= 18. CHAPTER 18 — EARTHQUAKE-RESISTANT STRUCTURES
= 18.10 — Special structural walls
== 18.10.1 Scope
=== 18.10.1.1 This section shall apply to special structural
walls, including ductile coupled walls, and all components
of special structural walls including coupling beams and
wall piers forming part of the seismic-force-resisting system.
=== 18.10.1.2 Special structural walls constructed using
precast concrete shall be in accordance with 18.11 in addition
to 18.10.
= R18.10 — Special structural walls
== R18.10.1 Scope
This section contains requirements for the dimensions
and details of special structural walls and all components
including coupling beams and wall piers. Wall piers are
defined in Chapter 2. Design provisions for vertical wall
segments depend on the aspect ratio of the wall segment
in the plane of the wall (hw/ℓw), and the aspect ratio of the
horizontal cross section (ℓw/bw), and generally follow the
descriptions in Table R18.10.1 . The limiting aspect ratios for
wall piers are based on engineering judgment. It is intended
that flexural yielding of the vertical reinforcement in the pier
should limit shear demand on the pier.
Table R18.10.1—Governing design provisions for
vertical wall segments[1]_
== 18.10.2 Reinforcement
=== 18.10.2.1 The distributed web reinforcement ratios, ρℓ and
ρt, for structural walls shall be at least 0.0025, except that
if Vu does not exceed 0.083λ sqrt(fc') Acv, ρt shall be permitted
to be reduced to the values in 11.6. Reinforcement spacing
each way in structural walls shall not exceed 450 mm. Reinforcement
contributing to Vn shall be continuous and shall
be distributed across the shear plane.
=== 18.10.2.2 At least two curtains of reinforcement shall be
used in a wall if Vu > 0.17λ sqrt(fc') Acv or hw/ℓw ≥ 2.0, in which hw
and ℓw refer to height and length of entire wall, respectively.
== R18.10.2 Reinforcement
Minimum reinforcement requirements in 18.10.2.1 follow
from preceding Codes. The requirement for distributed shear
reinforcement is related to the intent to control the width of
inclined cracks. The requirement for two layers of reinforcement
in walls resisting substantial design shears in 18.10.2.2
is based on the observation that, under ordinary construction
conditions, the probability of maintaining a single layer of
reinforcement near the middle of the wall section is quite
low. Furthermore, presence of reinforcement close to the
surface tends to inhibit fragmentation of the concrete in the
event of severe cracking during an earthquake. The requirement
for two layers of vertical reinforcement in more slender
walls is to improve lateral stability of the compression zone
under cyclic loads following yielding of vertical reinforcement
in tension.
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18 Seismic
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=== 18.10.2.3 Reinforcement in structural walls shall be developed
or spliced for fy in tension in accordance with 25.4,
25.5, and (a) through (d):
(a) Except at the top of a wall, longitudinal reinforcement
shall extend at least 3.6 m above the point at which it is no
longer required to resist flexure but need not extend more
than ℓd above the next floor level.
(b) At locations where yielding of longitudinal reinforcement
is likely to occur as a result of lateral displacements,
development lengths of longitudinal reinforcement shall
be 1.25 times the values calculated for fy in tension.
(c) Lap splices of longitudinal reinforcement within
boundary regions shall not be permitted over a height
equal to hsx above, and ℓd below, critical sections where
yielding of longitudinal reinforcement is likely to occur
as a result of lateral displacements. The value of hsx need
not exceed 6 m. Boundary regions include those within
lengths specified in 18.10.6.4(a) and within a length equal
to the wall thickness measured beyond the intersecting
region(s) of connected walls.
(d) Mechanical splices of reinforcement shall conform to
18.2.7 and welded splices of reinforcement shall conform
to 18.2.8.
=== R18.10.2.3 Requirements are based on provisions in
Chapter 25, with modifications to address issues specific
to structural walls, as well as to the use of high-strength
reinforcement. Because actual forces in longitudinal reinforcement
of structural walls may exceed calculated forces,
reinforcement should be developed or spliced to reach the
yield strength of the bar in tension. Termination of longitudinal
(vertical) reinforcement in structural walls should be
specified so that bars extend above elevations where they are
no longer required to resist design flexure and axial force;
extending bars ℓd above the next floor level is a practical
approach to achieving this requirement. A limit of 3.6 m
is included for cases with large story heights. Bar terminations
should be accomplished gradually over a wall height
and should not be located close to critical sections where
yielding of longitudinal reinforcement is expected, which
typically occurs at the base of a wall with a uniform, or
nearly uniform, cross section over the building height. Strain
hardening of reinforcement results in spread of plasticity
away from critical sections as lateral deformations increase.
Research (Aaletti et al. 2012; Hardisty et al. 2015) shows
that lap splices should be avoided in walls where flexural
yielding is anticipated, for example at the base of walls,
because they may lead to large localized strains and bar fractures.
!!Figure R18.10.2.3 illustrates boundary regions where
lap splices are not permitted.
At locations where yielding of longitudinal reinforcement
is expected, a 1.25 multiplier is applied to account for the
likelihood that the actual yield strength exceeds the specified
yield strength of the bar, as well as the influence of
strain hardening and cyclic load reversals. Where transverse
reinforcement is used, development lengths for straight and
hooked bars may be reduced as permitted in 25.4.2 and
25.4.3, respectively, because closely spaced transverse reinforcement
improves the performance of splices and hooks
subjected to repeated inelastic demands (ACI 408.2R).
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Fig. R18.10.2.3—Wall boundary regions within heights where lap splices are not permitted.
