Reported by ACI Committee 374 ACI 374.3R-16 · 2020. 5. 12. · ACI 374.3R-16 Guide to Nonlinear Modeling Parameters for Earthquake-Resistant Structures Reported by ACI Committee

Guide to Nonlinear Modeling Parameters for Earthquake-Resistant StructuresReported by ACI Committee 374

AC

I 374

.3R

-16

@Seismicisolation@Seismicisolation

https://telegram.me/seismicisolation

First PrintingSeptember 2016

ISBN: 978-1-945487-19-4

Guide to Nonlinear Modeling Parameters for Earthquake-Resistant Structures

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This guide provides information regarding nonlinear modeling of components in special moment frame and structural wall systems resisting earthquake loads. The reported modeling parameters provide a modeling option for licensed design professionals (LDPs) performing nonlinear analysis for performance-based seismic design of reinforced concrete building structures designed and detailed in accordance with ACI 318.

Keywords: backbone curve; beams; columns; coupling beams; earth-quake-resistant structures; flexure; joints; modeling parameters; nonlinear analysis; performance-based engineering; seismic design; shear; special concrete moment frames; special concrete shear walls; special structural walls.

CONTENTS

CHAPTER 1—INTRODUCTION AND SCOPE, p. 21.1—Introduction, p. 21.2—Scope, p. 2

CHAPTER 2—NOTATION AND DEFINITIONS, p. 32.1—Notation, p. 32.2—Definitions, p. 4

CHAPTER 3—GENERAL, p. 43.1—General, p. 43.2—Backbone curve selection procedure, p. 5

CHAPTER 4—NONLINEAR MODELING PARAMETERS FOR SPECIAL CONCRETE MOMENT FRAMES, p. 5

4.1—Modeling parameters for columns, p. 54.2—Modeling parameters for beams and beam-column

joints (ASCE/SEI 41), p. 5

Jeffrey J. Dragovich, Chair Insung Kim*, Secretary

ACI 374.3R-16

Guide to Nonlinear Modeling Parameters for Earthquake-Resistant Structures

Reported by ACI Committee 374

Mark A. AschheimJohn F. Bonacci

Joseph M. BracciSergio F. BrenaPaul J. BrienenNed M. Cleland

Juan Francisco Correal DazaJoe Ferzli

David C. Fields

Luis E. GarciaGarrett R. Hagen*

Wael Mohammed HassanMary Beth D. Hueste

Luis F. IbarraBrian E. Kehoe

James M. LaFaveAndres Lepage

Adolfo B. Matamoros

Stavroula J. PantazopoulouChris P. PantelidesJose A. Pincheira

Jeffrey RautenbergJose I. Restrepo

Mario E. RodriguezMurat SaatciogluFelipe Saavedra

Guillermo Santana

Mehrdad SasaniShamim A. Sheikh

Myoungsu ShinHitoshi Shiohara

Roberto StarkJohn H. TessemJohn W. Wallace

Tom C. XiaFernando Yanez

*Task group that developed this guide. Alvaro Celestino was also a member of the task group and primary author.

Consulting MembersSergio M. Alcocer Ronald Klemencic Andrew W. Taylor

Special acknowledgements to Laura Basualdo, Anna Birely, Reza Dashtpeyma, Wassim Ghannoum, and Andrew Shuck for their contributions to this guide.

ACI Committee Reports, Guides, and Commentaries are intended for guidance in planning, designing, executing, and inspecting construction. This document is intended for the use of individuals who are competent to evaluate the significance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. The American Concrete Institute disclaims any and all responsibility for the stated principles. The Institute shall not be liable for any loss or damage arising therefrom.

Reference to this document shall not be made in contract documents. If items found in this document are desired by the Architect/Engineer to be a part of the contract documents, they shall be restated in mandatory language for incorporation by the Architect/Engineer.

ACI 374.3R-16 was adopted and published September 2016.Copyright © 2016, American Concrete InstituteAll rights reserved including rights of reproduction and use in any form or by

any means, including the making of copies by any photo process, or by electronic or mechanical device, printed, written, or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors.

1



CHAPTER 5—NONLINEAR MODELING PARAMETERS FOR SPECIAL CONCRETE STRUCTURAL WALLS AND COUPLING BEAMS, p. 7

5.1—Modeling parameters for special structural walls and coupling beams controlled by flexure, p. 7

5.2—Modeling parameters for structural walls and coupling beams controlled by shear, p. 11

CHAPTER 6—SUMMARY AND CONCLUSIONS, p. 12

CHAPTER 7—REFERENCES, p. 12Authored documents, p. 13

CHAPTER 1—INTRODUCTION AND SCOPE

1.1—IntroductionThis guide provides nonlinear modeling parameters that

will assist the licensed design professional (LDP) in the use of performance-based seismic design of new concrete buildings. Performance objectives are assigned for the given structure and compliance with the performance objectives are then evaluated based on the deformation of structural elements rather than evaluated based on strength under prescriptive requirements. Deformations in structural components allow the LDP to understand damage levels related to seismic hazards.

There are currently several documents that provide general analysis procedures for the design of new build-ings using performance-based engineering (ASCE/SEI 7; Structural Engineers Association of Northern California [SEAONC] 2008; Los Angeles Tall Buildings Structural Design Council [LATBSDC] 2014; Pacific Earthquake Engineering Research Center [PEER] [PEER/ATC 2010]). Although these documents provide a means for seismic design indicative of earthquake hazards and acceptance criteria that are similar to ASCE/SEI 41, they do not provide the required information for modeling nonlinear behavior of a structural component based on detailing conditions, such as the development of force-deformation backbone curves shown in Fig. 1.1. This guide provides modeling parameters that can be used to generate the backbone curves of struc-tural members of special moment frame and structural wall systems detailed per Chapter 18 of ACI 318-14.

For example, an engineer modeling the nonlinear defor-mation of a structural wall with specific reinforcement configurations for new design can select from the following three alternatives: 1) develop modeling parameters from existing experimental data; 2) develop and implement a new testing program; or 3) create force-deformation curves using the information in the existing building standard (ASCE/SEI 41) or guideline (ACI 369R) developed for seismic evalu-ation and rehabilitation. The existing experimental data, however, are not always available, and new testing programs may be limited by budget and project schedule. In addition, the modeling parameters in the existing building standard do not always adequately represent the behavior of components designed according to current codes. Furthermore, they may not be directly applied to new design due to incongruences

in parameter definition and requirements across documents. This guide provides a set of nonlinear modeling parameters that can be used without performing one of the three alterna-tives given.

