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An ACI Standard
Standard Requirements for Seismic Evaluation and Retrofit of Existing Concrete Buildings
� '
(ACI 369.1M-17) and Commentary Reported by ACI Committee 369
I
~ '
•
m d/2
0.0030
0.0 1
0.2
0.00 1 5
0.005
0.01
Condition iii. beams controlled by inadequate development or splicing along the span! Stirrup spacing � d/2
0.0030
0.02
0.0
0.00 1 5
0.01
0.02
Stirrup spacing > d/2
0.0030
0.01
0.0
0.00 1 5
0.005
0.01
0.02
0.03
Condition iv. beams controlled b y inadequate embedment into beam-co1umn jointl 0.0 1 5
0.03
0.2
0.0 1
'Values between those listed in the table shall be determined by linear interpolation. twhere more than one of Conditions i, ii, iii, and iv occur for a given component, use the minimum appropriate numerical value from the table. :c and NC are abbreviations for conforming and nonconforming transverse reinforcement, respectively. Transverse reinforcement is conforming if, within the flexural plastic hinge region, hoops are spaced at :S d/3 , and if, for components of moderate and high ductility demand, the strength provided by the hoops ( V,) is at least three-fourths of the design shear. Otherwise, the transverse reinforcement is considered nonconforming.
§ V is the shear force from NSP or NDP. Note:fc£ in M Pa.
fs
=
1 .25
( )2/3 ;:eg
R.
fyeL
:s;
fyeu E
( 1 b)
In cases where .fs f/uE from Eq. ( l a) but the maximum applied longitudinal bar stress is larger than ls-deg given in Eq. ( 1 b), columns shall be deemed controlled by inadequate development or splicing and the capacity of the existing reinforcement taken as.J;eu£· c) For inadequate development or splicing of straight bars in beams and columns: for nonlinear procedures, it shall be permitted to assume that the reinforcement retains the calcu lated maximum stress evaluated using Eq. ( l a) up to the deformation levels defined by a11e in Tables 7 through 9; for linear procedures, the calculated maximum stress evaluated using Eq. ( 1 a) shall be used for strength calculations. For members other than beams and columns controlled by inad=
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opment and splices of reinforcement account for mechanical bond from deformations present in deformed bars as well as chemical bond. The length required to develop plain bars is much greater than for deformed bars and more sensitive to cracking in concrete. Testing and assessment procedures for tensile lap splices and development length for plain steel reinforcement are found in Concrete Reinforcing Steel Insti tute ( 1 98 1 ).
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STANDARD REQUIREMENTS FOR SEISMIC EVALUATION AND RETROFIT OF EXISTING CONCRETE BUILDINGS (ACI 369.1 M-17)
S TANDARD
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COMMENTARY
Table 8-Model ing parameters and nu merical acceptance criteria for nonli near procedures: reinforced concrete col umns other than circular with spiral reinforcement or seismic hoops as defined in ACI 318M Acceptance criteria
Modeling parameters
Plastic rotation angle, rad Performance level
Plastic rotation angles a,e and b,r, rad Residual strength ratio c,e
a,,
=
For
(
10
LS
CP
0.5 b }
0.7b,e!
e
0.7b,e
Columns not controlled by inadequate development or splicing along the clear height'
0.042 - 0.043 Nuo, + 0.63 p, - 0.023
Nw, Agfc£
-
::; 0.5
l
cn1
Agjc£
Vy£ J
VCo/0£
� 0.0 t
b,1
=
=
0.5 I J:' N_ UD_ _ ____sg_ 5 + __ 0.8AJ;£ p, /,.,£
0.01 � a,,
0 . 1 5a,e S 0.005
,
N _ � 0.0 0.24 - 0.4 ____\!Q_
Agfc�
Columns controlled by inadequate development or splicing along the clear height§
a,,
b,1
=
(
(I
p,J;.,£
= S Pef e£ y
J
� 0.0
Nuo + 1 2 , 0.0 1 2 - 0.085 � p
gh£
c,e = O. I 5
II
$ 0.025
rO.O � a,1
0.0
#
0. 5 b
,
::; 0.06
+ 36p, S 0.4
'p, shall not be taken greater than 0.0 1 75 in any case nor greater than 0.0075 when ties are not adequately anchored in the core. Equations in the table are not valid for columns with p1 smaller than 0.0005. V,E!Vco/O£ shall not be taken less than 0.2. Nuo shall be the maximum compressive axial load accounting for the effects of lateral forces as described in Eq. (7-34) of ASCE 4 1 - 1 7. Alternatively, it shall be permitted to evaluate Nuo based on a limit-state analysis. shall be reduced linearly for Nud(AJ',£) > 0.5 from its value at Nud(A,j',£) Wud(A,j',£) shall not be taken smaller than 0. 1 .
1b,,
=
0.5 to zero at Nud(AJ',E) = 0.7 but shall not be smaller than a,,.
iColumns are considered t o b e controlled b y inadequate development o r splices where the calculated steel stress at the splice exceeds the steel stress specified b y Eq. ( I a) o r ( I b). Modeling parameter for columns controlled by inadequate development or splicing shall never exceed those of columns not controlled by inadequate development or splicing. 11a,1
for columns controlled by inadequate development or splicing shall be taken as zero if the splice region is not crossed by at least two tie groups over its length.
'p, shall not be taken greater than 0.0075.
equate development or splicing and hooked anchorage, the developed stress shall be assumed to degrade from 1 .0fs, at a ductility demand or DCR equal to 1 .0, to 0.2fs at a ductility demand or DCR equal to 2.0. d) The strength of deformed straight, discontinuous bars embedded in concrete sections or beam-column joints, with clear cover over the embedded bar not less than 3db, shall be calculated according to Eq. (2)
lrs
17
r = - fl. e < - lyLJ
db
E
(MPa)
(2)
where fs is less than;;,LIE and the calculated stress in the bar caused by design loads equals or exceeds fs, the maximum developed stress shall be assumed to degrade from 1 .0fs, at a American Concrete Institute Copyrighted Material-www.concrete.org
STANDARD REQUIREMENTS FOR SEISMIC EVALUATION AND RETROFIT OF EXISTING CONCRETE BUILDINGS (ACI 369.1M-17)
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STANDARD
C OMMENTARY
Table 9-Modeling parameters and numerical acceptance criteria for non l i near procedures: reinforced concrete circular columns with spiral reinforcement or seismic hoops as defined in ACI 318M Acceptance criteria
Modeling parameters
Plastic rotation angle, rad Plastic rotation angles a,r and b,,, rad
Performance level
Residual strength ratio c,,
LS
10
a,1
For
=
(
CP
Columns not controlled by inadequate development or splicing along the clear height'
0.06 - 0.06
N"" Agfc£ -,
::;;
l
y£ ) � 0.0 :gfuoc£, + 1 .3p, - 0.037 :ColO£ t
0.5 b,,
c,,
=
=
0.65 N_ I ___s£ /,' + u.o_ _ 5 0.8AJ:r p, J;.,£
0.24 - 0.4
0.01 � a,1
0. 15a,e :S 0.005
0.5b,el
0.7b,}
:gf' � 0.0 c £
Columns controlled by inadequate development or splicing along the clear height§
a,,
b,1
=
(
=
(I ) ,
p, J; ,£ � 0.0 8 p J;.1£ ::;; 0.025
II
ro.o
Nuo 0.0 1 2 - 0.085 � + 1 2 p, � a.., J,£ $ 0.06 c,e =
#
0.0
0.5b,e
0.7b,e
0. 1 5 + 36p, :S 0.4
'p,
shall not be taken greater than 0.0 1 75 in any case nor greater than 0.0075 when ties are not adequately anchored in the core. Equations in the table are not valid for columns with p, smaller than 0.0005. V,.£/VcoJOE shall not be taken less than 0.2.
Nuo shall be the maximum compressive axial load accounting for the effects of lateral forces as described in Eq. (7-34) of ASCE 4 1 - 1 7. Alternatively, it shall be permitted to evaluate Nuo based on a limit-state analysis. lb.,,
shall be reduced linearly for Nuof(AJ',E) > 0.5 from its value at Nuof(AJ',,) = 0.5 to zero at Nuof(AJ',,) = 0.7 but shall not be smaller than a,1
INuof(A,j',E) shall not be taken smaller than 0. 1 . !Columns are considered to be controlled by inadequate development or splices where the calculated steel stress at the splice exceeds the steel stress specified by Eq. ( I a) or ( I b). Modeling parameter for columns controlled by inadequate development or splicing shall never exceed those of columns not controlled by inadequate development or splicing. 11a,1 for 'p,
columns controlled by inadequate development or splicing shall be taken as zero if the splice region is not crossed by at least two tie groups over its length.
shall not be taken greater than 0.0075.
ductility demand or DCR equal to 1 .0, to 0.2/s at a ductility demand or DCR equal to 2.0. In beams with bottom bar embedment length into beam-column joints less than the requirements of ACI 3 1 8M, flexural strength shall be calcu lated considering the stress limitation of Eq. (2). e) For plain straight, hooked, and lap-spliced bars, devel opment and splice lengths shall be taken as twice the values determined in accordance with ACI 3 1 8M, unless other lengths are justified by approved tests. f) Doweled bars added in seismic retrofit shall be assumed to develop yield stress where all the following conditions are satisfied: i. Drilled holes for dowel bars are cleaned ii. Embedment length le is not less than 1 Odb iii. Minimum dowel bar spacing is not less than 4le and minimum edge distance is not less than 2le
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STANDARD REQUIREMENTS FOR SEISMIC EVALUATION AND RETROFIT OF EXISTING CONCRETE BUILDINGS (ACI 369.1 M-17)
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Design values for dowel bars not satisfying these condi tions shall be verified by test data. Field samples shall be obtained to ensure that design strengths are developed in accordance with Chapter 3 . g) Square reinforcing bars in a building should b e classi fied as either twisted or straight. The developed strength of twisted square bars shall be as specified for deformed bars in this section, using an effective diameter calculated based on the area of the square bar. Straight square bars shall be considered plain bars, and the developed strength shall be as specified for plain bars in this section. 3.6-Con nections to existing concrete Connections used to connect two or more components shall be classified according to their anchoring systems as cast-in-place or as post-installed and shall be evaluated and designed according to Chapter 1 7 of ACI 3 1 8M- 14 as modi tied in this section. The properties of the existing anchors and connection systems obtained in accordance with 2.2 herein shall be considered in the evaluation. These provi sions do not apply to connections in plastic hinge zones.
C3.6-Connections to existing concrete Chapter 1 7 of ACI 3 1 8M- 14 accounts for the influence of cracking on the load capacity of connectors; however, cracking and spalling expected in plastic hinge zones is likely to be more severe than the level of damage for which Chapter 1 7 is applicable. ACI 3 5 5 .2 and ACI 355 .4M describe simulated seismic tests that can be used for qualifi cation of post-installed anchors. Such tests do not simulate the conditions expected in plastic hinge zones. The 2006 version of ASCE 41 required the load capacity of anchors placed in areas where cracking is expected to be reduced by a factor of 0.5. This provision was included in FEMA 273 for both cast-in-place and post-installed anchors, before the introduction of ACI 3 1 8M-02 Appendix D. Because cracking is now accounted for in ACI 3 1 8M, the 0.5 factor is not required in 3 .6 of this standard. Capacities of existing anchors should be evaluated based on the obtained properties in accordance with 2.2, and Chapter 1 7 of ACI 3 1 8M-14. If the anchors are not tested to failure but to a load based on the force-controlled action determined by the engineer for the seismic hazard under consideration, the procedure in Chapter 1 7 of ACI 3 1 8M- 14 can be used to calculate available strength based on the test results and the geometry of anchors measured or assumed by the engineer. To evaluate the capacity of existing cast-in-place and post-installed anchors using ACI 3 1 8M- 14 Chapter 17, it is necessary to know the geometry of the anchor (that is, embedment, edge distance, spacing, and anchor diameter) and material properties. Edge distance, spacing, and anchor diameter can be established from construction documents or by visual inspection. Unless known from construction docu ments, embedment and material properties of the anchor are more difficult to determine. Where failure of the anchor is not critical to meeting the target performance level, embed ment of post-installed anchors can be assumed equal to the minimum embedment required by manufacturer's speci fications for the anchor type in question. For cast-in-place anchors, embedment can be taken as less than or equal to the minimum embedment from the original design code for an embedded bolt of the same diameter. It is recommended that where the consequence of failure of an anchor is critical to satisfying the target performance level, anchor embedment not known from construction documents is determined by nondestructive testing (for example, ultrasonic testing).
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STANDARD REQUIREMENTS FOR SEISMIC EVALUATION AND RETROFIT OF EXISTING CONCRETE BUILDINGS (ACI 369.1M-17)
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Lower-bound properties for steel connector materials and concrete strength based on default values, construction documents, or test values can be assumed for anchor strength calculations. It is noted that direct testing of anchors can provide greater certainty and can provide higher capacities. Judgment should be exercised in the use of default lower bound material properties because doing so may not yield a conservative estimate of anchor capacity in cases where the steel strength is determined to govern the anchor capacity, and additional requirements ofACI 3 1 8M- 1 4 Chapter 1 7 for ductile behavior are waived as a result. Not all manufacturers of post-installed anchors publish information on the mean and the standard deviation ofthe ulti mate anchor capacity. Older testing for existing post-installed anchors is often reported at allowable stress design levels and may not comply with the requirements of Chapter 1 7 of ACI 3 1 8M- 1 4 for simulated seismic tests. Care and judgment should be used in determining pullout strength for anchors, particularly those that are critical to satisfying the target performance level. Where necessary, in-place strengths of anchors can be obtained or verified by static testing of repre sentative anchors. ACI 355 .2 and ACI 355.4M can be used for guidance on testing. Proper installation of post-installed anchors is critical to their performance and should be verified in all cases. 3.6.1 Cast-in-place anchors and connection systems-All
C3.6.1 Cast-in-place anchors and connection systems
component actions on cast-in-place anchors and connection systems shall be considered force-controlled. Lower-bound strength of the anchors and connections shall be nominal strength as specified in Chapter 1 7 of ACI 3 1 8M- 1 4 for the connections of structural components. The amplifica tion factor to account for the seismic overstrength, n0, shall be taken equal to unity for the connections of structural components. A strength reduction factor and amplification factor no shall be used for the connections ofnonstructural components.
The strength reduction factor in ACI 3 1 8M is taken equal to unity for the lower-bound connection strength of struc tural components, but the requirements in 1 7 .2.3 of ACI 3 1 8M- 1 4 need to be satisfied, including the reduction of the strength due to cracked concrete and cyclic loading. The component actions on the anchors and connection systems for structural components are considered as force-controlled actions according to 7.5.2 and 7.5.3 of ASCE 4 1 - 1 7, so further amplification of the seismic demand is not necessary. However, the seismic demand on nonstructural compo nents in Chapter 13 of ASCE 4 1 - 1 7 is based on that in ASCE 7. A strength reduction factor and amplification factor no should be consistent with the demand.
3.6.2 Post-installed anchors-All component actions on post-installed anchor connection systems shall be considered force-controlled. The lower-bound capacity of post-installed anchors shall be nominal strength, as specified in Chapter 1 7 of ACI 3 1 8M-14, or mean less one standard deviation of ultimate values published in approved test reports for the connections of structural components. The amplifica tion factor to account for the seismic overstrength, n0, shall be taken equal to unity for the connections of structural components. A strength reduction factor and amplification factor n0 shall be used for the connections of nonstructural components.
C3.6.2 Post-installed anchors-The strength reduction factor in ACI 3 1 8M is taken equal to unity for the lower bound connection strength of structural components, but the requirements in 1 7.2.3 of ACI 3 1 8M- 14 need to be satis fied, including the reduction of the strength due to cracked concrete and cyclic loading. The component actions on post installed anchors for structural components are considered force-controlled actions according to 7.5.2 and 7.5.3 of ASCE 4 1 - 1 7, so further amplification of the seismic demand is not necessary. However, the seismic demand on nonstructural compo nents in Chapter 1 3 of ASCE 4 1 - 1 7 is based on that in ASCE 7. Strength reduction factor and amplification factor no should be consistent with the demand.
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STANDARD REQUIREMENTS FOR SEISMIC EVALUATION AND RETROFIT OF EXISTING CONCRETE BUILDINGS (ACI 369.1 M-17)
S TANDARD
COMMENTARY
3.7-Retrofit measures Seismic retrofit measures for concrete buildings shall meet the requirements of this section and other provisions of this standard. Retrofit measures shall include replacement or retrofit of the component or modification of the structure so that the component is no longer deficient for the selected perfor mance objective. If component replacement is selected, the new component shall be designed in accordance with this standard and detailed and constructed in compliance with the applicable building code. Retrofit measures shall be evaluated to ensure that the completed retrofit achieves the selected performance objec tive. The effects of retrofit on stiffness, strength, and deform ability shall be taken into account in an analytical model of the rehabilitated structure. The compatibility of new and existing components shall be checked at displacements consistent with the selected performance level. Connections required between existing and new compo nents shall satisfy the requirements of 3 .6 and other require ments of this standard.
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STANDARD REQUIREMENTS FOR SEISMIC EVALUATION AND RETROFIT OF EXISTING CONCRETE BUILDINGS (ACI 369.1M-17)
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C OMMENTARY
CHAPTER 4-CONCRETE MOMENT FRAMES 4.1 -Types of concrete moment frames Concrete moment frames are defined as elements composed primarily of horizontal frame components, such as beams, slabs, or both; vertical frame components, such as columns; and joints connecting horizontal and vertical frame components. To resist seismic forces, these elements act alone or in conjunction with shear walls, braced frames, or other elements. Frames that are cast monolithically, including monolithic concrete frames created by the addition of new material, are addressed in this chapter. Frames addressed include reinforced concrete beam-column moment frames, post tensioned concrete beam-column moment frames, and slab column moment frames. The frame classifications in 4. 1 . 1 through 4. 1 .3 include existing construction, new construction, existing construc tion that has been retrofitted, frames intended as part of the seismic-force-resisting system, and frames not intended as part of the seismic-force-resisting system in the original design. 4.1.1 Reiriforced concrete beam-column momentframes
Reinforced concrete beam-column moment frames, addressed in 4.2, are defined by the following conditions: a) Frame components are beams with or without slabs, columns, and their connections. b) Frames are of monolithic construction that provide for moment and shear transfer between beams and columns. c) Primary reinforcement in components contributing to seismic-force resistance is nonprestressed. 4.1.2 Post-tensioned concrete beam-column moment frames Post-tensioned concrete beam-column moment -
frames, addressed in 4.3, are defined by the following conditions: a) Frame components are beams (with or without slabs), columns, and their connections. b) Frames are of monolithic construction that provide for moment and shear transfer between beams and columns. c) Primary reinforcement in beams contributing to seismic force resistance includes post-tensioned reinforcement with or without nonprestressed reinforcement. 4.1.3 Slab-column moment frames Slab-column moment frames, addressed in 2.4, are defined by the following conditions: a) Frame components are slabs with or without beams in the transverse direction, columns, and their connections. b) Frames are of monolithic construction that provide for moment and shear transfer between slabs and columns. c) Primary reinforcement in slabs contributing to seismic force resistance includes nonprestressed reinforcement, prestressed reinforcement, or both. -
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STANDARD REQUIREMENTS FOR SEISMIC EVALUATION AND RETROFIT OF EXISTING CONCRETE BUILDINGS (ACI 369.1 M-17)
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COMMENTARY
4.2-Reinforced concrete beam-col umn moment frames 4.2. 1 General-The analytical model for a beam-column frame element shall represent strength, stiffness, and defor mation capacity ofbeams, columns, beam-columnjoints, and other components of the frame, including connections with other elements. Potential failure in flexure, shear, and rein forcement development at any section along the component length shall be considered. Interaction with other elements, including nonstructural components, shall be included. Analytical models representing a beam-column frame using line elements with properties concentrated at compo nent centerlines shall be permitted. Where beam and column centerlines do not intersect, the eccentricity effects between frame centerlines shall be considered. Where the centerline of the narrower component falls within the middle one-third of the adjacent frame component measured transverse to the framing direction, this eccentricity need not be considered. Where larger eccentricities occur, the effect shall be repre sented either by reductions in effective stiffness, strength, and deformation capacity or by direct modeling of the eccentricity. The beam-column joint in monolithic construction is the zone having horizontal dimensions equal to the column cross-sectional dimensions and vertical dimension equal to the beam depth. A wider joint is acceptable where the beam is wider than the column. The beam-column joint shall be modeled according to 4.2.2 or as justified by experimental evidence. The model of the connection between columns and foundation shall be selected based on details of the column-foundation connection and rigidity of the founda tion-soil system. Action of the slab as a diaphragm interconnecting vertical components shall be considered. Action of the slab as a composite beam flange shall be considered in developing stiffness, strength, and deformation capacities of the beam component model per 3 . 1 .3 . Inelastic action shall be restricted to those components and actions listed in Tables 7 through 9, except where it is demonstrated by experimental evidence and analysis that other inelastic action is acceptable for the selected perfor mance level. Acceptance criteria are specified in 4.2.4.
