Special Reinforced Concrete Structural Wallssite.iugaza.edu.ps/sshihada/files/2012/02/Handout-6...continuous and shall be distributed a cross the shear plane. According to ACI 18.10.4.3,

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143

Special Reinforced Concrete Structural Walls

The requirements of this section apply to special reinforced concrete

structural walls serving as part of the earthquake force-resisting system.

Shear Strength:

Based on ACI 18.10.4.1, nominal shear strength nV of structural walls is not

to exceed

ytcccvn ffAV '

Where c is a coefficient defining the relative contribution of concrete

strength to wall strength, given as follows.

c = 0.80 for 5.1/ ww lh ;

c = 0.53 for 0.2/ ww lh ;

c = 0.53 to 0.80 (linear variation) for ww lh / between 1.5 and 2.0.

cvA = gross area of concrete section bounded by web thickness and length of

section in the direction of shear force considered, cm2.

Shear Reinforcement:

At least two curtains of reinforcement shall be used in a wall if the in-plane

factored shear force assigned to the wall exceeds ccv fA 53.0 or 0.2/ ww lh ,

as specified by ACI 18.10.2.2.

Based on ACI 18.10.2.1, the distributed web reinforcement ratios, l and

t for structural walls shall not be less than 0.0025, except if uV does not

exceed ccv fA 27.0 , l and t shall be permitted to be reduced to the

values required in ACI 11.6. Reinforcement spacing each way in structural

walls shall not exceed 45 cm. reinforcement contributing to uV shall be

continuous and shall be distributed a cross the shear plane.

According to ACI 18.10.4.3, walls are to be reinforced with shear

reinforcement in two orthogonal directions in the plane of the wall.

If 0.2/ ww lh , reinforcement ratio l shall be at least the reinforcement ratio

t .

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144

Design for Flexure and Axial Loads:

Based on ACI 18.10.5.1, structural walls and portions of such walls subject

to combined flexural and axial loads shall be designed in accordance with

ACI 22.4.

Horizontal Wall Segments:

ACI 2.3 defines a horizontal wall segment, shown in the Figure R18.10.4.5,

as a segment of structural wall, bounded vertically by two openings or by an

opening and an edge. A vertical wall segment is a segment of a structural

wall bounded horizontally by two openings, or by an opening and an edge;

wall piers are vertical wall segments. A vertical wall segment is referred to

as a coupling beam when openings are aligned vertically over the building

height.

Normal shear strength of horizontal wall segments shall be assumed not to

exceedccw fA '65.2 , where cwA is the cross-sectional area of a horizontal

wall segment or coupling beam, as specified in ACI 18.10.4.5.

Wall Piers:

ACI 2.3 defines a wall pier as a vertical wall segment within a structural

wall, bounded horizontally by two openings or by an opening and an edge,

with ratio of horizontal length to wall thickness ( ww bl / ) less than or equal to

6.0, and ratio of clear height to horizontal length ( ww lh / ) greater than or

equal to 2.0

ACI 18.10.4.4 states that normal shear strength of all wall segments sharing

a common lateral force, nV , shall not be taken larger than ccv fA 12.2 , where

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145

cvA is the total cross-sectional area of concrete bounded by web thickness

and length of section. The normal shear strength of any one of the individual

wall pier, nV , shall not be taken larger than ccw fA '65.2 , where cwA is the

cross-sectional area of the individual vertical wall segment considered.

In ACI 18.10.4.2, the value of ratio ww lh / used for determination of nV for

segments of a wall shall be the larger of the ratios for the entire wall and the

segment of wall considered.

Boundary Elements:

ACI 2.3 defines a boundary element as a portion along wall and diaphragm

edge, including edges of openings, strengthened by longitudinal and

transverse reinforcement.

Two design approaches for evaluating the need of boundary elements at the

edges of structural walls are provided in ACI 18.10.6.2 and explained below.

A- For walls or wall piers with 0.2/ ww lh that are effectively continuous

from the base of the structure to top of wall and designed to have a single

critical section for flexure and axial loads, ACI 18.10.6.2 requires that

compression zones be reinforced with special boundary elements where:

wu

w

h

lc

/5.1600

and c corresponds to the largest neutral axis depth calculated for the factored

axial force and nominal moment strength consistent with the direction of

design displacement u . The ratio wu h/ in the previous equation shall not be

taken less than 0.005.

