lecture 18 shear walls, deep beams and corbels (b&w)

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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan

Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures

Lecture-18

Shear Walls and Coupling beams

By: Prof Dr. Qaisar Ali

Civil Engineering Department

UET [email protected]

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Topics Addressed

Shear Wall

Introduction

Behavior

ACI Recommendations

Design Examples

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Topics Addressed

Coupling Beam

Introduction

Behavior

ACI Recommendations

Design Examples

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SHEAR WALLS

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3



Introduction

Shear Walls

The term “shear wall” is used to describe a wall

that resists lateral (wind or earthquake) loads

acting parallel to the plane of the wall in

addition to the gravity loads from the floors and

roof adjacent to the wall.

Such walls are also referred to as “structural

walls”.

Non structural walls and partitions, whether

directly considered or not also add to the total

lateral stiffness of the structure.

5



Introduction

Difference between Wall and Column

The differentiation between columns and walls in the code is based on the

principal use rather than on arbitrary relationships of height and cross-

sectional dimensions, ACI 318-02, Chapter 2 Definitions.

While a wall always encloses or separates spaces, it may also be used to

resist horizontal or vertical forces or bending.

A column is normally used as a main vertical member carrying axial loads

combined with bending and shear. It may, however, form a small part of

an enclosure or separation.

The code permits walls to be designed using the principles stated for

column design .

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4



Introduction

Difference between Wall, Column and Pier

For the sake of terminology, however, following difference is recognized

by the code.

Column: Member with a ratio of height-to-least lateral dimension

exceeding 3 used primarily to support axial compressive load.

Wall: Though not specifically mentioned in the code, members of height-

to-least lateral dimension NOT exceeding 3 are considered as WALLS.

Pier: This is a wall segment and refers to a part of a wall bounded by

openings or by an opening and an edge.

Traditionally, a vertical wall segment bounded by two window openings has

been referred to as a pier, ACI 318 -02, R21.7.4.2

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Introduction Other Definitions

DIAPHRAGM is a horizontal or nearly horizontal system acting totransmit lateral forces to the vertical-resisting elements. The term“diaphragm” includes horizontal bracing systems.

DIAPHRAGM or SHEAR WALL CHORD is the boundary element of adiaphragm or shear wall that is assumed to take axial stresses analogousto the flanges of a beam.

BOUNDARY ELEMENT is an element at edges of openings or atperimeters of shear walls or diaphragms.

COLLECTOR is a member or element provided to transfer lateral forcesfrom a portion of a structure to vertical elements of the lateral-force-resisting system.

STRUCTURAL DIAPHRAGMS are structural members,such as floor and roof slabs, which transmit inertial forcesto lateral- force-resisting members.

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5



Introduction

Other Definitions

1629.6.4 Moment-resisting frame system. A structural system with an essentially complete space frame providing support for gravity loads. Moment-resisting frames provide resistance to lateral load primarily by flexural action of members.

1629.6.5 Dual system. A structural system with the following features:

1. An essentially complete space frame that provides support

for gravity loads.

2. Resistance to lateral load is provided by shear walls or braced frames andmoment-resisting frames (SMRF, IMRF, MMRWF or steel OMRF). Themoment-resisting frames shall be designed to independently resist at least 25percent of the design base shear.

3. The two systems shall be designed to resist the total design base shear inproportion to their relative rigidities considering the interaction of the dualsystem at all levels.

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Introduction

Types of Shear Walls

Shape

Length to height ratio

Seismic demand

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6



Introduction

Importance of Shear Walls

Shear walls are extremely important in high-rise buildings. If unaided by walls,

high rise frames could not be efficiently designed to satisfy strength

requirements or to be within acceptable lateral drift limits.

Since frame buildings depend primarily on the rigidity of connections for their

resistance to lateral loads, they tend to be uneconomical beyond a certain

height range.

11 to 14 stories, in regions of high to moderate seismicity

15 to 20 stories, elsewhere.

Many times, however, shear walls are also provided in low rise (1 to 5) or

medium rise frame buildings (6 to 10) in order to reduce sizes of columns.

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Introduction

Locations of Shear Walls

It should be located such that the center of mass and center of rigidity of the

structure coincide.