C4.2-Rei nforced concrete beam-column moment frames C4.2.1 General-Nonstructural components should be included in the analytical model if such elements contribute significantly to building stiffness, modify dynamic prop erties, or have significant impact on the behavior of adja cent structural elements. Section 7.2.3.3 of ASCE 4 1 - 1 7 suggests that nonstructural components should b e included if their lateral stiffness exceeds 10 percent of the total initial lateral stiffness of a story. Partial infill walls and staircases are examples of nonstructural elements that can alter the behavior of adjacent concrete structural elements.
4.2.2 Stiffness of reinforced concrete beam-column momentframes
C4.2.2 Stiffness of reiriforced concrete beam-column momentframes
4.2.2.1 Linear static and dynamic procedures-Beams
C4.2.2. 1 Linear static and dynamic procedures-Various
shall be modeled considering flexural and shear stiffnesses, including the effect of the slab acting as a flange in mono lithic construction according to the provisions in 3 . 1 .3 . Columns shall b e modeled considering flexural, shear, and axial stiffnesses. Refer to 3 . 1 .2 to compute the effective stiff nesses. Where joint stiffness is not modeled explicitly, it shall be permitted to be modeled implicitly by adjusting a centerline model (Fig. 2): a) For 'L.Mco!EI''f£fi18 > 1 .2, column offsets are rigid and beam offsets are not.
approaches to explicitly model beam-column joints are available in El-Metwally and Chen (1 988), Ghobarah and Biddah ( 1 999), Shin and LaFave (2004), Mitra and Lowes (2007), and Lin and Restrepo (2002). For simplicity of implementation in commercial structural analysis software and agreement with calibration studies performed in the development of this standard, this section defines an implicit beam-column j oint modeling technique using centerline models with semi-rigid joint offsets. Figure 2 shows an example of an explicit joint model and illustrates the implicit
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STANDARD REQUIREMENTS FOR SEISMIC EVALUATION AND RETROFIT OF EXISTING CONCRETE BUILDINGS (ACI 369.1M-17)
STANDARD
a) Example of explicit joint model
C OMMENTARY
b) Offsets for implicit
joint model
Fig. 2-Beam-column joint modeling (hatched portions indicate rigid element).
b) For IJv!co!El'i)18£ < 0.8, beam offsets are rigid and column offsets are not. c) For 0.8 :S IJv!co!£/IJvf8£ :S 1 .2, half of the beam and column offsets are considered rigid. Mco!£ shall be calculated considering axial force from the gravity loads specified in Eq. (7-3) of ASCE 4 1 - 1 7. Because this modeling approach accounts only for joint shear flex ibility, stiffness values used for the beams and columns shall include the flexibility resulting from bar slip.
joint modeling approach. In the implicit joint model, only a portion of the beam, column, or both, within the geometric joint region is defined as rigid. In typical commercial soft ware packages, this portion can range from 0, in which case the model is a true centerline model, to 1 .0, where the entire joint region is rigid. Further commentary is provided in C3. 1 .2 . 1 , and background material is provided in Elwood et a!. (2007) and Birely et a!. (2009).
4.2.2.2 Nonlinear static procedure-Nonlinear load deformation relations shall comply with 3 . 1 .2. Nonlinear modeling parameters for beams, columns, and beam-column joints are provided in Tables 7, 8, 9, and 12. Beams and columns shall be modeled using concentrated or distributed plastic hinge models. Other models whose behavior represents the behavior of reinforced concrete beam and column components subjected to seismic loading shall be permitted. The beam and column model shall be capable of representing inelastic response along the compo nent length, except where it is shown by equilibrium that yielding is restricted to the component ends. Where nonlinear response is expected in a mode other than flexure, the model shall be established to represent such effects. Monotonic load-deformation relations shall be estab lished according to the generalized load-deformation rela tion shown in Fig. 1 , with the exception that different rela tions shall be permitted where verified by experiments. The overall load-deformation relation shall be established so that maximum resistance is consistent with the strength specifi cations of 3.2 and 4.2.3. For beams and columns, the generalized deformation in Fig. 1 is plastic hinge rotation. For beam-column joints, the generalized deformation is shear strain. Values of the gener-
C4.2.2.2 Nonlinear static procedure-The modeling parameters and acceptance criteria specified in Tables 8 and 9 reflect results from research on reinforced concrete columns and an updated database of columns tests that includes 3 1 9 rectangular and 1 7 1 circular column tests without lap splices (Ghannoum et a!. 20 1 5a,b), and a database of 39 rectangular columns containing lap splices (Ghannoum 20 1 7). Most circular columns in the database contained spiral reinforce ment. Separate tables are given for rectangular columns (Table 8) and spirally reinforced circular columns (Table 9). For circular columns reinforced with ties not conforming to ACI 3 1 8M seismic hoop designation, Table 8 should be used. The three parameters that are used in Tables 8 and 9 to calculate modeling parameters and acceptance criteria for columns not controlled by inadequate development or splicing are: axial load ratio, transverse reinforcement ratio, and ratio of shear demand at flexural yielding to shear capacity ( Vy£/ Vco!o£). For columns controlled by inadequate development or splicing, the same modeling parameters were introduced for rectangular and circular columns in Tables 8 and 9 and are related to: axial load ratio, transverse reinforcement ratio, and the ratio of transverse reinforcement to longitudinal reinforcement strength.
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STANDARD REQUIREMENTS FOR SEISMIC EVALUATION AND RETROFIT OF EXISTING CONCRETE BUILDINGS (ACI 369.1 M-17)
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COMMENTARY
Table C1 -Range of values of nonlinear modeling parameters for concrete col umns
Nud(AJ'c£)
p,
1/,£/V,E
0
0.0005
0
0.0005
0
0 . 0 1 75
Columns other than circular with spiral
Circular columns with spiral
reinforcement or seismic hoops
reinforcement or seismic hoops a"r' rad
a"e' rad
b"'' rad*
0.2
0.038
0.090
0.053
0. 1 20
1 .5
0.008
0.090
0.005
0. 1 20
0.2
0.048
0.090
0.075
0. 1 20
b"'' rad*
0
0.0 1 75
1 .5
0.0 1 9
0.090
0.027
0. 1 20
0.7
0.0005
0.2
0.008
0.008
0.0 1 1
0.0 1 1
0.7
0.0005
1 .5
0.0
0.0
0.0
0.0
0.7
0 . 0 1 75
0.2
0.0 1 8
0.0 1 8
0.033
0.033
0.7
0 . 0 1 75
1 .5
0.0
0.0
0.0
0.0
'b,, values obtained by
takingf',Eif·,£ � 0.067.
Table C2-M ultipl iers for concrete col umn modeling parameters to ach ieve specific probabil ities of exceedance Modeling parameter
Multiplier to achieve probability of exceedance 40 percent
25 percent
10 percent
Columns not controlled by inadequate development or splicing along the clear height Reinforced concrete columns other than circular with spiral reinforcement or seismic hoops as defined in ACI 3 1 8M Reinforced concrete circular columns with spiral reinforcement or seismic hoops as defined in ACI 3 1 8M
Gnt
0.80
0.62
bne
0.80
0.70
0.5
Gnt
0.70
0.57
0.42
bne
NA'
NA'
NA'
0.47
Columns controlled by inadequate development or splicing along the clear height All columns
ane
0.62
0.5
0.33
bne
NA'
NA'
NA'
'Multipliers not available due to limited test data.
alized deformation at Points B, C, and D shall be derived from experiments or rational analyses and shall take into account the interactions among flexure, axial load, and shear. Acceptance criteria in Tables 8 and 9 were selected as 1 5 percent of the a11e values for immediate occupancy, 50 percent of the b,e values for life safety, and 70 percent of the b, e values for collapse prevention. The fractions of b,e values were selected based on Table C2 to achieve low probabilities of axial failure for columns satisfying the acceptance criteria. These probabilities were 1 0 percent and 25 percent for life safety and collapse prevention, respectively. Note that the probabilities of exceedance in Table C l correspond to the probability of failure for a column given a plastic rotation demand equal to the modeling parameter scaled by the appropriate multiplier in Table C2. Most laboratory tests ignore some factors that can influence the drift capacity, such as loading history and bidirectional loading. The probabilities of exceedance in Table C2 can therefore be larger if these factors are considered. Databases used to assess the model conservatism consist of rectangular and circular columns subjected to unidirectional lateral forces applied parallel to either one of the column
The modeling parameters in Tables 8 and 9 define the plastic rotations according to Fig. l (a). As shown in Fig. 1 (a), modeling parameter a11 e provides the plastic rotation at significant loss of lateral force capacity. For the purposes of determining a11e values based on test data, it was assumed that this point represented a 20 percent or greater reduction in the lateral force resistance from the measured peak shear capacity. For columns expected to experience flexural failures ( Vy£/Vcoto£ :S 0.6), such loss of lateral load resistance can be caused by concrete crushing, bar buckling, and other flexural damage mechanisms. For columns expected to experience shear failures, either before or after flexural yielding ( Vy£/Vcoto£ > 0.6), loss of lateral load resistance is commonly caused by severe diagonal cracking indicative of shear damage. For columns with inadequate anchorage or splicing, loss of lateral load resistance is caused by bond splitting failures that gradually unload the longitudinal bars. Consistent with 7 .5. 1 .2 of ASCE 4 1 - 1 7, modeling parameter bn1 provides an estimate of the plastic rotation at the loss of gravity load support, that is, axial load failure. Modeling parameters given in Tables 8 and 9 represent median estimates of parameters extracted from columns in
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Table 1 0(a)-Numerical acceptance criteria for linear procedures: reinforced concrete columns other than circular with spiral reinforcement or seismic hoops as defined in ACI 318M
.
m-factors
Performance level
( NUD ) AJ,�
Component type Primary
V,.dVco/0£
p,
10
LS
Secondary CP
LS
CP
Columns not controlled by inadequate development or splicing along the clear height! �0. 1
2:0.0 1 75
2:0.7
2:0.0 1 75
�0. 1
�0.0005
2:0.7
�0.0005
�0. 1
2:0.0 1 75
2:0.7
2:0.0 1 75
�0. 1
�0.0005
2:0.7
�0.0005
2:0.2 0.6
No
II
_
II
_
II
_
I jl
_
II
_
Condition ii: post-tensioned slab-column connections!
v t ...JL vo
reinforcement!
0
Yes
Continuity
1 .5
2
2.5
2.5
3.25
0.6
Yes
1
1
1
2
2.25
>0.6
Yes
1
I
1
1 .5
1 .75
0
No
1 .25
1 .75
1 .75
1 .75
2
0.6
No
>0.6
No
I
I II
_
I
I II
_
II
_
I jl
_
II
_
Condition iii: slabs controlled by inadequate development or splicing along the spant II
_
II
_
II
_
3
4
3
4
Condition iv: slabs controlled by inadequate embedment into slab-column joint! 2
2
3
"Values between those listed in the table shall be determined by linear interpolation. twhcrc more than one of conditions i, ii, iii, and iv occur for a given component, use the minimum appropriate numerical value from the table. l Vg
is the gravity shear acting on the slab critical section as defined by ACI 3 1 8M, and V, is the direct punching shear strength as defined by ACI 3 1 8M.
§"Yes" shall be used where the area of effectively continuous main bottom bars passing through the column cage in each direction is greater than or equal to O.S V/(};). Where the slab is post-tensioned, "Yes" shall be used where at least one of the posttensioning tendons in each direction passes through the column cage. Otherwise, "No" shall be used. IIAction
shall be treated as force-controlled.
the greater of 1 .0 and m/2, the element shall be defined as a weak story element and shall be evaluated by the procedure for weak story elements in 4.2.4. 1 . 4.4.4.2 Nonlinear static and dynamic procedures
C4.4.4.2 Nonlinear static and dynamic procedures
Inelastic response shall be restricted to actions in Tables 8 and 1 5 , except where it is demonstrated by experimental evidence and analysis that other inelastic actions are accept-
Section C4.4.2.2 has a discussion ofTable 1 5 and acceptance criteria for reinforced concrete slab-column connections. Section C4.2.2.2 has a discussion of Table 8 and acceptance criteria for reinforced concrete columns.
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able for the selected performance levels. Other actions shall be defined as force-controlled. Calculated component actions shall satisfy the require ments of 5 .5.3.2 of ASCE 4 1 - 17. Maximum permissible inelastic deformations shall be taken from Tables 8 and 1 5. Alternative values shall be permitted where justified by experimental evidence and analysis. 4.4.5 Retrofit measures for slab-column momentframes
Seismic retrofit measures for slab-column moment frames shall meet the requirements of 3 . 7 and other provisions of this standard.
C4.4.5 Retrofit measures for slab-column moment fram es Retrofit measures described in C4.2.5 for rein -
forced concrete beam-column moment frames can also be effective in rehabilitating reinforced concrete slab-column moment frames. Further retrofit measures are found in FEMA 547.
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CHAPTER 5-PRECAST CONCRETE FRAM ES 5.1-Types of precast concrete frames Precast concrete frames shall be defined as those elements constructed from individually made beams and columns assembled to resist externally applied loads through frame action. These systems shall include those that are consid ered in design to resist seismic forces and those that are considered in design as secondary elements that do not resist seismic forces but must resist the effects of deformations resulting from seismic forces.
C5. 1 -Types of precast concrete frames
5.1.1 Precast concrete frames expected to resist seismic forces Frames of this classification are assembled using
C5.1.1 Precast concrete frames expected to resist seismic forces-These systems are recognized and accepted by
either wet or dry joints (connections are made by bolting, welding, post-tensioning, or other similar means) in a way that results in significant seismic force resistance in the frame element. Frames of this classification resist seismic forces either acting alone or acting in conjunction with shear walls, braced frames, or other seismic-force-resisting elements.
FEMA P-750 and are based on ACI 3 1 8M, which speci fies safety and serviceability levels expected from precast concrete frame construction. In the referenced documents, precast frames are not classified by the method of construc tion (wet or dry j oints), but by the expected behavior resulting from the detailing used. In addition to recognizing varying levels of ductile performance as a result of overall frame detailing, ACI 3 1 8M- 14, 1 8.9.2. 1 , 1 8 .9.2.2, and 1 8 .9.2.3, acknowledge three types of unit-to-unit connec tions that can result in the highest level of performance. Such connections are either strong or ductile, as defined in 4.2, 1 8.9.2 . 1 , 1 8 .9.2.2, and 1 8.9.2.3 ofACI 3 1 8M- 1 4 or have demonstrated acceptable performance where tested in accor dance with ACI 374. 1 .
-
5.1.2 Precast concrete frames not expected to resist seismic forces directly-Frames of this classification shall
be assembled using dry joints in a way that does not result in significant seismic force resistance in the frame element. Other structural elements or systems such as shear walls, braced frames, or moment frames provide the entire seismic force resistance, with the precast concrete frame system deforming in a manner that is compatible with the structure as a whole. 5.2-Precast concrete frames expected to resist seismic forces 5.2.1 General-The analytical model for a frame element of this classification shall represent strength, stiffness, and deformation capacity of beams, columns, beam-column joints, and other components of the frame. Potential failure in flexure, shear, and reinforcement development at any section along the component length shall be considered. Interaction with other components, including nonstructural components, shall be included. All other considerations of 4.2 . 1 shall be taken into account. In addition, the effects of shortening caused by creep, and other effects of prestressing and post-tensioning on member behavior, shall be evaluated. Where dry joints are used in assembling the precast system, consideration shall be given to the effect of those joints on overall behavior. Where connections yield under the speci fied seismic forces, the analysis model shall take this effect into account.
C5.2-Precast concrete frames expected to resist seism ic forces
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5.2.2 Stiffness ofprecast concreteframes expected to resist seismic forces Stiffness for analysis shall be as defined in
-
4.2.2. The effects of prestressing shall be considered where computing the effective stiffness values using Table 5 . Flex ibilities associated with connections shall be included in the analytical model. 5.2.3 Strength ofprecast concreteframes expected to resist seismic forces-Component strength shall be computed
according to the requirements of 4.2.3, with the additional requirement that the following effects be included in the analysis: a) Effects of prestressing that are present, including but not limited to reduction in rotation capacity, secondary stresses induced, and amount of effective prestress force remaining b) Effects of construction sequence, including the possi bility of construction of the moment connections occurring after portions of the structure are subjected to dead loads c) Effects of restraint caused by interaction with intercon nected wall or brace components d) Effects of connection strength, considered in accor dance with 3 . 6 5.2.4 Acceptance criteria for precast concrete frames expected to resist seismic forces Acceptance criteria for
-
precast concrete frames expected to resist seismic forces shall be as specified in 4.2.4, except that the factors defined in 5.2.3 shall also be considered. Connections shall comply with the requirements of 3.6. 5.2.5 Retrofit measures for precast concrete frames expected to resist seismic forces Seismic retrofit measures
C5.2.5 Retrofit measures for precast concrete frames expected to resist seismic forces-The retrofit measures
for precast concrete frames shall meet the requirements of 3. 7 and other provisions of this standard and ASCE 4 1 .
described in C4.2.5 for reinforced concrete beam-column moment frames can also be effective in retrofitting precast concrete moment frames. When installing new components or materials to the existing system, existing prestressing strands should be protected.
5.3-Precast concrete frames not expected to resist seismic forces directly 5.3.1 General-The analytical model for precast concrete frames that are not expected to resist seismic forces directly shall comply with the requirements of 5 .2. 1 and shall include the effects of deformations that are calculated to occur under the specified seismic loadings.
C5.3-Precast concrete frames not expected to resist seismic forces directly
5.3.2 Stiffness of precast concrete frames not expected to resist seismic forces directly-The analytical model
C5.3.2 Stiffness ofprecast concrete frames not expected to resist seismic forces directly-The stiffness used in
shall include realistic lateral stiffness of these frames to evaluate the effects of deformations under seismic forces. If the lateral stiffness is ignored in the analytical model, the effects of calculated building drift on these frames shall be evaluated separately. The analytical model shall consider the negative effects of connection stiffness on component response where that stiffness results in actions that can cause component failure.
the analysis should consider possible resistance that can develop under lateral deformation. In some cases, it may be appropriate to assume zero lateral stiffness. The North ridge earthquake graphically demonstrated that there are few instances where the precast column can be considered to be completely pinned top and bottom and, as a consequence, not resist any shear from building drift. Several parking
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structures collapsed as a result of this lack of fixity. Conser vative assumptions should be made. 5.3.3 Strength of precast concrete frames not expected to resist seismic forces directly-Component strength shall
be computed according to the requirements of 5.2.3. All components shall have sufficient strength and ductility to transmit induced forces from one member to another and to the designated seismic-force-resisting system. 5.3.4 Acceptance criteria for precast concrete frames not expected to resist seismic forces directly-Acceptance
criteria for components in precast concrete frames not expected to resist seismic forces directly shall be as specified in 5.2.4. All moments, shear forces, and axial loads induced through the deformation of the structural system shall be checked using appropriate criteria in the referenced section. 5.3.5 Retrofit measures for precast concrete frames not expected to resist seismic forces directly-Seismic retrofit
C5.3.5 Retrofit measures for precast concrete frames not expected to resist seismic forces directly-The retrofit
measures for precast moment frames shall meet the require ments of 3.7 and other provisions herein.
measures described in C4.2.5 for reinforced concrete beam column moment frames can also be effective in retrofitting precast concrete frames not expected to resist seismic forces directly. When installing new components or materials to the existing system, existing prestressing strands should be protected.
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CHAPTER 6-CONCRETE FRAMES WITH IN FILLS 6. 1 -Types of concrete frames with infills Concrete frames with infills consist of complete gravity-load canying concrete frames infilled with masoruy or concrete, constructed in such a way that the infill and the concrete frame interact when subjected to gravity and seismic forces. Infills are considered to be isolated from the surrounding frame when the minimum gap requirements specified in 1 1 .4. 1 of ASCE 4 1 - 1 7 are satisfied. If all infills in a frame are isolated, the frame shall be analyzed as an isolated frame according to provisions given in Chapters 6, 7, and 1 1 , and the isolated infill panels shall be analyzed according to the requirements of Chapter 1 1 of ASCE 4 1 - 17.