1.2—ScopeThis guide provides information about nonlinear modeling

parameters for:

Fig. 1.1—Generalized force-deformation relations for struc-tural concrete components (ASCE/SEI 41). (Note: a, b, d, e, f, and g are deformations as defined in the reported nonlinear modeling parameter tables.)

American Concrete Institute – Copyrighted © Material – www.concrete.org

2 GUIDE TO NONLINEAR MODELING PARAMETERS FOR EARTHQUAKE-RESISTANT STRUCTURES (ACI 374.3R-16)



(a) Special moment frames extracted from ASCE/SEI 41, for which definitions and requirements are converted to those of the codes for the design of new concrete buildings

(b) Special structural walls and coupling beams extracted from ASCE/SEI 41, for which definitions and requirements are converted to those of the codes for the design of new concrete buildings

(c) Special moment frames and structural walls developed from the latest experimental databases of structural compo-nents compliant with the requirements of Chapter 18 (ACI 318-14) for earthquake-resistant structures.

In regards to (c), the mean and mean minus one standard deviation modeling parameter values are provided for these code-compliant specimen databases in an effort to demon-strate a quantitative representation of data distribution for the LDP. The LDP can select modeling parameters based on ASCE/SEI 41, or the experimental database, depending on project constraints, jurisdiction requirements, or both.

The modeling parameters in this guide are meant to be used for the analytical modeling of structural components in earthquake-resistant systems as described. The guide, however, does not describe global behavior or provide interaction between different systems in the buildings, for example, diaphragms and moment frames.

CHAPTER 2—NOTATION AND DEFINITIONS

2.1—NotationAcv = gross area of concrete section bound by web thick-

ness and length of section in the direction of shear force considered, in.2 (mm2)

Ag = gross area of concrete section, in.2 (mm2)Aj = effective cross-sectional area within a joint in a

plane parallel to plane of beam reinforcement generating shear in the joint, in.2 (mm2) (ACI 318-14 Section 18.8.4.3)

As = area of nonprestressed longitudinal tension rein-forcement, in.2 (mm2)

As′ = area of compression reinforcement, in.2 (mm2)Av = area of shear reinforcement within spacing s, in.2

(mm2)b = width of compression face of member, in. (mm)bw = web width, or diameters of circular section, in. (mm)d = distance from extreme compression fiber to centroid

of longitudinal tension reinforcement, in. (mm)E = effect of horizontal and vertical earthquake-induced

forcesEc = modulus of elasticity of concrete, psi (MPa)Es = modulus of elasticity of reinforcement and struc-

tural steel, psi (MPa)fc′ = specified compressive strength of concrete, psi

(MPa, √fc′ in MPa = 12√fc′ in psi)fy = specified yield strength of reinforcement, psi (MPa)h = height of member along which deformations are

measured, in. (mm)hb = subgrade dimension from absolute base of wall to

grade level, in. (mm)

hc = average height of the beams framing into the joint in the direction of applied shear, in. (mm)

heff = effective shear span of wall, in. (mm)hw = height of entire wall from base to top, or clear

height of wall segment or wall pier, in. (mm)Icr = moment of inertia of cracked section transformed

to concrete, in.4 (mm4)Ig = moment of inertia of gross concrete section about

centroidal axis, neglecting reinforcement, in.4 (mm4)L = length of member along which deformations are

assumed to occur, in. (mm)ℓd = development length in tension of deformed bar,

deformed wire, or plain wire reinforcement, in. (mm)lp = assumed plastic hinge length, minimum of the

following: 0.5lw, the first-story height, and 0.5hw for wall segments, in. (mm)

lw = length of entire wall, or length of wall segment or wall pier considered in direction of shear force, in. (mm)

Mn = nominal flexural strength at section, in.-lb (N-mm)Mpr = probable flexural strength of members, with or

without axial load, determined using the properties of the member at the joint faces assuming a tensile stress in the longitudinal bars of at least 1.25fy and a strength reduction factor ϕ of 1.0, in.-lb (N-mm)

P = design axial force obtained from design load combinations that include overstrength factor or determined from limit-state analysis, lb (N)

Q = generalized force demand in a componentQy = yield strength of a components = center-to-center spacing of transverse reinforce-

ment, in. (mm)V = design shear force obtained from design load

combinations that include overstrength factor or determined from limit-state analysis, lb (N)

Ve = design shear force for load combinations including earthquake effects, lb (N) (refer to ACI 318-14 Sections 18.6.5.1 and 18.7.6.1.1)

Vn = nominal shear strength, lb (N)Vo = shear strength of a column per ASCE/SEI 41 Eq.

(10-3), lb (N)Vp = shear demand on a column at flexural yielding of

plastic hinges per ASCE/SEI 41 Section 10.4.2.2.2, lb (N)

Vsi = nominal shear strength provided by shear reinforce-ment, lb (N)

∆ = generalized deformation, in. (mm)∆y = generalized yield deformation, in. (mm)εy = yield strain of reinforcement, in./in. (mm/mm)θ = generalized deformation, radiansθy = generalized yield deformation, radiansϕ = strength reduction factorϕy = yield curvature at section, 1/in. (1/mm)ρ = ratio of nonprestressed tension reinforcementρ′ = ratio of nonprestressed compression reinforcementρb = ratio of As to bd producing balanced strain conditionρv = ratio of Av to bws


GUIDE TO NONLINEAR MODELING PARAMETERS FOR EARTHQUAKE-RESISTANT STRUCTURES (ACI 374.3R-16) 3



Ω0 = amplification factor to account for overstrength of the seismic-force-resisting system (overstrength factor)

2.2—DefinitionsACI provides a comprehensive list of definitions through

an online resource, “ACI Concrete Terminology,” https://www.concrete.org/store/productdetail.aspx?ItemID=CT16. Definitions provided herein complement that source.

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.

drift—horizontal deflection at the top of the story relative to the bottom of the story.

effective stiffness—stiffness of a structural member accounting for cracking, creep, and other nonlinear effects.

licensed design professional—an individual who is licensed to practice structural design as defined by the statu-tory requirements of the professional licensing laws of the state or jurisdiction in which the project is to be constructed, and who is in responsible charge of the structural design.

modeling parameter—deformation parameter that defines the shape of the nonlinear force-deformation enve-lope curve of a structural component.

performance objective—one or more pairings of a selected seismic hazard level with both a target structural performance level and a target nonstructural performance level.

probable strength—strength of a member determined using the properties of the member assuming a tensile stress in the reinforcing bars of at least 1.25fy and a strength reduc-tion factor ϕ of 1.0.

special moment frame—a cast-in-place beam-column frame complying with 18.2.3 through 18.2.8 and 18.6 through 18.8 of ACI 318-14.

special structural wall and coupling beam—a cast-in-place structural wall and connecting the structural walls in accordance with 18.2.3 through 18.2.8 and 18.10 of ACI 318-14.

