.2 

0.1

0.0  0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0  

T (s)

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Wall design Luis E. Garcia

The cases 

26 buildings with a total area of 243 000 m2  



5 office buildings



2 educational buildings



Height from 7 to 20 stories



12 stories in average

Building area from 1 200 to 50 000 



19 apartment buildings







Building location

m2 

9 400 m2  in average





6 buildings in Zone 1

N 

Zona 4 Zona 1 Zona 2 

4 buildings in the transition from Zone 1 to 2 

Zona 1 - Cerros

Zona 3

2 buildings in Zone 2 

0  2  4 6 8  10 km Escala

Zona 2 - Piedemonte Zona 3 - Lacustre A Zona 4 - Lacustre B Zona 5A - Terrazas y Conos

Zona 5B Zona 5A

12 buildings in Zone 3 2 buildings in Zone 4

-- 

rr Potencialmente Licuables

Vibration period T (s)

Lets look at the following parameter  1.50 





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



Capacity/demand ratio for horizontal seismic forces

1.25 

   )   s    (   y 1.00    n    ó    i   c   c   e   r 0.75     i    D   o    d   o 0.50     í   r   e    P

Zona 1 Trans 1-2 Zona 2 Zona 3 Zona 4

0.25 

0.00  0.00

0.25

0.50

0.75

1.00

1.25

1.50  

Período Dirección x (s)

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Wall design Luis E. Garcia

Effect of the wall section

Capacity/Demand

8 

     t     n     e

7 

6 

    o      M

Mean = 2.0

   ) 5     W   y   a    S4     (    /   y   n    V

Compression

= 0.01 = .

Compression Compression

Zona 1 Trans 1-2 Zona 2 Zona 3 Zona 4

3 

t

Tension

Tension Tension

Mean = 2.2 Compression

Compression Compression

1

Tension

Tension

Tension 0  0

1

2

3

4

5

6

7

8

 

Curvature

Vnx/(SaxW)

Experimental behavior of low walls under horizontal load

Typical wall failure modes 





Flexure 

Steel fails in tension





Concrete spalls in the compression zone





Lateral buckling in the compression zone

Shear  

Diagonal tension



Sliding 



Web buckling 

General buckling 

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 

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Wall design Luis E. Garcia

Experimental behavior of slender walls under horizontal load 



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.

Structural analysis of wall systems 

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



Global slenderness effects



Effect of the nonlinear response

--  horizontal steel ratio is lower. 

The strength for horizontal loads decreases as more cycles in the nonlinear range are performed.

Finite elements y

v4

P u4

Finite elements y

a

v3 u3

a

4

3

x

v4

b x

u1 P

(a)

1

2 

v1

v2

b

v3

a

4

3

u1

1

2 

u3

b x

u2

v1

(b)

v4 1

y a

u4

2

v2

(a) y a

b u2

v3

a

u4

4

3

u1

1

2 

u3

b x

M1

M 1 M2

M2

v1

v2

(c)

(c)

b u2

(b)

(d)

Page23

Wall design Luis E. Garcia

Wall requirements in ACI 318-08

ACI 318-08



Chapter 10 – Flexure and axial load 



Chapter 11 - Shear 



Chapter 14 - Walls



Chapter 21 – Seismic requirements

Minimum steel ratio

General requirements 

Cover 

20 mm



14.3.2 – Minimum steel ratio of vertical reinforceme reinforcement nt computed over gross section is: 

  0.0012 or de for med b ar s n ot l ar ger t han Nº 5 ( 5/ 8”)

16 M ( 16

mm), with f y not less than 420 MPa.



s

Maximum bar spacing 



s s

s

  0.0015 for other deformed bars.



  0.0012 for welded wire reinforcement with diameter not larger  than16 mm.

h

s

s s



3h 450 mm

14.3.3 - Minimum ratio of horizontal reinforcement area to gross concrete area, ρ t: 

  0.0020 for deformed bars not larger than Nº 5 (5/8”) ó 16M (16



  0.0025 for other deformed bars.



  0.0020 for welded wire reinforcement with diameter not larger 

mm), with f y not less than 420 MPa.

than16 mm.

s

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Wall design Luis E. Garcia

21.9 - Special structural walls and coupling beams eas wo cur a ns o re n orcemen must be used in a wall if Vu exceeds 0.17 Acv fc  (MPa) = 0.53 A cv fc 

(kgf/cm2)

21.9 - Special structural walls and coupling beams  performed, effective flange widths of flanged sections ( I , L, C or 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.

21.9 - Special structural walls and coupling beams Vn of structural walls shall not exceed 

Vn

Acv

fc

c

t fy

 

Recommendation for pre-dimensioning Minimum amount of walls Shear strength

w

(21-7)

bw

Viu 0.25 f c

(MPa)

bw

Slenderness

c

hw

.

h

4

w

0.17

hw

1.5

2.0

w

this slenderness ratio will lead to a maximum story drift ≤ 1% hp

w

Vu

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Wall design Luis E. Garcia

Recommendation for pre-dimensioning boundary elements

boundary elements n

bw

300 mm

Coupling beams

300 mm

bw

300 mm

300 mm

w

w

mm bw

hn 20 w

25

Wall boundary elements 

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 or not 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.

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Wall design Luis E. Garcia

Nonlinear wall deflection Curvature at yield 

Deflection at yield 

Nonlinear curvature

Moment-curvature diagram for wall section

Nonlinear deflection

M

w u

y

Ultimate curvature demand 

y

Mn

hw

p

The total deflection is:

y

p u

y

Mcr 0

We can solve for the ultimate curvature demand and obtain:

cr

y

n

u

Equation (21-8) deduction

What happens at section?

The rotation at the plastic hinge when the displacement demand dema nd (  u ) takes place is:

At level of displacement demand

cu u

Strain At level of nominal strength

s

At level of  s yield in tension of extreme reinforcement

y

n

c =

0.003

c <

0.003

With a plastic hinge length equal to half the wall horizontal length:

c cy

h

Then the curvature at the wall base when the displacement demand occurs is:

w

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