If there is eccentricity as illustrated in the fig, the building will undergo torsional

distortions. Though the structure can be designed for such effects, it would be

relatively uneconomical.

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Center of resistance

Eccentricity

Center of mass

Shear wall

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Introduction Locations of Shear Walls

Most multi-story buildings are constructed with a central core area.

The core usually contains, among other things, elevator, plumbing and HVAC

shafts etc.

Walls provided for such core can be used as Shear Walls.

Additional walls can be provided at other appropriate locations.

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Introduction

Frame-Wall Interaction

In a RC frame structure, the floor systems (RC slabs)

distribute the lateral loads to the vertical framing

elements in proportion to their rigidities.

Though the actual distribution of lateral loads will

depend on the relative rigidities of walls and columns,

the structural walls usually being substantially stiffer

than the columns attract major portion of the lateral

loads, leaving only small portion for the frame

members.

With adequate wall bracing, the frame can be

considered as non-sway for column design.

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8



Introduction


The analysis and design of the structural system for a building frame of moderate

height can be simplified if the structural walls are sized to carry the entire lateral

load.

Members of the frame (columns and beams or slabs) can be proportioned to resist

the gravity loads only.

Neglecting frame-wall interaction for buildings of moderate size and height will result

in reasonable member sizes and overall costs.

When the walls stiffness is much higher than the stiffness of the columns in a given

direction within a story, the frame takes only a small portion of the lateral loads.

Thus, for low-rise buildings, neglecting the contribution of frame action in resisting

lateral loads and assigning the total lateral load resistance to walls is an entirely

reasonable assumption.

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Introduction


In contrast, frame-wall interaction must be considered for high-rise structures

where the walls have a significant effect on the frame: in the upper stories,

the frame must resist more than 100 % of the story shears caused by the

wind loads.

Thus, neglecting frame-wall interaction would not be conservative at these

levels. Clearly, a more economical high-rise structure will be obtained when

frame-wall interaction is considered.

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9



Behavior of Shear Walls

A typical shear wall, which is part of a

lateral load resisting system, is

subjected to following actions.

In-plane shear and bending moment

(along major axis)

Out-of-plane shear and bending moment

(along minor axis)

Axial Load

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In-plane shear and bending

moment (along major axis)

In-plane shear

A variable shear, which reaches

a maximum at the base.

Both horizontal and vertical

reinforcement are provided for

shear.

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10




In-plane shear and bending moment (along

major axis)

In-plane bending moment

A variable bending moment which reaches a

maximum at the base and tends to cause

vertical tension near the loaded edge and

compression at the far edge.

Vertical distributed reinforcement (fig a) or

reinforcement at the edges in boundary

zones (fig b) will be required against this

action

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Fig a

Fig b




Out-of-plane shear and bending moment (along

minor axis)

Out-of-plane bending moment

Depending on a number of parameters, the wall may

bend in an out-of-plane mode either

as a whole from top to bottom called global bending or

as Individual wall segments in a story called local

bending

In both cases vertical reinforcement distributed all

along the length of the wall shall be provided.

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Out-of-plane shear and bending moment (along

minor axis)

Out-of-plane shear

Out-of-plane shear is not usually a problem in shear

walls.

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ACI Code Recommendations

Types of Walls according to Seismic Hazard (Definitions,

Chapter 21)

Walls located in regions of low to moderate seismic hazard (zones 1, 2a

and 2b UBC 97), shall comply with the requirements of ordinary reinforced

concrete structural walls of the chapter 14 of ACI 318-02.

There are no special requirements for structural walls located in regions of low to

moderate seismic hazard, except for the connection requirements.

Walls located in regions of high seismic hazard (zones 3 and 4 of UBC 97),

shall comply with the requirements of Special reinforced concrete

structural wall of chapter 21 of the ACI 318-02,, in addition to the

requirements for ordinary reinforced concrete structural walls.

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Types of Walls according to Seismic Hazard (Definitions,

Chapter 21)

The provisions for the design of Ordinary reinforced concrete

structural wall from chapter 14 will be presented first. Special

provisions for Special reinforced concrete structural wall from

chapter 21 will be presented next.

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Ordinary reinforced concrete structural wall (Chapter 14)

According to section 14.2.3, walls subjected to shear forces shall

be designed in accordance with the provisions of chapter 11,

section 11.10 on provisions of shear reinforcement for

structural walls.

