= 18. CHAPTER 18 — EARTHQUAKE-RESISTANT STRUCTURES
= 18.7 — Columns of special moment frames
== 18.7.1 Scope
=== 18.7.1.1 This section shall apply to columns of special
moment frames that form part of the seismic-force-resisting
system and are proportioned primarily to resist flexure,
shear, and axial forces.
== 18.7.2 Dimensional limits
=== 18.7.2.1 Columns shall satisfy (a) and (b):
(a) The shortest cross-sectional dimension, measured on a
straight line passing through the geometric centroid, shall
be at least 300 mm;
(b) The ratio of the shortest cross-sectional dimension to
the perpendicular dimension shall be at least 0.4.
== 18.7.3 Minimum flexural strength of columns
=== 18.7.3.1 Columns shall satisfy 18.7.3.2 or 18.7.3.3, except
at connections where the column is discontinuous above the
connection and the column factored axial compressive force
Pu under load combinations including earthquake effect, E,
are less than Ag fc′/10.
=== 18.7.3.2 The flexural strengths of the columns shall satisfy
ΣMnc ≥ (6/5)ΣMnb (18.7.3.2)
ΣMnc is sum of nominal flexural strengths of columns
framing into the joint, evaluated at the faces of the joint.
Column flexural strength shall be calculated for the factored
axial force, consistent with the direction of the lateral forces
considered, resulting in the lowest flexural strength.
ΣMnb is sum of nominal flexural strengths of the beams
framing into the joint, evaluated at the faces of the joint.
In T-beam construction, where the slab is in tension under
moments at the face of the joint, slab reinforcement within
an effective slab width defined in accordance with 6.3.2 shall
be assumed to contribute to Mnb if the slab reinforcement is
developed at the critical section for flexure.
Flexural strengths shall be summed such that the column
moments oppose the beam moments. Equation (18.7.3.2)
shall be satisfied for beam moments acting in both directions
in the vertical plane of the frame considered.
=== 18.7.3.3 If 18.7.3.2 is not satisfied at a joint, the lateral
strength and stiffness of the columns framing into that joint
shall be ignored when calculating strength and stiffness of
the structure. These columns shall conform to 18.14.
= R18.7 — Columns of special moment frames
== R18.7.1 Scope
This section applies to columns of special moment frames
regardless of the magnitude of axial force. Before 2014, the
Code permitted columns with low levels of axial stress to be
detailed as beams.
== R18.7.2 Dimensional limits
The geometric constraints in this provision follow from
previous practice (Seismology Committee of SEAOC 1996).
== R18.7.3 Minimum flexural strength of columns
The intent of 18.7.3.2 is to reduce the likelihood of yielding
in columns that are considered as part of the seismic-forceresisting
system. If columns are not stronger than beams
framing into a joint, there is increased likelihood of inelastic ...
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PART 5: EARTHQUAKE RESISTANCE 305
18 Seismic
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== R18.7.3 Continuation
action. In the worst case of weak columns, flexural yielding
can occur at both ends of all columns in a given story,
resulting in a column failure mechanism that can lead to
collapse. Connections with discontinuous columns above the
connection, such as roof-level connections, are exempted if
the column axial load is low, because special moment frame
columns with low axial stress are inherently ductile and
column yielding at such levels is unlikely to create a column
failure mechanism that can lead to collapse.
In 18.7.3.2, the nominal strengths of the beams and
columns are calculated at the joint faces, and those strengths
are compared directly using Eq. (18.7.3.2). The 1995 and
earlier Codes required design strengths to be compared at
the center of the joint, which typically produced similar
results but with added calculation effort.
In determining the nominal moment strength of a beam
section in negative bending (top in tension), longitudinal
reinforcement contained within an effective flange width of a
top slab that acts monolithically with the beam increases the
beam strength. French and Moehle (1991), on beam-column
subassemblies under lateral loading, indicates that using the
effective flange widths defined in 6.3.2 gives reasonable
estimates of beam negative moment strengths of interior
connections at story displacements approaching 2 percent of
story height. This effective width is conservative where the
slab terminates in a weak spandrel.
If 18.7.3.2 cannot be satisfied at a joint, 18.7.3.3 requires
that any positive contribution of the column or columns
involved to the lateral strength and stiffness of the structure
is to be ignored. Negative contributions of the column or
columns should not be ignored. For example, ignoring the
stiffness of the columns ought not to be used as a justification
for reducing the design base shear. If inclusion of those
columns in the analytical model of the building results in an
increase in torsional effects, the increase should be considered
as required by the general building code. Furthermore,
the column must be provided with transverse reinforcement
to increase its resistance to shear and axial forces.
== 18.7.4 Longitudinal reinforcement
=== 18.7.4.1 Area of longitudinal reinforcement, Ast, shall be
at least 0.01Ag and shall not exceed 0.06Ag.