=== 18.10.2.4 Walls or wall piers with hw/ℓw ≥ 2.0 that are
effectively continuous from the base of structure to top of
wall and are designed to have a single critical section for
flexure and axial loads shall have longitudinal reinforcement
at the ends of a vertical wall segment that satisfies (a)
through (c).
=== R18.10.2.4 This provision is based on the assumption that
inelastic response of the wall is dominated by flexural action
at a critical, yielding section. The wall should be proportioned
so that the critical section occurs where intended.
If there is potential for more than one critical section, it is
prudent to provide the minimum boundary reinforcement at
all such sections.
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18 Seismic
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=== 18.10.2.4 continuation
(a) Longitudinal reinforcement ratio within 0.15ℓw from
the end of a vertical wall segment, and over a width equal
to the wall thickness, shall be at least 0.5 sqrt(fc')/fy .
(b) The longitudinal reinforcement required by 18.10.2.4(a)
shall extend vertically above and below the critical section
at least the greater of ℓw and Mu/3Vu.
(c) No more than 50 percent of the reinforcement required
by 18.10.2.4(a) shall be terminated at any one section.
=== R18.10.2.4 continuation
The requirement for minimum longitudinal reinforcement
in the ends of the wall is to promote the formation of
well-distributed secondary flexural cracks in the wall plastic
hinge region to achieve the required deformation capacity
during earthquakes (Lu et al. 2017; Sritharan et al. 2014).
Furthermore, significantly higher in-place concrete strengths
than used in design calculations may be detrimental to the
distribution of cracking. 18.10.2.4(a) specifies the required
reinforcement ratio in the end tension zones, as shown for
different wall sections in Fig. R18.10.2.4 .
The longitudinal reinforcement required by 18.10.2.4(a)
should be located at a critical section where concentrated
yielding of longitudinal reinforcement is expected (typically
the base of a cantilever wall) and must continue to a sufficient
elevation of the wall to avoid a weak section adjacent
to the intended plastic hinge region. A height above or below
the critical section of Mu/3Vu is used to identify the length
over which yielding is expected.
Fig. R18.10.2.4—Locations of longitudinal reinforcement required by 18.10.2.4(a) in different configurations of wall sections.
=== 18.10.2.5 Reinforcement in coupling beams shall be developed
for fy in tension in accordance with 25.4, 25.5, and (a)
and (b):
(a) If coupling beams are reinforced according to 18.6.3.1,
the development length of longitudinal reinforcement
shall be 1.25 times the values calculated for fy in tension.
(b) If coupling beams are reinforced according to 18.10.7.4,
the development length of diagonal reinforcement shall be
1.25 times the values calculated for fy in tension.
== 18.10.3 Design forces
== R18.10.3 Design forces
The possibility of yielding in components of structural
walls should be considered, as in the portion of a wall between
two window openings, in which case the actual shear may be
in excess of the shear indicated by lateral load analysis based
on factored design forces.
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=== 18.10.3.1 The design shear force Ve shall be calculated by:
Ve = Ωv.ωv.Vu ≤ 3Vu (18.10.3.1)
where Vu, Ωv, and ωv are defined in 18.10.3.1.1, 18.10.3.1.2,
and 18.10.3.1.3, respectively.
==== 18.10.3.1.1 Vu is the shear force obtained from code lateral
load analysis with factored load combinations.
==== 18.10.3.1.2 Ωv shall be in accordance with
Table 18.10.3.1.2 .
Table 18.10.3.1.2—Overstrength factor Ωv at critical
section_
==== 18.10.3.1.3 For walls with hwcs/ℓw < 2.0, ωv shall be taken
as 1.0. Otherwise, ωv shall be calculated as:
ωv = 0.9 + ns/10, ns <=6
ωv = 1.3 + ns/30 <=1.8, ns > 6
(18.10.3.1.3)
where ns shall not be taken less than the quantity 0.00028.hwcs.
=== R18.10.3.1 Design shears for structural walls are obtained
from lateral load analysis with appropriate load factors
increased to account for: (i) flexural overstrength at critical
sections where yielding of longitudinal reinforcement is
expected; and (ii) dynamic amplification due to higher mode
effects, as illustrated in Fig. R18.10.3.1 . The approach used
to determine the amplified shear forces is similar to that used
in New Zealand Standard 3101 (2006). Because Mn and Mpr
depend on axial force, which varies for different load combinations,
and loading direction for flanged and coupled walls,
the condition producing the largest value of Ωv should be
used. Although the value of 1.5 in 18.10.3.1.2 is greater than
the minimum value obtained for the governing load combination
with a ϕ factor of 0.9 and a tensile stress of at least 1.25fy
in the longitudinal reinforcement, a value greater than 1.5 may
be appropriate if provided longitudinal reinforcement exceeds
that required. Dynamic amplification is not significant in
walls with hw/ℓw < 2. A limit of 0.007hwcs is imposed on ns to
account for buildings with large story heights. The application
of ΩV to Vu does not preclude the application of a redundancy
factor if required by the general building code.
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18 Seismic
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Fig. R18.10.3.1—Determination of shear demand for walls with hw/ℓw ≥ 2.0 (Moehle et al 2011).
== 18.10.4 Shear strength
=== 18.10.4.1 Vn shall be calculated by:
Vn = (αc.lambda.sqrt(fc') + rho_t.fyt) Acv ... (18.10.4.1)
where:
αc = 0.25 for hw/ℓw ≤ 1.5
αc = 0.17 for hw/ℓw ≥ 2.0
It shall be permitted to linearly interpolate the value of αc
between 0.25 and 0.17 for 1.5 < hw/ℓw < 2.0.
