ACI 318-19 Code Cases
A
CI has received written requests for clarification of
the intent or application of the provisions for special
structural walls as stated in ACI CODE-318-19:
Building Code Requirements for Structural Concrete and
Commentary. Requests were submitted by the Structural
Engineers Association of Washington (SEAW), Structural
Engineers Association of Northern California (SEAONC), and
Los Angeles Tall Buildings Structural Design Council
(LATBSDC). In response, ACI Committee 318, Structural
Concrete Building Code, has developed, balloted, and
approved three code cases to clarify the relevant Code
sections. The code cases are listed in the following text by
organizational submittal:
Code Case 318-19 Submitted by SEAW
Subject: Strength reduction factor, ϕ, for use with
Eq. (18.10.3.1)
Background: ACI 318-19, Section 21.2.4.1, notes that for
any member designed to resist earthquake-induced forces E, ϕ
for shear shall be 0.6 if the nominal shear strength of the
member is less than the shear corresponding to the
development of the nominal moment strength of the member.
Otherwise, ϕ for shear shall be 0.75 per Table 21.2.1 item (b).
Section 18.10.3.1 requires that the design shear force Ve for
shear walls shall be computed as the shear demand Vu,
amplified by the overstrength factor Ωv, as computed per
Table 18.10.3.1.2. Per this table, for walls with aspect ratios
greater than 1.5, Ωv is taken as the larger of either 1.5 or the
ratio of the probable moment strength to the moment demand.
This calculation effectively results in the wall being designed
such that the nominal shear strength of the member exceeds
the shear corresponding to the development of the nominal
moment strength of the member, satisfying the requirement of
Section 21.2.4.1.
Section 18.10.3.1 also provides an upper limit for the
amplification factor on Vu as 3.0 per Eq. (18.10.3.1).
Questions:
1. This code case requests clarification that whenever a
value of Ωv is computed exceeding 1.0, including when this
upper limit of 3.0 is used, that ϕ for shear may be taken as
0.75 as the intent of shear amplification per Section 21.2.4.1
has been satisfied.
2. Similarly, Section 18.10.8.1(a) requires that qualifying
wall piers shall have their design shear force amplified, but
this value need not exceed Ω0, which is the ASCE 7-161
overstrength factor and different from Ωv from Section
18.10.3.1. The intent of the amplification factor is the same,
namely that the walls can remain elastic in shear. This code
case also requests clarification that ϕ for shear may be taken
as 0.75 for wall piers when the shear demands have been
amplified by Ω0, and that both Ω0 and Ωv do not need to be
applied to Ve at the same time.
Interpretations:
1. The intent of Section 21.2.4.1 is that, if Ωv ≥ 1.5, f for
shear shall be permitted to be taken equal to 0.75 at the critical
section and at all sections.
2. According to Section 18.10.8.1, wall piers are required
to be designed either for the shear corresponding to the
development of Mpr, at the top and bottom of the wall pier
(capacity design approach), accounting for the axial force in
the pier, or for the shear from structural analysis amplified by
W0. For either case, f = 0.75 is intended, and Ωv need not be
applied in addition to Ω0.
Subject: Clarification about calculation methods for Mpr
and Mu
Background: For walls with a height-to-length ratio
greater than 1.5, the overstrength factor Ωv is calculated as the
greater of Mpr /Mu or 1.5, where Mpr is the probable flexural
strength of the member and Mu is the factored moment at the
section. Because the calculation of the axial-flexural strength
for a wall section can be complicated, additional clarification
about these parameters would be helpful.
Questions:
1. For ductile coupled walls, or special structural walls
otherwise separated into separate design segments by coupling
beams, clarify if Mpr and Mu are intended to reference the
individual design segments of the wall, or the overall wall as a
whole. Note that for an overall wall as a whole, separated by
coupling beams, the strain in the concrete and nonprestressed
reinforcement is not proportional to the distance from the
neutral axis as required by ACI 318-19, Section 22.2.1.2.
2. Please clarify the load combinations and loading
conditions intended to be used for the calculation of Mpr and
Mu. Due to the large number of load combinations, many
values of Mpr and Mu are considered during the design of a
special structural wall, and a typical design would have
calculated ratios that don’t control the design of the section
that exceed 3 or more. As a suggestion, should it be clarified
that Mu be calculated using the load combination of ACI
318-19, Eq. (5.3.1e) for the load combination with the
maximum seismic moment?