=== 18.7.4.2 In columns with circular hoops, there shall be at
least six longitudinal bars.
== R18.7.4 Longitudinal reinforcement
The lower limit of the area of longitudinal reinforcement
is to control time-dependent deformations and to have the
yield moment exceed the cracking moment. The upper limit
of the area reflects concern for reinforcement congestion,
load transfer from floor elements to column (especially in
low-rise construction) and the development of high shear
stresses.
Spalling of the shell concrete, which is likely to occur
near the ends of the column in frames of typical configuration,
makes lap splices in these locations vulnerable. If lap
splices are to be used at all, they should be located near the
midheight where stress reversal is likely to be limited to a
smaller stress range than at locations near the joints. Transverse
reinforcement is required along the lap-splice length ...
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== R18.7.4 Continuation
because of the uncertainty in moment distributions along the
height and the need for confinement of lap splices subjected
to stress reversals (Sivakumar et al. 1983).
=== 18.7.4.3 Over column clear height, longitudinal reinforcement
shall be selected such that 1.25ℓd ≤ ℓu/2.
=== R18.7.4.3 Bond splitting failure along longitudinal bars
within the clear column height may occur under earthquake
demands (Ichinose 1995; Sokoli and Ghannoum 2016).
Splitting can be controlled by restricting longitudinal bar
size, increasing the amount of transverse reinforcement, or
increasing concrete strength, all of which reduce the development
length of longitudinal bars (ℓd) over column clear
height (ℓu). Increasing the ratio of column-to-beam moment
strength at joints can reduce the inelastic demands on longitudinal
bars in columns under earthquake demands.
=== 18.7.4.4 Mechanical splices shall conform to 18.2.7 and
welded splices shall conform to 18.2.8. Lap splices shall be
permitted only within the center half of the member length,
shall be designed as tension lap splices, and shall be enclosed
within transverse reinforcement in accordance with 18.7.5.2
and 18.7.5.3.
== 18.7.5 Transverse reinforcement
=== 18.7.5.1 Transverse reinforcement required in 18.7.5.2
through 18.7.5.4 shall be provided over a length ℓo from each
joint face and on both sides of any section where flexural
yielding is likely to occur as a result of lateral displacements
beyond the elastic range of behavior. Length ℓo shall be at
least the greatest of (a) through (c):
(a) The depth of the column at the joint face or at the
section where flexural yielding is likely to occur
(b) One-sixth of the clear span of the column
(c) 450 mm
=== 18.7.5.2 Transverse reinforcement shall be in accordance
with (a) through (f):
(a) Transverse reinforcement shall comprise either single
or overlapping spirals, circular hoops, or single or overlapping
rectilinear hoops with or without crossties.
(b) Bends of rectilinear hoops and crossties shall engage
peripheral longitudinal reinforcing bars.
(c) Crossties of the same or smaller bar size as the hoops
shall be permitted, subject to the limitation of 25.7.2.2.
Consecutive crossties shall be alternated end for end along
the longitudinal reinforcement and around the perimeter
of the cross section.
(d) Where rectilinear hoops or crossties are used, they
shall provide lateral support to longitudinal reinforcement
in accordance with 25.7.2.2 and 25.7.2.3.
(e) Reinforcement shall be arranged such that the spacing
hx of longitudinal bars laterally supported by the corner of
a crosstie or hoop leg shall not exceed 350 mm around the
perimeter of the column.
(f) Where Pu > 0.3Ag fc′ or fc′ > 70 MPa in columns with
rectilinear hoops, every longitudinal bar or bundle of bars
around the perimeter of the column core shall have lateral
support provided by the corner of a hoop or by a seismic
hook, and the value of hx shall not exceed 200 mm. Pu
shall be the largest value in compression consistent with
factored load combinations including E.
== R18.7.5 Transverse reinforcement
This section is concerned with confining the concrete and
providing lateral support to the longitudinal reinforcement.
=== R18.7.5.1 This section stipulates a minimum length over
which to provide closely-spaced transverse reinforcement at
the column ends, where flexural yielding normally occurs.
Research results indicate that the length should be increased
by 50 percent or more in locations, such as the base of a
building, where axial loads and flexural demands may be
especially high (Watson et al. 1994).
=== R18.7.5.2 Sections 18.7.5.2 and 18.7.5.3 provide requirements
for configuration of transverse reinforcement for
columns and joints of special moment frames. Figure
=== R18.7.5.2 shows an example of transverse reinforcement
provided by one hoop and three crossties. Crossties with
a 90-degree hook are not as effective as either crossties
with 135-degree hooks or hoops in providing confinement.