=== 18.10.4.2 In 18.10.4.1, the value of ratio hw/ℓw used to
calculate Vn for segments of a wall shall be the greater of the
ratios for the entire wall and the segment of wall considered.
=== 18.10.4.3 Walls shall have distributed shear reinforcement
in two orthogonal directions in the plane of the wall. If hw/ℓw
does not exceed 2.0, reinforcement ratio ρℓ shall be at least
the reinforcement ratio ρt.
=== 18.10.4.4 For all vertical wall segments sharing a common
lateral force, Vn shall not be taken greater than 0.66 sqrt(fc') Acv.
For any one of the individual vertical wall segments, Vn shall
not be taken greater than 0.83 sqrt(fc') Acw, where Acw is the area
of concrete section of the individual vertical wall segment
considered.
=== 18.10.4.5 For horizontal wall segments and coupling
beams, Vn shall not be taken greater than 0.83 sqrt(fc') Acv,
where Acw is the area of concrete section of a horizontal wall
segment or coupling beam.
== R18.10.4 Shear strength
Equation (18.10.4.1) recognizes the higher shear strength
of walls with high shear-to-moment ratios (Hirosawa 1977;
Joint ACI-ASCE Committee 326 1962; Barda et al. 1977).
The nominal shear strength is given in terms of the gross area
of the section resisting shear, Acv. For a rectangular section
without openings, the term Acv refers to the gross area of the
cross section rather than to the product of the width and the
effective depth.
A vertical wall segment refers to a part of a wall bounded
horizontally by openings or by an opening and an edge. For
an isolated wall or a vertical wall segment, ρt refers to horizontal
reinforcement and ρℓ refers to vertical reinforcement.
The ratio hw/ℓw may refer to overall dimensions of a wall,
or of a segment of the wall bounded by two openings, or an
opening and an edge. The intent of 18.10.4.2 is to make certain
that any segment of a wall is not assigned a unit strength
greater than that for the entire wall. However, a wall segment
with a ratio of hw/ℓw higher than that of the entire wall should
be proportioned for the unit strength associated with the ratio
hw/ℓw based on the dimensions for that segment.
To restrain the inclined cracks effectively, reinforcement
included in ρt and ρℓ should be appropriately distributed along
the length and height of the wall (refer to 18.10.4.3). Chord
reinforcement provided near wall edges in concentrated
amounts for resisting bending moment is not to be included in
determining ρt and ρℓ. Within practical limits, shear reinforcement
distribution should be uniform and at a small spacing.
If the factored shear force at a given level in a structure is
resisted by several walls or several vertical wall segments of
a perforated wall, the average unit shear strength assumed for
the total available cross-sectional area is limited to 0.66 sqrt(fc')
with the additional requirement that the unit shear strength
assigned to any single vertical wall segment does not exceed
0.83 sqrt(fc') . The upper limit of strength to be assigned to any
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== R18.10.4 continuation
one member is imposed to limit the degree of redistribution
of shear force.
Horizontal wall segments in 18.10.4.5 refer to wall
sections between two vertically aligned openings (refer
to Fig. R18.10.4.5 ). It is, in effect, a vertical wall segment
rotated through 90 degrees. A horizontal wall segment is also
referred to as a coupling beam when the openings are aligned
vertically over the building height. When designing a horizontal
wall segment or coupling beam, ρt refers to vertical
reinforcement and ρℓ refers to horizontal reinforcement.
Fig. R18.10.4.5—Wall with openings.
=== 18.10.4.6 The requirements of 21.2.4.1 shall not apply to
walls or wall piers designed according to 18.10.6.2.
=== R18.10.4.6 Section 21.2.4.1 does not apply because walls
designed according to 18.10.6.2 are controlled by flexural
yielding, and code level shear forces have been amplified.
== 18.10.5 Design for flexure and axial force
=== 18.10.5.1 Structural walls and portions of such walls
subject to combined flexure and axial loads shall be designed
in accordance with 22.4. Concrete and developed longitudinal
reinforcement within effective flange widths, boundary
elements, and the wall web shall be considered effective.
The effects of openings shall be considered.
=== 18.10.5.2 Unless a more detailed analysis is performed,
effective flange widths of flanged sections shall extend from
the face of the web a distance equal to the lesser of one-half
the distance to an adjacent wall web and 25 percent of the
total wall height above the section under consideration.
== R18.10.5 Design for flexure and axial force
=== R18.10.5.1 Flexural strength of a wall or wall segment
is determined according to procedures commonly used for
columns. Strength should be determined considering the
applied axial and lateral forces. Reinforcement concentrated
in boundary elements and distributed in flanges and webs
should be included in the strength calculations based on a
strain compatibility analysis. The foundation supporting the
wall should be designed to resist the wall boundary and web
forces. For walls with openings, the influence of the opening
or openings on flexural and shear strengths is to be considered
and a load path around the opening or openings should
be verified. Capacity-design concepts and the strut-and-tie
method may be useful for this purpose (Taylor et al. 1998).
=== R18.10.5.2 Where wall sections intersect to form L-,
T-, C-, or other cross-sectional shapes, the influence of the
flange on the behavior of the wall should be considered by
selecting appropriate flange widths. Tests (Wallace 1996)
show that effective flange width increases with increasing
drift level and the effectiveness of a flange in compression
differs from that for a flange in tension. The value used for
the effective compression flange width has little effect on
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18 Seismic
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=== R18.10.5.2 continuation
the strength and deformation capacity of the wall; therefore,
to simplify design, a single value of effective flange width
based on an estimate of the effective tension flange width is
used in both tension and compression.