C6.1 -Types of concrete frames with infills
6.1 . 1 Types offrames-The provisions of Chapter 6 shall apply to concrete frames, as defined in Chapters 4, 5, and 9, which interact with infills. 6.1.2 Masonry infills-The provisions of Chapter 4 shall apply to masonry infills, as defined in Chapter 1 1 of ASCE 4 1 - 1 7, which interact with concrete frames. 6.1.3 Concrete infills-The provisions of Chapter 6 shall apply to concrete infills that interact with concrete frames, where the infills were constructed to fill the space within the bay of a complete gravity frame without special provision for continuity from story to story. The concrete of the infill shall be evaluated separately from the concrete of the frame.
C6.1.3 Concrete infills-The construction of concrete infilled frames is similar to that of masonry-infilled frames, except that the infill is of concrete instead ofmasonry units. In older existing buildings, concrete infill commonly contains nominal reinforcement, which often does not extend into the surrounding frame elements. The concrete used in the infill is often lower quality than that used in the frame elements and should be evaluated separately from investigations of the frame concrete.
6.2-Concrete frames with masonry infills 6.2.1 General-The analytical model for a concrete frame with masoruy infills shall represent strength, stiff ness, and deformation capacity of beams, slabs, columns, beam-column joints, masonry infills, and all connections and components of the element. Potential failure in flexure, shear, anchorage, reinforcement development, or crushing at any section shall be considered. Interaction with nonstruc tural components shall be included. For a concrete frame with masonry infill resisting seismic forces within its plane, modeling of the response using a linear elastic model shall be permitted, provided that the infill does not crack when subjected to design seismic forces. If the infill does not crack when subjected to design seismic forces, modeling the assemblage of frame and infill as a homogeneous medium shall be permitted. For a concrete frame with masonry infills that cracks when subjected to design seismic forces, modeling of the response using a diagonally braced frame model, in which the columns act as vertical chords, the beams act as hori zontal ties, and the infill acts as an equivalent compression strut, shall be permitted. Requirements for the equivalent
C6.2-Concrete frames with masonry infills C6.2.1 General-The licensed design professional is referred to FEMA 274 and FEMA 306 for additional infor mation regarding the behavior of masoruy infills.
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compression strut analogy shall be as specified in Chapter 1 1 of ASCE 4 1 - 1 7. Frame components shall be evaluated for forces imparted to them through interaction of the frame with the infill, as specified in Chapter 1 1 of ASCE 4 1 - 1 7. In frames with full-height masonry infills, the evaluation shall include the effect of strut compression forces applied to the column and beam, eccentric from the beam-column joint. In frames with partial-height masonry infills, the evaluation shall include the reduced effective length of the columns above the infilled portion of the bay. 6.2.2 Stiffness ofconcrete frames with masonry infills 6.2.2.1 Linear static and dynamic procedures-In frames having infills in some bays and no infill in other bays, the restraint of the infill shall be represented as described in 6.2. 1 . Bays without infills shall b e modeled as frames as specified in appropriate portions of Chapters 4, 5, and 9. Where infills are discontinuous over the height, the effects of the discontinuity on overall building performance shall be evaluated. Effective stiffnesses shall be in accordance with 3 . 1 .2. 6.2.2.2 Nonlinear static procedure Nonlinear load deformation relations for use in analysis by the NSP shall follow the requirements of 3 . 1 .2.2. Modeling beams and columns using nonlinear truss elements shall be permitted in infilled portions of the frame. Beams and columns in non infilled portions of the frame shall be modeled using the relevant specifications of Chapters 4, 5, and 9. The model shall be capable of representing inelastic response along the component lengths. Monotonic load-deformation relations shall be according to the generalized relation shown in Fig. 1 , except different relations shall be permitted where verified by tests. Numer ical quantities in Fig. 1 shall be derived from tests or by analytical procedures, as specified in Chapter 7 of ASCE 4 1 - 1 7, and shall take into account the interaction between frame and infill components. Alternatively, the following procedure shall be permitted for monolithic reinforced concrete frames: a) For beams and columns in bays without infills, where the generalized deformation is taken as rotation in the flex ural plastic hinge zone, the plastic hinge rotation capacities shall be as defined by Tables 7 and 8. b) For masonry infills, the generalized deformations and control points shall be as defined in Chapter 1 1 of ASCE 4 1 - 1 7. c) For beams and columns in bays with infills, where the generalized deformation is taken as elongation or compres sion displacement of the beams or columns, the tension and compression strain capacities shall be as specified in Table 1 7 . -
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Table 1 7-Modeling parameters and nu merical acceptance criteria for non l i near procedures-rei nforced concrete infilled frames
.
Modeling parameters
Acceptance criteria Total strain
Residual strength ratio
Total strain Conditions
d i:
e
c
Performance level 10
LS
CP
Columns modeled as compression chordst
Columns confined along entire length!
0.02
0.04
0.4
0.003
0.03
0.04
All other cases
0.003
0.01
0.2
0.002
0.0 1
0.01
0.0 1
0.04
0.05
0.02
0.03
ii: Columns modeled as tension chords! Columns with well-confined splices or no splices
0.05
0.05
0.0
All other cases
§
0.03
0.2
-
'Interpolation shall not be permitted. l]f load reversals result in both Conditions i and ii applying to a single column, both conditions shall be checked. !A column shall be permitted to be considered confined along its entire length where the quantity of hoops along the entire story height including the joint is equal to three-fourths of that required by ACI 3 1 8M for boundary components of concrete shear walls. The maximum longitudinal spacing of sets of hoops shall not exceed either h/3 or 8db. §Potential for splice failure shall be evaluated directly to determine the modeling and acceptance criteria. For these cases, refer to the generalized procedure of6.3.2.
using properties verified by tests. Unloading and reloading properties shall represent stiffness and strength degradation characteristics. 6.2.3 Strength of concrete frames with masonry in/ills
Strengths of reinforced concrete components shall be calculated according to the general requirements of 3 .2, as modified by other provisions of this standard. Strengths of masonry infills shall be calculated according to the require ments of Chapter 1 1 of ASCE 4 1 - 1 7. Strength calculations shall consider the following: a) Limitations imposed by beams, columns, and joints in noninfilled portions of frames b) Tensile and compressive capacity of columns acting as boundary components of infilled frames c) Local forces applied from the infill to the frame d) Strength of the infill e) Connections with adjacent components 6.2.4 Acceptance criteria for concrete frames with masonry irifi.lls 6.2.4.1 Linear static and dynamic procedures-All compo nent actions shall be classified as either deformation-controlled or force-controlled, as defined in 7.5 . 1 of ASCE 4 1 - 1 7. In primary components, deformation-controlled actions shall be restricted to flexure and axial actions in beams, slabs, and columns, and lateral deformations in masonry infill panels. In secondary components, deformation-controlled actions shall be restricted to those actions identified for the isolated frame in Chapters 4, 5, and 9, as appropriate, and for the masonry infill in 1 1 .4 ofASCE 4 1 - 1 7. Design actions shall be determined as prescribed in Chapter 7 of ASCE 4 1 - 1 7. Where calculated DCR values
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Table 1 8-Numerical acceptance criteria for linear procedures-reinforced concrete infil led frames .
m-factors
Performance level Component type Primary Conditions
10
LS
Secondary CP
LS
CP
i : Columns modeled as compression chords! Columns confined along entire lengthl
I
3
4
4
5
All other cases
I
I
I
I
I
ii: Columns modeled as tension chords! Columns with well-confined splices or no splices
3
4
5
5
6
All other cases
I
2
2
3
4
·Interpolation shall not be permitted. l]fload reversals result in both Conditions i and ii applying to a single column, both conditions shall be checked. lA column
is permitted to be considered confined along its entire length where the quantity of hoops along the entire story height. including the joint, is equal to three-fourths of that required by ACI 3 1 8M for boundary components of concrete shear walls. The maximum longitudinal spacing of sets of hoops shall not exceed either h/3 or 8d,.
exceed unity, the following design actions shall be deter mined using limit analysis principles as prescribed in Chapter 7 of ASCE 4 1 - 1 7: 1) moments, shears, torsions, and development and splice actions corresponding to develop ment of component strength in beams, columns, or masonry infills; and 2) column axial load corresponding to develop ment of the flexural capacity of the infilled frame acting as a cantilever wall. Design actions shall be compared with strengths in accor dance with 7.5.2.2 ofASCE 4 1 - 17. Values ofm-factors shall be as specified in 1 1 .4.2.4 ofASCE 4 1 - 1 7 for masonry infills; applicable portions of Chapters 4, 5, and 9 for concrete frames; and Table 1 8 for columns modeled as tension and compression chords. Those components that have design actions less than strengths shall be assumed to satisfy the performance criteria for those components. 6.2.4.2 Nonlinear static and dynamic procedures-In
the design model, inelastic response shall be restricted to those components and actions that are permitted for isolated frames as specified in Chapters 4, 5, and 9, and for masonry infills as specified in 1 1 .4 of ASCE 4 1 - 1 7. Calculated component actions shall satisfy the require ments of 7.5.3.2 of ASCE 4 1 - 1 7 and shall not exceed the numerical values listed in Table 17; the relevant tables for isolated frames given in Chapters 4, 5, and 9; and the rele vant tables for masonry infills given in Chapter 1 1 of ASCE 4 1 - 1 7. Component actions not listed in Tables 7, 8, and 1 0 shall b e treated a s force-controlled. Alternative approaches or values shall be permitted where justified by experimental evidence and analysis. 6.2.5 Retrofit measures for concrete frames with masonry infills Seismic retrofit measures for concrete frames with
C6.2.5 Retrofit measures for concrete frames with masonry infills-The retrofit measures described in relevant
masonry infills shall meet the requirements of 3 .7 and other provisions herein.
commentary of Chapters 4, 5 , and 9 for isolated frames, and retrofit measures described in relevant commentary of
-
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1 1 .4 of ASCE 4 1 - 1 7 for masonry infills, can also be effec tive in retrofitting concrete frames with masonry infills. The licensed design professional is referred to FEMA 308 for further information in this regard. In addition, the following retrofit measures can be effective in rehabilitating concrete frames with infills: a) Post-tensioning existing beams, columns, or joints using external post-tensioned reinforcement. Vertical post tensioning can be effective in increasing tensile capacity of columns acting as boundary zones. Anchorages should be located away from regions where inelastic action is antici pated and should be designed considering possible force variations caused by seismic forces. b) Modification of the element by selective material removal from the existing element. Either the infill should be completely removed from the frame or gaps should be provided between the frame and the infill. In the latter case, the gap requirements of Chapter 1 1 of ASCE 4 1 - 1 7 should be satisfied and adequate measures must be taken to guar antee the out-of-plane stability of the infill. c) Changing the building system to reduce the demands on the existing element. Examples include the addition of supple mentary seismic-force-resisting elements such as walls, steel braces, or buttresses; seismic isolation; and mass reduction. 6.3-Concrete frames with concrete infills 6.3.1 General-The analytical model for a concrete frame with concrete infills shall represent the strength, stiff ness, and deformation capacity of beams, slabs, columns, beam-column joints, concrete infills, and all connections and components of the elements. Potential failure in flexure, shear, anchorage, reinforcement development, or crushing at any section shall be considered. Interaction with nonstruc tural components shall be included. The analytical model shall be established considering the relative stiffness and strength of the frame and the infill, as well as the level of deformations and associated damage. For low deformation levels, and for cases where the frame is relatively flexible, the infilled frame shall be permitted to be modeled as a shear wall, with openings modeled where they occur. In other cases, the frame-infill system shall be permitted to be modeled using a braced-frame analogy such as that described for concrete frames with masonry infills in 6.2. Frame components shall be evaluated for forces imparted to them through interaction of the frame with the infill as speci fied in Chapter 1 1 of ASCE 41-17. In frames with full-height infills, the evaluation shall include the effect of strut compres sion forces applied to the column and beam eccentric from the beam-column joint. In frames with partial-height infills, the evaluation shall include the reduced effective length of the columns above the infilled portion of the bay. In frames with infills in only some bays, the restraint of the infill shall be represented as described in this section. Bays without infills shall be modeled as frames as specified in appropriate portions of Chapters 4, 5, and 9. Where infills create a discontinuous wall over the height, the effects of
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C6.3-Concrete frames with concrete infills
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the discontinuity on overall building performance shall be evaluated. 6.3.2 Stiffness ofconcrete frames with concrete infills 6.3.2.1 Linear static and dynamic procedures-Effective
stiffnesses shall be calculated according to the principles of 3 . 1 .2 . 1 and the procedure of 6.2.2. 1 . 6.3.2.2 Nonlinear static procedure-Nonlinear load deformation relations for use in analysis by NSP shall follow the requirements of 3 . 1 .2.2. Monotonic load-deformation relations shall be according to the generalized relation shown in Fig. 1 , except that different relations shall be permitted where verified by tests. Numerical quantities in Fig. 1 shall be derived from tests or by analysis procedures specified in 7.6 of ASCE 4 1 - 1 7 and shall take into account the interactions between frame and infill components. Alternatively, the procedure of 4.2.2.2 shall be permitted for the development ofnonlinear modeling parameters for concrete frames with concrete infills. 6.3.2.3 Nonlinear dynamic procedure-Nonlinear load deformation relations for use in analysis by NDP shall model the complete hysteretic behavior of each component using properties verified by tests. Unloading and reloading properties shall represent stiffness and strength degradation characteristics. 6.3.3 Strength of concrete frames with concrete irifills
Strengths of reinforced concrete components shall be calculated according to the general requirements of 4.2, as modified by other specifications of this chapter. Strength calculations shall consider the following: a) Limitations imposed by beams, columns, and joints in unfilled portions of frames b) Tensile and compressive capacity of columns acting as boundary components of infilled frames c) Local forces applied from the infill to the frame d) Strength of the infill e) Connections with adjacent components Strengths of existing concrete infills shall be determined considering shear strength of the infill panel. For this calcu lation, procedures specified in 7.2.3 shall be used for calcu lation of the shear strength of a wall segment. Where the frame and concrete infill are assumed to act as a monolithic wall, flexural strength shall be based on continuity of vertical reinforcement in both the columns acting as boundary components and the infill wall, including anchorage of the infill reinforcement in the boundary frame. 6.3.4 Acceptance criteria for concrete frames with concrete irifills-The acceptance criteria for concrete frames
with concrete infills shall comply with relevant acceptance criteria of 6.2.4, Chapter 7, and Chapter 8. American Concrete Institute Copyrighted Material-www.concrete.org
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6.3.5 Retrofit measures for concrete frames with concrete inills Seismic retrofit measures for concrete frames with concrete infills shall meet the requirements of 3 . 7 and other provisions of this standard and AS CE 4 1 .
C6.3.5 Retrofit measuresfor concreteframes with concrete infills Retrofit measures described in C6.2.5 for concrete
f
-
-
frames with masonry infills can also be effective in reha bilitating concrete frames with concrete infills. In addition, application of shotcrete to the face of an existing wall to increase the thickness and shear strength can be effective. For this purpose, the face of the existing wall should be roughened, a mat of steel reinforcement should be doweled into the existing structure, and shotcrete should be applied to the desired thickness. The licensed design professional is referred to FEMA 308 for further information regarding retrofit of concrete frames with concrete inti!!.
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CHAPTER 7-CONCRETE STRUCTURAL WALLS 7.1 -Types of concrete structural walls and associated components The provisions of Chapter 7 shall apply to all reinforced concrete structural walls in all types of structural systems that incorporate reinforced concrete structural walls. These types include isolated structural walls, structural walls used in wall-frame systems, coupled structural walls, and discon tinuous structural walls. Structural walls shall be permitted to be considered as solid walls if they have openings that do not significantly influence the strength or inelastic behavior of the wall. Perforated structural walls shall be defined as walls that have a regular pattern of openings in both hori zontal and vertical directions that creates a series of wall pier (vertical wall segment) and deep beam components (hori zontal wall segment). Coupling beams shall comply with provisions of 7.2 and shall be exempted from the provisions for beams covered in Chapter 4.
C7.1 -Types of concrete structural walls and associated components Concrete structural walls are planar vertical elements or combinations of interconnected planar elements that serve as lateral-load-resisting elements in concrete structures. Struc tural walls (or wall segments) shall be considered slender if their aspect ratio (h,jfw [height/length]) is greater than 3.0 and shall be considered short or squat if their aspect ratio is less than 1 .5 . Slender walls are normally controlled by flex ural behavior; short walls are normally controlled by shear behavior. The response of walls with intermediate aspect ratios is influenced by both flexure and shear. Identification of component types in concrete structural wall elements depends, to some degree, on the relative strengths ofthe wall segments based on expected or measured material properties. Vertical segments are often termed "wall piers", whereas horizontal segments can be called "coupling beams" or "spandrels". The licensed design professional is referred to FEMA 3 06 for additional information regarding the behavior of concrete wall components. Selected infor mation from FEMA 306 has been reproduced in Table C3 and Fig. C3 to clarify wall component identification.
7.1 . 1 Monolithic reinforced concrete structural walls and wall segments-Monolithic reinforced concrete structural
C7.1.1 Monolithic reinforced concrete structural walls and wall segments-The wall reinforcement is normally
walls shall consist of vertical cast-in-place elements, either uncoupled or coupled, in open or closed shapes. These walls shall have relatively continuous cross sections and rein forcement and shall provide both vertical and lateral force resistance, in contrast with infilled walls defined in 6. 1 .3 . Structural walls or wall segments with axial loads greater than 0.3 5P0 shall not be considered effective in resisting seismic forces. For the purpose of determining effectiveness of structural walls or wall segments, the use of axial loads based on a limit state analysis shall be permitted.
continuous in both the horizontal and vertical directions, and bars are typically lap-spliced for tension continuity. The reinforcement mesh can also contain horizontal ties around vertical bars that are concentrated either near the vertical edges of a wall with constant thickness or in boundary members formed at the wall edges. The amount and spacing of these ties is important for determining how well the concrete at the wall edge is confined and, thus, for deter mining the lateral deformation capacity of the wall. In general, slender reinforced concrete structural walls are governed by flexure and tend to form a plastic flexural hinge near the base of the wall under severe lateral loading. The ductility of the wall is a function of the percentage of longitudinal reinforcement concentrated near the bound-
Table C3-Reinforced concrete shear wall component types Component type per FEMA 306
Description
ASCE 41 designation
Stronger than beam or spandrel components that can frame into it so that nonlinear behavior
RC I
Isolated wall or stronger
(and damage) is generally concentrated at the base, with a flexural plastic hinge or shear
wall pier
failure. Includes isolated (cantilever) walls. If the component has a major setback or cutoff of reinforcement above the base, this section should be also checked for nonlinear behavior.
RC2 RC3
Weaker wall pier
Weaker than the spandrels to which it connects; characterized by flexural hinging top and
Weaker than the wall piers to which it connects; characterized by hinging at each end, shear
coupling beam
failure, or sliding shear failure.
Stronger spandrel
RC5
Pier-spandrel panel zone
wall segment
bottom or shear failure.
Weaker spandrel or
RC4
Monolithic reinforced concrete wall or vertical
Horizontal wall segment
Should not suffer damage because it is stronger than attached wall piers. If this component is damaged, it should probably be reclassified as Typically not a critical area in
or coupling beam
RC3.
RC walls.
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Wall segment
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\
CJ DD DD CJCJ
.---::0=----> D D D
Squat wall
Slender wall
Strongly coupled perforated wall
(a) Cantilever Wall Mechanisms RC3
D
Strong pier I weak spandrel
Weak pier / strong spandrel
Weakly coupled perforated wall
(b) Pier I Spandrel Mechanisms
_ _ _
pq
pq _
_ _ _
(c) Mixed Mechanisms Fig. C3-Identification ofcomponent types in concrete shear wall elements (FEMA 3 6).
aries of the wall, level of axial load, amount of lateral shear required to cause flexural yielding, thickness, reinforcement used in the web portion of the shear wall, and transverse reinforcement in the boundary elements, including the ratio of the transverse reinforcement spacing to the diameter of the longitudinal reinforcing bars. In general, higher axial load stresses and higher shear stresses reduce the flexural ductility and energy-absorbing capability of the wall. Short or squat structural walls are normally governed by shear. These walls normally have a limited ability to deform beyond the elastic range and continue to resist seismic forces. Thus, these walls are typically analyzed either as displacementAmerican Concrete Institute Copyrighted Material-www.concrete.org
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controlled components with low ductility capacities or as force-controlled components. 7.1.2 Reinforced concrete columns supporting discon tinuous structural walls-Reinforced concrete columns
C7.1.2 Reinforced concrete columns supporting discon tinuous structural walls-In structural wall buildings, it is
supporting discontinuous structural walls shall be analyzed in accordance with the requirements of 4.2.
not uncommon to find that some walls are terminated either to create commercial space in the first story or to create parking spaces in the basement. In such cases, the walls are commonly supported by columns. Such designs are not recommended in seismic zones because very large demands can be placed on these columns during earthquake loading. In older buildings, such columns often have standard longi tudinal and transverse reinforcement; the behavior of such columns during past earthquakes indicates that tightly spaced closed ties with well-anchored 1 35-degree hooks are required for the building to survive severe seismic forces.