CHAPTER 3—GENERAL

3.1—GeneralIn the following sections, tables of nonlinear modeling

parameters are provided for components of special moment frames, special structural walls, and special coupling beam components designed in accordance with Chapter 18 of ACI 318. An experimental database of component specimens compliant with the detailing requirements of ACI 318 was available for columns (Ghannoum and Sivaramakrishnan 2012a,b) and flexure-controlled structural walls (Birely 2012) only. Therefore, while tables derived from ASCE/SEI 41 are available for all component types including columns, beams, beam-column joints, and shear-controlled wall elements, tables derived from the test database are only available for columns and flexure-controlled walls.

The nonlinear force-deformation response of a compo-nent can be generalized as a backbone curve by a series of linear relations dictated by the provided nonlinear modeling parameters. This guide adopted the generalization methods

used in ASCE/SEI 41. Figure 1.1 presents examples of general force-deformation backbone curves and modeling parameters. A typical backbone curve is described by a linear response from Point A (unloaded deformation) to Point B (effective yield), then a linear response from Point B to C (post-yield deformation without degradation of strength), followed by a linear response from Point C to D (strength degradation), and a final line from Point D to E (total loss of strength and deformation capacity limit). The slope from Point A to B (initial stiffness) is selected according to Table 3.1. The stiffness values presented for flexure-controlled elements are meant to represent a secant to yield level forces, neglecting initial stiffness properties prior to flexural cracking. The initial variation of stiffness is not a critical factor for esti-mation of plastic deformation capacity and is generally lost after the first significant cycle of dynamic loading. It is critical that the effective stiffness values presented be used instead of the stiffness values from Section 6.6.3 of ACI 318 because the modeling parameters based on ASCE/SEI 41 (plastic rotations) were calculated as total deformation minus yield deformation, based on the effective stiffness values defined in this document. The yield strength Qy of a component is defined as the nominal strength—that is, Mn or Vn calculated in accordance with ACI 318 Chapter 18, without the inclu-sion of a strength reduction factor ϕ. The slope from Point B to C corresponds to the increase of the component strength, considering the difference between nominal strength and the probable strength associated with strain hardening of the steel reinforcement—that is, 1.25fy. The linear relations between Points C, D, and E are determined by the modeling param-eters representing the strength degradation at higher defor-mations. Although ASCE/SEI 41 general backbone curves in Fig. 1.1(a) and (c) show a sudden strength loss from Point C to D, a more realistic approach for ductile concrete compo-

Table 3.1—Effective initial stiffness (ASCE/SEI 41-13 Table 10-5, modified)

Component Flexural rigidity Shear rigidity

Beams* 0.3EcIg 0.4EcAw

Columns with compression due to design gravity loads ≥ 0.5Agfc′†

0.7EcIg 0.4EcAw

Columns with compression due to design gravity loads < 0.1Agfc or

with tension†

0.3EcIg 0.4EcAw

Beam-column joints

Rigid column offsets and non-rigid beam offsets based on the beam stiffness (Fig. 4.2a)

Structural walls

Constant stiffness coefficient method: Refer to 5.1.1.1 0.4EcAcv

Constant yield curvature method:Refer to 5.1.2.1 0.4EcAcv

*For T-beams, Ig can be taken as twice the value of Ig of the web alone. Otherwise, Ig is based on the effective width as defined in Section 6.3 of ACI 318-14.†For columns with axial compression falling between the limits provided, flexural rigidity is determined by linear interpolation.





nents can consider a gradual slope for the strength loss branch, degrading from Point C directly to E (ASCE/SEI 41; PEER/ATC 2010); this approach, demonstrated with dashed lines in Fig. 1.1(a) and (c), should be taken for construction of back-bone curves using this guide.

When components are modeled using nonlinear force-deformation relationships according to this guide, they should be evaluated and designed using a deformation-based approach rather than a force-based approach, in accor-dance with the deformation acceptance criteria included in the selected design standards or guidelines for the project. The structural components intended to remain elastic—for example, diaphragm connections to seismic-resisting components or columns under discontinuous structural walls—should be evaluated using demands from either the analysis model or capacity-based methods, and compared against nominal strength values obtained from ACI 318, with consideration of the strength reduction factor ϕ.

For nonlinear static procedures such as pushover analyses, components can be modeled using the modeling parameters provided in this document without supplementary informa-tion. For nonlinear dynamic procedures, information regarding cyclic behavior of components, also called hysteresis, is also required. Hysteretic modeling recommendations are beyond the scope of this document. The unloading and reloading stiff-ness and strength, and any pinching of the force-versus-defor-mation hysteresis loops, should reflect the behavior observed in a test specimen similar to the one under investigation.

When design forces on components are required to be calculated to determine conditions for selecting modeling parameters, these forces can be calculated using either limit-state analysis (capacity-based design) or taken as the design force corresponding to the unreduced hazard-level earthquake under consideration. As an example for when ASCE/SEI 7 is used for design, the design axial force and shear force for a wall, P and V, used to determine modeling parameters, should be obtained from the design load combinations that include earthquake load E increased by the overstrength factor Ω0. The earthquake demand amplified by the overstrength factor Ω0E provides a demand comparable to that required for evalu-ation of force-controlled actions in ASCE/SEI 41.

3.2—Backbone curve selection procedureThe steps involved in creating a typical backbone curve

(Fig. 1.1) are:(1) Determine nominal strengths per ACI 318 (for

example, Vn or Mn).(2) Determine the probable strength per ACI 318, associ-

ated with strain hardening of the steel reinforcement.(3) Determine Point B with the coordinates in accordance

with the nominal strength and effective stiffness values in Table 3.1.

(4) Calculate the conditions (for example P/(Agfc′) or ρv = Av/(bws)) required by the modeling parameter table and select modeling parameters by linear interpolation.

(5) Determine Points C and E with the coordinates in accordance with the probable strength and the selected modeling parameters.