According to section 14.4, Walls subjected to flexure load, axial

load or combined flexure and axial load shall be designed in

accordance with the provisions for flexure and axial loads of

chapter 10. (like column design)

Walls shall be properly anchored into all intersecting elements, such

as floors, columns, other walls, and footings.

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13




Wall sizing

A minimum of 6 in thickness will be required for a wall with a single

layer of reinforcement and 10 in for a wall with double layer.(ACI

14.3.4)

Moreover, according to (ACI 318-89) the shear wall must have a total

stiffness of at least six times the sum of stiffness of all columns in a

given direction within the story

I(walls) > 6I(columns)

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Shear: (Section 11.10, ACI 318-02)

Shear Wall Capacity contributed by concrete alone is given as

ФVc =0.75 x 2 x √fc′ x h x d (ACI 11.10.4)

where d = 0.8 lw ( ACI 11.10.4)

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lw

hw

Vu

h

14





Minimum reinforcement for shear

Both horizontal and vertical shear reinforcement shall be provided as per following criterion.

ρh = ratio of horizontal shear reinforcement area to gross concrete area of vertical section ρn = ratio of vertical shear reinforcement area to gross concrete area of horizontal section

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Conditions Horizontal Shear Reinforcement Vertical Shear Reinforcement

Vu ≤ ФVc /2(11.10.8)

ρh = 0.0020 for #5 and smallerρh = 0.0025 for other bars(14.3)

ρn = 0.0012 for #5 and smaller with fy>60ksiρn= 0.0015 for other bars(14.3)

ФVc/2 ≤ Vu ≤ ФVc

(11.10.8)ρh = 0.0025 (11.10.9.2) ρn = 0.0025 (11.10.9.4)

Vu > ФVc

(11.10.8)s =0.75 x Av x fy x d / (Vu – ФVc) ρn = 0.0025 +0.5(2.5-hw / lw )(ρh - 0.0025)

(11.10.9.4)






Maximum Spacing of Shear reinforcement

Horizontal Shear reinforcement

Spacing of horizontal shear reinforcement shall not exceed

Iw/5 , 3h nor 18 inch, (whichever is less)

Vertical Shear reinforcement

Spacing of vertical shear reinforcement shall not exceed

Iw/3 , 3h nor 18 inch, (whichever is less )

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15





The ACI code additionally requires that

Vu < Ф 10√f c h(0.8lw ) ( ACI 318-02,11.10.3)

Increase thickness of wall, if this happens

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Flexure (14.2, 14.3)

Walls must be designed as compression members by the strength

design provisions in Chapter 10 for flexure and axial loads.

Vertical reinforcement, however, need not be enclosed by lateral ties if

vertical reinforcement area is not greater than 0.01 times gross

concrete area.

Minimum ratio of vertical reinforcement area to gross concrete areashall be

(a) 0.0012 for deformed bars not larger than No. 5 with a specified yield

strength not less than 60,000 psi; or

(b) 0.0015 for other deformed bars

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16




Placement of Reinforcement (14.3.4)

Walls more than 10 in. thick, except basement walls, shall have

reinforcement for each direction placed in two layers parallel with faces

of wall in accordance with the following:

(a) One layer consisting of not less than one-half and not more than two-

thirds of total reinforcement required for each direction shall be placed not

less than 2 in. nor more than one-third the thickness of wall from the exterior

surface;

(b) The other layer, consisting of the balance of required reinforcement in

that direction, shall be placed not less than 3/4 in. nor more than one-third

the thickness of wall from the interior surface.

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Reinforcement around openings (14.3.7)

In addition to the minimum reinforcement, not less than two No. 5 bars

shall be provided around all window and door openings. Such bars shall

be extended to develop the bar beyond the corners of the openings but

not less than 24 in.

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Design of Ordinary Reinforced Concrete Structural Wall

General

In the case of low-rise walls, shear requirements usually govern, so

a preliminary thickness can be determined based on shear.

In high-rise structures, a preliminary wall thickness is not as

obvious. In such structures, the wall thickness can vary a number of

times over the height of the structure, and a thickness is usually

determined from experience.