Special boundary element reinforcement shall extend vertically above and

below the critical section at least the greater of wl and uu VM 4/ , except when

the critical section occurs at wall base, the boundary element transverse

reinforcement at the wall base shall extend into the support at least dl of the

largest longitudinal reinforcement in the special boundary element. Where

the special boundary element terminates on a footing, mat, or pile cap,

special boundary element transverse reinforcement shall extend at least 30

cm into the footing, mat, or pile cap, unless a greater extension is required

by ACI 18.13.2.3.

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146

The above design approach uses a displacement-based model. In this

method, the wall is displaced an amount equal to 1.5 the expected design

displacement, and boundary elements are required to confine the concrete

when the strain at the extreme compression fiber of the wall exceeds a

critical value.

Boundary Element Requirements (ACI 18.10.6.2)

B- Structural walls not designed to the provisions of ACI 18.10.6.2, shall

have special boundary elements at boundaries and edges around openings of

structural walls where the maximum extreme fiber compressive stress,

corresponding to factored forces including earthquake effect, exceeds cf 2.0 .

The special boundary element shall be permitted to be discontinued where

the calculated compressive stress is less than cf 15.0 , as stated in ACI

18.10.6.3.

Stresses are calculated for the factored forces using a linearly elastic model

and gross section properties, as given here

g

wu

g

u

I

lM

A

Pf

2/

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147

Boundary Element Requirements (ACI 18.10.6.3)

Boundary Element Dimensions:

As required by ACI 18.10.6.4, boundary elements are to extend horizontally

from the extreme compression fiber a distance not less than the larger of

wlc 1.0 and .2/c

Width of the flexural compression zone, b, over the horizontal distance

calculated above, including flange if present, shall be at least 16/uh , where

uh is equivalent to ul . For walls or wall piers with 0.2/ ww lh and with

8/3/ wlc , width of flexural compression zone shall be greater than or equal

to 30 cm.

Boundary Element Transverse Reinforcement:

The boundary element transverse reinforcement shall satisfy the

requirements of ACI 18.7.5.2(a) through (e) and 18.7.5.3, except the value

of xh in 18.7.5.2 shall not exceed the lesser of 35 cm and two-thirds of the

boundary element thickness, and the transverse reinforcement spacing limit

of 18.7.5.3(a) shall be one-third of the least dimension of the boundary

element.

The amount of transverse reinforcement shall be in accordance with Table

18.10.6.4(f).

The above requirements are summarized below:

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148

Transverse reinforcement shall be provided by either single or overlapping

hoops. Crossties of the same bar size and spacing as the hoops shall be

permitted. Each end of the crossties shall engage a peripheral long

reinforcing bar. Consecutive crossties shall be alternated end for end and

along the longitudinal reinforcement. Spacing of crossties or legs of

rectangular hoops, xh within a cross section of the member shall not exceed

35 cm on center.

where:

shA total cross-sectional area of transverse reinforcement, including

crossties, within spacing s and perpendicular to dimension cb , cm2.

gA gross area of concrete section, cm2.

chA cross-sectional area of a member measured to the outside edges of

transverse reinforcement, cm2.

s = spacing of transverse reinforcement measured along the longitudinal

axis of the structural member, center-to-center.

cb = cross-sectional dimension of member core measured to the outside

edges of the transverse reinforcement composing area shA , cm.

xs = maximum center-to-center spacing of longitudinal bars supported by

corners of crossties or hoop legs around the perimeter of the boundary

element.

ytf = specified yield strength of transverse reinforcement.

cf = specified compressive strength of concrete.

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149

Based on ACI 18.7.5.3, spacing of transverse reinforcement shall not exceed

the smallest of (a) through (c):

(a) one-third of the minimum member dimension (as modified by ACI

18.10.6.4(e)),

(b) six times the diameter of the smallest longitudinal bar

(c) s as calculated by:

3

h3510s x

The value of s shall not exceed 15 cm and need not be taken less than 10

cm.

In ACI 18.10.6.5, where special boundary elements are not required by ACI

18.10.6.2 or 18.10.6.3, (a) and (b) shall be satisfied.