CHAPTER 4—NONLINEAR MODELING PARAMETERS FOR SPECIAL CONCRETE

MOMENT FRAMES

4.1—Modeling parameters for columns4.1.1 Modeling parameters from ASCE/SEI 41—Table

4.1.1 was developed for columns in special concrete moment frames by modifying Table 10-8 of ASCE/SEI 41, which consists of modeling parameters for existing components. The modeling parameter values in Table 10-8 (ASCE/SEI 41) that did not satisfy the detailing criteria in ACI 318—for example, lap splice requirements or transverse reinforcement ratio—were deleted or modified by linear interpolation. Defi-nitions and condition requirements were modified to conform to language and criteria in ACI 318 as well. Due to differences in definitions and symbols, some conditions were modified in Table 4.1.1. For example, in the second footnote (†) of Table 4.1.1, the conditions are expressed in terms of Ve, Vn, and ϕ instead of Vp and V0, as in Table 10-8 of ASCE/SEI 41. ASCE/SEI 41 symbols are replaced by those in ACI 318.

4.1.2 Modeling parameters from subset database—The databases (Ghannoum and Sivaramakrishnan 2012a,b) used to develop the ASCE/SEI 41 column modeling parameter tables contain test results from various test specimens. Values derived solely from tests of ACI 318-compliant components were filtered from the ASCE/SEI 41 test databases to develop a new set of modeling parameters. The database included a total of 38 rectangular column specimens and 25 circular column specimens conforming to the intent of ACI 318-14 detailing requirements. The data for rectangular and circular columns were separated and two sets of modeling param-eters—one for rectangular columns (Table 4.1.2a) and the other for circular columns (Table 4.1.2b)—were developed. The procedure recommended in Section 7.6 of ASCE/SEI 41 was used to develop the modeling parameters in Tables 4.1.2a and 4.1.2b for consistency and to allow comparisons with Table 4.1.1. Values of modeling parameters equal to mean and mean minus one standard deviation are provided based on statistical analysis of the database.

Figure 4.1.2 presents an example of a comparison between test data and modeling parameters based on ASCE/SEI 41 and the experimental database. Mean values should be used for nonlinear analysis to minimize skewing of the analysis results (Ghannoum and Matamoros 2014). The mean minus one stan-dard deviation values are presented to provide insight to the scatter of the data used to develop these tables. Accordingly, acceptance criteria should be carefully selected considering the distribution and scatter of the data, which are represented by the mean minus one standard deviation value.

4.2—Modeling parameters for beams and beam-column joints (ASCE/SEI 41)

Tables 4.2a and 4.2b provide modeling parameters for beams and for beam-column joints in special moment frames, respectively. The parameters shown are based on those given in Tables 10-7 and 10-10 of ASCE/SEI 41. Data-bases for beams and beam-column joints were not available to the committee. Initial stiffness values (slope from Point





Table 4.1.2a—Nonlinear modeling parameters for rectangular columns in special moment frames based on database

Conditions Plastic rotation angle, radians*†

Residual strength

ratio‡

P/(Agfc′) ρv = Av/(bws)

Mean

Mean minus one standard

deviation

a b a b c

= 0.1 ≥ 0.015 0.065 0.085 0.035 0.055 0.2

≥ 0.6 ≥ 0.015 0.020 0.030 0.005 0.005 0.2

= 0.1 = 0.006 0.040 0.070 0.020 0.045 0.2

≥ 0.6 = 0.006 0.010 0.010 0.005 0.005 0.2*The modeling parameters should apply where Ve/ϕVn ≤ 0.8.†The strength provided by the hoops or spirals (ϕVs) should be at least three-fourths of the design shear force V. Design axial force P shall be based on the maximum expected axial load due to gravity and earthquake loads.‡Values between those listed in the table should be determined by linear interpolation.

Table 4.1.1—Nonlinear modeling parameters for columns in special moment frames (ASCE/SEI 41 Table 10-8, modified)

Conditions

Modeling parameters*

Plastic rotation angle, radians

Residual strength

ratio

a b c

Condition i. Ve/ϕVn ≤ 0.8†

P/(Agfc′)‡ ρv = Av/(bws)

≤0.1 ≥ 0.006 0.035 0.060 0.2

≥0.6 ≥ 0.006 0.010 0.010 0.0

≤0.1 = 0.0036§ 0.030§ 0.044§ 0.2

≥0.6 = 0.0036§ 0.007§ 0.007§ 0.0

Condition ii. 0.8 ≤ Ve/ϕVn ≤ 1.0†

P/(Agfc′)‡ ρv = Av/(bws)V/bwd√fc′#, psi (MPa)

≤ 0.1 ≥ 0.006 ≤ 3 (0.25) 0.032 0.060 0.2

≤ 0.1 ≥ 0.006 ≥ 6 (0.50) 0.025 0.060 0.2

≥ 0.6 ≥ 0.006 ≤ 3 (0.25) 0.010 0.010 0.0

≥ 0.6 ≥ 0.006 ≥ 6 (0.50) 0.008 0.008 0.0

≤ 0.1 = 0.0036§ ≤ 3 (0.25) 0.023§ 0.039§ 0.2

≤ 0.1 = 0.0036§ ≥ 6 (0.50) 0.017§ 0.036§ 0.2

≥ 0.6 = 0.0036§ ≤ 3 (0.25) 0.007§ 0.007§ 0.0

≥ 0.6 = 0.0036§ ≥ 6 (0.50) 0.005§ 0.005§ 0.0*Values between those listed in the table should be determined by linear interpolation.†The strength provided by the hoops or spirals (ϕVs) should be at least three-fourths of the design shear force Ve.‡Design axial force P shall be based on the maximum expected axial load due to gravity and earthquake loads.§The transverse reinforcement ratio values in ASCE/SEI 41 were modified per the minimum requirement in ACI 318, and the modeling parameter values were modified by linear interpolation.#V is the design shear force Ve per Section 18.7.6.1.1 of ACI 318, unless determined by a nolinear analysis.

Table 4.1.2b—Nonlinear modeling parameters for circular columns in special moment frames based on database

Conditions Plastic rotation angle, radians*†Residual strength

ratio‡

P/(Agfc′) ρv = Av/(bws)

MeanMean minus one

standard deviation

a b a b c

= 0.1 ≥ 0.012 0.070 0.085 0.035 0.035 0.2

≥ 0.6 ≥ 0.012 0.015 0.020 0.010 0.010 0.2

= 0.1 = 0.0036 0.060 0.070 0.030 0.030 0.2

≥ 0.6 = 0.0036 0.010 0.015 0.010 0.010 0.2*The modeling parameters should apply where Ve/ϕVn ≤ 0.8.†The strength provided by the hoops or spirals (ϕVs) should be at least three-fourths of the design shear force V. Design axial force P should be based on the maximum expected axial load due to gravity and earthquake loads.‡Values between those listed in the table should be determined by linear interpolation.