While fire resistance requirements will seldom govern wall

thickness, the governing building code requirements should not be

overlooked.

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General

The size of openings required for stairwells and elevators will

usually dictate minimum wall plan layouts. Thus, the lengths of

walls are usually dictated by architectural considerations.

Therefore, the first step in the design procedure is to determine a

preliminary thickness of the wall.

From a practical standpoint, a minimum thickness of 6 inches will

be required for a wall with a single layer of reinforcement, and 10

inches for a wall with a double layer.

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18




General

In low-rise walls, which are typically governed by shear

requirements, it is common practice to determine the amount of

vertical and horizontal reinforcement based on the shear provisions

of Section 11.10.

The flexural and axial force requirements of the appropriate design

method are then checked based on the reinforcement for shear.

It is not uncommon for low-rise walls to have minimum amounts of

reinforcement over their entire height.

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General

In the case of high-rise walls, wall sections at the base of the

structure will usually, but not always, be governed by the

requirements for flexure and axial load. Once the required amount

of reinforcement is established for those requirements, the shear

requirements of Section 11.10 are checked.

The amounts of reinforcement are typically varied over the height of

high-rise walls.

In no case shall the provided areas of reinforcement be less than

the minimum values prescribed in the code.

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Shear

ФVn = ФVc + ФVs

ФVs =Vu – ФVc = 0.75 x Av x fy x d/ s

Therefore s = 0.75 x Av x fy x d /(Vu – ФVc)

“s” is center to center to center spacing of horizontal reinforcement in inches

Av is single bar area for one curtain and two times bar area for two

curtains of reinforcement.

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lw

hw

Vu

h



Shear

Horizontal and vertical shear reinforcement Ash & Asv from minimum

reinforcement ratio “ρ” can be calculated as follows

Ash or Asv = (inch2 per foot ) = ρ x 12 x h ; h is thickness of wall

Spacing “s” (inch c/c) = (Av /Ash ) x 12

s = Av /(ρ x 12 x h ) x 12 (substituting Ash )

s = Av /(ρ x h )

ρ = Av /(s x h )

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h

lw

h

hw

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Flexure

In general, when designing a wall as a compression member, an

interaction diagram needs to be constructed for sections subjected to

combined flexure and axial load, and the applied factored moments

must be magnified to account for slenderness effects.

Details on how to construct such a diagram have been discussed

earlier.

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Flexure

Approximate procedure for design of In-plane bending

For buildings of moderate height, walls with uniform cross-sections and

uniformly distributed vertical and horizontal reinforcement are usually the

most economical.

Concentration of the reinforcement at the extreme ends of a wall or small

segment (boundary zones) is usually not required except in high and

moderate seismic zones (special walls).

Uniform distribution of the vertical wall reinforcement required for shear

wall usually provides adequate moment strength as well.

Minimum amounts of reinforcement will usually be sufficient for both

shear and moment requirements.

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21



Flexure


In general, walls that are subjected to axial load or combined axial and

flexure load need to be designed as compression members according to

the provisions given in ACI Chapter 10.

For rectangular shear walls containing uniformly distributed vertical

reinforcement and subjected to an axial load smaller than that producing

balance failure, the following approximate equation can be used to

determine the nominal moment capacity of the wall. ( Cardens A.E et. al,

Design Provisions for Shear walls,” Journal of the ACI, Vol 70, No. 3

March 1973, pp 221-230)

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Flexure


• 0.5 1 1

• Where = total area of vertical reinforcement, in.2

= horizontal length of wall, in.

= factored axial compressive load, kips

= yield strength of reinforcement = 60 ksi

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Flexure


43




Flexure


44


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Flexure


45




Flexure


46


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Flexure


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Flexure

Out-of-plane bending

As wall is mostly slender along its minor axis, moment magnification

shall be done before wall is designed for out-of-plane bending

Once moment is magnified, wall shall be designed for this moment

either using interaction diagram or approximate procedure.