7.1.3 Reinforced concrete coupling beams-Reinforced concrete coupling beams used to link two shear walls together shall be evaluated and rehabilitated to comply with the requirements of7.2.
C7.1.3 Reinforced concrete coupling beams-Coupled walls are generally much stiffer and stronger than they would be if they acted independently. Coupling beams typically have a small span-depth ratio, and their inelastic behavior is normally affected by the high shear forces acting in these components. Coupling beams in most older reinforced concrete buildings commonly have conventional reinforce ment that consists of longitudinal flexural steel and trans verse steel for shear. In some more modern buildings, or in buildings where coupled structural walls are used for seismic retrofit, the coupling beams can use diagonal reinforcement as the primary reinforcement for both flexure and shear. The inelastic behavior of coupling beams that use diagonal rein forcement has been shown experimentally to be much better with respect to retention of strength, stiffness, and energy dissipation capacity than the observed behavior of coupling beams with nonprestressed reinforcement.
7.2-Rei nforced concrete structural walls, wal l segments, and cou pling beams 7.2.1 General-The analytical model for a structural wall element shall represent the stiffness, strength, and deforma tion capacity of the wall. Potential failure in flexure, shear, and reinforcement development at any point in the wall shall be considered. Interaction with other structural and nonstructural components shall be included. Slender structural walls and wall segments shall be permitted to be modeled as equivalent beam-column elements that include both flexural and shear deforma tions. The flexural strength of beam-column elements shall include the interaction of axial load and bending, and shall be calculated based on expected material properties. The rigid connection zone at beam connections to this equivalent beam-column element shall represent the distance from the wall centroid to the edge of the wall. Unsymmetrical wall sections shall be modeled with the different bending capaci ties for the two loading directions. A beam element that incorporates both bending and shear deformations shall be used to model coupling beams. The
C7.2-Reinforced concrete structural walls, wall segments, and coupling beams C7.2.1 General-For rectangular structural walls, wall segments with h,j£\V :S 2.5 and flanged wall sections with h,/EIV :S 3 .5, either a modified beam-column analogy or a multiple-node, multiple-spring approach should be used. Because structural walls usually respond in single curvature over a story height, one multiple-spring element per story can be used for modeling walls. Wall segments should be modeled with either the beam-column element or with a multiple-spring model with two elements over the length of the wall segment. Coupling beams that have diagonal reinforcement satis fying ACI 3 1 8M requirements commonly have a stable hysteretic response under large load reversals. Therefore, these members could adequately be modeled with beam elements used for typical frame analyses.
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inelastic response shall account for the loss of shear strength and stiffness during reversed cyclic loading to large defor mations. For coupling beams that have diagonal reinforce ment satisfying ACI 3 1 8M requirements, a beam element representing flexure only shall be permitted. The diaphragm action of concrete slabs that interconnect shear walls and frame columns shall be represented in the model. 7 .2.2 Stiffness ofreinforced concrete structural walls, wall segments, and coupling beams-The effective stiffness of all
C7.2.2 Stiffness of reinforced concrete structural walls, wall segments, and coupling beams-Element stiffness
the elements discussed in Chapter 9 shall be defined based on the material properties, component dimensions, rein forcement quantities, boundary conditions, and current state of the member with respect to cracking and stress levels. Alternatively, use of values for effective stiffness given in Table 5 shall be permitted. For coupling beams, the effective stiffness values given in Table 5 for nonprestressed beams shall be used unless alter native stiffnesses are determined by more detailed analysis.
recommendations for flexure-controlled structural walls are intended to provide a secant-to-yield stiffness, neglecting the effect of wall stiffness properties prior to flexural cracking on the calculated response. When significant flexural cracking is expected to occur, the initial wall stiffness is not considered to have a significant effect on calculated nonlinear deforma tions because demands generally exceed the cracking load during the first significant cycle of dynamic loading. In cases where little to no cracking is expected to occur, the licensed design professional can use iterative analytical techniques to obtain a more accurate approximation of the wall stiffness. To calculate the effective stiffness to yield of flexure controlled walls, the 20 1 3 version of ASCE 4 1 recom mended using a reduction factor for the gross moment of inertia of 0.5 times Ig. However, experimental studies of slender walls pushed to yield-level drifts have shown lower stiffness reduction factors, in the range of 0. 1 5 to 0.25 times the gross moment of inertia (PEER 20 1 0; Panagiotou and Restrepo 2007; Priestley et al. 2007). An important limi tation of this type of approach is that the calculated effec tive wall stiffness is independent of parameters such as the vertical reinforcement ratio and axial load. For a given concrete cross section, studies have shown that yield curvature is not sensitive to reinforcing ratio and axial loads (Wallace and Moehle 1992). Equations that rely on the yield curvature to calculate the effective stiffness (Priestley and Kowalski 1998) have been shown to provide estimates of effec tive stiffness that are in reasonable agreement with experimen tally measured values when axial loads and reinforcement ratios are relatively low. For the case where Nuci(AJ�E) :S 0. 1 5 and Pe :S 0.0 1 , the effective yield curvature tPy£ can be approximated for planar concrete walls as yE
2fye
= fEE w
(C4)
s
For flexural deformations without the effect of bond slip, the effective flexural rigidity (EI)eff can be calculated in accordance with Eq. (C5) (C5) where My£ is evaluated using an applied axial load NUG·
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Alternatively, moment-curvature analysis can be used, and a more general relationship for wall flexural rigidity can be derived (C6) where AfJyE is evaluated using an applied axial load Nuc· Where inadequate anchorage or splices are present, the calculated moment strength used to evaluate wall flexural rigidity should be based on the reduced reinforcement capacity in accordance with 3 . 5 . When bond slip is expected at the interface between the structural wall and the anchoring supporting element, the additional flexibility at the interface should be accounted for. A rigid-body rotation associated with bond slip of the longitudinal reinforcing bars within the foundation occurs at the wall-to-foundation interface, which adds to wall defor mations. Where this type of behavior is anticipated, the additional flexibility can be accounted for either implicitly by reducing the wall effective flexural rigidity or explicitly by introducing a flexible rotational spring. There are several methodologies available for approximating bond slip. For continuous walls, an acceptable approach for capturing the effects of bond slip is to modify the effective flexural rigidity of the wall in the story directly above the interface as follows (EJ)
eff
=
Mfy£
h1
fy£
[-h_l-l hi + £ s
(C7)
p
Equation (C7) assumes a constant yield curvature profile over the first-floor height and compares well against shake table testing from multi-story building prototypes. With this method, the flexibility associated with bar slip is lumped within the story above the interface, and only the moment of inertia over the height is modified for bond slip. Above the height Eq. (C6) can be used to estimate wall flexural rigidity using yield moments and curvatures at wall hinges or using the expected maximum moments and associated curvatures at the levels considered. The strain penetration depth fsp in this equation is meant to approximate the length over which flexural longitudinal bar strains penetrate into the foundation system and can be approximated as follows for the purpose of approximating bar slip. Equation (C5) was derived assuming an average bond stress of l .O 'ifc ' (MPa), which was shown to be an appropriate estimate of average bar stresses into the founda tion under earthquake excitations (Ghannoum and Moehle 2012). Other equations and methodologies have been proposed to account for strain penetration and deformations from bar slip (Priestley et al. 2007).
h� ,
h1
(CS)
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For plane bars, lsp can be taken as twice the value obtained from Eq. (C8). As an alternative to modifying the flexural rigidity to account for bar slip, a rotational spring can be used to explicitly capture slip, where the spring stiffness is defined as KR
=
2Mfy£ 0.05
0.75
1 .0
0.4
0.0
0.6
0.40
0.75
1 .0
ii: Shear wall coupling beams! Longitudinal reinforcement and
v
transverse reinforcement!
t"C ,fj;;
Conventional longitudinal
::;0.25
0.02
0.030
0.60
0.006
0.020
0.030
transverse reinforcement
�0.5
0.0 1 6
0.024
0.30
0.005
0.0 1 6
0.024
Conventional longitudinal
::;0.25
0.0 1 2
0.025
0.40
0.006
0.0 1 0
0.020
�0.5
0.008
0.0 1 4
0.20
0.004
0.007
0.012
reinforcement with conforming
reinforcement with nonconforming transverse reinforcement
"For shear walls and wall segments, use drift; for coupling beams, use chord rotation; refer to Fig. 5 and 6. I Fo r shear walls and wall segments where inelastic behavior i s governed b y shear, the axial load on the member must be less than o r equal t o O. I SA,j;'; otherwise, the member must be treated as a force-controlled component. lFor coupling beams spanning less than 2400 mm, with bottom reinforcement continuous into the supporting walls, acceptance criteria values shall be permitted to be doubled for LS and CP performance. !Conventional longitudinal reinforcement consists oftop and bottom steel parallel to the longitudinal axis of the coupling beam. Conforming transverse reinforcement consists of: (a) closed stirrups over the entire length of the coupling beam at a spacing less than or equal to d/3; and (b) strength of closed stirrups V, � 3/4 of required shear strength of the coupling beam.
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The flexural strength of structural walls or wall segments, My, shall be determined using the fundamental principles given in Chapter 22 of ACI 3 1 8M-14. For calculation of flex ural strength, as represented by Point B in Fig. l (a), the effec tive compression and tension flange widths defined in 7.2.2 shall be used, except that the first limit shall be changed to one-tenth of the wall height. Where calculating the maximum inelastic flexural strength of the wall, MP,., as represented by Point C in Fig. 1 (a), the effects from strain hardening shall be accounted for by substitutingJ;e£ with 1 .25J;eE· For all moment strength calculations, the yield strength of the longitudinal reinforcement shall be taken as lower bound or expected material properties as applicable to deformation-controlled or force-controlled actions, respectively. For all moment strength calculations, the axial load acting on the wall shall include gravity loads, as defined in 7.2.2 ofASCE 4 1 - 1 7. The nominal shear strength of a structural wall or wall segment shall be determined based on the principles and equations given in Chapter 1 8 of ACI 3 1 8M- 1 4, except that the restriction on spacing, reinforcement ratio, and the number of curtains of reinforcement shall not apply to existing walls. There shall be no difference between the yield and nominal shear strengths, as represented by Points B and C in Fig. I . Where an existing shear wall or wall segment has a trans verse reinforcement percentage p1 less than 0.00 1 5 or where the cracking moment strength exceeds the yield strength, the wall shall be considered force-controlled. Splice lengths for primary longitudinal reinforcement shall be evaluated using the procedures given in 3.5. Reduced flexural strengths shall be evaluated at locations where splices govern the usable stress in the reinforcement. The need for confinement reinforcement in boundary elements shall be evaluated by the procedure in ACI 3 1 8M or other approved procedure. The nominal flexural and shear strengths of coupling beams shall be evaluated using the principles and equations contained in Chapter 1 8 of ACI 3 1 8M- 14. The expected strength of longitudinal or diagonal reinforcement shall be used.
between the strength of walls with one or two curtains of web reinforcement (Elwood et a!. 2007).
7.2.4 Acceptance criteria for reiriforced concrete struc tural walls, wall segments, and coupling beams 7.2.4.1 Linear static and dynamic procedures-Structural
C7.2.4.1 Linear static and dynamic procedures-For
walls, wall segments, and coupling beams shall be classi fied as either deformation- or force-controlled, as defined in 5 .5 . 1 of ASCE 4 1 - 1 7. In these components, deformation controlled actions shall be restricted to flexure or shear. All other actions shall be treated as force-controlled. The flexural strength of a structural wall or wall segment shall be used to determine the maximum shear force in struc tural walls and wall segments. For cantilever structural walls, the shear force shall be equal to the magnitude of the lateral force required to develop the nominal flexural strength at the base ofthe wall, assuming that the lateral force is distributed uniformly over the height of the wall. For wall segments, the shear force shall be equal to the shear corresponding to the
shear-controlled coupling beams, ductility is a function of the shear in the member as determined by the expected shear capacity of the member. In accordance with 3 .2, expected strengths are calculated using the procedures specified in ACI 3 1 8M. For coupling beams, the concrete contribution to shear strength is nearly always zero.
(ciCiJ
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development of the positive and negative nominal moment strengths at opposite ends of the wall segment. Design actions (flexure, shear, axial, or force transfer at reinforcing bar anchorages and splices) on components shall be determined as prescribed in Chapter 7 of ASCE 4 1 - 1 7. Where determining the appropriate value for the design actions, proper consideration shall be given to gravity loads and to the maximum forces that can be transmitted consid ering nonlinear action in adjacent components. Design actions shall be compared with strengths in accordance with 7.5 .2.2 of ASCE 4 1 -1 7. Tables 21 and 22 specify m-factors for use in Eq. (7-36) of ASCE 41-17. Alternate m-factors shall be permitted where justified by experimental evidence and analysis. Table 21-Numerical acceptance criteria for l i near procedures: reinforced concrete shear walls and associated components controlled by flexure m-factors Performance level Component type Primary Conditions
10
LS
Secondary CP
LS
CP
i : Shear walls and wall segments•
(A, - A;)JyE + p t
V,.J;�
:
v
Confined
tj,..,fl:;
boundary§
:00. 1
:00.33
Yes
2
4
6
6
8
:00. 1
�0.5
Yes
2
3
4
4
6
�.25
:00.33
Yes
1 .5
3
4
4
6
�.25
�0.5
Yes
1 .25
2
2.5
2.5
4
:00. 1
:00.33
No
2
2.5
4
4
6
:00. 1
�0.5
No
1 .5
2
2.5
2.5
4
1.5
2
2
3
1.5
1 . 75
1 .75
2
�.25
:00.33
No
1 .25
�.25
�0.5
No
1 .25
ii: Shear wall coupling beamsll Longitudinal reinforcement and transverse
v
:
reinforcement•
t,l,.-J]:;
Conventional longitudinal reinforcement with
:00.25
2
4
6
6
9
conforming transverse reinforcement
�0. 5
1 .5
3
4
4
7
:00.25
1 .5
3.5
5
5
8
�0.5
1 .2
1.8
2.5
2.5
4
NA
2
5
7
7
10
Conventional longitudinal reinforcement with nonconforming transverse reinforcement Diagonal reinforcement
•Linear interpolation between values listed in the table shall be pennitted.
tP is the design axial force in the member. Alternatively, use of axial loads determined based on a limit state analysis shall be permitted. l V is
the shear force calculated using limit-state analysis procedures in accordance with 7.2.4.
§A boundary element shall be considered confined where transverse reinforcement exceeds 7 5 percent o fthe requirements given i n ACI 3 1 8M and spacing o ftransverse reinforcement does not exceed 8d,. It shall be permitted to take modeling parameters and acceptance criteria as 80 percent of confined values where boundary elements have at least 50 percent of the requirements given in ACI 3 1 8M and spacing of transverse reinforcement does not exceed Sd,. Otherwise, boundary elements shall be considered not confined. llfor secondary coupling beams spanning less than 2400 mm, with bottom reinforcement continuous into the supporting walls, secondary values shall be permitted to be doubled. 'Conventional longitudinal reinforcement consists of top and bottom steel parallel to the longitudinal axis of the coupling beam. Conforming transverse reinforcement consists of: a) closed stirrups over the entire length of the coupling beam at a spacing less than or equal to d/3 ; and b) strength of closed stirrups V, � 3/4 of required shear strength of the coupling beam. American Concrete Institute Copyrighted Material-www.concrete.org
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Table 22-Numerical acceptance criteria for l inear procedures: reinforced concrete shear walls and associated components controlled by shear m-factors Performance level Component type Primary Conditions
LS
10
Secondary CP
LS
CP
i: Shear walls and wall segments'
(A, - A:)Jy£ + p 1,/-.J:£ (A, - A:)f,.£ + p 1,/- ,J:£
< 0.05
2
2.5
3
4.5
6
> 0.05
1.5
2
3
3
4
3
4
4
6
i i : Shear wall coupling beams! Longitudinal reinforcement and transverse
v
§
reinforcement'
1,/.., J]:;
Conventional longitudinal reinforcement with
::;0.25
1.5
conforming transverse reinforcement Conventional longitudinal reinforcement with nonconforming transverse reinforcement
20.5
1.2
2
2.5
2.5
3.5
::;0.25
1.5
2.5
3
3
4
20.5
1.2
1 .2
1 .5
1 .5
2.5
'The shear shall be considered to be a force-controlled action for shear walls and wall segments where inelastic behavior is governed by shear and the design axial load is greater than 0. 1 5Ag};'. It shall be permitted to calculate the axial load based on a limit state analysis. 1For secondary coupling beams spanning less than 2400 mm, with bottom reinforcement continuous into the supporting walls, secondary values shall be permitted to be doubled. !Conventional longitudinal reinforcement consists of top and bottom steel parallel to the longitudinal axis of the coupling beam. Conforming transverse reinforcement consists of: a) closed stirrups over the entire length of the coupling beam at a spacing less than or equal to d/3; and b) strength of closed stirrups V, 2 3/4 of required shear strength of the coupling beam. § V is the shear force calculated using limit-state analysis procedures in accordance with 7.2.4. I .
7.2.4.2 Nonlinear static and dynamic procedures-In the design model, inelastic response shall be restricted to those components and actions listed in Tables 1 9 and 20, except where it is demonstrated that other inelastic actions are justi fied for the selected performance levels. For members expe riencing inelastic behavior, the magnitude of other actions (forces, moments, or torque) in the member shall correspond to the magnitude of the action causing inelastic behavior. The magnitude of these other actions shall be shown to be below their nominal capacities. Components experiencing inelastic response shall satisfy the requirements of7 .5 .3 .2 ofASCE 4 1 - 1 7, and the maximum plastic hinge rotations, drifts, or chord rotation angles shall not exceed the values given in Tables 1 9 and 20 for the selected performance level. Linear interpolation between tabulated values shall be used if the member under analysis has condi tions that are between the limits given in the tables. 7 .2.5 Retrofit measures for reinforced concrete structural walls, wall segments, and coupling beams-Seismic retrofit
C7.2.5 Retrofit measures for reinforced concrete shear walls, wall segments, and coupling beams-The following
measures for reinforced concrete structural walls, wall segments, coupling beams, and columns supporting discon tinuous structural walls shall meet the requirements of 3.7 and other provisions herein.
measures can be effective in retrofitting reinforced struc tural walls, wall segments, coupling beams, and reinforced concrete columns supporting discontinuous structural walls:
(ciCiJ
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a) Addition of wall boundary elements: Addition of boundary elements can be an effective measure in strength ening walls or wall segments that have insufficient flexural strength. These members can be either cast-in-place rein forced concrete components or steel sections. In both cases, proper connections should be made between the existing wall and the added components. The shear demand and shear capacity of the retrofitted wall should be reevaluated. b) Addition of confinement j ackets at wall boundaries: Increasing the confinement at the wall boundaries by the addition of a steel or reinforced concrete jacket can be an effective measure in improving the flexural deformation capacity of a structural wall. For both types of jackets, the longitudinal steel should not be continuous from story to story unless the jacket is also being used to increase the flex ural capacity. The minimum thickness for a concrete jacket should be 75 mm. Carbon fiber wrap should be permitted for improving the confinement of concrete in compression. c) Reduction of flexural strength: Reduction in the flex ural capacity of a structural wall to change the governing failure mode from shear to flexure can be an effective retrofit measure. It can be accomplished by saw-cutting a specified number of longitudinal bars near the edges of the wall. d) Increased shear strength of wall: Increasing the shear strength of the web of a structural wall by casting additional reinforced concrete adjacent to the wall web can be an effec tive retrofit measure. The new concrete should be at least 1 00 mm thick and should contain horizontal and vertical reinforcement. The new concrete should be properly bonded to the existing web of the structural wall. The use of carbon fiber sheets, epoxied to the concrete surface, should also be permitted to increase the shear capacity of a shear wall. e) Confinement j ackets to improve deformation capacity of coupling beams and columns supporting discontinuous structural walls: The use of confinement
j ackets described previously as a retrofit measure for wall boundaries, and in Chapter 2 for frame elements, can also be effective in increasing both the shear capacity and the defor mation capacity of coupling beams and columns supporting discontinuous structural walls. f) Infilling between columns supporting discontinuous structural walls: Where a discontinuous structural wall is supported on columns that lack either sufficient strength or deformation capacity to satisfy design criteria, making the wall continuous by infilling the opening between these columns can be an effective retrofit measure. The infill and existing columns should be designed to satisfy all the requirements for new wall construction, including any strengthening of the existing columns required by adding a concrete or steel jacket for strength and increased confine ment. The opening below a discontinuous structural wall should also be permitted to be infilled with steel bracing. The bracing members should be sized to satisfy all design requirements, and the columns should be strengthened with a steel or a reinforced concrete j acket. American Concrete Institute Copyrighted Material-www.concrete.org
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All the aforementioned retrofit measures require an evalu ation of the wall foundation, diaphragms, and connections between existing structural elements and any elements added for retrofit purposes.