Fig. 4.1.2—Example of test data and modeling parameters based on ASCE/SEI 41 and the subset database (modeling parameter b for rectangular columns versus transverse rein-forcement ratio).

Table 4.2a—Nonlinear modeling parameters for beams in special moment frames (ASCE/SEI 41 Table 10-7, modified)

Conditions Modeling parameters*

(ρ – ρ′)/ρb

V/bwd√fc′†‡, psi (MPa)


Residual strength ratio

a b c

≤ 0.0 ≤ 3 (0.25) 0.025 0.05 0.2

≤ 0.0 ≥ 6 (0.50) 0.02 0.04 0.2

≤ 0.5 ≤ 3 (0.25) 0.02 0.03 0.2

≤ 0.5 ≥ 6 (0.50) 0.015 0.02 0.2*Values between those listed in the table should be determined by linear interpolation.†The strength provided by the hoops (ϕVs) should be at least three-fourths of the design shear V.‡V is the design shear force Ve per Section 18.6.5.1 of ACI 318, unless determined by a nonlinear analysis.





A to B in Fig. 1.1) of beams and beam-column joints should be selected based on Table 3.1, and the nonlinear modeling parameters a, b, and c should be selected from Tables 4.2a and 4.2b. The initial stiffness of a beam-column joint is obtained by considering rigid offsets (Fig. 4.2a). The nonlinear modeling parameters for beam-column joints are selected based on the joint classification shown in Fig. 4.2b.

CHAPTER 5—NONLINEAR MODELING PARAMETERS FOR SPECIAL CONCRETE

STRUCTURAL WALLS AND COUPLING BEAMS

5.1—Modeling parameters for special structural walls and coupling beams controlled by flexure

5.1.1 Modeling parameters from ASCE/SEI 41—This document provides two approaches for developing the nonlinear backbone of structural walls, as indicated in Fig. 1.1. The design professional can follow the ASCE/SEI 41 approach, using a constant elastic stiffness and modeling parameters adopted from ASCE/SEI 41 in Table 5.1.1. The elastic stiffness (slope from Point A to B in Fig. 1.1) is based

Table 4.2b—Nonlinear modeling parameters for beam-column joints in special moment frames (ASCE/SEI 41 Table 10-10, modified)

Conditions

Modeling parameters*†


Residual strength ratio

a b c

Condition i. Interior joints (Note: For classification of joints, refer to Fig. 4.2b)

P/(Agfc′)‡ V/Vn§

≤ 0.1 ≤ 1.2 0.015 0.03 0.2

≤ 0.1 ≥ 1.5 0.015 0.03 0.2

≥ 0.4 ≤ 1.2 0.015 0.025 0.2

≥ 0.4 ≥ 1.5 0.015 0.02 0.2

Condition ii. Other joints (Note: For classification of joints, refer to Fig. 4.2b)

P/(Agfc′)‡ V/Vn§

≤ 0.1 ≤ 1.2 0.01 0.02 0.2

≤ 0.1 ≥ 1.5 0.01 0.03 0.2

≥ 0.4 ≤ 1.2 0.01 0.025 0.2

≥ 0.4 ≥ 1.5 0.01 0.02 0.2*Values between those listed in the table should be determined by linear interpolation.†The modeling parameters only can be used if the joint transverse reinforcement is spaced at ≤ hc/3 within the joint. hc is average height of the beams framing into the joint in the direction of applied shear.‡P is the design axial force on the column above the joint, and Ag is the gross cross-sectional area of the joint.§V is the design shear force, and Vn is the shear strength for the joint. The shear strength should be calculated according to Section 18.8.4 of ACI 318, except for knee joints. For knee joints with or without transverse beams, V f An c j= ′8 should replace the strength requirement in Section 18.8.4.1 of ACI 318.

Fig. 4.2a—Beam-column joint modeling (ASCE/SEI 41). (Note: Hatched portions indicate rigid element.)

Fig. 4.2b—Joint classification for response in the plane of the page (ASCE/SEI 41).





on either a constant percentage of the wall gross section properties (a constant stiffness coefficient (5.1.1.1)) or on the assumption that the yield curvature remains constant for a given concrete cross section (5.1.2). Once the elastic stiff-ness is defined, plastic rotation or total drift to Points C and D can be identified from either Table 5.1.1, based on ASCE/SEI 41 values, or by using Table 5.1.2, which was developed based on a subset database from ACI-compliant wall speci-mens. This section defines the steps required for the more traditional constant stiffness coefficient methodology, while 5.1.2.1 outlines the steps involved when assuming a constant yield curvature.

Table 5.1.1 is provided for flexure-controlled special structural walls and coupling beams, defined for elements in which Ve/Vn is less than or equal to 1.0, where Ve is the design shear force per ACI 318 Section 18.7.6.1.1. The modeling parameters found in Table 5.1.1, based on plastic deforma-tion, consist of table values from ASCE/SEI 41, modified to

correspond to the design requirements for walls prescribed in ACI 318. Descriptions and requirements associated with elements not conforming to ACI 318 were removed. Also, because of the difference in definitions and symbols, some of the conditions were modified.

5.1.1.1 Element properties: constant stiffness coefficient methodology—This guide provides two approaches for developing the nonlinear backbone curve of structural walls, as indicated in Fig. 1.1. The main difference between the two approaches is that the elastic stiffness (slope from Point A to B in Fig. 1.1) is calculated based on either a percentage of the wall gross section properties (a stiffness coefficient) or on the assumption that the yield curvature is insensitive to changes in axial load ratio and flexural reinforcement content for a given concrete cross section. This section defines the steps required for the stiffness coefficient methodology, while 5.1.2.1 outlines the steps involved when calculating the slope based on the yield curvature.