(a) If the longitudinal reinforcement ratio at the wall boundary is

greater than yf/28 , boundary transverse reinforcement shall

satisfy 18.7.5.2(a) through (e) over the distance calculated in

accordance with 18.10.6.4(a). The maximum longitudinal spacing

of transverse reinforcement in the boundary shall not exceed the

lesser of 20 cm and bd8 ;

(b) Except when uV in the plane of the wall is less than

ccv fA 265.0 , horizontal reinforcement terminating at the edges

of structural walls without boundary elements shall have a standard

hook engaging the edge reinforcement or the edge reinforcement

shall be enclosed in U-stirrups having the same size and spacing as

and spliced to the horizontal displacement.

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150

Reinforcement Details for Boundary Elements

Anchorage and Splicing of Reinforcement:

In ACI 18.8.5.1, the development length dhl for a bar with a standard 90

degree hook shall not be less than the largest of bd8 , 15 cm, and the length

required by the following equation, which is applicable to bar diameters

ranging from 10 mm to 36 mm.

c

yb

dhf

fdl

'17

The 90-degree hook shall be located within the confined core of a boundary

element.

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151

In ACI 18.8.5.3, for bar diameters 10 mm through 36 mm, the development

length dl , in tension, for a straight bar shall not be less than (a) and (b):

(a) 2.5 times the length required by the above-mentioned equation if

the depth of the concrete cast in one lift beneath the bar does not

exceed 30 cm, and

(b) 3.25 times the length provided by the same equation if the depth of

the concrete cast in one lift beneath the bar exceeds 30 cm.

In ACI 18.8.5.4, straight bars terminated at a joint shall pass through the

confined core of a boundary element. Any portion of dl not within the

confined core shall be increased by a factor of 1.6.

The next figures show boundary element requirements for special shear

walls.

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152

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153

Example (7):

Redesign shear wall 'A' in example (6) as a special shear wall using ACI

318-14 for reinforced concrete design.

Use 22 /4200 and /300 cmkgfcmkgf yc .

Solution:

Design for shear: -1

At least two curtains of reinforcement shall be used in a wall if the in-plane

factored shear force exceeds ccv 'fA53.0 or 0.2/ ww lh .

tonsfAV ccvn 08.551000/3003002053.053.0

21.2075.0

16.15

uV> 55.08 tons

Since 83

24/ ww lh , two curtains of reinforcement are required.

1-1 Horizontal shear reinforcement:

0025.0t

cm45S max,2

cm/cm05.0S

A and 200025.0h0025.0

S

A 2

2

t

2

t

For two curtains of reinforcement and trying 10 mm bars

max,22

2

Scm4.31S ,05.0S

785.02 . Use 10 mm bars @ 30cm.

tons374.17tons06.281000/3003002027.0'fA27.0 ccv

Thus t and l may be reduced based according to ACI 11.6. Nevertheless,

it will not be reduced in this example.

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154

1-2 Vertical shear reinforcement:

cm45S max,1

For two curtains of reinforcement, and trying 10 mm bars

11

l

S

0.7852 200025.0h0025.0

S

A

and max,11 Scm40.31S . Use 10mm bars @ 30cm.

Check for shear reinforcement capacity

tonsVn 21.2075.0/16.15

ytcccvn f'fAV

83

24/ ww lh ,i.e.

53.0c

KOtonstons

ffAV ytcccvn

.21.2008.1181000/42000025.030053.030020

max,

2- Design for flexure and axial loads:

Boundary elements are required where the maximum fiber compression

stress > c'f2.0 , calculated from the following equation:

g

wu

g

u

I

2/lM

A

Pf

The boundary elements may be disconnected where the compressive stress

< c'f15.0

wys

uwysu

l

c1

fA

P1lfA5.0M

where:

1w 85.02l

c

,

'fhl

fA

cw

ys and

'fhl

p

cw

u

For the vertical shear reinforcement of 10 mm

@30cm, 2s cm28.17A 836.0280300

70

05.085.0 ,

04032.030020300

420028.17

'fhl

fA

cw

ys

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155

, u

u

cw

u P00055.030020300

1000P

'fhl

p ,

79124.0

P00055.004032.0

836.085.004032.02

P00055.004032.0

l

c uu

w

Load combinations are

EDS QDS 2.02.1

EDS QDS 2.09.0

For first storey:

tonsPu 92.435.22432.022.1

3002.0/81.9512/30020

2/30010000047.265

30020

100092.43 2

3 cmkgf

i.e., special boundary elements are required at wall ends.