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CHAPTER 8-PR ECAST CONCRETE STRUCTURAL WALLS 8.1 -Types of precast structural walls Precast concrete structural walls shall consist of story high or half-story-high precast wall segments that are made continuous through the use of either mechanical connec tors or reinforcement splicing techniques with or without a cast-in-place connection strip. Connections between precast segments shall be permitted along both the horizontal and vertical edges of a wall segment. The following types of precast structural walls are addressed in Chapter 8: a) Effectively monolithic construction, defined as construc tion in which the reinforcement connections are made to be stronger than the adjacent precast panels so that the lateral load response of the precast wall system is comparable to that for monolithic structural walls b) Jointed construction, defined as construction in which inelastic action is permitted to occur at the connections between precast panels c) Tilt-up construction, defined as a special technique for precast wall construction where there are vertical joints between adjacent panels and horizontal joints at the founda tion level, and where the roof or floor diaphragm connects with the tilt-up panel 8.1.1 Effectively monolithic construction-For this type of precast wall, the connections between precast wall elements are designed and detailed to be stronger than the panels they connect. Precast structural walls and wall segments of effectively monolithic construction shall be evaluated by the criteria defined in Chapter 7.
8.1.2 Jointed construction-Precast structural walls and wall segments of jointed construction shall be evaluated by the criteria defined in 8.2.
C8. 1 -Types of precast structural walls
C8.1.1 Effectively monolithic construction-When the precast structural wall is subjected to lateral loading, any yielding and inelastic behavior should take place in the panel elements away from the connections. If the reinforcement detailing in the panel is similar to that for cast-in-place struc tural walls, then the inelastic response of a precast structural wall should be similar to that for a cast-in-place wall. Modern building codes permit the use ofprecast structural wall construction in high seismic zones if it satisfies the criteria for cast-in-place structural wall construction. C8.1.2 Jointed construction-For most older structures that contain precast structural walls, and for some modern construction, inelastic activity can be expected in the connec tions between precast wall panels during severe lateral loading. Because joints between precast walls in older build ings have often exhibited brittle behavior during inelastic load reversals, jointed construction was not permitted in high seismic zones. Therefore, where evaluating older build ings that contain precast walls that are likely to respond as j ointed construction, the permissible ductilities and rotation capacities provided in the following, which are less than those given in Chapter 7, should be reduced. For some modern structures, precast structural walls have been constructed with special connectors that are detailed to exhibit ductile response and energy absorption character istics. Many of these connectors are proprietary, and only limited experimental evidence concerning their inelastic behavior is available. Although this type of construction is clearly safer than j ointed construction in older buildings,
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the experimental evidence is not sufficient to permit the use of the same ductility and rotation capacities given for cast in-place construction. Thus, the permissible values given in Chapter 5 should be reduced. Section 9.6 of FEMA 450 provides testing criteria that can be used to validate design values consistent with the highest performance of monolithic structural wall construction. 8.1.3 Tilt-up construction-Structural walls and wall segments of tilt-up type of precast walls shall be evaluated by the criteria defined in 8.2.
C8.1.3 Tilt-up construction-Tilt-up construction should be considered a special case of jointed construction. The walls for most buildings constructed by the tilt-up method are longer than their height. Shear would usually govern their in-plane design, except where there are significant openings in the wall panels-for example, door openings at loading dock areas of warehouses. The major concern for most tilt-up construction is the connection between the tilt-up wall and the roof diaphragm. That connection should be analyzed carefully to be sure the diaphragm forces can be transmitted safely to the precast wall system.
8.2-Precast concrete structural walls and wall segments 8.2.1 General-The analytical model for a precast concrete structural wall or wall segment shall represent the stiffness, strength, and deformation capacity of the overall member, as well as the connections and joints between any precast panel components that compose the wall. Potential failure in flexure, shear, and reinforcement development at any point in the wall panels or connections shall be consid ered. Interaction with other structural and nonstructural components shall be included. Modeling of precast concrete structural walls and wall segments within the precast panels as equivalent frame elements that include both flexural and shear deforma tions shall be permitted. The rigid-connection zone at beam connections to these equivalent frame elements shall repre sent the distance from the wall centroid to the edge of the wall or wall segment. The different bending capacities for the two loading directions of unsymmetrical precast wall sections shall be modeled. For precast structural walls and wall segments where shear deformations have a more significant effect on behavior than flexural deformation, a multiple spring model shall be used. The diaphragm action of concrete slabs connecting precast structural walls and frame columns shall be represented in the model.
C8.2-Precast concrete structural walls and wall segments
8.2.2 Stiffness of precast concrete structural walls and wall segments-The modeling assumptions defined in 7 .2.2
for monolithic concrete structural walls and wall segments shall also be used for precast concrete walls. In addition, the analytical model shall model the axial, shear, and rotational deformations of the connections between the precast compo nents that compose the wall by either softening the model used to represent the precast panels or by adding spring elements between panels.
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8.2.2.1 Linear static and dynamicprocedures-The modeling procedures given in 7 .2.2 . 1 , combined with a procedure for including connection deformations as noted previously, shall be used. 8.2.2.2 Nonlinear static procedure Nonlinear load deformation relations shall comply with the requirements of 3 . 1 .2. The monotonic load-deformation relationships for analytical models that represent precast structural walls and wall segments within precast panels shall be in accordance with the generalized relation shown in Fig. I , except that alternative approaches shall be permitted where verified by experiments. Where the relations are according to Fig. 1 , the following approach shall be permitted. Values for plastic hinge rotations or drifts at Points B, C, and E in Fig. 1 for the two general shapes shall be as defined in the following. The strength levels at Points B and C shall correspond to the yield strength and expected flexural strength or lower-bound flexural strength, as is appropriate in accordance with 7.2.3 . The residual strength for the Line Segment D-E shall be as defined in the following. For precast structural walls and wall segments whose inelastic behavior under lateral loading is governed by flexure, the general load-deformation relationship shall be defined as in Fig. 1 (a). For these members, the x-axis of Fig. ! (a) shall be taken as the rotation over the plastic hinging region at the end of the member, as shown in Fig. 2. If the requirements for effectively monolithic construc tion are satisfied, the value of the hinge rotation at Point B shall correspond to the yield rotation 8y and shall be calcu lated by Eq. (5). The same expression shall also be used for wall segments within a precast panel if flexure controls the inelastic response of the segment. If the precast wall is of jointed construction and flexure governs the inelastic response of the member, then the value of 8y shall be increased to account for rotation in the joints between panels or between the panel and the foundation. For precast structural walls and wall segments whose inelastic behavior under lateral loading is governed by shear, the general load-deformation relationship shall be defined as in Fig. 1 (b). For these members, the x-axis of Fig. 1 (b) shall be taken as the story drift for structural walls and as the element drift for wall segments, as shown in Fig. 3 . For effectively monolithic construction, the values for the variables a11e, h11e, and C11e, required to define the loca tion of Points C, D, and E in Fig. ! (a), shall be as specified in Table 1 9. For construction classified as jointed construc tion, the values of a11e, h11e, and C11e specified in Table 19 shall be reduced to 50 percent of the given values, unless experi mental evidence is available to justify higher values. In no case, however, shall values larger than those specified in Table 1 9 be used. For effectively monolithic construction, values for the variables d11e, e11e, and C11e, required to find the Points C, D, and E in Fig. 1 (b), shall be as specified in Table 20 for the appropriate member conditions. For construction classi-
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fied as jointed construction, the values of d e, e11e, and Cne specified in Table 20 shall be reduced to 50 percent of the specified values unless experimental evidence is available to justify higher values. In no case, however, shall values larger than those specified in Table 20 be used. For Tables 19 and 20, linear interpolation between tabu lated values shall be permitted if the member under analysis has conditions that are between the limits given in the tables. 11
8.2.2.3 Nonlinear dynamic procedure-Nonlinear load deformation relations for use in analysis by NDP shall model the complete hysteretic behavior of each component using properties verified by experimental evidence. The general ized relation shown in Fig. 1 shall be taken to represent the envelope for the analysis. The unloading and reloading stiff nesses and strengths, and any pinching of the load-versus rotation hysteresis loops, shall reflect the behavior experi mentally observed for wall elements similar to the one under investigation. 8.2.3 Strength of precast concrete structural walls and wall segments-The strength of precast concrete structural
C8.2.3 Strength ofprecast concrete structural walls and wall segments-In older construction, attention should
walls and wall segments within the panels shall be computed according to the general requirement of3 .2, except as modified herein. For effectively monolithic construction, the strength calculation procedures given in 7.2.3 shall be followed. For jointed construction, calculations of axial, shear, and flexural strength of the connections between panels shall be based on fundamental principles of structural mechanics. Expected yield strength for steel reinforcement of connec tion hardware used in the connections shall be used where calculating the axial and flexural strength of the connec tion region. The unmodified specified yield strength of the reinforcement and connection hardware shall be used where calculating the shear strength of the connection region. For all precast concrete structural walls ofjointed construc tion, no difference shall be taken between the computed yield and nominal strengths in flexure and shear. The values for strength represented by the Points B and C in Fig. 1 shall be computed following the procedures given in Section 7.2.3 .
be given to the technique used for splicing reinforcement extending from adjacent panels into the connection. These connections can be insufficient and often can govern the strength of the precast shear wall system.
8.2.4 Acceptance criteria for precast concrete struc tural walls and wall segments-The acceptance criteria for
C8.2.4 Acceptance criteriafor precast concrete structural walls and wall segments-The procedures outlined in 9.6 of
precast concrete structural walls shall be as per 8.2.4. 1 or 8 .2.4.2 or by other approved methods.
FEMA 450-04 can be used to establish acceptance criteria for precast structural walls.
8.2.4.1 Linear static and dynamic procedures-For
precast wall construction that is effectively monolithic and for wall segments within a precast panel, the acceptance criteria defined in 7.2.4. 1 shall be followed. For precast wall construction defined as jointed construction, the accep tance criteria procedure given in 7 .2.4. 1 shall be followed; however, the m-factors specified in Tables 21 and 22 shall be reduced by 50 percent, unless experimental evidence justi fies the use of a larger value. An m-factor need not be taken American Concrete Institute Copyrighted Material-www.concrete.org
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as less than 1 .0 and in no case shall be taken as larger than the values specified in these tables. 8.2.4.2 Nonlinear static and dynamic procedures
Inelastic response shall be restricted to those structural walls (and wall segments) and actions listed in Tables 1 9 and 20, except where it is demonstrated by experimental evidence and analysis that other inelastic action is acceptable for the selected performance levels. For components experiencing inelastic behavior, the magnitude of the other actions (forces, moments, or torques) in the component shall correspond to the magnitude of the action causing the inelastic behavior. The magnitude of these other actions shall be shown to be below their nominal capacities. For precast walls that are effectively monolithic and wall segments within a precast panel, the maximum plastic hinge rotation angles or drifts during inelastic response shall not exceed the values specified in Tables 1 9 and 20. For precast walls of jointed construction, the maximum plastic hinge rotation angles or drifts during inelastic response shall not exceed one-half of the values specified in Tables 19 and 20 unless experimental evidence justifies a higher value. However, in no case shall deformation values larger than those specified in these tables be used for jointed type construction. Alternative approaches or values shall be permitted where justified by experimental evidence and analysis. 8.2.5 Retrofit measuresfor precast concrete structural walls and wall segments-Seismic retrofit measures for precast
C8.2.5 Retrofit measures for precast concrete structural walls and wall segments-Precast concrete structural wall
concrete structural walls and wall segments shall meet the requirements of 3.7 and other provisions of this standard.
systems can suffer from some of the same deficiencies as cast in-place walls. These deficiencies include inadequate flexural capacity, inadequate shear capacity with respect to flexural capacity, lack of confinement at wall boundary elements, and inadequate splice lengths for longitudinal reinforcement in wall boundaries. A few deficiencies unique to precast wall construction are inadequate connections between panels, to the foundation, and to floor or roof diaphragms. The retrofit measures described in Section 7.2.5 can be effective in retrofitting precast concrete structural walls. In addition, the following retrofit measures can be effective: a) Enhancement of connections between adjacent or intersecting precast wall panels: Mechanical connectors such as steel shapes and various types of drilled-in anchors, or cast-in-place strengthening methods, or a combina tion of the two, can be effective in strengthening connec tions between precast panels. Cast-in-place strengthening methods can include exposing the steel reinforcement at the edges of adjacent panels, adding vertical and transverse (tie) reinforcement, and placing new concrete. b) Enhancement of connections between precast wall panels and foundations: Increasing the shear capacity of the wall panel-to-foundation connection by using supple mental mechanical connectors or by using a cast-in-place overlay with new dowels into the foundation can be an effec tive retrofit measure. Increasing the overturning moment
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capacity of the panel-to-foundation connection by using drilled-in dowels within a new cast-in-place connection at the edges of the panel can also be an effective retrofit measure. Adding connections to adjacent panels can also be an effec tive retrofit measure in eliminating some of the forces trans mitted through the panel-to-foundation connection. c) Enhancement of connections between precast wall panels and floor or roof diaphragms: Strengthening these connections by using either supplemental mechan ical devices or cast-in-place connectors can be an effective retrofit measure. Both in-plane shear and out-of-plane forces should be considered where strengthening these connections.
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CHAPTER 9-CONCRETE BRACED FRAMES 9.1 -Types of concrete-braced frames Reinforced concrete-braced frames shall be defined as those frames with monolithic, nonprestressed, reinforced concrete beams, columns, and diagonal braces that are coin cident at beam-column joints and that resist seismic forces primarily through truss action. Where masonry infills are present in concrete-braced frames, requirements for masonry-infilled frames specified in Chapter 4 shall also apply. 9.2-General The analytical model for a reinforced concrete-braced frame shall represent the strength, stiffness, and deforma tion capacity of beams, columns, braces, and all connections and components of the frame. Potential failure in tension, compression (including instability), flexure, shear, anchorage, and reinforcement development at any section along the component length shall be considered. Interaction with other structural and nonstructural components shall be included. The use of analytical models that represent the framing with line elements with properties concentrated at compo nent centerlines shall be permitted. Analytical models shall also comply with the requirements specified in 4.2. 1 . In frames that have braces only in some bays, the restraint of the brace shall be represented in the analytical model as specified previously, and the nonbraced bays shall be modeled as frames in compliance with the applicable provi sions in other sections of this standard. Where braces create a vertically discontinuous frame, the effects of the disconti nuity on overall building performance shall be considered. Inelastic deformations in primary components shall be restricted to flexure and axial load in beams, columns, and braces. Other inelastic deformations shall be permitted in secondary components. 9.3-Stiffness of concrete braced frames 9.3.1 Linear static and dynamic procedures-Modeling of beams, columns, and braces in braced portions of the frame considering only axial tension and compression flexibilities shall be permitted. Nonbraced portions of frames shall be modeled according to procedures described in Chapters 4, 5 , and 9 of this standard for frames. Effective stiffnesses shall be according to 3 . 1 .2. 9.3.2 Nonlinear static procedure-Nonlinear load-defor mation relations shall comply with the requirements of 3 . 1 .2 . Beams, columns, and braces i n braced portions shall be modeled using nonlinear truss components or other models whose behavior has been demonstrated to adequately repre sent behavior of concrete components dominated by axial tension and compression loading. Models for beams and columns in nonbraced portions shall comply with require ments for frames specified in 4.2.2.2. The model shall be
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capable of representing inelastic response along the compo nent lengths, as well as within connections. Monotonic load-deformation relations shall be according to the generalized load-deformation relation shown in Fig. 1 , except that different relations are permitted where verified by experiments. The overall load-deformation relation shall be established so that the maximum resistance is consistent with the strength specifications of 3.2 and 4.2.3 . Numerical quantities in Fig. 1 shall be derived from tests, rational anal yses, or criteria of 6.2.2.2, with braces modeled as columns in accordance with Table 1 7 . 9.3.3 Nonlinear dynamic procedure-Nonlinear load deformation relations for use in analysis by NDP shall model the complete hysteretic behavior of each component using properties verified by experimental evidence. Unloading and reloading properties shall represent stiffness and strength degradation characteristics.
9.4-Strength of concrete-braced frames Component strengths shall be computed according to the general requirements of 3.2 and the additional requirements of 4.2.3 . The possibility of instability of braces in compres sion shall be considered. 9.5-Acceptance criteria for concrete-braced frames 9.5.1 Linear static and dynamic procedure-All actions shall be classified as being either deformation-controlled or force-controlled, as defined in 7.5 . 1 of ASCE 4 1 - 1 7. In primary components, deformation-controlled actions shall be restricted to flexure and axial actions in beams and columns as well as axial actions in braces. In secondary components, deformation-controlled actions shall be restricted to those actions identified for the braced or isolated frame in this standard. Calculated component actions shall satisfy the require ments of 7.5 .2.2 of ASCE 4 1 - 1 7. The m-factors for concrete frames shall be as specified in other applicable sections of this standard, and m-factors for beams, columns, and braces modeled as tension and compression components shall be as specified for columns in Table 1 8 . The m-factors shall be reduced to half the values in that table but need not be less than 1 .0 where component buckling is a consideration. Alternate approaches or values shall be permitted where justified by experimental evidence and analysis. 9.5.2 Nonlinear static and dynamic procedures-Calcu
lated component actions shall satisfy the requirements of 7.5.2.2 of ASCE 4 1 - 1 7 and shall not exceed the numerical values listed in Table 1 7 or the relevant tables for isolated frames specified in other sections herein. Where inelastic action is indicated for a component or action not listed in these tables, the performance shall be deemed unacceptable. Alternate approaches or values shall be permitted where justified by experimental evidence and analysis.
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9.6-Retrofit measu res for concrete-braced frames Seismic retrofit measures for concrete-braced frame components shall meet the requirements of 3 . 7 and other provisions of this standard.
C9.6-Retrofit measures for concrete-braced frames Retrofit measures that can be effective in retrofitted concrete braced frames include the general approaches listed for other concrete elements in this standard and ASCE 4 1 , plus other approaches based on rational principles.
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CHAPTER 1 0-CAST-IN-PLACE CONCRETE DIAPH RAGMS 1 0 . 1 -Components of cast-in-place concrete d iaphragms Cast-in-place concrete diaphragms transmit inertial forces within a structure to vertical seismic-force-resisting elements. Concrete diaphragm systems shall be made up of slabs, struts, collectors, and chords. Alternatively, diaphragm action is permitted to be provided by a struc tural truss in the horizontal plane. Diaphragms consisting of structural concrete topping on metal deck shall comply with the requirements of 9. 8.2 of ASCE 4 1 - 1 7.
C10.1 -Components of cast-i n-place concrete d iaphragms
10.1.1 Slabs-Slabs shall consist of cast-in-place concrete systems that, in addition to supporting gravity loads, transmit inertial loads developed within the structure from one vertical seismic-force-resisting element to another and provide out of-plane bracing to other portions of the building. 10.1.2 Struts and collectors-Collectors are components that serve to transmit the inertial forces within the diaphragm to elements of the seismic-force-resisting system. Struts are components of a structural diaphragm used to provide conti nuity around an opening in the diaphragm. Struts and collec tors shall be monolithic with the slab, occurring either within the slab thickness or being thicker than the slab. 10.1.3 Diaphragm chords-Diaphragm chords are compo nents along diaphragm or opening edges with concentrated longitudinal and, in some cases, added transverse reinforce ment, acting primarily to resist tension and compression forces generated by bending in the diaphragm. Exterior walls shall be permitted to serve as chords, provided there is adequate strength to transfer shear between the slab and the wall.