== 18.10.6 Boundary elements of special structural walls
=== 18.10.6.1 The need for special boundary elements at the
edges of structural walls shall be evaluated in accordance
with 18.10.6.2 or 18.10.6.3. The requirements of 18.10.6.4
and 18.10.6.5 shall also be satisfied.
== R18.10.6 Boundary elements of special structural walls
=== R18.10.6.1 Two design approaches for evaluating
detailing requirements at wall boundaries are included in
18.10.6.1. Provision 18.10.6.2 allows the use of displacement-
based design of walls, in which the structural details
are determined directly on the basis of the expected lateral
displacements of the wall. The provisions of 18.10.6.3 are
similar to those of the 1995 Code, and have been retained
because they are conservative for assessing required transverse
reinforcement at wall boundaries for many walls.
Provisions 18.10.6.4 and 18.10.6.5 apply to structural walls
designed by either 18.10.6.2 or 18.10.6.3.
=== 18.10.6.2 Walls or wall piers with hwcs/ℓw ≥ 2.0 that are
effectively continuous from the base of structure to top of
wall and are designed to have a single critical section for
flexure and axial loads shall satisfy (a) and (b):
(a) Compression zones shall be reinforced with special
boundary elements where_
1.5δu/hwcs >= lw/(600c)
(18.10.6.2a)
and c corresponds to the largest neutral axis depth calculated
for the factored axial force and nominal moment
strength consistent with the direction of the design
displacement δu. Ratio δu/hwcs shall not be taken less than
0.005.
(b) If special boundary elements are required by (a), then
(i) and either (ii) or (iii) shall be satisfied.
(i) Special boundary element transverse reinforcement
shall extend vertically above and below the critical
section a least the greater of ℓw and Mu/4Vu, except as
permitted in 18.10.6.4(i).
(ii) b >= sqrt(0.025.c.lw)
(iii) δc/hwcs ≥ 1.5δu/hwcs, where:
δc/hwcs=(1/400)[4-1/50(lw/b)(c/b)-Ve/(0.66.sqrt(fc').Acv)]
(18.10.6.2b)
The value of δc/hwcs in Eq. (18.10.6.2b) need not be taken
less than 0.015.
=== R18.10.6.2 This section is based on the assumption that
inelastic response of the wall is dominated by flexural action
at a critical, yielding section. The wall should be proportioned
and reinforced so that the critical section occurs
where intended.
Equation (18.10.6.2a) follows from a displacementbased
approach (Moehle 1992; Wallace and Orakcal 2002).
The approach assumes that special boundary elements are
required to confine the concrete where the strain at the
extreme compression fiber of the wall exceeds a critical
value when the wall is displaced to 1.5 times the design
displacement. Consistent with a displacement-based design
approach, the design displacement in Eq. (18.10.6.2a) is
taken at the top of the wall, and the wall height is taken as
the height above the critical section. The multiplier of 1.5
on design displacement was added to Eq. (18.10.6.2) in the
2014 Code to produce detailing requirements more consistent
with the building code performance intent of a low probability
of collapse in Maximum Considered Earthquake level
shaking. The lower limit of 0.005 on the quantity δu/hwcs
requires special boundary elements if wall boundary longitudinal
reinforcement tensile strain does not reach approximately
twice the limit used to define tension-controlled
beam sections according to 21.2.2. The lower limit of 0.005
on the quantity δu/hwcs requires moderate wall deformation
capacity for stiff buildings.
The neutral axis depth c in Eq. (18.10.6.2) is the depth
calculated according to 22.2 corresponding to development
of nominal flexural strength of the wall when displaced in
the same direction as δu. The axial load is the factored axial
load that is consistent with the design load combination that
produces the design displacement δu.
The height of the special boundary element is based on
estimates of plastic hinge length and extends beyond the
zone over which yielding of tension reinforcement and
spalling of concrete are likely to occur.
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=== R18.10.6.2 continuation
Equation (18.10.6.2b) is based on the mean top-of-wall
drift capacity at 20 percent loss of lateral strength proposed
by Abdullah and Wallace (2019). The requirement that drift
capacity exceed 1.5 times the drift demand results in a low
probability of strength loss for the design earthquake. The
expression for b in (ii) is derived from Eq. (18.10.6.2b),
assuming values of Vu/(0.66Acv.sqrt(fc')) and δu/hwcs of approximately
1.0 and 0.015, respectively. If b varies over c, an
average or representative value of b should be used. For
example, at the flanged end of a wall, b should be taken equal
to the effective flange width defined in 18.10.5.2, unless c
extends into the web, then a weighted average should be
used for b. At the end of a wall without a flange, b should be
taken equal to the wall thickness. If the drift capacity does
not exceed the drift demand for a trial design, then changes
to the design are required to increase wall drift capacity,
reduces wall drift demand, or both, such that drift capacity
exceeds drift demand for each wall in a given building.
=== 18.10.6.3 Structural walls not designed in accordance with
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 load combinations including earthquake effects
E, exceeds 0.2fc′. The special boundary element shall be
permitted to be discontinued where the calculated compressive
stress is less than 0.15fc′. Stresses shall be calculated for
the factored loads using a linearly elastic model and gross
section properties. For walls with flanges, an effective flange
width as given in 18.10.5.2 shall be used.
=== R18.10.6.3 By this procedure, the wall is considered to
be acted on by gravity loads and the maximum shear and
moment induced by earthquake in a given direction. Under
this loading, the compressed boundary at the critical section
resists the tributary gravity load plus the compressive resultant
associated with the bending moment.