For lower values of Pu/Ag fc′ and lower concrete compressive
strengths, crossties with 90-degree hooks are adequate
if the ends are alternated along the length and around the
perimeter of the column. For higher values of Pu/Ag fc′, for
which compression-controlled behavior is expected, and for
higher compressive strengths, for which behavior tends to be
more brittle, the improved confinement provided by having
corners of hoops or seismic hooks supporting all longitu- ...
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PART 5: EARTHQUAKE RESISTANCE 307
18 Seismic
No further reproduction or distribution is permitted.
=== R18.7.5.2 Continuation
dinal bars is important to achieving intended performance.
Where these conditions apply, crossties with seismic hooks
at both ends are required. The 200 mm limit on hx is also
intended to improve performance under these critical conditions.
For bundled bars, bends or hooks of hoops and crossties
need to enclose the bundle, and longer extensions on
hooks should be considered. Column axial load Pu should
reflect factored compressive demands from both earthquake
and gravity loads.
In past editions of the Code, the requirements for transverse
reinforcement in columns, walls, beam-column joints, and
diagonally reinforced coupling beams referred to the same
equations. In the 2014 edition of the Code, the equations and
detailing requirements differ among the member types based
on consideration of their loadings, deformations, and performance
requirements. Additionally, hx previously referred to
the distance between legs of hoops or crossties. In the 2014
edition of the Code, hx refers to the distance between longitudinal
bars supported by those hoops or crossties.
Fig. R18.7.5.2—Example of transverse reinforcement in
columns.
=== 18.7.5.3 Spacing of transverse reinforcement shall not
exceed the least of (a) through (d):
(a) One-fourth of the minimum column dimension
(b) For Grade 420, 6db of the smallest longitudinal bar
(c) For Grade 550, 5db of the smallest longitudinal bar
(d) so, as calculated by:
so = 100 + ( (350-hx)/3 )
(18.7.5.3)
The value of so from Eq. (18.7.5.3) shall not exceed 150
mm and need not be taken less than 100 mm.
=== 18.7.5.4 Amount of transverse reinforcement shall be in
accordance with Table 18.7.5.4 .
The concrete strength factor kf and confinement effectiveness
factor kn are calculated according to Eq. (18.7.5.4a) and
(18.7.5.4b).
(a) kf = fc'/175 + 0.6 >= 1.0; (18.7.5.4a)
(b) kn = nl / (nl - 2); (18.7.5.4b)
where nl is the number of longitudinal bars or bar bundles
around the perimeter of a column core with rectilinear hoops
that are laterally supported by the corner of hoops or by
seismic hooks.
Table 18.7.5.4—Transverse reinforcement for
columns of special moment frames_
=== R18.7.5.3 The requirement that spacing not exceed onefourth
of the minimum member dimension or 150 mm is for
concrete confinement. If the maximum spacing of crossties or
legs of overlapping hoops within the section is less than 350
mm, then the 100 mm limit can be increased as permitted by
Eq. (18.7.5.3). The spacing limit as a function of the longitudinal
bar diameter is intended to provide adequate longitudinal
bar restraint to control buckling after spalling.
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308 ACI 318-19: BUILDING CODE REQUIREMENTS FOR STRUCTURAL CONCRETE
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=== R18.7.5.4 The effect of helical (spiral) reinforcement and
adequately configured rectilinear hoop reinforcement on
deformation capacity of columns is well established (Sakai
and Sheikh 1989). Expressions (a), (b), (d), and (e) in
Table 18.7.5.4 have historically been used in ACI 318 to calculate
the required confinement reinforcement to ensure that
spalling of shell concrete does not result in a loss of column
axial load strength. Expressions (c) and (f) were developed
from a review of column test data (Elwood et al. 2009) and
are intended to result in columns capable of sustaining a drift
ratio of 0.03 with limited strength degradation. Expressions
(c) and (f) are triggered for axial load greater than 0.3Ag fc′,
which corresponds approximately to the onset of compression-
controlled behavior for symmetrically reinforced
columns. The kn term (Paultre and Légeron 2008) decreases
the required confinement for columns with closely spaced,
laterally supported longitudinal reinforcement because such
columns are more effectively confined than columns with
more widely spaced longitudinal reinforcement. The kf term
increases the required confinement for columns with fc′ > 70
MPa because such columns can experience brittle failure if
not well confined. Concrete strengths greater than 100 MPa
should be used with caution given the limited test data for
such columns. The concrete strength used to determine the
confinement reinforcement is required to be the same as that
specified in the construction documents.
Expressions (a), (b), and (c) in Table 18.7.5.4 are to be
satisfied in both cross-sectional directions of the rectangular
core. For each direction, bc is the core dimension perpendicular
to the tie legs that constitute Ash, as shown in Fig. R18.7.5.2 .