C 10.L3 Diaphragm chords-When evaluating an existing building, special care should be taken to evaluate the condi tion of the lap splices. Where the splices are not confined by closely spaced transverse reinforcement, splice failure is possible if stress levels reach critical values. In retrofit construction, new lap splices should be confined by closely spaced transverse reinforcement.
1 0.2-Analysis, modeling, and acceptance criteria for cast-in-place concrete diaphragms 1 0.2.1 General The analytical model for a diaphragm shall represent the strength, stiffness, and deformation capacity of each component and the diaphragm as a whole. Potential failure in flexure, shear, buckling, and bond or anchorage of reinforcement shall be considered. Modeling of the diaphragm as a continuous or simple span horizontal beam supported by elements of varying stiffness shall be permitted. The beam shall be modeled as rigid, stiff, or flexible considering the deformation characteristics of the actual system.
C10.2-Analysis, modeling, and acceptance criteria for cast-in-place concrete d iaphragms C10.2.1 General-Computer models are often based on the assumption that diaphragms are rigid for motion in the plane of the diaphragm. Due to their thickness, most cast in-place diaphragms would be considered rigid in the plane of the diaphragm. Thin concrete slabs cast over metal decks might be considered rigid or flexible for motion in the plane of the diaphragm depending on the length-to-width ratio of the diaphragm.
1 0.2.2 Stiffness of cast-in-place concrete diaphragms
f C10.2.2 Stifness ofcast-in-place concrete diaphragms
Diaphragm stiffness shall be modeled according to 1 0.2. 1 and shall be determined using a linear elastic model and gross section properties. The modulus of elasticity used shall be that of the concrete as specified in ACI 3 1 8M. Where the length-to-width ratio of the diaphragm exceeds 2.0 (where
The concern is for relatively flexible vertical members that can be displaced by the diaphragm and for relatively stiff vertical members that can be overloaded by the same diaphragm displacement.
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the length is the distance between vertical elements), the effects of diaphragm flexibility shall be considered where assigning lateral forces to the resisting vertical elements. 10.2.3 Strength of cast-in-place concrete diaphragms
Strength of cast-in-place concrete diaphragm components shall comply with the requirements of 3.2 as modified in this section. The maximum component strength shall be determined considering potential failure in flexure, axial load, shear, torsion, bond, anchorage, and other actions at all points in the component under the actions of design gravity and lateral load combinations. The shear strength shall be calculated as specified in ACI 3 1 8M. Strut, collector, and chord strengths shall be as determined for frame components in 4.2.3 . 10.2.4 Acceptance criteria for cast-in-place concrete diaphragms-Diaphragm shear and flexure shall be consid
ered deformation-controlled. Acceptance criteria for slab component actions shall be as specified for shear walls in 7.2.4, with m-factors taken according to similar components in Tables 2 1 and 22 for use in Eq. (7-36) of ASCE 4 1 - 1 7. Acceptance criteria for struts, chords, and collectors shall be as specified for frame components in 4.2.4. Connections shall be considered force-controlled. 1 0.3-Retrofit measures for cast-in-place concrete diaphragms Seismic retrofit measures for cast-in-place concrete diaphragms shall meet the requirements of 3.7 and other provisions herein and ASCE 4 1 .
C10.3-Retrofit measures for cast-in-place concrete diaphragms Two general alternatives that can be effective in retrofitting cast-in-place concrete diaphragms include the following: either improve the strength and ductility or reduce the demand in accordance with FEMA 1 72. Providing additional reinforcement and encasement can be an effective measure to strengthen or improve individual components. Increasing the diaphragm thickness can also be effective, but the added weight can overload the footings and increase the seismic loads. Lowering seismic demand by providing additional seismic-force-resisting elements, introducing additional damping, or isolating the base of the structure can also be effective retrofit measures.
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CHAPTER 1 1 -PR ECAST CONCRETE DIAPH RAGMS 1 1.1 -Components of precast concrete d iaphragms Precast concrete diaphragms are elements made up of primarily precast components with or without topping that transmit shear forces from within a structure to vertical seismic-force-resisting elements. Precast concrete diaphragms shall be classified as topped or untopped. A topped diaphragm shall be defined as one that includes a reinforced structural concrete topping slab poured over the completed precast horizontal system. An untapped diaphragm shall be defined as one constructed of precast components without a structural cast-in-place topping.
C11.1 -Components of precast concrete d iaphragms Chapter 1 1 provides a general overview of concrete diaphragms. Components of precast concrete diaphragms are similar in nature and function to those of cast-in-place diaphragms with a few critical differences. One difference is that precast diaphragms do not possess the inherent unity of cast-in-place monolithic construction. Additionally, precast components can be highly stressed because of prestressed forces. These forces cause long-term shrinkage and creep, which shorten the component over time. This shortening tends to fracture connections that restrain the component. Most floor systems have a topping system, but some hollow-core floor systems do not. The topping slab generally bonds to the top of the precast components, but it can have an inadequate thickness at the center of the span or can be inadequately reinforced to effectively resist seismic forces. Also, extensive cracking of joints can be present along the panel j oints. Shear transfer at the edges of precast concrete diaphragms is especially critical. Some precast roof systems are constructed as untapped systems. Untapped precast concrete diaphragms have been limited to areas of lower seismic hazard by recent versions of ASCE 7. This limitation has been imposed because of the brittleness of connections and lack of test data concerning the various precast systems. Special consideration shall be given to diaphragm chords in precast construction.
1 1.2-Analysis, model ing, and acceptance criteria for precast concrete diaphragms Analysis and modeling of precast concrete diaphragms shall conform to 1 0.2.2, with the added requirement that the analysis and modeling shall account for the segmental nature of the individual components. Component strengths shall be determined in accordance with 1 0.2.3 . Welded connection strength shall be based on rational procedures, and connections shall be assumed to have little ductility capacity unless test data verify higher ductility values. Precast concrete diaphragms with rein forced concrete topping slabs shall be considered deforma tion-controlled in shear and flexure. m-factors shall be taken as 1 .0, 1 .25, and 1 .5 for IO, LS, and CP performance levels, respectively. Untopped precast concrete diaphragms shall be considered force-controlled.
C11.2-Analysis, model ing, and acceptance criteria for precast concrete d iaphragms Welded connection strength can be determined using PCI MNL 1 20. A discussion of design provisions for untapped precast diaphragms can be found in the appendix to Chapter 9 of FEMA 368. The appendix to Chapter 9 of FEMA 450 provides discussion of the behavior of untapped precast diaphragms and outlines a design approach that can be used for such diaphragms to satisfy the requirements of this standard.
1 1.3-Retrofit measures for precast concrete d iaphragms Seismic retrofit measures for precast concrete diaphragms shall meet the requirements of 3 . 7 and other provisions of this standard.
C11.3-Retrofit measures for precast concrete d iaphragms Section 1 0.3 provides guidance for retrofit measures for concrete diaphragms in general. Special care should be taken to overcome the segmental nature of precast concrete diaphragms and to avoid damaging prestressing strands when adding connections.
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CHAPTER 1 2-CONCR ETE FOUNDATIONS 1 2.1-Types of concrete foundations Foundations shall be defined as those components of a building that serve to transmit loads from the vertical structural subsystems, such as columns and walls, to the supporting soil or rock. Concrete foundations for buildings shall be classified as either shallow or deep foundations as defined in Chapter 8 of ASCE 4 1 - 1 7. Requirements of Chapter 12 shall apply to shallow foundations that include spread or isolated footing, strip or line footing, combina tion footing, and concrete mat footing and to deep founda tions that include pile foundations and cast-in-place piers. Concrete grade beams shall be permitted in both shallow and deep foundation systems and shall comply with the require ments of Chapter 1 2 .
C12.1-Types of concrete foundations
12.1.1 Shallow concrete foundations-Existing spread footings, strip footings, and combination footings are rein forced or unreinforced. Vertical loads are transmitted by these footings to the soil by direct bearing; seismic forces are transmitted by a combination of friction between the bottom of the footing and the soil, and passive pressure of the soil on the vertical face of the footing. Concrete mat footings are reinforced to resist the flexural and shear stresses resulting from the superimposed concen trated and line structural loads and the distributed resisting soil pressure under the footing. Seismic forces are resisted by friction between the soil and the bottom of the footing and by passive pressure developed against foundation walls that are part of the system. 12.1.2 Deep concretefoundations 12.1.2.1 Driven concrete pile foundations-Concrete pile foundations shall be composed of a reinforced concrete pile cap supported on driven piles. The piles shall be concrete (with or without prestressing), steel shapes, steel pipes, or composite (concrete in a driven steel shell). Vertical loads are transmitted to the piles by the pile cap. Pile foundation resistance to vertical loads shall be calculated based on the direct bearing of the pile tip in the soil, the skin friction or cohesion of the soil on the surface area of the pile, or based on a combination of these mechanisms. Seismic force resis tance shall be calculated based on passive pressure of the soil on the vertical face of the pile cap, in combination with interaction of the piles in bending and passive soil pressure on the pile surface.
C12.1.2.1 Driven concrete pile foundations-In poor soils, or soils subject to liquefaction, bending of the piles can be the only dependable resistance to seismic forces.
12.1.2.2 Cast-in-place concrete pile foundations-Cast
C12.1.2.2 Cast-in-place concrete pile foundations
in-place concrete pile foundations shall consist of reinforced concrete placed in a drilled or excavated shaft. Cast-in-place pile foundation resistance to vertical and seismic forces shall be calculated in the same manner as that of driven pile foun dations specified in 1 2. 1 .2. 1 .
Segmented steel cylindrical liners are available to form the shaft in weak soils and allow the liner to be removed as the concrete is placed. Various slurry mixtures are often used to protect the drilled shaft from caving soils. The slurry is then displaced as the concrete is placed by the tremie method.
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1 2.2-Analysis of existing concrete foundations For concrete buildings, it is permitted to consider compo nents fixed against rotation and translation at the top of the foundation ifthe connections between components and foun dations, the foundations, and supporting soil are shown to be capable of resisting the induced forces and the foundation is rotationally stiff relative to the component stiffness. Where components or foundations are not designed to resist flexural moments, or the connections between components and foun dations are not capable of resisting the induced moments, it is permitted to model the components with pinned ends at the top of the foundation. In such cases, the component base shall be evaluated for the ability to accommodate the neces sary end rotation of the component. The effects of base stiff ness of components shall be taken into account at the point of maximum displacement of the superstructure. If fixed or pinned boundary conditions cannot be justified, a more rigorous analysis procedure shall be used. Appro priate vertical, lateral, and rotational soil springs shall be incorporated in the analytical model as described in 8.4 of ASCE 4 1 - 1 7. The spring characteristics shall be as specified in Chapter 8 of ASCE 4 1 - 1 7. Rigorous analysis of structures with deep foundations in soft soils shall be based on special soil-pile interaction studies to determine the probable loca tion of the point of fixity in the foundation and the resulting distribution of forces and displacements in the superstruc ture. In these analyses, the appropriate representation of the connection of the pile to the pile cap shall be included in the model. Piles with less than 1 5 0 mm of embedment without any dowels into the pile cap shall be modeled as being pinned to the cap. Unless the pile and pile cap connection detail is identified as otherwise from the available construc tion documents, the pinned connection shall be used in the analytical model. Where the foundations are included in the analytical model, the responses of the foundation components shall be considered. The reactions of structural components attached at the foundation (axial loads, shears, and moments) shall be used to evaluate the individual components of the founda tion system.
C12.2-Analysis of existing concrete foundations Engineering judgment should be practiced when modeling the effects of the foundation elements. The determination of the appropriate boundary condition to be used can often be quickly performed by comparing the relative strengths and stiffness of the superstructure component with the founda tion element. For example, the base of a column can typi cally be modeled as fixed when it connects to a mat or pile foundation; similarly, the ends of a concrete shear wall can typically be modeled as pinned when connecting to shallow foundations. The engineer is permitted to use simple boundary conditions (that is, fixed or pinned) when they can be justified. A more rigorous approach is required when a simple approach cannot be justified. In place of a more rigorous analysis approach, the engineer may also consider bounding the analysis by using both a fixed boundary condi tion analysis approach and a pinned boundary condition analysis approach.
1 2.3-Evaluation of existing condition Allowable soil capacities (subgrade modulus, bearing pres sure, and passive pressure) and foundation displacements for the selected performance level shall be as prescribed in Chapter 8 of ASCE 4 1 - 1 7 or as established with project specific data. All components of existing foundation systems and all new material, components, or components required for retrofit shall be evaluated as force-controlled actions. However, the capacity of the foundation components need not exceed 1 .25 times the capacity of the supported vertical structural component or element (column or wall).
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1 2.4-Retrofit measu res for concrete foundations Seismic retrofit measures for concrete foundations shall meet the requirements of 3.7 and other provisions of this standard.
C12.4-Retrofit measures for concrete foundations The measures described in this section can be effective in retrofitting existing shallow and deep foundations. For shallow concrete foundations: a) Enlarging the existing footing by lateral addi tions: Enlarging the existing footing can be an effective retrofit measure. The enlarged footing can be considered to resist subsequent actions produced by the design loads, as long as adequate shear and moment transfer capacity are provided across the joint between the existing footing and the additions. b) Underpinning the footing: Underpinning an existing footing involves the removal of unsuitable soil underneath, coupled with replacement using concrete, soil cement, suit able soil, or other material. Underpinning should be staged in small increments to prevent endangering the stability of the structure. This technique can be used to enlarge an existing footing or to extend it to a more competent soil stratum. c) Providing tension tie-downs: Tension ties (soil and rock anchors, prestressed and unstressed) can be drilled and grouted into competent soils and anchored in the existing footing to resist uplift. Increased soil-bearing pressures produced by the ties should be checked against the accep tance criteria for the selected performance level specified in Chapter 8 of ASCE 4 1 - 1 7. Piles or drilled piers can also be effective in providing tension tie-downs of existing footings. d) Increasing effective depth of footing: This method involves pouring new concrete to increase shear and moment capacity of the existing footing. The new concrete should be adequately doweled or otherwise connected so that it is inte gral with the existing footing. New horizontal reinforcement should be provided, if required, to resist increased moments. e) Increasing the effective depth of a concrete mat foun dation with a reinforced concrete overlay: This method involves pouring an integral topping slab over the existing mat to increase shear and moment capacity. f) Providing pile supports for concrete footings or mat foundations: Adding new piles can be effective in providing support for existing concrete footing or mat foundations, provided that the pile locations and spacing are designed to avoid overstressing the existing foundations. g) Changing the building structure to reduce the demand on the existing elements: This method involves removing mass or height of the building or adding other materials or components (such as energy-dissipation devices) to reduce the load transfer at the base level. New shear walls or braces can be provided to reduce the demand on existing foundations. h) Adding new grade beams: This approach involves the addition of grade beams to tie existing footings together where poor soil exists, to provide fixity to column bases, and to distribute seismic forces between individual footings, pile caps, or foundation walls. i) Improving existing soil: This approach involves grouting techniques to improve existing soil. For deep foundations:
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a) Providing additional piles or piers: Providing addi tional piles or piers can be effective, provided that extension and additional reinforcement of existing pile caps follow guidance provided for retrofit measures of shallow founda tions provided previously. b) Increasing the effective depth of the pile cap: New concrete and reinforcement added to the top of the pile cap can be effective in increasing its shear and moment capacity, provided that the interface is designed to transfer actions between the existing and new materials. c) Improving soil adjacent to the existing pile cap: Soil improvement adjacent to existing pile caps can be effective if undertaken in accordance with guidance provided in 8.3 ofASCE 4 1 - 1 7. d) Increasing passive pressure bearing area of pile cap: The addition of new reinforced concrete extensions to the existing pile cap can be effective in increasing the vertical foundation bearing area and load resistance. e) Changing the building system to reduce the demands on the existing elements: New lateral-load-resisting elements can be effective in reducing demand. f) Adding batter piles or piers: Adding batter piles or piers to existing pile or pier foundations can be effective in resisting seismic forces. It should be noted that batter piles have performed poorly in recent earthquakes where liquefi able soils were present. This problem is especially important to consider around wharf structures and in areas that have a high water table. Addition of batter piles to foundations in areas of such seismic hazards should be in accordance with requirements in 8 .4 of ASCE 4 1 - 1 7. g) Increasing tension tie capacity from pile or pier to superstructure: Added reinforcement should satisfy the requirements of Chapter 3 .