Recognizing that this loading condition may be repeated
many times during the strong motion, the concrete is to be
confined where the calculated compressive stresses exceed
a nominal critical value equal to 0.2fc′. The stress is to be
calculated for the factored forces on the section assuming
linear response of the gross concrete section. The compressive
stress of 0.2fc′ is used as an index value and does
not necessarily describe the actual state of stress that may
develop at the critical section under the influence of the
actual inertia forces for the anticipated earthquake intensity.
=== 18.10.6.4 If special boundary elements are required by
18.10.6.2 or 18.10.6.3, (a) through (k) shall be satisfied:
(a) The boundary element shall extend horizontally from
the extreme compression fiber a distance at least the
greater of c – 0.1ℓw and c/2, where c is the largest neutral
axis depth calculated for the factored axial force and
nominal moment strength consistent with δu.
(b) Width of the flexural compression zone, b, over the
horizontal distance calculated by 18.10.6.4(a), including
flange if present, shall be at least hu/16.
(c) For walls or wall piers with hw/ℓw ≥ 2.0 that are effectively
continuous from the base of structure to top of
wall, designed to have a single critical section for flexure
and axial loads, and with c/ℓw ≥ 3/8, width of the flexural
compression zone b over the length calculated in
18.10.6.4(a) shall be greater than or equal to 300 mm
(d) In flanged sections, the boundary element shall incl.
ude the effective flange width in compression and shall
extend at least 300 mm into the web.
=== R18.10.6.4 The horizontal dimension of the special
boundary element is intended to extend at least over the
length where the concrete compressive strain exceeds the
critical value. For flanged wall sections, including box
shapes, L-shapes, and C-shapes, the calculation to determine
the need for special boundary elements should include
a direction of lateral load consistent with the orthogonal
combinations defined in ASCE/SEI 7. The value of c/2 in
18.10.6.4(a) is to provide a minimum length of the special
boundary element. Good detailing practice is to arrange the
longitudinal reinforcement and the confinement reinforcement
such that all primary longitudinal reinforcement at the
wall boundary is supported by transverse reinforcement.
A slenderness limit is introduced into the 2014 edition
of this Code based on lateral instability failures of slender
wall boundaries observed in recent earthquakes and tests
(Wallace 2012; Wallace et al. 2012). For walls with large
cover, where spalling of cover concrete would lead to a
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18 Seismic
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=== 18.10.6.4 continuation
(e) The boundary element transverse reinforcement shall
satisfy 18.7.5.2(a) through (d) and 18.7.5.3, except the
transverse reinforcement spacing limit of 18.7.5.3(a)
shall be one-third of the least dimension of the boundary
element. The maximum vertical spacing of transverse
reinforcement in the boundary element shall also not
exceed that in Table 18.10.6.5(b) .
(f) Transverse reinforcement shall be arranged such that the
spacing hx between laterally supported longitudinal bars
around the perimeter of the boundary element shall not
exceed the lesser of 350 mm and two-thirds of the boundary
element thickness. Lateral support shall be provided by a
seismic hook of a crosstie or corner of a hoop. The length of
a hoop leg shall not exceed two times the boundary element
thickness, and adjacent hoops shall overlap at least the lesser
of 150 mm and two-thirds the boundary element thickness.
(g) The amount of transverse reinforcement shall be in
accordance with Table 18.10.6.4(g) .
Table 18.10.6.4(g)—Transverse reinforcement for
special boundary elements_
(h) Concrete within the thickness of the floor system at
the special boundary element location shall have specified
compressive strength at least 0.7 times fc′ of the wall.
(i) For a distance above and below the critical section
specified in 18.10.6.2(b), web vertical reinforcement shall
have lateral support provided by the corner of a hoop or
by a crosstie with seismic hooks at each end. Transverse
reinforcement shall have a vertical spacing not to exceed
300 mm and diameter satisfying 25.7.2.2.
(j) Where the critical section occurs at the wall base, the
boundary element transverse reinforcement at the wall
base shall extend into the support at least ℓd, in accordance
with 18.10.2.3, 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 300 mm into the footing, mat, or pile cap, unless a
greater extension is required by 18.13.2.4.
=== R18.10.6.4 continuation
significantly reduced section, increased boundary element
thickness should be considered.
A value of c/ℓw ≥ 3/8 is used to define a wall critical
section that is not tension-controlled according to 21.2.2. A
minimum wall thickness of 300 mm is imposed to reduce the
likelihood of lateral instability of the compression zone after
spalling of cover concrete.
Where flanges are highly stressed in compression, the
web-to-flange interface is likely to be highly stressed and
may sustain local crushing failure unless special boundary
element reinforcement extends into the web.
Required transverse reinforcement at wall boundaries
is based on column provisions. Expression (a) of
Table 18.10.6.4(g) was applied to wall special boundary elements
prior to the 1999 edition of this Code. It is reinstated in the
2014 edition of this Code due to concerns that expression
(b) of Table 18.10.6.4(g) by itself does not provide adequate
transverse reinforcement for thin walls where concrete
cover accounts for a significant portion of the wall thickness.
For wall special boundary elements having rectangular
cross section, Ag and Ach in expressions (a) and (c) in Table 18.10.6.4(g)
are defined as Ag = ℓbe.b and Ach = bc1.bc2, where
dimensions are shown in Fig. R18.10.6.4b . This considers
that concrete spalling is likely to occur only on the exposed
faces of the confined boundary element. Tests (Thomsen
and Wallace 2004) show that adequate performance can be
achieved using vertical spacing greater than that permitted
by 18.7.5.3(a). The limits on spacing between laterally
supported longitudinal bars are intended to provide more
uniform spacing of hoops and crossties for thin walls.