3. Is the calculation of Mpr using the critical capacity method
acceptable? The critical capacity method minimizes the
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where the seismic flexural demand is largely an axial behavior.
Interpretations:
1. The intent of Section 18.10.3.1.2 is to treat structural
walls in coupled wall systems as individual walls when
determining Mpr and Mu at critical sections for shear
amplification requirements.
2. The intent of Table 18.10.3.1.2 footnote [1] is to only
use load combinations that include earthquake effect E.
3. ACI 318-19, Section 18.10.3.1.2, does not specify which
method shall be used; the licensed design professional may
exercise judgment in using any reasonable approach.
Fig. 1: Edited schematic figure of critical capacity method taken from
spColumn v7.00 manual
distance between the ultimate load point and the point on the
capacity curve (Fig. 1). Use of this method would more
accurately represent the available overstrength in coupled walls
where axial forces increase together with seismic moments, or
Subject: Use of the redundancy factor when calculating
amplified forces
Background: ASCE 7-16 requires the use of load
combinations, including an earthquake force multiplied by an
overstrength factor Ω0 to approximate the maximum seismic
load for the design of critical elements. ASCE 7-16, Section
12.3.4.1, states that the redundancy factor ρ is intended to be
1.0 for load combinations that include this overstrength factor.
The last sentence of Commentary Section R18.10.3.1
states, “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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Question:
1. Please clarify this commentary sentence. Is the intent of
this commentary that the redundancy factor ρ per ASCE 7-16
is allowed to be 1.0 when using Eq. (18.10.3.1), similar to the
design of critical elements in other structural systems?
Interpretation:
1. The intent of Section 18.10.3.1 is that, where a
redundancy factor of 1.3 is applied according to ASCE 7-16,
Section 12.3.4, Ve, due to lateral forces, need not exceed three
times the factored shear obtained from elastic analysis of the
structure under code-prescribed seismic forces with a
redundancy factor of 1.0.
Code Case 318-19 Submitted by SEAONC
Subject: Use of mechanical splices for Grade 80 in
structural walls
Background: Per Section 18.2.7.2 (Fig. 2), Type 2
mechanical splices for Grade 80 are not permitted within 2D
from a critical section of the wall, because it is expected that
reinforcement will yield in this region. This provision is in
contradiction with Section 18.10.2.3(c), which, for lap splices,
states that yielding of the reinforcement is expected in height
equal to hsx above and ℓd below the critical section (Fig. 3).
The second paragraph of the commentary provides
exception if testing data show that coupler successfully meets
performance requirements. This process will require using
alternative means and methods, and hence can complicate the
design, and will be subjective to authority having jurisdiction
(AHJ) on how the commentary is interpreted and what tests,
how many specimens, and what the required performance is.
This part should be codified so that when test data is
presented, it shall be accepted.
Questions:
ACI 318-19 extends the use of high-strength reinforcement
in seismic regions. It is expected that engineers will use Grade
80 more often to avoid congestion problems in the wall
boundary elements. ACI 318-19 further introduces significant
restrictions on lap and mechanical splices. Section 18.2.7.2 on
mechanical splices appears to be written primarily for moment
frame elements and then was extended to structural walls. As
such, it is inconsistent with definition of yielding region in
Section 18.10.
1. We seek confirmation that the mechanical splices should
be only restricted from the same zones as lap splices.
2. We also ask to include into the Code part minimum
performance requirements on mechanical splices for Grade 80,
so they can be used in locations of expected yielding, and what
type of testing and how many successful tests are required.
Interpretations:
1. ACI 318-19 specifies different heights over which
restrictions apply to lap splices and mechanical splices of
longitudinal reinforcement, as follows:
(a) According to Section 18.10.2.3 (refer to Fig. R18.10.2.3),
lap-splices of longitudinal reinforcement are not permitted
above (by one story height) and below (by ℓd) a wall critical
section.
(b) According to Sections 18.2.7.2 and 18.2.8.1, respectively,
mechanical couplers of longitudinal reinforcement (except for
Type 2 on Grade 60 reinforcement) and welded splices of
CODE
COMMENTARY
Fig. 2: Excerpt of ACI 318-19, Section 18.2.7.2
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Fig. 3: Clarification of “No splice region” for lap splices (ACI 318-19, Fig. R18.10.2.3)
longitudinal reinforcement, are not permitted within a distance
equal to twice the member depth of a critical section, where
yielding of the reinforcement is likely to occur.