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Flexure


Moment Magnification

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Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures50


Flexure


Moment Magnification

Cracked moment of inertia, Icr

Icr = Es

Ec

As +Pu

fy

(d – c)2 + wc3

3

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Flexure


out-of-plan deflection requirements

51


s = 5Mc

2

48EcIe

c

150

M = Msa

5Psc2

1 –48EcIe



ACI Provisions for Special reinforced concrete structural walls

52

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Provisions for Special Boundary Elements

The minimum reinforcement ratio for both the longitudinal and transversereinforcement is 0.0025, unless the design shear force does not exceed Acv fc , whereAcv is the net area of concrete bounded by the web thickness and the length of thewall in the direction of analysis; in this case, the minimum reinforcement must not beless than that given in 14.3. The reinforcement provided for shear strength must becontinuous and distributed uniformly across the shear plane with a maximum spacingof 18 in. At least two curtains of reinforcement are required if the in-plane factoredshear force assigned to the wall exceeds Acv fc

n = ratio of area of distributed reinforcement parallel to the plane of Acv to gross concrete area perpendicular to that reinforcement.(horizontal, denoted by h in chapter 14)

v = ratio of area of distributed reinforcement perpendicular to the plane of Acv to gross concrete area Acv.(vertical, denoted by n in chapter 14)

Acp = area of concrete section, resisting shear, of an individual pier or horizontal wall segment, in.2

Acv = gross area of concrete section bounded by web thickness and length of section in the direction of shear force considered, in.2

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21.7.2.1:1. If Vu ≤ Acv ′, provide minimum reinforcement as given for

ordinary reinforced structural walls, where Acv is the net area of concrete

bounded by the web thickness and the length of the wall in the direction of

analysis

Acv = h × lw

’

h h

lw




21.7.2.2: 2. If Vu> Acv ′ , both the longitudinal (v)and transversereinforcement (n ) must not be less than 0.0025

21.7.2.2: 3. If Vu>2 Acv ′ , Two curtains of reinforcement are required inboth directions.

21.7.2.3:4. Anchoring or splicing of reinforcement as per 21.5.4

21.7.4: Shear Strength.

Vn = Acv (c ′ + n fy)

c = 3 (for hw/lw ≤ 1.5) &c= 2 (for hw/lw ≥ 2.0) & varies linearly for

other values. (c = 2.0 conservatively)

21.7.4.3: Walls shall have distributed reinforcement providing resistance in twoorthogonal directions in the plane of the wall. If the ratio hw/lw does not exceed2.0 then reinforcement v shall not be less than n

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R 21.7.4: The ratio hw/lw may refer to overall dimensions of a wall, or of asegment of the wall bounded by two openings or an opening and an edge.

To restrain the inclined cracks effectively, reinforcement included in n and v

should be appropriately distributed along the length and height of the wall.

Chord reinforcement provided near wall edges in concentrated amounts forresisting bending moments is not to be included in determining n and V.

21.7.5: Design of flexure and axial loads.

21.7.5.1:

21.7.5.2:



21.7.6 Boundary Elements of Special Reinforced Concrete Structural Walls

21.6.3. Compression zones shall includes special boundary elements where themaximum extreme fiber stress corresponding to the factored forces, includingearthquake effects, exceeds 0.2 fc’ (see Fig. 29-21).

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Fig 29-21: Special Boundary Element Requirements per 21.7.6.3




When special boundary elements are required, they must extend horizontallyfrom the extreme compression fiber a distance not less than the larger of c – 0.1lw and c/2 (21.7.6.4(a); see Fig. 29-20).

In the vertical direction, the special boundary elements must extend from thecritical section a distance greater than or equal to the larger of lw or Mu/4Vu

(21.7.6.2). This distance is based on upper bound estimates of plastic hingelengths, and is beyond the zero over which concrete spalling is likely to occur.

From earlier codes, it is 0.15 to 0.25 lw

See chapter 6 simplifired approach.