Flexural capacity at section of maximum moment:

08094.0

79124.0

92.4300055.004032.0

wl

c

cmc 28.2430008094.0 , and length of boundary element is not less than the

larger of wl1.0c and cmc 14.122/

mtMu .54.144 and

mtM u .93.12054.14447.265' For a boundary element 35 cm in length, additional reinforcement in each of

the two boundaries is given as follows

2

, 40.15785.0426142009.0

10000093.120cmA additionals

Use 8 16 mm bars in each of the two boundary elements.

Boundary element transverse reinforcement:

The larger of:

yt

ccsh

f

bsfA

09.0

yt

c

ch

g

shf

f

A

AA

130.0

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156

cms

cm

cm

ofsmallesttheS

22.173

33.133510

6.96.16

67.63/20

max

where xh is the lesser of 35 cm and (20x2/3)

and

maxS is taken as 5 cm.

For the longer direction of boundary, cmbc 1242201

For the shorter direction of boundary, cmbc 314352

239.04200

30012509.0cmAsh

213.14200

3001

3112

203551230.0 cmAsh

Use 2-legged mm10 ties @ 5 cm

Anchorage of horizontal shear reinforcement:

For 10 mm bars hooked at 180 degree,

cm

f

dfA

c

by

sh 26.1430017

14200

17

For straight bars

cmld 91.4926.145.3 , taken as 50 cm, N.O.K

For second storey: tonsPu 43.385.22132.022.1

`

157

3002.0/74.7912/30020

2/30010000099.219

30020

100043.38 2

3 cmkgf



0771.0

79124.0

43.3800055.004032.0

wl

c



mtMu .3.138 and



2

, 42.11785.0426142009.0




The larger of:

yt

ccsh

f

bsfA

09.0

yt

c

ch

g

shf

f

A

AA

130.0

cms

cm

cm

ofsmallesttheS

22.173

33.133510

6.96.16

67.63/20

max


and



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158


239.04200

30012509.0cmAsh

213.14200

3001

3112

203551230.0 cmAsh




cm

f

dfA

c

by

sh 26.1430017

14200

17

For straight bars


For third storey:

tonsPu 94.325.21832.022.1

3002.0/96.6312/30020

2/30010000041.175

30020

100094.32 2

3 cmkgf



0733.0

79124.0

94.3200055.004032.0

wl

c

cmc 223000733.0 , and length of boundary element is not less than the

larger of wl1.0c and cmc 112/

mtMu .0.132 and



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159

2

, 54.7785.0426142009.0




The larger of:

The larger of:

yt

ccsh

f

bsfA

09.0

yt

c

ch

g

shf

f

A

AA

130.0

cms

cm

cm

ofsmallesttheS

22.173

33.133510

6.96.16

67.63/20

max


and




239.04200

30012509.0cmAsh

213.14200

3001

3112

203551230.0 cmAsh




cm

f

dfA

c

by

sh 26.1430017

14200

17

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160

For straight bars


For fourth storey:

tonsPu 45.275.21532.022.1

3002.0/88.4812/30020

2/30010000090.132

30020

100045.27 2

3 cmkgf

i.e., special boundary elements are required at wall ends, and will be

discontinued when 30015.0f . Nevertheless, the boundary will be used

throughout the entire fourth floor.


06950.0

79124.0

45.2700055.004032.0

wl

c



mtMu .65.125 and



2

, 87.3785.0426142009.0




The larger of:

yt

ccsh

f

bsfA

09.0

yt

c

ch

g

shf

f

A

AA

130.0

`

161

cms

cm

cm

ofsmallesttheS

22.173

33.133510

6.96.16

67.63/20

max


and




239.04200

30012509.0cmAsh

213.14200

3001

3112

203551230.0 cmAsh




cm

f

dfA

c

by

sh 26.1430017

14200

17

For straight bars


For fifth storey:

tonsPu 96.215.21232.022.1

3002.0/92.3412/30020

2/30010000078.93

30020

100096.21 2

3 cmkgf

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162

and < 0.15 (300)

i.e., special boundary elements are no longer required at wall ends.


0657.0

79124.0

96.2100055.004032.0

wl

c

mtmtMu .78.93.24.119

Thus, no additional reinforcement is required at wall ends.

For sixth, seventh and eighth storeys

No additional reinforcement is required.

Documents

Special Reinforced Concrete Structural Wallssite.iugaza.edu.ps/sshihada/files/2012/02/Handout-6...continuous and shall be distributed a cross the shear plane. According to ACI 18.10.4.3,