Commentary Sections R18.2.7 and R18.10.2.3 both refer to
these (different) lengths in (a) and (b) as potential yielding
regions. The Committee will consider clarifying this issue as
new business.
2. ACI Committee 318 has not evaluated test data that
would enable developing minimum performance requirements
for mechanical splices for Grade 80 reinforcement. The
Committee will consider this as new business.
Subject: Shear wall web ties
Background: ACI 318-19, Section 18.10.6.4(i), requires
135-135 degree web ties or hoops (Fig. 4). The vertical extent
of the web ties is the same as the extent of the special
boundary element (SBE) per Section 18.10.6.2. However,
Section 18.10.6.4 applies to walls with the SBE determined by
either of Sections 18.10.6.2 or 18.10.6.3. However, Section
18.10.6.2 is intended only for higher-aspect-ratio walls. The
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Fig. 4: Excerpt from ACI 318-19, Section 18.10.6.4(i)
code language is not clear on whether the web ties are
required only for walls with the SBE required by Section
18.10.6.2. (Additional note: Section 18.10.6.2(b)(i) should
reference Section 18.10.6.4(j) for limits of extent of the SBE).
Question:
1. ACI 318-19 introduces web ties to prevent the loss of
axial load-carrying capacity. The tests used as reference in
commentary focused mostly on high-aspect-ratio walls where
(a)
(b)
Fig. 5: Excerpts from ACI 318-19, Section 18.10.3: (a) Table 18.10.3.1.2; and (b) Section 18.10.3.1
the compressive stresses at the inside face of the SBE can be
quite high. On the other hand, the stress trigger in Section
18.10.6.3 for requirement of the SBE is relatively low, and
hence the web crossties may not be justified.
We seek confirmation that web ties are only required for
walls with the SBE per Section 18.10.6.2. If that is not the
case, we seek confirmation that the vertical extent of web ties
need not exceed the height of the SBE. We suggest reevaluation of the requirements on vertical and horizontal
extent of the web ties for the walls.
Interpretation:
1. ACI 318-19, Section 18.10.6.1, indicates that, if SBEs
are required by either Section 18.10.6.2 or 18.10.6.3, the
requirements of Section 18.10.6.4 apply. As indicated by
Section 18.10.6.4, all subsections ((a) through (k)) must be
satisfied. Therefore, all subsections of Section 18.10.6.4 apply
to walls designed according to either Section 18.10.6.2 or
18.10.6.3, if the SBE is required.
For walls designed according to Section 18.10.6.2, the
height of the SBE is specified in Section 18.10.6.2(b)(i),
whereas for walls designed according to Section 18.10.6.3, the
SBE may be discontinued when the stress trigger drops below
0.15 fc′. The requirements of Section 18.10.6.4 apply only over
the height of the SBE; therefore, the web crossties need not be
used above the height of the SBE.
Note that Section 18.10.6.2(b)(i) referencing Section
18.10.6.4(i) is an erratum that has been identified and
corrected (to Section 18.10.6.4(j)).
Subject: Wall shear amplification
Background: ACI 318, Section 18.10.3, introduces shear
amplification on shear walls. The shear amplification consists
of two parts: flexural overstrength and dynamic amplification.
We found points herein that are open to interpretation and
should be clarified.
1. The flexural overstrength is based on horizontal critical
section (Fig. 5(a)). However, the Code specifies that design
shear force Ve is calculated as amplified shear (Fig 5(b)).
While unlikely, this can be interpreted as not only horizontal
shear forces but also vertical design forces on coupling beams.
2. The load case for calculating flexural amplification is
not clear. Current language in footnote [1] of Table 18.10.3.1.2
requires load combination that produces maximum value of
Mpr/Mu. This can imply calculating this ratio at nonseismic
load combination that would produce very large overstrength
because the Mu value is low.
Questions: We seek confirmation:
1. That amplification of shear is only required for
horizontal shear; and
2. On the load case that is to be used for calculation of
flexural overstrength.
Interpretations:
1. The shear amplification of Section 18.10.3.1 is not
required for design of coupling beams.
2. Footnote [1] in Table 18.10.3.1.2 indicates that the
overstrength factor Ωv is calculated for the load combination
producing the highest value of Ωv. Load combinations are
specified in ACI 318-19, Section 5.3. The intent is that the
overstrength factor Ωv is calculated only for the load
combinations that include load effect E—that is, Table 5.3.1
load combinations (5.3.1e) and (5.3.1g).