Configuration requirements for boundary element transverse
reinforcement and crossties for web longitudinal
reinforcement are summarized in Fig. R18.10.6.4a . A limit
is placed on the relative lengths of boundary element hoop
legs because tests (Segura and Wallace 2018; Welt et al.
2017; Arteta 2015) show that a single perimeter hoop with
supplemental crossties that have alternating 90-degree and
135-degree hooks are not as effective as overlapping hoops
and crossties with seismic hooks at both ends if ℓbe exceeds
approximately 2b.
These tests also show that loss of axial load-carrying
capacity of a wall can occur immediately following damage
to the wall boundary elements if web vertical reinforcement
within the plastic hinge region is not restrained. Use of web
crossties outside of boundary elements also results in a less
abrupt transition in transverse reinforcement used to provide
concrete confinement and restrain buckling of longitudinal
reinforcement, which addresses potential increases in the
neutral axis depth due to shear (diagonal compression) and
uncertainties in axial load.
Requirements for vertical extensions of boundary elements
are summarized in Fig. R18.10.6.4c (Moehle et al. 2011).
The horizontal reinforcement in a structural wall with low
shear-to-moment ratio resists shear through truss action,
with the horizontal bars acting like the stirrups in a beam.
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=== 18.10.6.4 continuation
(k) Horizontal reinforcement in the wall web shall extend
to within 150 mm of the end of the wall. Reinforcement
shall be anchored to develop fy within the confined core
of the boundary element using standard hooks or heads.
Where the confined boundary element has sufficient length
to develop the horizontal web reinforcement, and As.fy/s of
the horizontal web reinforcement does not exceed As.fyt/s
of the boundary element transverse reinforcement parallel
to the horizontal web reinforcement, it shall be permitted
to terminate the horizontal web reinforcement without a
standard hook or head.
=== R18.10.6.4 continuation
Thus, the horizontal bars provided for shear reinforcement
must be developed within the confined core of the boundary
element and extended as close to the end of the wall as cover
requirements and proximity of other reinforcement permit.
The requirement that the horizontal web reinforcement be
anchored within the confined core of the boundary element
and extended to within 150 mm from the end of the wall
applies to all horizontal bars whether straight, hooked, or
headed, as illustrated in Fig. R18.10.6.4c .
The requirements in 18.10.2.4 apply to the minimum
longitudinal reinforcement in the ends of walls, including
those with special boundary elements.
Fig. R18.10.6.4a—Configurations of boundary transverse reinforcement and web crossties.
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18 Seismic
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Fig. R18.10.6.4b—Development of wall horizontal reinforcement
in confined boundary element.
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Fig. R18.10.6.4c—Summary of boundary element requirements for special walls.
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PART 5: EARTHQUAKE RESISTANCE 329
18 Seismic
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=== 18.10.6.5 Where special boundary elements are not required
by 18.10.6.2 or 18.10.6.3, (a) and (b) shall be satisfied:
(a) Except where Vu in the plane of the wall is less than
0.083λ .sqrt(fc').Acv, 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 reinforcement.
(b) If the maximum longitudinal reinforcement ratio at the
wall boundary exceeds 2.8/fy, 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
vertical spacing of transverse reinforcement at the wall
boundary shall be in accordance with Table 18.10.6.5(b) .
Table 18.10.6.5(b)—Maximum vertical spacing of
transverse reinforcement at wall boundary
=== R18.10.6.5 Cyclic load reversals may lead to buckling
of boundary longitudinal reinforcement even in cases
where the demands on the boundary of the wall do not
require special boundary elements. For walls with moderate
amounts of boundary longitudinal reinforcement, ties are
required to inhibit buckling. The longitudinal reinforcement
ratio is intended to include only the reinforcement at
the wall boundary, as indicated in Fig. R18.10.6.5 . A greater
spacing of ties relative to 18.10.6.4(e) is allowed due to the
lower deformation demands on the walls. Requirements of
=== 18.10.6.5 apply over the entire wall height and are summarized
in Fig. R18.10.6.4c for cases where special boundary
elements are required (Moehle et al. 2011).
The addition of hooks or U-stirrups at the ends of horizontal
wall reinforcement provides anchorage so that the
reinforcement will be effective in resisting shear forces. It
will also tend to inhibit the buckling of the vertical edge
reinforcement. In walls with low in-plane shear, the development
of horizontal reinforcement is not necessary.
Limits on spacing of transverse reinforcement are intended
to prevent bar buckling until reversed cyclic strains extend
well into the inelastic range. To achieve similar performance
capability, smaller spacing is required for higher-strength
longitudinal reinforcement.
Fig. R18.10.6.5—Longitudinal reinforcement ratios for
typical wall boundary conditions.
== 18.10.7 Coupling beams
=== 18.10.7.1 Coupling beams with (ℓn/h) ≥ 4 shall satisfy the
requirements of 18.6, with the wall boundary interpreted as
being a column. The provisions of 18.6.2.1(b) and (c) need
not be satisfied if it can be shown by analysis that the beam
has adequate lateral stability.
=== 18.10.7.2 Coupling beams with (ℓn/h) < 2 and with Vu ≥
0.33λ.sqrt(fc').Acw shall be reinforced with two intersecting groups
of diagonally placed bars symmetrical about the midspan,
unless it can be shown that loss of stiffness and strength of the
== R18.10.7 Coupling beams
Coupling beams connecting structural walls can provide
stiffness and energy dissipation. In many cases, geometric
limits result in coupling beams that are deep in relation to
their clear span. Deep coupling beams may be controlled by
shear and may be susceptible to strength and stiffness deterioration
under earthquake loading. Test results (Paulay and
Binney 1974; Barney et al. 1980) have shown that confined
diagonal reinforcement provides adequate resistance in deep
coupling beams.