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Fig 29-20: Special Boundary Element Requirements per 21.7.6.2



Section 21.7.6.4 contains the details of he reinforcement when specialboundary elements are required by 21.7.6.2 or 21.7.6.3. The transversereinforcement must satisfy the same requirements as per special momentframe members subjected to bending and axial load (21.4.4.1 through21.4.4.3), excluding Eq. (21-3) (21.7.6.4(c); see Fig. 29-22). Also, thetransverse reinforcement shall extend in the support a distance not lessthan the development length of the largest longitudinal bar in the specialboundary element; for footing or mats, the transverse reinforcement shallextend at least 12 in. into the footing or mat (21.7.6.4(d)). Horizontalreinforcement in the wall web shall be anchored within the confined core ofthe boundary element within the confined core of the boundary element todevelop its specified yield strength (21.7.6.4(c)). To achieve this anchorage,90-deg hooks or mechanical anchorages are recommended. Mechanicalsplices and welded splices of the longitudinal reinforcement in theboundary elements shall conform to 21.2.6 and 21.2.7, respectively(21.7.6.4(d) )


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when special boundary elements are not required, the provisions of21.7.6.5must be satisfied. For the cases when the longitudinalreinforcement ratio at the wall boundary is greater than 400/fy, transversereinforcement, spaced not more than 8 in. on center, shall be provided thatsatisfies 21.4.4.1(c), 21.4.4.3, and 21.7.6.4(c)(21.7.6.5(a)). Thisrequirement helps in preventing bucking of the longitudinal reinforcementthat can be caused by cyclic load reversals. The longitudinal reinforcementratio to be used includes only the reinforcement at the end of the wall asindicated in Fig. R21.7.6.5. Horizontal reinforcement terminating at theedges of structural walls must be properly anchored per 21.7.6.5(b)in orderfor the reinforcement to be effective in resisting shear and to help inpreventing buckling of the vertical edge reinforcement. The provisions of21.7.6.5(b)are not required to be satisfied when the factored shear force Vu

is less than Acv ′





Fig 29-22: Reinforcement Details for Special Boundary Elements

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When adequately proportioned and detailed, coupling beams betweenstructural wall can provide an efficient means of energy dissipation underseismic forces, and can provide a higher degree of overall stiffness to thestructure. Due to their relatively large depth to clear span ratio, ends ofcoupling beams are usually subjected to large inelastic rotations. Adequatedetailing and shear reinforcement are necessary to prevent shear failureand to ensure ductility and energy dissipation.

coupling beams with ln/h ≥ 4 shall satisfy the requirement of 21.3for flexuremembers of special moment frames, excluding 21.3.1.3and 21.3.1.4(a)if itcan be shown that the beam has adequate lateral stability (21.7.7.1). Whenln/h < 4, coupling beams with two intersecting groups of diagonally-placedbars symmetrical about the midspan is permitted (21.7.7.2). The diagonalbars are required for deep coupling beams (ln/h < 2) with a factored shearforce Vu greater than 4 ′Acp, unless it can be shown otherwise thatsafety and stability are not compromised (21.7.7.3). Experiments haveshown that diagonally oriented reinforcement is effective only if the bars canbe placed at large inclination.

21.7.7 Coupling Beams



Note that in 2002 code, h replaces d in the definition of the aspect ratio(clear span/depth) and Acp replaces bwd in the shear equations. The firstchange simplifies the code requirements, since d is not always readilyknown for beams with multiple layers of reinforcement. The second changeremoves an inconsistency between 21.6.4.5 and 21.6.7.4 of the 1999 code;Acp is now consistently used in 21.7.4.5and 21.7.7.4.

Section 21.7.7.4 contains the reinforcement details for the two intersectinggroups of diagonally placed bars. Figure 29-23 provides a summary ofthese requirements. The requirement on side dimensions of the cage andits core is to provide adequate toughness and stability when the bars arestressed beyond yielding. The nominal shear strength of a coupling beam iscomputed from the following (21.7.7.4(b)):

Vn = 2Avdfysin ≤ 10 ′AcpEq. (21-9)


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The additional reinforcement specified in 21.7.7.4(f) is used to confine theconcrete outside of the diagonal cores.

Fig 29-23: Coupling Beam with Diagonally Oriented Reinforcement



References

70

ACI 318-02

Design of Concrete Structures (13th Ed.) by Nilson,

Darwin and Dolan

PCA Notes on ACI 318-02

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The End

71



Ordinary reinforced concrete structural wall

Flexure

Wall design is further complicated by the fact that slenderness is a

consideration in practically all cases of out-of-plane bending.

The approximate evaluation of slenderness effects prescribed in Section

10.11 may be used

72

Design of Shear Wall

37


Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures 73

Ash

Asv

lecture 18 shear walls, deep beams and corbels (b&w)

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