Subject: Transverse reinforcement configurations
Background: A large part of Section 18.10.6.4 was revised
for ACI 318-19. The revisions include enhanced detailing
based on tests of flexural (large aspect ratio) walls. We found
that some of the requirements are unclear (1) on whether
135-135 are always required. While the code language seems
to allow it (see our interpretation in Fig. 6), the commentary
and example figure in commentary contradict it. Given that
the special moment frame (SMF) columns can use 135-90
degree crossties, we seek confirmation that the 135-90 degree
crossties can also be used in SBE as long as the spacing of
vertical bars supported by a seismic hook meets the code
requirement.
We seek confirmation that alternative transverse
reinforcement configurations, such as “uni-ties,” that are in
general agreement with the Code can be used instead of
overlapping hoops and crossties (2) or headed bars instead of
crossties (3). In addition, we suggest re-evaluation of the
requirements on enhanced detailing (enhanced from ACI
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(a)
(b)
Fig. 6: Per our interpretation of Section 18.10.6.4(f), both of the following are acceptable: (a) SBE transverse reinforcement of two cross
sections above each other using 135-90 degree crossties having vertical bars laterally supported by a seismic hook or bend of a hoop at 14 in.
on-center; and (b) SBE transverse reinforcement with 135-135 degree crossties having vertical bars laterally supported by a seismic hook or
bend of a hoop at 14 in. on-center
(a)
(b)
Fig. 7: Excerpts from ACI 318-19: (a) Section 18.10.6.4(e) and (f); and (b) Fig. R18.10.6.4
318-14 requirements) for walls with SBE that are expected to
experience low stress and strain levels (4).
Questions:
1. ACI 318-19 Commentary Fig. R18.10.6.4 and
Commentary Section 18.10.6.4 suggest that all crossties in
SBE should have 135-135 degree hooks (Fig. 7). However,
Section 18.10.6.4(e) references SMF column sections that do
not require that and Section 18.10.6.4(f) requires that vertical
bars spaced lesser than 14 in. and 2/3 of SBE width are
supported by a seismic hook. It seems that if the bars are
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spaced at 7 in., only every other bar would require a seismic
hook. The Code should explicitly clarify whether each
crosstie needs to be 135-135 degrees or under which
circumstances that would be the case.
2. ACI 318-19, Section 18.10.6.4(e) and (f), requires an
exterior hoop or overlapping hoops depending on SBE lengthto-width ratio with additional crossties. These requirements
provide appropriate restraint for vertical bars and
confinement. Similar confinement and restraint can also be
achieved by using continuous wound ties (“serpentine ties” or
“uni-ties”). However, it is unclear whether uni-ties meet the
exterior hoop requirement. Similarly, this applies to Section
18.7.5.2 for moment frame columns and Section 18.10.6.4(i)
for web crossties.
3. Headed bars appear to be a viable alternative to crossties
with seismic hooks in providing required confinement. Is the
head of the headed bar conforming to ACI 318-19, Section
20.2.1.6, equivalent to a seismic hook?
4. ACI 318-19, Section 18.10.6.4(e) and (f), requires
exterior hoop or overlapping hoops depending on SBE
length-to-width ratio with additional crossties. The
overlapping hoops are required to improve the confinement
and are based on tests for high-aspect-ratios walls undergoing
large inelastic strains in SBEs. Given the low stress limit
requirement on SBE in Section 18.10.6.3, it is not expected
that all walls would undergo high compressive strains. As
such, ACI should clarify whether the overlapping hoops are
required for all walls with SBE or only for walls with high
rotational or stress demands.
Interpretations:
1. The intent of Section 18.10.6.4(f) is that all crossties
within the SBE shall have a seismic hook at both ends,
regardless of the horizontal spacing between supported
longitudinal bars.
2. According to ACI 318-19, Section 25.7.4, continuously
wound bars or wires can be considered as ties; therefore,
provided that the aspect ratios of the hoops created by the
continuously wound tie do not exceed 2.0, and overlap as
required, they satisfy the intent of Section 18.10.6.4(f).
Similarly, continuously wound ties can meet the intent of
Section 18.7.5.2 for confining reinforcement in columns of
SMFs and Section 18.10.6.4(i) for confining reinforcement in
webs (regions between SBEs) of special structural walls.