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CHAPTER 1 3-NOTATION AND DEFINITIONS 1 3.1 -Notation gross area of concrete section bounded by web thickness and length of section in the direction of shear force considered in the case of walls, and gross area of concrete section in the case of diaphragms, not to exceed the thickness times the width of the diaphragm, mm2 gross area of column, mm2 Ag effective cross-sectional area of a beam-column A1 joint, in a plane parallel to the plane of reinforce ment generating shear in the joint, mm2 area of nonprestressed tension reinforcement, mm2 As total area oflongitudinal reinforcement in a section, Ase mm2 area of compression reinforcement, mm2 As' area of shear reinforcement, mm2 Av area of the web cross section, = bwd, mm2 Acv =
Aw a11e
parameter used to measure deformation capacity in component load-deformation curves, Fig. I ; same as a in ASCE 4 1 b section width, mm bne parameter used to measure deformation capacity in component load-deformation curves, Fig. 1 ; same as b in ASCE 4 1 beff effective width of slab when using an effective beam width model, mm bw web width, mm parameter used to measure residual strength; same C11e as c in ASCE 4 1 size ofrectangular or equivalent rectangular column, c1 capital, or bracket measured in the direction of the span for which moments are being determined, mm size of rectangular or equivalent rectangular c2 column, capital, or bracket measured in perpendic ular to the direction of the span for which moments are being determined, mm DCR= demand-capacity ratio, computed in accordance with Eq. (7- 1 6) in ASCE 4 1 - 1 7 distance from extreme compression fiber to centroid d of tension reinforcement, mm; it shall be permitted to assume that d 0. 8h, where h is the dimension of the column in the direction of shear, mm nominal diameter of reinforcing bar, mm db de column core depth measured out-to-out of ties, mm parameter used to measure deformation capacity, d11e Fig. 1 ; same as d in ASCE 4 1 E Young's modulus of elasticity, MPa modulus of elasticity of concrete; evaluated using EcE expected material properties, MPa (EI)efF effective flexural rigidity of a section, N.mm2 Es modulus of elasticity of reinforcement, MPa e11e = parameter used to measure deformation capacity, Fig. 1 ; same as e in ASCE 4 1 =
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!cuE' =
/s-deg =
huE = he
hn =
gne h
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effective prestressing force of a prestressing tendon, mm2 parameter used to measure deformation capacity, Fig. 1 ; same asfin ASCE 4 1 specified compressive strength of concrete, MPa expected compressive strength of concrete, MPa lower-bound compressive strength of concrete, MPa lower-bound or expected concrete comprehensive strength, as applicable to force-controlled or defor mation-controlled actions, respectively, MPa average compressive stress in concrete caused by effective prestress force only, after allowance for all prestress losses, MPa maximum stress that can be developed in anchored or spliced reinforcement, Eq. ( I a), MPa maximum stress that can be developed in anchored or spliced reinforcement after inelastic deforma tions or damage reduce the effective anchorage length to eb-deg, MPa, Eq. (1 b), MPa specified yield strength for nonprestressed rein forcement, MPa expected yield strength of steel reinforcement, MPa lower-bound yield strength of steel reinforcement, MPa lower-bound or expected yield strength of rein forcement, as applicable to force-controlled or deformation-controlled actions, respectively, MPa specified yield strength of longitudinal steel rein forcement, MPa lower-bound yield strength of longitudinal steel reinforcement, MPa lower-bound yield strength of longitudinal steel reinforcement, MPa lower-bound or expected yield strength of longi tudinal reinforcement, as applicable to force controlled or deformation-controlled actions, respectively, MPa specified yield strength of transverse reinforce ment, MPa expected yield strength of transverse reinforce ment, MPa lower-bound yield strength of transverse reinforce ment, MPa lower-bound or expected yield strength oftransverse reinforcement, as applicable to force-controlled or deformation-controlled actions, respectively, MPa parameter used to measure deformation capacity, Fig. 1 ; same as g in ASCE 4 1 height o f member along which deformations are measured, mm overall thickness of member, mm structural wall height, mm effective height over which bond slip is distributed, taken as the clear height of the wall at the story directly above the anchorage interface, mm American Concrete Institute Copyrighted Material-www.concrete.org
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he I Ig
COMMENTARY
gross cross-sectional dimension of column core measured in the direction of joint shear, mm moment of inertia, mm4 moment of inertia of gross concrete or masonry section about centroidal axis, neglecting reinforce ment, mm4
stiffness of rotational spring used to explicitly capture bar slip, N.mm/rad k11e coefficient used for calculation of column shear strength based on displacement ductility, Eq. (3). k11e = 1 .0 in regions where displacement ductility demand is less than or equal to 2, 0.7 in regions where displacement ductility demand is greater than or equal to 6, and varies linearly for displace ment ductility between 2 and 6 L length of member along which deformations are assumed to occur, mm length of slab span in a slab-column in the direction £1 of seismic forces, mm length of slab span in a slab-column in the direction £2 perpendicular to the seismic forces, mm lb available length of straight development, lap splice, or standard hook, Eq. ( l a), mm lb.deg= adjusted available straight development, or lap splice length for column bars passing through regions where inelastic deformations and damage are expected, Eq. ( 1 b), mm. lb.deg shall be evaluated by subtracting from lb a distance of 2!3d from the point of maximum flexural demand in any direc tion damage is anticipated within the column; with d calculated in the direction of the largest cross sectional dimension., mm required length of development for a straight bar, £" splice, or hook, evaluated in accordance with ACI 3 1 8M; Eq. ( l a) and ( lb) of this document, mm le length of embedment of reinforcement, Eq. (2), mm lp Length of plastic hinge used for calculation of inelastic deformation capacity, Eq. (5), mm lw = length of entire wall or a segment of wall consid ered in the direction of shear force, mm Ms£ = moment strength at beam section; evaluated using expected material properties Mcoe� moment strength at column section; evaluated using expected material properties, N.mm MfY£= moment at section at first yield, defined as the moment at which the yield strain of the steel rein forcement is first reached in tension, or a concrete strain of 0.002 is reached in compression; evalu ated using expected material properties, N.mm Msecs£ = moment strength of the slab column strip; evalu ated using expected material properties, N.mm Mse� positive or negative flexural strengths of a section of slab between lines that are two-and-one-half slab or drop panel thicknesses outside opposite faces of the column or capital, N.mm KR
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Muo=
member design moment evaluated based on Eq. (7-34) of ASCE 4 1 - 1 7, N.mm Muo.cs =moment caused by gravity loads acting on the slab column strip; to be calculated according to the procedures of ACI 3 1 8M for the gravity loads specified in 7 .2.2 of ASCE 4 1 - 1 7, N.mm Muox= design bending moment about the x-axis for axial load PuF, N.mm Muoy= design bending moment about the y-axis for axial load PuF, N.mm My£ = moment strength at section; evaluated per ACI 3 1 8M without strength reduction factors and using expected material properties, or using Eq. (C l O), N.mm component demand modification factor to account m for expected ductility associated with this action at the selected structural performance level m = value of m for bending about the x-axis of a member my = value of m for bending about the y-axis of a member Nuo = member design axial force evaluated based on Eq. (7-34) of ASCE 4 1 - 1 7, N Nua = member design axial force evaluated based on Eq. (7-3) of ASCE 4 1 - 1 7; set to zero for tension force in Eq. (3), N number of prestressed strands nominal axial load strength at zero eccentricity, N lower-bound of vertical compressive strength for wall or wall pier, N PC£ = expected gravity compressive force applied to a wall or pier component stress, N PeL = lower-bound axial strength of a column, wall, or wall pier, N Puo = deformation-controlled axial force evaluated per ASCE 4 1 - 17, 7.5.2, N PuF = force-controlled axial force evaluated per ASCE 4 1 -1 7 , 7.5 .2, N generalized force in a component, Fig. 1 Q Qc£ = expected strength of a deformation controlled action of an element at the deformation level under consideration lower-bound estimate of the strength of a force controlled action of an element at the deformation level under consideration deformation-controlled action caused by gravity Quo = loads and earthquake forces force-controlled action caused by gravity loads and earthquake forces yield strength of a component, Fig. 1 substitute yield strength s spacing of transverse reinforcement, Eq. (3) and (C l ), mm thickness of wall web, mm fw shear force at section concurrent with moment M, N v Vcot = shear strength of concrete columns, Eq. (3); evalu ated using lower-bound or expected material propX
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erties as applicable to force-controlled or deforma tion-controlled actions, respectively, N Vco10= shear strength of concrete columns at a displace ment ductility demand not exceeding 2.0, Eq . (3); evaluated using lower-bound or expected mate rial properties as applicable to force-controlled or deformation-controlled actions, respectively, N !ot= shear strength of concrete columns at a displace c Vo ment ductility demand not exceeding 2.0, Eq . (3); evaluated using expected material properties, N VcPun£ = punching shear strength provided by the concrete as defined in ACI 3 1 8M ; evaluated using expected material properties, N beam-column joint shear strength calculated using V1 the general procedures of ACI 3 1 8M, as modified by Eq. (4), N shear strength provided by shear reinforcement, N v. Vuo = member design shear force evaluated based on Eq. (7-34) of ASCE 4 1 - 1 7, N shear demand resulting in flexural yielding of the plastic hinges; evaluated using a longitudinal steel stress of/ye£, N shear at yield in the direction under consideration, N/m dimensionless parameter for evaluating the effec Uco/ tiveness of transverse reinforcement in resisting shear forces in Eq . (3); ac01 1 .0 for sld :S 0.75, 0.0 for sld 2: 1 .0, and varies linearly for sld between 0.75 and 1 .0 effective stiffness factor for cracked section of a �eff slab modeled using an effective beam width model, Eq. (C3) L'1 calculated deflection of diaphragm, wall, or bracing element; or generalized deformation, Fig. 1 strength reduction factor � curvature at section at first yield, defined as the �fy£ curvature at which the yield strain of the steel rein forcement is first reached in tension, or a concrete strain of 0.002 is reached in compression; evalu ated using expected material properties, rad/mm curvature in the effective bilinear moment-curva �y£ ture relationship associated with My£; evaluated using expected material properties, rad/mm coefficient for calculation of joint shear strength, y Eq. (4) fraction of unbalanced moment transferred by y1 flexure at slab-column connections knowledge factor used to reduce component K strength based on the level of knowledge obtained for individual components during data collection A correction factor related to unit weight of concrete, Eq. (3) and (4) coefficient of shear friction ll generalized deformation, radians, Fig. 1 8 angle between lower edge of compressive strut and eb beam, rad s
=
=
=
=
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STANDARD Elc
Ely£ p p p
' "
Pbae = Pe
p,
Pv Pw
C OMMENTARY
angle between lower edge of compressive strut and column, rad yield rotation, radians, Eq. (5); evaluated using expected material properties ratio of nonprestressed tension reinforcement to effective section area = A/bd ratio of nonprestressed compression reinforcement volumetric ratio of horizontal confinement rein forcement in a joint reinforcement ratio producing balanced strain conditions Ratio of area of distributed longitudinal reinforce ment to gross concrete area perpendicular to that reinforcement ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that rein forcement = A/(bs) vertical reinforcement ratio in a wall or wall pier ratio of As to bwd
1 3.2-Definitions acceptance criteria-limiting values of properties, such as drift, strength demand, and inelastic deformation, used to determine the acceptability of a component at a given performance level. action-an internal moment, shear, torque, axial force, deformation, displacement, or rotation corresponding to a displacement caused by a structural degree of freedom; designated as force- or deformation-controlled. aspect ratio-ratio of full height to length for concrete and masonry shear walls; ratio of span to depth for hori zontal diaphragms. assembly-two or more interconnected components. beam-a structural member whose primary function is to carry loads transverse to its longitudinal axis. boundary component-a structural component at the boundary of a shear wall or a diaphragm or at an edge of an opening in a shear wall or a diaphragm that possesses tensile or compressive strength to transfer lateral forces to the seismic-force-resisting system. braced frame--a vertical seismic-force-resisting element consisting of vertical, horizontal, and diagonal components joined by concentric or eccentric connections. building performance level-a limiting damage state for a building, considering structural and nonstructural compo nents, used in the definition of performance objectives. capacity-the permissible strength or deformation for a component action. chord-see diaphragm chord. closed stirrups or ties-transverse reinforcement defined
in ACI 3 1 8M consisting of standard stirrups or ties with hooks having a bend angle of at least 90 degrees, and lap splices in a pattern that encloses longitudinal reinforcement. collector-see diaphragm collector. column (or beam) j acketing-a retrofit method in which
a concrete column or beam is encased in a steel, concrete, or American Concrete Institute Copyrighted Material-www.concrete.org
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FRP (fiber-reinforced polymer) jacket to strengthen or repair the member by confining the concrete. component-a part of an architectural, mechanical, elec trical, or structural system of a building. concrete masonry-masonry constructed with solid or hollow units made of concrete; can be ungrouted or grouted. connection-a link that transmits actions from one component or element to another component or element, categorized by type of action (moment, shear, or axial). connectors-nails, screws, lags, bolts, split rings, shear plates, headed studs, and welds used to link components to other components. coupling beam-a component that ties or couples adja cent shear walls acting in the same plane. critical action-the component action that reaches its elastic limit at the lowest level oflateral deflection or loading of the structure. crosstie-a component that spans the width of the diaphragm and delivers out-of-plane wall forces over the full depth of the diaphragm. deep foundation-driven piles made of steel, concrete, or wood, cast-in-place concrete piers, or drilled shafts of concrete. deformability-the ratio of the ultimate deformation to the limit deformation. deformation-controlled action-an action that has an associated deformation that is allowed to exceed the yield value of the element being evaluated. the extent of permis sible deformation beyond yield is based on component modification factors (m-factors). deformation-sensitive component-a component that is sensitive to deformation imposed by the drift or deforma tion of the structure, including deflection or deformation of diaphragms. demand-the amount of force or deformation imposed on an element or component. design earthquake-a user-specified earthquake for the evaluation or retrofit of a building that has ground-shaking criteria described in Chapter 2 of ASCE 4 1 - 1 7. design resistance (force or moment, as appropriate)
resistance provided by a member or connection; the product of adjusted resistance, the resistance factor, and the time effect factor. diaphragm-a horizontal (or nearly horizontal) structural element, such as a floor or roof system, used to transfer iner tial lateral forces to vertical elements of the seismic-force resisting system. diaphragm chord-a boundary component perpendic ular to the applied force that is provided to resist tension or compression caused by the diaphragm moment. diaphragm collector-a component parallel to the applied force that transfers lateral forces from the diaphragm of the structure to vertical elements of the seismic-force resisting system. diaphragm ratio-see aspect ratio. diaphragm strut-see diaphragm tie. American Concrete Institute Copyrighted Material-www.concrete.org
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diaphragm tie-a component parallel to the applied load that is provided to transfer wall anchorage or diaphragm inertial forces within the diaphragm; also called diaphragm strut; see crosstie, for case where diaphragm tie spans the entire diaphragm width. drift-horizontal deflection at the top of the story relative to the bottom of the story. edge distance-the distance from the edge of the member to the center of the nearest fastener. effective stiffness-the value of the lateral force in the building, or an element thereof, divided by the corresponding lateral displacement. element-an assembly of structural components that act together in resisting forces, including gravity frames, moment-resisting frames, braced frames, shear walls, and diaphragms. evaluation-an approved process or methodology of evaluating a building for a selected performance objective. expected material property-the mean value of the material property from material tests; as defined in ASCE 4 1 - 1 7, 7.5.1 .4. expected strength-the mean value of resistance of a component at the deformation level anticipated for a popula tion of similar components, including consideration of the variability in material strength as well as strain-hardening and plastic section development; evaluated using expected material properties as defined in ASCE 4 1 - 17, 7.5 . 1 .4. flexible diaphragm-a diaphragm with horizontal defor mation along its length twice or more than twice the average story drift. force-controlled action-an action that is not allowed to exceed the nominal strength of the element being evaluated. foundation system-an assembly of structural compo nents, located at the soil-structure interface, that transfers loads from the superstructure into the supporting soil. hoops-transverse reinforcement defined in 25.7.4 of ACI 3 1 8M consisting of closed ties with 1 35-degree hooks embedded into the core and no lap splices. in-plane wall-see shear wall. infill-a panel ofmasonry placed within a steel or concrete
frame. Panels separated from the surrounding frame by a gap are termed "isolated infills". Panels that are in full contact with a frame around its full perimeter are termed "shear infills". joint-an area where ends, surfaces, or edges of two or more components are attached; categorized by type of fastener or weld used and method of force transfer. knee joint-a joint that in the direction of framing has one column and one beam. level of seismicity-a degree of expected seismic hazard. For this standard, levels are categorized as very low, low, moderate, or high, based on mapped acceleration values and site amplification factors, as defined in 2.5 (Table 2-5) of ASCE 4 1 - 1 7. licensed design professional-All references in this stan dard to the licensed design professional shall be understood
(ciCiJ
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to mean the person who is licensed and responsible for, and in charge of, the inspection, evaluation, structural design, or retrofit design. lightweight concrete--structural concrete that has an air-dry unit weight not exceeding 1 800 kg/m3. linear dynamic procedure (LDP)-a response-spec trum-based modal analysis procedure defined in ASCE 4 1 , the use of which is required where the distribution of lateral forces is expected to depart from that assumed for the linear static procedure. linear static procedure (LSP)-a lateral force analysis procedure defined in ASCE 4 1 , using a pseudo-lateral force. This procedure is used for buildings for which the linear dynamic procedure is not required. load path-a path through which seismic forces are delivered from the point at which inertial forces are gener ated in the structure to the foundation and, ultimately, the supporting soil. lower-bound material property-the mean value of the material property from material tests minus one standard deviation; as defined in ASCE 4 1 - 1 7, 7.5 . 1 .4. lower-bound strength-the mean-minus-one standard deviation of the governing strength for a population of similar components; evaluated using lower-bound material properties as defined in ASCE 4 1 - 1 7, 7.5 . 1 .4. masonry-the assemblage of masonry units, mortar, and possibly grout or reinforcement; classified with respect to the type of masonry unit, including clay-unit masonry, concrete masonry, or hollow-clay tile masonry. moment frame (MF)-a frame capable of resisting hori zontal forces caused by the members (beams, columns, and slabs) and joints resisting forces primarily by flexure. nominal strength-the capacity of a structure or compo nent to resist the effects of loads, as determined by: 1 ) computations using specified material strengths and dimen sions, and formulas derived from accepted principles of structural mechanics; or 2) field tests or laboratory tests of scaled models, allowing for modeling effects and differences between laboratory and field conditions. nonstructural component-an architectural, mechan ical, or electrical component of a building that is perma nently installed in, or is an integral part of, a building system. overturning-behavior that results when the moment produced at the base of vertical seismic-force-resisting elements is larger than the resistance provided by the building weight and the foundation resistance to uplift. perforated wall or perforated infill panel-a wall or panel not meeting the requirements for a solid wall or infill panel. performance objective--one or more pairings of a selected seismic hazard level with both an acceptable or desired structural performance level and an acceptable or desired nonstructural performance level. pier-vertical portion of a wall between two horizontally adj acent openings or by an opening and an edge; piers resist American Concrete Institute Copyrighted Material-www.concrete.org
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axial stresses from gravity forces and bending moments from combined gravity and lateral forces. primary component-an element that is required to resist the seismic forces and accommodate seismic deformations for the structure to achieve the selected performance level. required member resistance (or required strength)
action on a component or connection, determined by struc tural analysis, resulting from the factored loads and the crit ical load combinations. resistance-the capacity of a structure, component, or connection to resist the effects of loads. retrofit-improving the seismic performance of structural or nonstructural components of a building. retrofit measures-modifications to existing compo nents, or installation of new components, that correct defi ciencies identified in a seismic evaluation as part of a scheme to rehabilitate a building to achieve a selected performance objective. retrofit method-one or more procedures for improving the seismic performance of existing buildings. retrofit strategy-a technical approach for developing rehabilitation measures for a building to improve seismic performance. rigid diaphragm-a diaphragm with horizontal deforma tion along its length less than half the average story drift. secondary component-an element that accommodates seismic deformations but is not required to resist the seismic forces it can attract for the structure to achieve the selected performance level. seismic-force-resisting system-those elements of the structure that provide its basic strength and stiffness to resist seismic forces. shallow foundation-isolated or continuous spread foot ings or mats. shear wall-a wall that resists lateral forces applied parallel with its plane; also known as an in-plane wall. solid wall or solid infill panel-a wall or infill panel with openings not exceeding 5 percent of the wall surface area. The maximum length or height of an opening in a solid wall must not exceed 1 0 percent of the wall width or story height. Openings in a solid wall or infill panel must be located within the middle 50 percent of a wall length and story height and must not be contiguous with adjacent openings. stiff diaphragm-a diaphragm that is neither flexible nor rigid. story-the portion of a structure between the tops of two successive finished floor surfaces and, for the topmost story, from the top of the floor finish to the top of the roof structural element. strength-the maximum axial force, shear force, or moment that can be resisted by a component. strong-column, weak-beam-a connection where the total moment capacity of the columns in any moment frame joint is greater than the total moment capacity of the beams, ensuring inelastic action in the beams. American Concrete Institute Copyrighted Material-www.concrete.org
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structural component-a component of a building that provides gravity- or lateral-load resistance as part of a continuous load path to the foundation, including beams, columns, slabs, braces, walls, wall piers, coupling beams, and connections; designated as primary or secondary. structural performance level a limiting struc tural damage state; used in the definition of performance objectives. structural system-an assemblage of structural compo nents that are joined together to provide regular interaction or interdependence. subassembly-a portion of an assembly. superstructure-the portion of the structure above the foundation or isolation system. tie-see diaphragm tie. wall pier vertical portion of a wall between two hori zontally adjacent openings or an opening and an edge. -
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C OMMENTARY R EFERENCES ACI committee documents and documents published by other organizations that are cited in the commentary are listed by document number, year of publication, and full title, followed by authored documents listed alphabetically. American Concrete Institute
ACI 20 1 . 1 R-08-Guide for Conducting a Visual Inspec tion of Concrete in Service ACI 2 1 4.4R- 10(1 6)-Guide for Obtaining Cores and Interpreting Compressive Strength Results ACI 228 . 1 R-03-In-Place Methods to Estimate Concrete Strength ACI 228.2R- 1 3-Report on Nondestructive Test Methods for Evaluation of Concrete in Structures ACI 3 1 8M-02-Building Code Requirements for Struc tural Concrete and Commentary ACI 3 1 8M- 14-Building Code Requirements for Struc tural Concrete and Commentary ACI 3 52R-02( 1 0)-Recommendations for Design of Beam-Column Connections in Monolithic Reinforced Concrete Structures ACI 355 .2-07-Qualification of Post-Installed Mechan ical Anchors in Concrete and Commentary ACI 355.4M- 1 1-Qualification of Post-Installed Adhe sive Anchors in Concrete and Commentary ACI 364 . 1 R-07-Guide for Evaluation of Concrete Struc tures before Rehabilitation ACI 374. 1 -05(1 4)-Acceptance Criteria for Moment Frames Based on Structural Testing and Commentary ACI 408R-03(1 2)-Bond and Development of Straight Reinforcing Bars in Tension ACI 437R-03-Strength Evaluation of Existing Concrete Buildings ACI 562M- 16-Code Requirements for Assessment, Repair, and Rehabilitation of Existing Concrete Structures and Commentary American Institute ofSteel Construction
AISC 3 60- 1 0-Specification for Structural Steel Buildings American Society of Civil Engineers
ASCE 7- 1 0-Minimum Design Loads for Buildings and Other Structures ASCE 4 1 -06-Seismic Evaluation and Retrofit of Existing Buildings ASCE 4 1 - 1 3-Seismic Evaluation and Retrofit of Existing Buildings ASCE 4 1 - 1 7-Seismic Evaluation and Retrofit of Existing Buildings SEI/ASCE 1 1 -99-Standard Guideline for Structural Condition Assessment of Existing Buildings ASTM International
ASTM A370- 1 7-Standard Test Methods and Definitions for Mechanical Testing of Steel Products American Concrete Institute Copyrighted Material-www.concrete.org
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ASTM A41 6/A4 1 6M- 1 7-Standard Specification for Steel Strand, Uncoated Seven-Wire for Prestressed Concrete ASTM A42 1 /A42 1M-1 5-Standard Specification for Uncoated Stress-Relieved Steel Wire for Prestressed Concrete ASTM A706/A706M- 1 6-Standard Specification for Deformed and Plain Low-Alloy Steel Bars for Concrete Reinforcement ASTM A722/A722M- 1 5-Standard Specification for High-Strength Steel Bars for Prestressed Concrete ASTM C39/C39M- 17-Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens ASTM C42/C42M- 1 6-Standard Test Method for Obtaining and Testing Drilled Cores and Sawed Beams of Concrete ASTM C496/C496M- 1 1-Standard Test Method for Split ting Tensile Strength of Cylindrical Concrete Specimens ASTM E 1 78-1 6a-Standard Practice for Dealing with Outlying Observations ASTM E488/E488M- 1 5-Standard Test Methods for Strength of Anchors in Concrete Elements Federal Emergency Management Agency
FEMA 1 72-92-NEHRP Handbook of Techniques for the Seismic Rehabilitation of Existing Buildings FEMA 273-97-NEHRP Guidelines for the Seismic Rehabilitation of Buildings FEMA 274-97-NEHRP Commentary on the Guidelines for Seismic Rehabilitation of Buildings FEMA 306-98-Evaluation of Earthquake-Damaged Concrete and Masonry Wall Buildings- Basic Procedures Manual FEMA 307-98-Evaluation of Earthquake-Damaged Concrete and Masonry Wall Buildings- Technical Resources FEMA 308-98-Repair of Earthquake Damaged Concrete and Masonry Wall Buildings FEMA 368-0 1-NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Struc tures (2000 edition) FEMA 450-04--NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Struc tures (2004 edition) FEMA 547-07-Techniques for the Seismic Rehabilita tion of Existing Buildings FEMA P-750- 1 0-NEHRP Recommended Provisions for Seismic Provisions for New Buildings and Other Structures (2009 edition) Precast/Prestressed Concrete Institute
PCI MNL 120- 1 0-PCI Design Handbook: Precast and Prestressed Concrete, Seventh Edition
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C OMMENTARY Authored references Allen, F., and Darvall, P., 1 977, "Lateral Load Equivalent Frame," A CI Journal Proceedings, V. 74, No. 7, July, pp. 294-299. Bartlett, F. M., and MacGregor, J. G., 1 995, "Equivalent Specified Concrete Strength from Core Test Data," Concrete International, V. 1 7, No. 3, Mar. 1 995, pp. 52-58. Bartlett, F. M., and MacGregor, J. G., 1 996, "Statis tical Analysis of the Compressive Strength of Concrete in Structures," A CI Materials Journal, V. 93, No. 2, Mar. Apr. pp. 1 5 8- 1 68 . Berry, M . , and Eberhard, M . , 2005, "Practical Perfor mance Model for Bar Buckling," Journal of Structural Engineering, V. 1 3 1 , No. 7, pp. 1 060- 1 070. doi: 1 0 . 1 06 1/ (ASCE)0733-9445(2005) 1 3 1 :7(1 060) Birely, A.; Lowes, L. N.; and Lehman, D. E., 2009, "A Practical Model for Beam-Column and Connection Behavior in Reinforced Concrete Frames," Proceedings of the ATC-SEI Conference on Improving the Seismic Perfor mance ofExisting Buildings and Other Structures, San Fran
cisco, CA. Biskinis, D. E.; Roupakias, G. K.; and Fardis, M. N., 2004, "Degradation of Shear Strength of Reinforced Concrete Members with Inelastic Cyclic Displacements," A CI Struc tural Journal, V. 1 0 1 , No. 6, Nov.-Dec., pp. 773-783. Brown, J., and Kunnath, S. K., 2004, "Low Cycle Fatigue Failure of Reinforcing Steel Bars," A CI Materials Journal, V. 1 0 1 , No. 6, Nov.-Dec. pp. 457-466. Caltrans, 2006, "Seismic Design Criteria," California Department of Transportation, Sacramento, CA. Cardenas, A. E.; Hanson, J. M.; Corley, W. G.; and Hognestad, E., 1 973, "Design Provisions for Shear Walls," A CI Journal Proceedings, V. 70, No. 3, Mar., pp. 22 1 -230. Cho, J.-Y., and Pincheira, J. A., 2006, "Inelastic Analysis of Reinforced Concrete Columns with Short Lap Splices Subjected to Reversed Cyclic Loads," A CI Structural Journal, V. 103, No. 2, Mar.-Apr., pp. 280-290. Concrete Reinforcing Steel Institute, 1 98 1 , Evaluation of Reinforcing Steel Systems in Old Reinforced Concrete Struc tures, CRSI, Schaumburg, IL, 16 pp.