Research results indicate that high strength reinforcement
can be used effectively as confinement reinforcement.
Section 20.2.2.4 permits a value of fyt as high as 690 MPa to
be used in Table 18.7.5.4.
=== 18.7.5.5 Beyond the length ℓo given in 18.7.5.1, the column
shall contain spiral reinforcement satisfying 25.7.3 or hoop
and crosstie reinforcement satisfying 25.7.2 and 25.7.4 with
spacing s not exceeding the least of 150 mm, 6db of the smallest
Grade 420 longitudinal column bar, and 5db of the smallest
Grade 550 longitudinal column bar, unless a greater amount
of transverse reinforcement is required by 18.7.4.4 or 18.7.6.
=== R18.7.5.5 This provision is intended to provide reasonable
protection to the midheight of columns outside the length
ℓo. Observations after earthquakes have shown significant
damage to columns in this region, and the minimum hoops
or spirals required should provide more uniform strength of
the column along its length.
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PART 5: EARTHQUAKE RESISTANCE 309
18 Seismic
No further reproduction or distribution is permitted.
=== 18.7.5.6 Columns supporting reactions from discontinued
stiff members, such as walls, shall satisfy (a) and (b):
(a) Transverse reinforcement required by 18.7.5.2 through
18.7.5.4 shall be provided over the full height at all levels
beneath the discontinuity if the factored axial compressive
force in these columns, related to earthquake effect,
exceeds Ag fc′/10. Where design forces have been magnified
to account for the overstrength of the vertical elements
of the seismic-force-resisting system, the limit of Ag fc′/10
shall be increased to Ag fc′/4.
(b) Transverse reinforcement shall extend into the discontinued
member at least ℓd of the largest longitudinal
column bar, where ℓd is in accordance with 18.8.5. Where
the lower end of the column terminates on a wall, the
required transverse reinforcement shall extend into the
wall at least ℓd of the largest longitudinal column bar at the
point of termination. Where the column terminates on a
footing or mat, the required transverse reinforcement shall
extend at least 300 mm into the footing or mat.
=== R18.7.5.6 Columns supporting discontinued stiff
members, such as walls or trusses, may develop considerable
inelastic response. Therefore, it is required that these ...
columns have the specified reinforcement throughout their
length. This covers all columns beneath the level at which
the stiff member has been discontinued, unless the factored
forces corresponding to earthquake effect are low. Refer to
R18.12.7.6 for discussion of the overstrength factor Ωo.
=== 18.7.5.7 If the concrete cover outside the confining transverse
reinforcement required by 18.7.5.1, 18.7.5.5, and
18.7.5.6 exceeds 100 mm, additional transverse reinforcement
having cover not exceeding 100 mm and spacing not
exceeding 300 mm shall be provided.
=== R18.7.5.7 The unreinforced shell may spall as the column
deforms to resist earthquake effects. Separation of portions
of the shell from the core caused by local spalling creates a
falling hazard. The additional reinforcement is required to
reduce the risk of portions of the shell falling away from the
column.
== 18.7.6 Shear strength
=== 18.7.6.1 Design forces
==== 18.7.6.1.1 The design shear force Ve shall be calculated
from considering the maximum forces that can be generated
at the faces of the joints at each end of the column. These
joint forces shall be calculated using the maximum probable
flexural strengths, Mpr, at each end of the column associated
with the range of factored axial forces, Pu, acting on the
column. The column shears need not exceed those calculated
from joint strengths based on Mpr of the beams framing into
the joint. In no case shall Ve be less than the factored shear
calculated by analysis of the structure.
=== 18.7.6.2 Transverse reinforcement
==== 18.7.6.2.1 Transverse reinforcement over the lengths ℓo,
given in 18.7.5.1, shall be designed to resist shear assuming
Vc = 0 when both (a) and (b) occur:
(a) The earthquake-induced shear force, calculated in
accordance with 18.7.6.1, is at least one-half of the
maximum required shear strength within ℓo.
(b) The factored axial compressive force Pu including
earthquake effects is less than Ag fc′/20.
== R18.7.6 Shear strength
=== R18.7.6.1 Design forces
==== R18.7.6.1.1 The procedures of 18.6.5.1 also apply to
columns. Above the ground floor, the moment at a joint may
be limited by the flexural strength of the beams framing
into the joint. Where beams frame into opposite sides of
a joint, the combined strength is the sum of the negative
moment strength of the beam on one side of the joint and
the positive moment strength of the beam on the other side
of the joint. Moment strengths are to be determined using a
strength reduction factor of 1.0 and reinforcement with an
effective yield stress equal to at least 1.25fy. Distribution of
the combined moment strength of the beams to the columns
above and below the joint should be based on analysis.
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[ Lanjut Ke 18.8—Joints of special moment frames ... ]

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