Table 5.1.1—Nonlinear modeling parameters: reinforced concrete special structural walls and coupling beams controlled by flexure (ASCE/SEI 41 Table 10-19, modified)

Conditions†

Modeling parameters*

Plastic hinge rotation angle, radiansResidual strength

ratio

a b c

Condition i. Structural walls and wall segments

( )A A f Ps s y

cv cA f− ′ +

′

‡

V/Acv√fc′, psi (MPa)‡ Confined boundary§

≤ 0.1 ≤ 4 (0.33) Yes 0.015 0.020 0.75

≤ 0.1 ≥ 6 (0.50) Yes 0.010 0.015 0.40

≥ 0.25 ≤ 4 (0.33) Yes 0.009 0.012 0.60

≥ 0.25 ≥ 6 (0.50) Yes 0.005 0.010 0.30

≤ 0.1 ≤ 4 (0.33) No 0.008 0.015 0.60

≤ 0.1 ≥ 6 (0.50) No 0.006 0.010 0.30

≥ 0.25 ≤ 4 (0.33) No 0.003 0.005 0.25

≥ 0.25 ≥ 6 (0.50) No 0.002 0.004 0.20

Conditions†

Chord rotation, radiansResidual strength

ratio

d e c

Condition ii. Structural wall coupling beams

Longitudinal reinforcement and transverse reinforcement# V/Acv√fc′, psi (MPa)‡

Conventional longitudinal reinforcement with conforming

transverse reinforcement

≤3 (0.25) 0.025 0.050 0.75

≥6 (0.50) 0.020 0.040 0.50

Diagonal reinforcement NA 0.030 0.050 0.80*Values between those listed in the table should be determined by linear interpolation.†Reinforced concrete special structural walls and coupling beams are controlled by flexure when Ve/ϕVn ≤ 1.0, and Ve is the design shear force per ACI 318 Section 18.7.6.1.1. For cantilever structural walls, the design shear force should be equal to the magnitude of the lateral force required to develop Mpr at the base of the wall, assuming the lateral force is distributed uniformly over the height of the wall. For vertical or horizontal wall segments, the design force should be equal to the shear corresponding to the development of Mpr at opposite ends of the wall segment.‡V is the design shear force Ve per ACI 318-14 Section 18.7.6.1.1, unless determined by a nonlinear analysis. The design axial force P should be based on the maximum expected axial demand due to gravity and earthquake loads.§Walls should be considered to have confined boundaries when special boundary elements are provided in accordance with ACI 318-14 Section 18.10.6.#Transverse reinforcement should have a strength of closed stirrups Vs ≥ 3/4 of required shear strength of the coupling beam to use modeling parameters defined in this table.





In reference to Fig. 1.1, the slope from Point A to B (initial stiffness) for flexural walls is assumed to be a constant percentage of the gross moment of inertia (constant stiff-ness coefficient), where the effective flexural stiffness EcIcr is defined as 0.5EcIg. Note that the 0.5 coefficient is also consistent with the recommendations in ACI 318-14 Section 6.6.3.1. This effective stiffness is meant to represent the secant stiffness to yield level forces, consistent with the assumed component stiffness in the ASCE/SEI 41 standard. Element shear stiffness is taken as 0.4EcAcv, which assumes no shear cracking. The yield rotation θy can be determined using an assumed plastic hinge length as follows in Eq. (5.1.1.1)

θ y

n

c crp

ME I

=

�

(5.1.1.1)

The definition of effective stiffness for coupling beams is the same as that for walls described previously. Note, however, that reported coupling beam modeling parameters are for chord rotation (Fig. 1.1(b) and 5.1.1.1(b)), not plastic rotation as for walls (Fig. 1. 1(a) and 5.1.1.1(a)).

5.1.2 Modeling parameters from subset database—The tabulated modeling parameters in Table 5.1.2 were devel-oped from experimental wall data (Birely 2012) that was isolated for flexure-controlled walls conforming to the intent of ACI 318 detailing requirements. Parameters reported in this section are for total wall drift (Fig. 1.1(b)), not plastic deformation (Fig. 1.1(a)), as those reported in Table 5.1.1. Total drift was reported so that values were independent of the chosen elastic stiffness and defined yield rotation. Depending on the chosen analytical approach, reported drifts can be converted to plastic rotations by subtracting wall yield rotations calculated per either the constant stiff-ness coefficient (5.1.1.1) or the constant yield curvature (5.1.2.1) methodologies.

Note that the available experimental data (Birely 2012) for ACI-compliant wall specimens is limited. The database included a total of 20 wall specimens with confined bound-aries and nine with unconfined boundaries. The maximum reported axial load ratio was 0.15, and there were a small number of wall specimens with shear demand ratios toward the upper limits of the ASCE/SEI 41 tables. Thus, the axial load and shear parameters were adjusted from ASCE/SEI 41 limits so that trend lines matched experimental data trends and then converged to ASCE/SEI 41 values when param-eters exceeded the range of included data; ASCE/SEI 41 values were converted to total drift by adding averaged wall yield rotations.

The basis for developing modeling parameters for indi-vidual wall specimens is consistent with the guidelines of ASCE/SEI 41 Section 7.6. Note that a large portion of tests within the database were concluded prior to reaching 20 percent strength degradation. Accordingly, modeling parameter d was defined as the maximum drift at 20 percent strength loss or the maximum test-reported drift, whichever was smaller. Similarly, modeling parameter e, defined as the

Fig. 5.1.1.1—Reported measures of deformation in struc-tural walls and coupling beams (ASCE/SEI 41).





drift at total loss of lateral-load-resisting capacity, was deter-mined based on the ASCE/SEI 41-defined slope between Point C and E, as shown in Fig. 1.1(b). The residual strength ratio c was taken directly from ASCE/SEI 41, and interpola-tion was used for each experimental wall and corresponding shear and axial demand ratios.

Modeling parameters in Table 5.1.2 are provided based on statistical analysis of the database mean values and mean minus one standard deviation values. An example of a comparison between test data and the modeling parameters developed based on ASCE/SEI 41 and the database is shown in Fig. 5.1.2. Mean values should be used for nonlinear anal-ysis to minimize skewing of the analysis results (Ghannoum and Matamoros 2014). The mean minus one standard devia-tion values are presented to provide insight into the scatter of the data used to develop the tables. Accordingly, accep-tance criteria should be carefully selected considering the distribution and scatter of the data, which are represented by the mean minus one standard deviation values. Note that the standard deviation for wall specimens with uncon-fined boundaries was sufficiently large such that the user is advised to refer to Table 5.1.1 values when mean minus one standard deviation values are desired, or lower bound drift values of 0.004 and 0.006 can be conservatively chosen for d and e, respectively. The standard deviation values were large in this case because of the limited number of specimens within the dataset.