Dovich, L. M., and Wight, J. K., 2005, "Effective Slab Width Model for Seismic Analysis ofFlat Slab Frames," A CI Structural Journal, V. 1 02, No. 6, Nov.-Dec., pp. 868-875. El-Metwally, S. E., and Chen, W. F., 1 988, "Moment Rotation Modeling of Reinforced Concrete Beam-Column Connections," A CI Structural Journal, V. 85, No. 4, Nov. Dec., pp. 3 84-394. Elwood, K. J., and Eberhard, M. 0., 2009, "Effective Stiffness of Reinforced Concrete Columns," A CI Structural Journal, V. 1 06, No. 4, July-Aug., pp. 476-484. Elwood, K. J.; Matamoros, A.; Wallace, J. W. ; Lehman, D. E.; Heintz, J. A.; Mitchell, A. D.; Moore, M. A.; Valley, M. T. ; Lowes, L.; Comartin, C.; and Moehle, J. P., 2007, "Update ofASCE/SEI 41 Concrete Provisions," Earthquake Spectra, V. 23, No. 3, pp. 493-523. doi: 1 0. 1 1 93/1 .27577 1 4 American Concrete Institute Copyrighted Material-www.concrete.org
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Elwood, K. J., and Moehle, J. P., 2004, "Evaluation of Existing Reinforced Concrete Columns," Proceedings of the Thirteenth World Conference on Earthquake Engineering,
Vancouver, British Columbia. Elwood, K. J., and Moehle, J. P., 2005a, "Drift Capacity of Reinforced Concrete Columns with Light Transverse Rein forcement," Earthquake Spectra, Earthquake Engineering Research Institute, Oakland, California, V. 2 1 , No. 1 , pp. 7 1 -89. Elwood, K. J., and Moehle, J. P. , 2005b, "Axial Capacity Model for Shear-Damaged Columns," A CJ Structural Journal, V. 1 02, No. 4, pp. 578-587. Fardis, M. N., and Biskinis, D. E., 2003, "Deformation Capacity of RC Members, as Controlled by Flexure or Shear," Otani Symposium, Tokyo, Japan, pp. 5 1 1 -530. Furlong, R. W. ; Hsu, C. T. T. ; and Mirza, S. A., 2004, "Analysis and Design of Concrete Columns for Biaxial Bending-Overview," ACJ Structural Journal, V. 1 0 1 , No. 3, May-June, pp. 4 1 3-423 . Ghannoum, W.; Sivaramakrishnan, B.; Pujol, S.; Catlin, A. C.; Fernando, S.; Yoosuf, N.; and Wang, Y., 20 1 5a, "NEES : ACI 369 Rectangular Column Database," https:!/ datacenterhub.org/resources/25 5 (accessed Sept. 1 1 , 20 1 7). Ghannoum, W.; Sivaramakrishnan, B.; Puj ol, S.; Catlin, A. C.; Fernando, S.; Yoosuf, N.; and Wang, Y. , 20 1 5b, "NEES : ACI 369 Circular Column Database," https://datacenterhub. org/resources/254 (accessed Sept. 1 1 , 20 1 7). Ghannoum, W. M., 20 17, "Updates to Modeling Param eters and Acceptance Criteria for Non-Ductile and Splice Deficient Concrete Columns," 1 6th World Conference on Earthquake Engineering, Santiago, Chile, pp. 1 - 12 . Ghannoum, W. M., and Matamoros, A . B., 20 14, "Nonlinear Modeling Parameters and Acceptance Criteria for Concrete Columns," Seismic Assessment of Existing Reinforced Concrete Buildings, SP-297, K. J. Elwood, J. Dragovich, and I. Kim, eds., American Concrete Institute, Farmington Hills, MI, pp. 1-24. Ghannoum, W. M., and Moehle, J. P., 2012, "Dynamic Collapse Analysis of a Concrete Frame Sustaining Column Axial Failures," A CI Structural Journal, V. 1 09, No. 3, May June, pp. 403-4 1 2. Ghobarah, A., and Biddah, A., 1 999, "Dynamic Analysis of Reinforced Concrete Frames Including Joint Shear Defor mation," Engineering Structures, V. 2 1 , No. 1 1 , pp. 97 1 -987. doi: 1 0 . 1 0 1 6/S0 1 4 1 -0296(98)00052-2 Henkhaus, K., 20 1 0, "Axial Failure of Vulnerable Rein forced Concrete Columns Damaged by Shear Reversals," PhD dissertation, Purdue University, West Lafayette, IN. Hidalgo, P. A.; Ledezma, C. A.; and Jordan, R., 2002, "Seismic Behavior of Squat Reinforced Concrete Shear Walls," Earthquake Spectra, V. 1 8, No. 2, 2002, pp. 287-308. doi: 1 0 . 1 1 93/ 1 . 149035 3 Hognestad, E ., 1952, "Fundamental Concepts i n Ulti mate Load Design of Reinforced Concrete Members," A CJ Journal Proceedings, V. 49, No. 1 0, pp. 809-830. American Concrete Institute Copyrighted Material-www.concrete.org
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Hsu, C. T. T., 1 988, "Analysis and Design of Square and Rectangular Columns by Equation of Failure Surface," A CI Structural Journal, V. 85, No. 2, Apr.-May, pp. 1 67-1 79. Hwang, S.-J., and Moehle, J. P., 2000, "Models for Later ally Load Slab-Column Frames," A CI Structural Journal, V. 97, No. 2, Mar.-Apr., pp. 345-353. Ichinose, T., 1 995, "Splitting Bond Failure of Columns under Seismic Action," ACI Structural Journal, V. 92, No. 5, Sept.-Oct., pp. 535-542. Kang, T. H.-K., and Wallace, J. W., 2005, "Dynamic Responses of Flat Plate Systems with Shear Reinforce ment," ACI Structural Journal, V. 1 02, No. 5, Sept.-Oct., pp. 763-773 . Kang, T. H.-K., and Wallace, J. W., 2006, "Punching of Reinforced and Post-Tensioned Concrete Slab-Column Connections," A CI Structural Journal, V. 1 04, No. 4, July Aug., pp. 53 1 -540. Kang, T. H.-K.; Wallace, J. W. ; and Elwood, K. J., 2009, "Nonlinear Modeling of Flat-Plate Systems," Journal of Structural Engineering, V. 1 3 5 , No. 2, pp. 1 47-158. doi: 1 0. 1 06 1 /(ASCE)0733-9445(2009) 1 35 :2(147) Lin, C. M., and Restrepo, J. I., 2002, "Seismic Behaviour and Design of Reinforced Concrete Interior Beam-Column Joints," Bulletin of the New Zealand Societyfor Earthquake Engineering, V. 35, No. 2, pp. 108-128. Luo, Y. H.; Durrani, A. J.; and Conte, J. P., 1 994, "Equivalent Frame Analysis of Flat Plate Buildings for Seismic Loading," Journal of Structural Engineering, V. 1 20, No. 7, pp. 2 1 372 1 55 . doi: 1 0. 1 06 1 /(ASCE)0733-9445(1 994) 1 20:7(2 1 37) Lynn, A. C.; Moehle, J. P.; Mahin, S. A.; and Holmes, W. T., 1 996, "Seismic Evaluation of Existing Reinforced Concrete Building Columns," Earthquake Spectra, V. 1 2, No. 4, pp. 7 1 5 -739. doi: 1 0 . 1 193/1 . 1 585907 Matamoros, A. B.; Matchulat, L.; and Woods, C., 2008, "Axial Load Failure of Shear Critical Columns Subj ected to High Levels of Axial Load," 1 4th World Conference on Earthquake Engineering, Beijing, China. Mitra, N., and Lowes, L. N., 2007, "Evaluation, Cali bration and Verification of a Reinforced Concrete Beam-Column Joint Model," Journal of Structural Engineering, V. 1 3 3, No. 1 , pp. 1 05- 1 20. doi: 1 0 . 1 06 1/ (ASCE)0733-9445(2007) 1 3 3 : 1 (1 05) Pacific Earthquake Engineering Research Center (PEER), 201 0, "Modeling and Acceptance Criteria for Seismic Design and Analysis of Tall Buildings," 72- 1 , PEER/ATC, Applied Technology Council (ATC), Oct., 242 pp. Panagiotakos, T. B., and Fardis, M. N., 2001 , "Deforma tion of Reinforced Concrete Members at Yielding and Ulti mate," A CI Structural Journal, V. 98, No. 2, Mar.-Apr., pp. 1 35- 1 48. Panagiotou, M., and Restrepo, J. I., 2007, "Design and Computational Model for the UCSD 7 -Story Structural Wall Building Slice," SSRP 07-09 Rep., Department of Structural Engineering, University of California, La Jolla, CA.
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Pecknold, D. A., 1 975, "Slab Effective Width for Equiva lent Frame Analysis," A CI Journal Proceedings, V. 72, No. 4, Apr., pp. 294-299. PEERIEERI, 2006, "New Information on Seismic Perfor mance of Concrete Buildings," Pacific Earthquake Engi neering Research Center/Earthquake Engineering Research Institute, seminar video download, EERI.org. Priestley, M. J. N.; Calvi, G. M.; and Kowalsky, M. J., 2007, "Displacement-Based Seismic Design of Structures," IUSS Press, Pavia, Italy, 771 pp. Priestley, M. J. N., and Kowalski, M. J., 1 998, "Aspects of Drift and Ductility Capacity of Cantilever Structural Walls" Bulletin, NZNSEE 3 1 , 2 pp. Qaisrani, A.-N., 1993, "Interior Post-Tensioned Flat Plate Connections Subjected to Vertical and Biaxial Lateral Loading," PhD thesis, Department of Civil Engineering, University of California-Berkeley, Berkeley, CA, 284 pp. Saatcioglu, M.; Alsiwat, J. M.; and Ozcebe, G., 1 992, "Hysteretic Behavior of Anchorage Slip in RIC Members," Journal of Structural Engineering, V. 1 1 8, No. 9, pp. 24392458 . doi: 1 0 . 1 061/(ASCE)0733-9445( 1 992) 1 1 8: 9(2439) Sezen, H., 2002, "Seismic Response and Modeling of Lightly Reinforced Concrete Building Columns," PhD dissertation, Department of Civil and Environmental Engi neering, University of California, Berkeley, CA. Sezen, H., and Moehle, J. P., 2004, "Shear Strength Model for Lightly Reinforced Concrete Columns," Journal of Structural Engineering, V. 1 30, No. 1 1 , pp. 1 692- 1 703 . doi: 1 0 . 1 06 1/(ASCE)0733-9445(2004) 1 30: 1 1 ( 1 692) Shin, M., and LaFave, J. M., 2004, "Modeling of Cyclic Joint Shear Deformation Contribution in RC Beam-Column Connections to Overall Frame Behavior," Structural Engi neering and Mechanics, V. 1 8, No. 5, pp. 645-669. doi: 1 0 . 1 2989/sem.2004 . 1 8 .5 .645 Simpson, B., and Matamoros, A., 20 1 2, "Criteria for Evaluating the Effect of Displacement History and Span to-Depth Ratio on the Risk of Collapse of RIC Columns," Proceedings of the 15th World Coriference on Earthquake Engineering, Lisbon, Portugal, 8 pp.
Sokoli, D., and Ghannoum, W. M., 20 1 6, "High-Strength Reinforcement in Columns under High Shear Stresses," A CI Structural Journal, V. 1 1 3, No. 3, May-June, pp. 605-6 14. doi: 1 0 . 1 43 59/5 1 688203 Sozen, M. A., and Moehle, J. P., 1 993, "Stiffness of rein forced Concrete Walls Resisting In-Plane Shear," Electric Power Research Institute, Research Project 3094-0 1 . Sperry, J.; Al-Yasso, S . ; Searle, N.; DeRubeis, M.; Darwin, D.; O'Reilly, M .; Matamoros, A.; Feldman, L.; Lepage, A.; Lequesne, R. ; andAjaam, A., 2005, "Anchorage of High-Strength Reinforcing Bars with Standard Hooks," Structural Engineering and Engineering Materials SM Report No. 1 1 1 , University of Kansas Center for Research,
Inc., Lawrence, KS. Vanderbilt, M . D., and Corley, W. G., 1 983, "Frame Analysis of Concrete Buildings," Concrete International, V. 5, No. 1 2, Dec., pp. 3 3-43 . American Concrete Institute Copyrighted Material-www.concrete.org
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Wallace, J. W., 1 994, "New Methodology for Seismic Design of RC Shear Walls," Journal of Structural Engi neering, V. 1 20, No. 3 , pp. 863-884. doi: 10. 1 06 1/ (ASCE)0733-9445( 1 994) 1 20:3(863) Wallace, J. W. , 1 995, "Seismic Design ofRC Shear Walls; Part I: New Code Format," Journal of Structural Engi neering, V. 1 2 1 , No. 1 , pp. 75-87. Wallace, J. W. , and Moehle, J. P., 1 992, "Ductility and Detailing Requirements of Bearing Wall Buildings," Journal of Structural Engineering, V. 1 1 8, No. 6, 1 992, pp. 1 6251 644. doi: 1 0. 1 06 1 /(ASCE)0733-9445(1 992) 1 1 8:6( 1 625) Wire Reinforcement Institute, 2009, "Historical Data on Wire, Triangular Wire Fabric/Mesh and Welded Wire Concrete Reinforcement (WWR)," TF 101-09, Wire Rein forcement Institute, Hartford, CT. Wood, S. L., 1 990, "Shear Strength of Low-Rise Rein forced Concrete Walls," A C1 Structural Journal, V. 87, No. 1 , Jan.-Feb., pp. 99- 1 07. Woods, C., and Matamoros, A., 20 1 0, "Effect of Longitu dinal Reinforcement Ratio on the Failure Mechanism of RIC Columns Most Vulnerable to Collapse," 9th US National and 1Oth Canadian Conference on Earthquake Engineering,
Toronto, ON, Canada, July.
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As ACI begins its second century of advancing concrete knowledge, its original chartered purpose remains "to provide a comradeship in finding the best ways to do concrete work of all kinds and in spreading knowledge." In keeping with this purpose, ACI supports the following activities: Technical committees that produce consensus reports, guides, specifications, and codes. Spring and fall conventions to facilitate the work of its committees. Educational seminars that disseminate reliable information on concrete. Certification programs for personnel employed within the concrete industry. Student programs such as scholarships, internships, and competitions. Sponsoring and co-sponsoring international conferences and symposia. Formal coordination with several international concrete related societies. Periodicals: the ACI Structural Journal, Materials Journal, and Concrete International. Benefits of membership include a subscription to Concrete International and to an ACI Journal. ACI members receive discounts of up to 40% on all ACI products and services, including documents, seminars
and convention registration fees.
As a member of ACI, you join thousands of practitioners and professionals worldwide who share a commitment to maintain the highest industry standards for concrete technology, construction, and practices. In addition, ACI chapters provide opportunities for interaction of professionals and practitioners at a local level.
American Concrete Institute 38800 Country Club Drive Farmington Hills, MI 48331 Phone: +1.248.848.3700 Fax:
+1.248.848.3701 www. concrete.org
American Concrete Institute Always advancing
38800 Country C l u b Drive Farmington H i l l s , Ml 48331 USA +1 . 248.848.3700 www.con crete.org
The A m e r i c a n C o n c rete I n stitute (AC I ) is a l e a d i n g a utho rity a n d resou rce worldwide for the deve l o p m e nt a n d d i stri bution of c o n s e n s u s-based sta n d a rd s a n d tec h n i c a l reso u rces, ed ucati o n a l pro g r a m s , and certifi cati o n s for i n d ivid u a l s a n d o rga n i zati o n s i nvo lved i n c o n c rete d es i g n , c o n st r u ct i o n , a n d materia l s , w h o s h a re a co m m itment to p u rs u i n g the best u s e o f c o n crete. I n d ivi d u a l s i nterested in the a ctivities of ACI a re e n c o u ra g e d to explore the ACI website fo r m e m b e rs h i p o p p o rtu n ities, c o m m ittee activities, and a wide va ri ety of c o n crete reso u rces. As a vo l u nteer m e m be r-d riven o rg a n izati o n , A C I i nvites p a rt n e rs h i p s a n d w e l c o m e s a l l con crete p rofess i o n a l s w h o w i s h to be p a rt of a res pecte d , c o n n ecte d , soc i a l g ro u p t h at p rovides a n op portu n ity for p rofessi o n a l g rowth, n etwo r k i n g a n d e nj oy m e nt.
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