3. ACI 318 only defines the use of crossties with seismic
hooks at one end and a bend at least 90 degrees on the other
end, or in the situation identified in Section 18.10.6.4(f),
seismic hooks at both ends. ACI Committee 318 has not
adopted the use of headed reinforcement for crossties because
of concerns about whether the heads can be effectively
interlocked with adjacent reinforcement and whether that
interlocking can be maintained during concrete placement.
Because of these concerns, Section 25.7.4 explicitly prohibits
the use of interlocking headed bars to make up hoops.
4. ACI 318-19, Section 18.10.6.4, requires the same
detailing provisions for walls designed using either Section
18.10.6.2 or 18.10.6.3; therefore, overlapping hoops are
required for SBEs of walls designed using either Section
18.10.6.2 or 18.10.6.3 if the hoop aspect ratio exceeds 2, as
required by Section 18.10.6.4(f).
Code Case 318-19 Submitted by LATBSDC
Questions:
1. The amplification factors Wv and wv amplify the entire
demand Vu determined from ASCE 7-16. Is it the intent that Vu
should be separated into portions due to nonseismic (if
appropriate) and lateral seismic, and only the portion of shear
demand associated with horizontal earthquake loading Eh be
amplified?
2. Is it the intent that Vu not be amplified in Section 18.10.3.1
for horizontal wall segments (including coupling beams) and
wall piers because other Provisions 21.2.4.1 (18.10.7) and
18.10.8 address these cases?
3. The maximum amplification factor Wvwv is 3.0. It is
unclear why this is not limited to W0 in ASCE 7-16 and how
the redundancy factor r should be treated. Would the intent of
Section 18.10.3.1 be satisfied if Ve is taken equal to WvVu with
redundancy factor taken as 1.0, as is allowed in overstrength
load combinations of ASCE 7, Section 12.4.3?
4. Is it the intent that only load combinations with E be
considered to determine the ratio of Mpr/Mu according to
footnote [1] in Table 18.10.3.1.2?
5. If only load combinations with E are considered in the
calculation of Mpr/Mu, is it the intent that Mpr can be
determined for the expected axial load, for example, 1.0D +
0.25Lu or as specified in ASCE 7-16?
6. For coupled walls and particularly for core walls
subjected to biaxial demands, the calculation of Mpr/Mu is
overly complicated and uncertain. We ask for clarification on
how this should be accomplished. If using an expected axial
load is acceptable (Q5), and given the complication and
uncertainty, is use of Mpr/Mu = 1.5 sufficient? We ask because
it appears that a lot of effort is required to determine a Mpr/Mu
that is likely to be between about 1.25 and 1.75. Also, for a
value of wv = 1.5, the value of Mpr/Mu is not required to be
taken greater than 2.0 (to reach Wvwv = 3.0). If the upper limit
is set as Wvwv = W0 in ASCE 7-16 (Q2), then, for wv = 1.5, the
value of Mpr/Mu is not required to be taken greater than 1.67
(to reach Wvwv = W0 = 2.5).
7. For coupled walls, is it the intent that the amplified
shear can be based on the average (or gravity) axial load for
the coupled walls because amplifying shear for each pier
(tension, compression; compression, tension) including the
worst-case axial load due to overturning for both ±Eh would
produce an unreasonably high shear demand for each pier?
Or, can an average value be used for each direction of
loading (which would be similar to using gravity load)?
Again, setting Mpr/Mu = 1.5 (or some value) would eliminate
this complication.
8. The dynamic amplification factor wv in Eq. (18.10.3.1.3)
appears to be based on using the equivalent lateral force
(ELF) procedure of ASCE 7-16, Section 12.8, based on a
review of the original paper and NZS 3101.2 Where a modal
response spectrum procedure is used, is it the intent that the
use of an alternative equation is appropriate (as noted in the
SEAOC Blue Book3), because use of modal analysis includes
at least some portion of the dynamic amplification factor?
9. If Wv is taken greater or equal to 1.5, is it the intent that
the f-factor for shear be taken as 0.75?
10. The requirement for overlapping hoops at wall
boundaries in Section 18.10.6.4(f) is based on the studies by
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Segura and Wallace4 and Abdullah and Wallace.5 These
studies indicate that overlapping hoops are required to
improve the deformation capacity (lateral instability of the
compression zone) of relatively thin wall boundaries
subjected to significant compression (and shear) demands.