5.1.2.1 Element properties: constant yield curvature meth-odology—An alternative approach to the constant stiffness coefficient methodology per ASCE/SEI 41 described in 5.1.1.1 is offered in this section. For a given concrete cross section, experimental evidence and first-principle mechanics suggest that yield curvature, rather than elastic stiffness, is generally insensitive to reinforcement ratio and axial load (Priestley et al. 2007). The equations developed using this

Table 5.1.2—Nonlinear modeling parameters; reinforced concrete special structural walls controlled by flexure (ACI 318-compliant wall specimen database)

Structural walls and wall segments

Conditions*

Chord rotation, radians†

Residual strength ratio†Mean Mean minus one standard deviation

d e d e c

( )A A

As s y

cv c

f Pf

− ′ +′

‡

V/Acv√fc′, psi (MPa)‡ Confined boundary§

= 0.00 ≤ 4 (0.33) Yes 0.025 0.030 0.019 0.023 0.75

= 0.00 ≥ 6 (0.50) Yes 0.018 0.023 0.015 0.018 0.4

= 0.15 ≤ 4 (0.33) Yes 0.019 0.024 0.013 0.018 0.6

= 0.15 ≥ 6 (0.50) Yes 0.014 0.019 0.009 0.014 0.3

≥ 0.25 ≤ 4 (0.33) Yes 0.011 0.014 0.011 0.014 0.6

≥ 0.25 ≥ 6 (0.50) Yes 0.007 0.012 0.007 0.012 0.3

≤ 0.1 = 0 No# 0.017 0.024 0.005 0.007 0.6

≤ 0.1 ≥ 6 (0.50) No# 0.009 0.016 0.005 0.007 0.6

≤ 0.1 ≥ 6 (0.50) No# 0.004 0.006 0.005 0.007 0.3*Reinforced concrete special structural walls and coupling beams are controlled by flexure when Ve/ϕVn ≤ 1.0, and Ve is the design shear force per ACI 318-14 Section 18.7.6.1.1. For cantilever structural walls, the design shear force should be equal to the magnitude of the lateral force required to develop Mpr at the base of the wall, assuming the lateral force is distributed uniformly over the height of the wall. For vertical or horizontal wall segments, the design force should be equal to the shear corresponding to the development of Mpr at opposite ends of the wall segment.†Values between those listed in the table should be determined by linear interpolation.‡V is the design shear force Ve per ACI 318-14 Section 18.7.6.1.1, unless determined by a nonlinear analysis. The design axial force P should be based on the maximum expected axial demand due to gravity and earthquake loads. A normalized axial compression demand of 0.1Acvfc′ is recommended as an upper limit for use of table values for unconfined walls due to the limited set of data with high axial load and to prevent the likelihood of a nonductile failure mechanism.§Walls should be considered to have confined boundaries when special boundary elements are provided in accordance with ACI 318-14 Section 18.10.6.#Because standard deviation was large for unconfined walls, provided values are intended to serve as a conservative lower bound. Alternatively, Table 5.1.1 values can be used. Values are converted from plastic hinge rotation to total drift by adding the yield rotation calculated in accordance with 5.1.2.1.

Fig. 5.1.2—Example of experimental data versus proposed table values, e-parameter in relation to normalized shear demand (ASCE/SEI 41).





methodology compare well with the experimental force-displacement profiles in the database, whereas the traditional constant stiffness methodology tends to largely overestimate wall stiffness.

Using the constant yield curvature methodology, the yield rotation is defined for walls with rigid-base restraints at grade level and for walls that extend below grade as follows.

Walls analyzed with rigid-base restraints at grade level:

θ φy y

eff dh= +

3 2

�

(5.1.2.1a)

Walls that extend below grade (Fig. 5.1.2.1):

θ

φy

yeff bh h= +

3( )

(5.1.2.1b)

where

ϕy = 2εy/ℓw (5.1.2.1c) (Priestley et al. 2007)

εy = fy/Es (5.1.2.1d)

For analytical modeling using the constant yield curvature methodology, the effective stiffness should be converted from the aforementioned equations as defined in the following.

Walls analyzed with rigid base restraints at grade level:

E IM

h

c crn

yd

eff

=

+

φ 1

1 5. �

(5.1.2.1e)

Walls that extend below grade:

E I

Mc cr

n

y

=φ

(5.1.2.1f)

Note the following when using the aforementioned equations:(a) Included in the equation for walls with rigid base

restraints, the development length ld is a term associated with bond slip at the foundation interface. Greater slip is expected for larger reinforcing bars at wall boundary elements; user to input ℓd associated with largest bar diameter at the wall end.

(b) Concrete wall buildings often have basement levels, in which case walls extend below grade and an idealized rigid base restraint at grade level is not appropriate. For this case, the development length term associated with bond-slip is removed and a simplified linear moment profile is assumed to begin with zero magnitude at a height of heff (Fig. 5.1.2.1), rise to Mn at grade level, and then decrease back to zero magnitude at the wall base.

(c) The term heff is defined as the height from grade level to the applied load. For wall experiments, heff generally corre-sponds to the height of the wall. For buildings with multiple levels, heff should relate to the effective shear span and can

be approximated by dividing the base moment at grade by the base shear at grade from first-mode response.

(d) Where shear cracking is considered in the analysis, the user may refer to PEER/ATC (2010) for recommendations of reduced shear stiffness in addition to the cracked flexural stiffness parameters formulated previously.

5.2—Modeling parameters for structural walls and coupling beams controlled by shear

5.2.1 Modeling parameters from ASCE/SEI 41—Table 5.2.1 provides nonlinear modeling parameters for walls and coupling beams controlled by shear. The values for shear-controlled elements were taken directly from ASCE/SEI 41, modified to correspond to ACI 318 requirements. Modeling parameters associated with elements not conforming to ACI 318 requirements were removed.

Modeling parameters for shear-controlled structural walls are for total wall drift (Fig. 1.1(c) and 5.1.1.1(c)). As shown in Fig. 1.1(c), a typical trilinear backbone curve for shear-governed walls is defined by:

(1) A linear response from Point A (unloaded deformation) to F (initial shear cracking)

(2) Then a linear response with a reduced slope from Point F to B (effective yield)

(3) Followed by a zero-slope linear response from Point B to C (post yield deformation without degradation of strength)

(4) Then a linear, negative-slope response from Point C to D (strength degradation)

(5) Finally, a line of constant residual strength starting at Point D and the ultimate deformation capacity at Point E.

For the initial stiffness (slope from Point A to F), refer to the constant-stiffness coefficient method (5.1.1.1). The yield strength Qy of a component (Point B) is defined as the nominal strength Vn calculated in accordance with ACI 318 Chapter

Fig. 5.1.2.1—Effective wall height for wall continuing below grade.





18 without the inclusion of a strength reduction factor ϕ. The slope from Point F to B is a function of the initial stiffness, parameters g and f, and the calculated nominal shear strength. The final slope considers a gradual degradation from Point C to E, similar to flexure-controlled elements.

A typical backbone curve for shear-controlled coupling beams is composed of a series of linear relations similar to coupling beams controlled by flexure. Note that the modeling parameters for coupling beams in Table 5.2.1 are consistent with ASCE/SEI 41, developed for nonconforming detailing, and, thus, conservative for code-compliant coupling beams.

