Lecture 18 Shear Walls, Deep Beams and Corbels (b&w)
description
Transcript of 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
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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
Topics Addressed
Shear Wall
Introduction
Behavior
ACI Recommendations
Design Examples
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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
Topics Addressed
Coupling Beam
Introduction
Behavior
ACI Recommendations
Design Examples
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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
SHEAR WALLS
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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
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.
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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
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Introduction
Types of Shear Walls
Shape
Length to height ratio
Seismic demand
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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
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Introduction
Frame-Wall Interaction
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Introduction
Frame-Wall Interaction
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Behavior of Shear Walls
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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
Behavior of Shear Walls
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
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Behavior of Shear Walls
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Behavior of Shear Walls
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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ACI Code Recommendations
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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ACI Code Recommendations
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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
Ordinary reinforced concrete structural wall (Chapter 14)
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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ACI Code Recommendations
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Ordinary reinforced concrete structural wall (Chapter 14)
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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ACI Code Recommendations
lw
hw
Vu
h
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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
Ordinary reinforced concrete structural wall (Chapter 14)
Shear: (Section 11.10, ACI 318-02)
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)
ACI Code Recommendations
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Ordinary reinforced concrete structural wall (Chapter 14)
Shear: (Section 11.10, ACI 318-02)
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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ACI Code Recommendations
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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
Ordinary reinforced concrete structural wall (Chapter 14)
Shear: (Section 11.10, ACI 318-02)
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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ACI Code Recommendations
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Ordinary reinforced concrete structural wall (Chapter 14)
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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ACI Code Recommendations
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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
Ordinary reinforced concrete structural wall (Chapter 14)
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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ACI Code Recommendations
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Ordinary reinforced concrete structural wall (Chapter 14)
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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ACI Code Recommendations
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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
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Design of Ordinary Reinforced Concrete Structural Wall
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Design of Ordinary Reinforced Concrete Structural Wall
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Design of Ordinary Reinforced Concrete Structural Wall
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Design of Ordinary Reinforced Concrete Structural Wall
lw
hw
Vu
h
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Design of Ordinary Reinforced Concrete Structural Wall
h
lw
h
hw
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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
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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Design of Ordinary Reinforced Concrete Structural Wall
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Design of Ordinary Reinforced Concrete Structural Wall
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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
Flexure
Approximate procedure for design of In-plane bending
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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Design of Ordinary Reinforced Concrete Structural Wall
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Flexure
Approximate procedure for design of In-plane bending
• 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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Design of Ordinary Reinforced Concrete Structural Wall
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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
Flexure
Approximate procedure for design of In-plane bending
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Design of Ordinary Reinforced Concrete Structural Wall
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Flexure
Approximate procedure for design of In-plane bending
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Design of Ordinary Reinforced Concrete Structural Wall
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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
Flexure
Approximate procedure for design of In-plane bending
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Design of Ordinary Reinforced Concrete Structural Wall
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Flexure
Approximate procedure for design of In-plane bending
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Design of Ordinary Reinforced Concrete Structural Wall
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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
Flexure
Approximate procedure for design of In-plane bending
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Design of Ordinary Reinforced Concrete Structural Wall
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Design of Ordinary Reinforced Concrete Structural Wall
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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
Flexure
Out-of-plane bending
Moment Magnification
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Design of Ordinary Reinforced Concrete Structural Wall
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures50
Design of Ordinary Reinforced Concrete Structural Wall
Flexure
Out-of-plane bending
Moment Magnification
Cracked moment of inertia, Icr
Icr = Es
Ec
As +Pu
fy
(d – c)2 + wc3
3
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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
Flexure
Out-of-plane bending
out-of-plan deflection requirements
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Design of Ordinary Reinforced Concrete Structural Wall
s = 5Mc
2
48EcIe
c
150
M = Msa
5Psc2
1 –48EcIe
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
ACI Provisions for Special reinforced concrete structural walls
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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
ACI Provisions for Special reinforced concrete structural walls
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
ACI Provisions for Special reinforced concrete structural walls
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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
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Provisions for Special Boundary Elements
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
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Provisions for Special Boundary Elements
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
Provisions for Special Boundary Elements
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:
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
21.7.6 Boundary Elements of Special Reinforced Concrete Structural Walls
Fig 29-21: Special Boundary Element Requirements per 21.7.6.3
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
21.7.6 Boundary Elements of Special Reinforced Concrete Structural Walls
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
21.7.6 Boundary Elements of Special Reinforced Concrete Structural Walls
Fig 29-20: Special Boundary Element Requirements per 21.7.6.2
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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) )
21.7.6 Boundary Elements of Special Reinforced Concrete Structural Walls
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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
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 ′
21.7.6 Boundary Elements of Special Reinforced Concrete Structural Walls
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
21.7.6 Boundary Elements of Special Reinforced Concrete Structural Walls
Fig 29-22: Reinforcement Details for Special Boundary Elements
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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
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
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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)
21.7.7 Coupling Beams
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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
21.7.7 Coupling Beams
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
Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
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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Department of Civil Engineering, University of Engineering and Technology Peshawar, Pakistan
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced Concrete Structures
The End
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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
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
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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 73
Ash
Asv