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=== 18.10.7.2 Continuation
coupling beams will not impair the vertical load-carrying ability
of the structure, the egress from the structure, or the integrity of
nonstructural components and their connections to the structure.
=== 18.10.7.3 Coupling beams not governed by 18.10.7.1 or
=== 18.10.7.2 shall be permitted to be reinforced either with two
intersecting groups of diagonally placed bars symmetrical
about the midspan or according to 18.6.3 through 18.6.5,
with the wall boundary interpreted as being a column.
=== 18.10.7.4 Coupling beams reinforced with two intersecting
groups of diagonally placed bars symmetrical about
the midspan shall satisfy (a), (b), and either (c) or (d), and
the requirements of 9.9 need not be satisfied:
(a) Vn shall be calculated by
Vn = 2Avd.fysinα ≤ 0.83.sqrt(fc')Acw (18.10.7.4)
where α is the angle between the diagonal bars and the
longitudinal axis of the coupling beam.
(b) Each group of diagonal bars shall consist of a minimum
of four bars provided in two or more layers.
(c) Each group of diagonal bars shall be enclosed by rectilinear
transverse reinforcement having out-to-out dimensions
of at least bw/2 in the direction parallel to bw and bw/5
along the other sides, where bw is the web width of the
coupling beam. The transverse reinforcement shall be in
accordance with 18.7.5.2(a) through (e), with Ash not less
than the greater of (i) and (ii):
(i) 0.09 sbc fc'/fy
(ii) 0.3 sbc ( Ag/Ach - 1 ).fc'/fyt
For the purpose of calculating Ag, the concrete cover
in 20.5.1 shall be assumed on all four sides of each
group of diagonal bars. The transverse reinforcement
shall have spacing measured parallel to the diagonal
bars satisfying 18.7.5.3(d) and not exceeding 6db of
the smallest diagonal bars, and shall have spacing of
crossties or legs of hoops measured perpendicular to the
diagonal bars not exceeding 350 mm. The transverse
reinforcement shall continue through the intersection of
the diagonal bars. At the intersection, it is permitted to
modify the arrangement of the transverse reinforcement
provided the spacing and volume ratio requirements are
satisfied. Additional longitudinal and transverse reinforcement
shall be distributed around the beam perimeter
with total area in each direction of at least 0.002bws
and spacing not exceeding 300 mm.
(d) Transverse reinforcement shall be provided for the
entire beam cross section in accordance with 18.7.5.2(a)
through (e) with Ash not less than the greater of (i) and (ii):
== R18.10.7 Continuation
Experiments show that diagonally oriented reinforcement
is effective only if the bars are placed with a large inclination.
Therefore, diagonally reinforced coupling beams are
restricted to beams having aspect ratio ℓn/h < 4. The 2008
edition of this Code was changed to clarify that coupling
beams of intermediate aspect ratio can be reinforced
according to 18.6.3 through 18.6.5.
Diagonal bars should be placed approximately symmetrically
in the beam cross section, in two or more layers. The
diagonally placed bars are intended to provide the entire
shear and corresponding moment strength of the beam.
Designs deriving their moment strength from combinations
of diagonal and longitudinal bars are not covered by these
provisions.
Two confinement options are described. According to
18.10.7.4(c), each diagonal element consists of a cage of
longitudinal and transverse reinforcement, as shown in
Fig. R18.10.7a . Each cage contains at least four diagonal
bars and confines a concrete core. The requirement on side
dimensions of the cage and its core is to provide adequate
stability to the cross section when the bars are loaded beyond
yielding. The minimum dimensions and required reinforcement
clearances may control the wall width. Revisions
were made in the 2008 Code to relax spacing of transverse
reinforcement confining the diagonal bars, to clarify that
confinement is required at the intersection of the diagonals,
and to simplify design of the longitudinal and transverse
reinforcement around the beam perimeter; beams with these
new details are expected to perform acceptably. The expressions
for transverse reinforcement Ash are based on ensuring
compression capacity of an equivalent column section is
maintained after spalling of cover concrete.
Section 18.10.7.4(d) describes a second option for
confinement of the diagonals introduced in the 2008 Code
(refer to Fig. R18.10.7b ). This second option is to confine
the entire beam cross section instead of confining the individual
diagonals. This option can considerably simplify field
placement of hoops, which can otherwise be especially challenging
where diagonal bars intersect each other or enter the
wall boundary.
For coupling beams not used as part of the lateral-force-resisting
system, the requirements for diagonal reinforcement
may be waived.
Test results (Barney et al. 1980) demonstrate that beams
reinforced as described in 18.10.7 have adequate ductility
at shear forces exceeding 0.83  sqrt(fc') bwd. Consequently, the
use of a limit of 0.83 sqrt(fc') Acw provides an acceptable upper
limit.
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PART 5: EARTHQUAKE RESISTANCE 331
18 Seismic
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=== 18.10.7.4 Continuation
(i) 0.09 sbc fc'/fyt
(ii) 0.3 sbc (Ag/Ach - 1) fc'/fyt
Longitudinal spacing of transverse reinforcement
shall not exceed the lesser of 150 mm and 6db of the
smallest diagonal bars. Spacing of crossties or legs of
hoops both vertically and horizontally in the plane of
the beam cross section shall not exceed 200 mm. Each
crosstie and each hoop leg shall engage a longitudinal
bar of equal or greater diameter. It shall be permitted to
configure hoops as specified in 18.6.4.3.