Section 18.10.6.4(f) could be interpreted to require
overlapping hoops for cases where the SBE is required within
a wall flange or around the perimeter of a core wall. Is it the
intent that overlapping hoops need not be provided for walls
with flanges that provide lateral support to the compression
zone?
Interpretations:
1. The intent of Section 18.10.3.1 is that only the factored
shear force from load combinations (5.3.1e) and (5.3.1g) in
Table 5.3.1 associated with horizontal seismic load effect Eh
need be amplified.
2. The intent of Section 18.10.3.1 is that Vu is not amplified
for horizontal wall segments (including coupling beams) and
wall piers because other Provisions 21.2.4.1 (18.10.7) and
18.10.8 address these cases.
3. The intent of Section 18.10.3.1 is that, where a
redundancy factor of 1.3 is applied according to ASCE 7-16,
Section 12.3.4, Ve due to lateral forces need not exceed three
times the factored shear obtained from elastic analysis of the
structure under code-prescribed seismic forces with a
redundancy factor of 1.0. Therefore, the intent of Section
18.10.3.1 is not satisfied if Ve is taken equal to W0Vu with
redundancy factor taken as 1.0. The Committee will consider
this possibility as new business.
4. Footnote [1] in Table 18.10.3.1.2 indicates that the
overstrength factor Ωv is calculated for the load combination
producing the highest value of Ωv. Load combinations are
specified in ACI 318-19, Section 5.3 (Table 5.3.1). The intent
is that the overstrength factor Ωv is calculated only for the
load combinations that include load effect E—that is, Table
5.3.1 load combinations (5.3.1e) and (5.3.1g).
5. See response to Item 4. The intent of the footnote [1] in
Table 18.10.3.1.2 would not be satisfied using expected axial
load. The Committee will consider this as new business.
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6. The intent of Section 18.10.3.1 (Table 18.10.3.1.2) is
that Wv be taken as the greater of Mpr/Mu and 1.5, unless a
more detailed analysis demonstrates a smaller value; however,
Ωv shall not be taken less than 1.0 (refer to Table 18.10.3.1.2,
footnote [2]). Therefore, the intent of Section 18.10.3.1 is not
satisfied if Mpr/Mu equal to 1.5 is used as an upper bound. The
Committee will consider simplifying this requirement as new
business.
7. The intent of Section 18.10.3.1.2 is to treat structural
walls in coupled wall systems as individual walls when
determining Mpr and Mu at critical sections for shear
amplification requirements. However, ACI 318-19, Section
18.10.3.1.2, does not specify how to calculate Mpr/Mu for
coupled walls; therefore, the licensed design professional may
exercise judgment in using any reasonable approach.
8. If a dynamic analysis procedure (for example, response
spectrum analysis) is used to compute Vu, the intent of Section
18.10.3.1.3 is satisfied using the following expression for
dynamic amplification in the SEAOC Blue Book3
ꞷv = 1.2 + ns / 50
The Committee suggests an alternative, simplified
expression that also considers differences in story heights
between those used in the original study for buildings in New
Zealand and for buildings more typical of the U.S. practice
ꞷv = 1.0 + 0.09hn1/3
where hn is the structural height from the base to the highest
level of the seismic force-resisting system of the structure, in
feet, where the base is the level at which the horizontal
seismic ground motions are considered to be imparted to the
structure.
9. The intent of Section 21.2.4.1 is that, if Ωv ≥ 1.5, f for
shear shall be permitted to be taken equal to 0.75 at the critical
section and at all sections.
10. The intent of Section 18.10.6.4(f) is that overlapping
hoops are not required for the SBE located where a wall web
and flange intersect.
References
1. ASCE 7-16, “Minimum Design Loads for Buildings and Other
Structures,” American Society of Civil Engineers, Reston, VA, 2017,
800 pp.
2. NZS 3101-2006—Concrete Structure Standard, Part 1: The Design
of Concrete Structures: Part 2: Commentary on the Design of Concrete
Structures, Standards New Zealand, 2006, 754 pp
3. SEAOC Seismology Committee, “SEAOC Blue Book: Seismic
Design Recommendations,” Structural Engineers Association of
California (SEAOC), Sacramento, CA, 2009, 296 pp.
4. Segura, C.L. Jr., and Wallace, J.W., “Impact of Geometry and
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Selected for reader interest by the editors.