Although ACI 318 does not consider an upper bound cap for wall axial load ratio, Table 5.2.1 values should not be used for axial demands greater than 0.15Acvfc′, as indi-cated in Footnote 3 of ASCE/SEI 41 Table 10-20. If axial loads exceed this limit, the elements should be designed based on force demands rather than relying on nonlinear deformations.

CHAPTER 6—SUMMARY AND CONCLUSIONSSets of modeling parameters are reported, based on the

values provided in ASCE/SEI 41 and statistical analyses of experimental test databases, for the following two cases: 1) special moment frame components including columns, beams, and beam-column joints; and 2) special struc-tural wall and coupling beam components. The reported modeling parameters provide an alternate modeling option for LDPs performing nonlinear analysis for performance-based design of new building structures. This guide provides information regarding modeling of components

in special moment frame and structural wall systems that can be used for performance-based design procedures described in standards or guidelines currently available that provide design seismic hazards and corresponding acceptance criteria.

Because an experimental database was available for columns and flexure-controlled walls only, modeling param-eters developed based on statistical analysis of the database were provided for columns and flexure-controlled walls, while values for beams, beam-column joints, coupling beams, and shear-controlled walls were provided based on ASCE/SE0I 41. Future work will include the development of improved modeling parameter tables for beams, beam-column joints, coupling beams, and shear-controlled walls upon availability of experimental specimens conforming to newer versions of ACI 318. In addition, other earthquake-resisting structural systems in Chapter 18 of ACI 318-14 will be included in the scope of future work.

CHAPTER 7—REFERENCESCommittee documents are listed first by document number

and year of publication followed by authored documents listed alphabetically.

American Concrete InstituteACI 318-14—Building Code Requirements for Structural

Concrete and CommentaryACI 369R-11—Guide for Seismic Rehabilitation of

Existing Concrete Frame Buildings and Commentary

Table 5.2.1—Modeling parameters for nonlinear procedures: reinforced concrete special structural walls and coupling beams controlled by shear (ASCE/SEI 41 Table 10-20, modified)

Conditions‡

Total drift ratio, %*† Strength ratio*

d e g c f

Condition i. Structural walls and wall segments§

( ).

A As s y

cv c

f PA f

− ′≤

+′

0 05 1.0 2.0 0.4 0.20 0.6

( ).

A As s y

cv c

f PA f

− ′>

+′

0 05 0.75 1.0 0.4 0.0 0.6

Condition ii. Structural wall coupling beams

Conditions‡

Chord rotation, radians*† Residual strength ratio*

d e c

Longitudinal reinforcement and transverse reinforcement#

V/Acv√fc′, psi (MPa)

Conventional longitudinal reinforcement with conforming

transverse reinforcement

≤3 (0.25) 0.02 0.030 0.60

≥6 (0.50) 0.016 0.024 0.30*Values between those listed in the table should be determined by linear interpolation.†For structural walls and wall segments, use drift. For coupling beams, use chord rotation. Refer to Fig. 5.1.1.1(c) and Fig. 5.1.1.1(b), respectively.‡Reinforced concrete special structural walls and coupling beams are controlled by shear when Ve/ϕVn > 1.0, and Ve is the design shear force per ACI 318-14 Section 18.7.6.1.1. For cantilever structural walls, the design shear force should be equal to the magnitude of the lateral force required to develop Mpr at the base of the wall, assuming the lateral force is distributed uniformly over the height of the wall. For vertical or horizontal wall segments, the design force should be equal to the shear corresponding to the development of Mpr at opposite ends of the wall segment.§The design axial force P should be based on the maximum expected axial demand due to gravity and earthquake loads. Values shown in this table are applicable for walls and wall segments with an axial load of less than 0.15Acvfc′.#Conventional longitudinal reinforcement consists of top and bottom steel parallel to the longitudinal axis of the coupling beam. Transverse reinforcement should have a strength of closed stirrups, Vs ≥ 3/4 of required shear strength of the coupling beam to use modeling parameters defined in this table.





American Society of Civil EngineersASCE/SEI 7-10—Minimum Design Loads for Buildings

and Other StructuresASCE/SEI 41-13—Seismic Evaluation and Retrofit of

Existing Buildings

Authored documentsBirely, A., 2012, “Seismic Performance of Slender Rein-

forced Concrete Structural Walls,” PhD dissertation, Univer-sity of Washington, Seattle, WA, 448 pp.

Ghannoum, W. M., and Matamoros, A. B., 2014, “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 Hill, MI, 24 pp.

Ghannoum, W. M., and Sivaramakrishnan, B., 2012a, “ACI 369 Circular Column Database,” NEEShub, Network for Earthquake Engineering Simulation (NEES), Purdue University, West Lafayette, IN. https://nees.org/resources/3658 (accessed July 19, 2016).

Ghannoum, W. M., and Sivaramakrishnan, B., 2012b, “ACI 369 Rectangular Column Database,” Neeshub, Network for Earthquake Engineering Simulation (NEES),

Purdue University, West Lafayette, IN. https://nees.org/resources/3659 (accessed July 19, 2016).

Los Angeles Tall Buildings Structural Design Council (LATBSDC), 2014, “An Alternative Procedure for Seismic Analysis and Design of Tall Buildings Located in the Los Angeles Region,” Los Angeles, CA, 51 pp.

Pacific Earthquake Engineering Research Center, 2010, “Tall Buildings Initiative Guidelines for Performance-Based Seismic Design of Tall Buildings,” Report No. 2010/05, Version 1.0, University of California, Berkeley, CA, Nov., 85 pp.

Pacific Earthquake Engineering Research Center/Applied Technology Council (PEER/ATC), 2010, “Modeling and Acceptance Criteria for Seismic Design and Analysis of Tall Buildings,” Task 7 Report for the Tall Buildings Initiative, PEER, Redwood City, CA, Oct., 242 pp.

Priestley, M. J. N.; Calvi, G. M.; and Kowalsky, M. J., 2007, Displacement-Based Seismic Design of Structures, IUSS Press, Pavia, Italy, May, 771 pp.

Structural Engineers Association of Northern California (SEAONC), 2008, “Recommended Administrative Bulletin on the Seismic Design & Review of Tall Buildings Using Non-Prescriptive Procedures,” SEAONC, San Francisco, CA, AB-083 Tall Buildings Task Group, Apr., 10 pp.











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Reported by ACI Committee 374 ACI 374.3R-16 · 2020. 5. 12. · ACI 374.3R-16 Guide to Nonlinear Modeling Parameters for Earthquake-Resistant Structures Reported by ACI Committee