Fig. R18.10.7a—Confinement of individual diagonals in coupling beams with diagonally oriented reinforcement. Wall boundary
reinforcement shown on one side only for clarity.
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332 ACI 318-19: BUILDING CODE REQUIREMENTS FOR STRUCTURAL CONCRETE
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Fig. R18.10.7b—Full confinement of diagonally reinforced concrete beam section in coupling beams with diagonally oriented
reinforcement. Wall boundary reinforcement shown on one side only for clarity.
== 18.10.8 Wall piers
=== 18.10.8.1 Wall piers shall satisfy the special moment frame
requirements for columns of 18.7.4, 18.7.5, and 18.7.6, with
joint faces taken as the top and bottom of the clear height of
the wall pier. Alternatively, wall piers with (ℓw/bw) > 2.5 shall
satisfy (a) through (f):
(a) Design shear force shall be calculated in accordance
with 18.7.6.1 with joint faces taken as the top and bottom
of the clear height of the wall pier. If the general building
code includes provisions to account for overstrength of
the seismic-force-resisting system, the design shear force
== R18.10.8 Wall piers
Door and window placements in structural walls sometimes
lead to narrow vertical wall segments that are considered
to be wall piers. The dimensions defining wall piers are
given in Chapter 2. Shear failures of wall piers have been
observed in previous earthquakes. The intent of this section
is to provide sufficient shear strength to wall piers such that
inelastic response, if it occurs, will be primarily in flexure.
The provisions apply to wall piers designated as part of the
seismic-force-resisting system. Provisions for wall piers not
designated as part of the seismic-force-resisting system are
given in 18.14. The effect of all vertical wall segments on the
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PART 5: EARTHQUAKE RESISTANCE 333
18 Seismic
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== 18.10.8 Continuation
need not exceed Ωo times the factored shear calculated by
analysis of the structure for earthquake load effects.
(b) Vn and distributed shear reinforcement shall satisfy
18.10.4.
(c) Transverse reinforcement shall be hoops except it shall
be permitted to use single-leg horizontal reinforcement
parallel to ℓw where only one curtain of distributed shear
reinforcement is provided. Single-leg horizontal reinforcement
shall have 180-degree bends at each end that
engage wall pier boundary longitudinal reinforcement.
(d) Vertical spacing of transverse reinforcement shall not
exceed 150 mm_
(e) Transverse reinforcement shall extend at least 300 mm
above and below the clear height of the wall pier.
(f) Special boundary elements shall be provided if required
by 18.10.6.3.
=== 18.10.8.2 For wall piers at the edge of a wall, horizontal
reinforcement shall be provided in adjacent wall segments
above and below the wall pier and be designed to transfer
the design shear force from the wall pier into the adjacent
wall segments.
== R18.10.8 Continuation
response of the structural system, whether designated as part
of the seismic-force-resisting system or not, should be considered
as required by 18.2.2. Wall piers having (ℓw/bw) ≤ 2.5
behave essentially as columns. Provision 18.10.8.1 requires
that such members satisfy reinforcement and shear strength
requirements of 18.7.4 through 18.7.6. Alternative provisions
are provided for wall piers having (ℓw/bw) > 2.5.
The design shear force determined according to 18.7.6.1
may be unrealistically large in some cases. As an alternative,
=== 18.10.8.1(a) permits the design shear force to be determined
using factored load combinations in which the earthquake
effect has been amplified to account for system overstrength.
Documents such as the NEHRP provisions (FEMA P749),
ASCE/SEI 7, and the 2018 IBC represent the amplified
earthquake effect using the factor Ωo.
Section 18.10.8.2 addresses wall piers at the edge of a
wall. Under in-plane shear, inclined cracks can propagate
into segments of the wall directly above and below the
wall pier. Unless there is sufficient reinforcement in the
adjacent wall segments, shear failure within the adjacent
wall segments can occur. The length of embedment of the
provided reinforcement into the adjacent wall segments
should be determined considering both development length
requirements and shear strength of the wall segments (refer
to Fig. R18.10.8 ).
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Fig. R18.10.8—Required horizontal reinforcement in wall
segments above and below wall piers at the edge of a wall.
== 18.10.9 Ductile coupled walls
=== 18.10.9.1 Ductile coupled walls shall satisfy the requirements
of this section.
=== 18.10.9.2 Individual walls shall satisfy hwcs/ℓw ≥ 2 and the
applicable provisions of 18.10 for special structural walls.
=== 18.10.9.3 Coupling beams shall satisfy 18.10.7 and (a)
through (c) in the direction considered.
(a) Coupling beams shall have ℓn/h ≥ 2 at all levels of the
building.
(b) All coupling beams at a floor level shall have ℓn/h ≤ 5
in at least 90 percent of the levels of the building.
(c) The requirements of 18.10.2.5 shall be satisfied at both
ends of all coupling beams.
== R18.10.9 Ductile coupled walls
The aspect ratio limits and development length requirements
for ductile coupled walls are intended to induce an
energy dissipation mechanism associated with inelastic
deformation reversal of coupling beams. Wall stiffness and
strength at each end of coupling beams should be sufficient
to develop this intended behavior.
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PART 5: EARTHQUAKE RESISTANCE 335
18 Seismic
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== 18.10.10 Construction joints
=== 18.10.10.1 Construction joints in structural walls shall be
specified according to 26.5.6, and contact surfaces shall be
roughened consistent with condition (b) of Table 22.9.4.2 .
== 18.10.11 Discontinuous walls
=== 18.10.11.1 Columns supporting discontinuous structural
walls shall be reinforced in accordance with 18.7.5.6.
[ Lanjut Ke 18.11—Special structural walls constructed
using precast concrete ... ]

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