ACI ITG 4.3R-07 (Report on Structural Design and Detailing for High-Strength Concrete in Moderate to High Seismic Applications)

ACI ITG-4.3R-07

Report on Structural Design and Detailing for High-Strength Concrete in Moderate to High Seismic Applications

Reported by ACI Innovation Task Group 4 and Other Contributors

First Printing September 2007 America Ameri can n Con Concr cret ete e Ins Insti titu tute te Advanc Adv ancing ing con concre crete te kno knowle wledge dge

®

Report on Structural Design and Detailing for High-Strength Concrete in Moderate to High Seismic Applications Copyright by the American Concrete Institute, Farmington Hills, MI. All rights reserved. This material may not be reproduced or copied, in whole or part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of ACI. The technical committees responsible for ACI committee reports and standards strive to avoid ambiguities, omissions, and errors in these documents. In spite of these efforts, the users of ACI documents occasionally find information or requirements that may be subject to more than one interpretation or may be incomplete or incorrect. Users who have suggestions for the improvement of ACI documents are requested to contact ACI. Proper use of this document includes periodically checking for errata at www.concrete.org/committees/errata.asp for www.concrete.org/committees/errata.asp for the most up-to-date revisions. ACI committee documents are 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. Individuals who use this publication in any way assume all risk and accept total responsibility for the application and use of this information. All information in this publication is provided “as is” without warranty of any kind, either express or implied, including but not limited to, the implied warranties of merchantability, fitness for a particular purpose or non-infringement. ACI and its members disclaim liability for damages of any kind, including any special, indirect, incidental, or consequential damages, including without limitation, lost revenues or lost profits, which may result from the use of this publication. It is the responsibility of the user of this document to establish health and safety practices appropriate to the specific circumstances involved with its use. ACI does not make any representations with regard to health and safety issues and the use of this document. The user must determine the applicability of all regulatory limitations before applying the document and must comply with all applicable laws and regulations, including but not limited to, United States Occupational Safety and Health Administration (OSHA) health and safety standards. Order information: ACI information: ACI documents are available in print, by download, on CD-ROM, through electronic subscription, or reprint and may be obtained by contacting ACI. Most ACI standards and committee reports are gathered g athered together in the annually revised Concrete Practice (MCP). (MCP). American Concrete Institute 38800 Country Club Drive Farmington Hills, MI 48331 U.S.A. Phone: 248-848-3700 Fax: 248-848-3701

www.concrete.org ISBN 978-0-87031-254-0

ACI Manual of

ACI ITG-4.3R-07

Report on Structural Design and Detailing for High-Strength Concrete in Moderate to High Seismic Applications Reported by ACI Innovation Task Group 4 and Other Contributors ACI Innovation Task Task Group 4

S. K. Ghosh Chair Joseph M. Bracci

D. Kirk Harman

Adolfo Matamoros

Michael A. Caldarone

Daniel C. Jansen

Andrew W. Taylor

Other contributors

Dominic J. Kelly

Andres Lepage

ACI ITG-4.3R ITG-4.3R presents presents a literature literature review review on seismic design using highstrength concrete. The document is organized in chapters addressing the structural design of columns, beams, beam-column joints, and structural walls made with high-strength concrete, and focuses on aspects most relevant for seismic design. Each chapter concludes with a series of recommended recommended modifications to ACI 318-05 based on the findings of the literature review. The recommendations recommendations include proposals for the modification of the equivalent rectangular stress block, equations to calculate the axial strength of columns subjected to concentric loading, column confinement requirements, limits on the specified yield strength of confinement reinforcement, strut factors, factors, and provisi provisions ons for the the develo developmen pmentt of straight straight bars and hooks. hooks. An accompanying standard, ITG-4.1, is written in mandatory language in a format that can be adopted by local jurisdictions, and will allow building officials to approve the use of high-strength concrete on projects that are being constructed under the provisions of ACI 301, “Specifications for Structural Concrete,” and ACI 318, “Building Code Requirements for Structural Concrete.” ITG 4 has also developed another nonmandatory language document: ITG-4.2 R. It addresses materi als and quali ty consi derati ons and is the supporting document for ITG-4.1. Keywords: bond; confinement; drift; flexure; high-strength concrete; highyield-strength reinforcement; seismic application; shear; stress block; strutand-tie.

ACI Committee Reports, Guides, Standard Practices, 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.

Henry G. Russell

CONTENTS Chapter 1—Introduction, p. ITG-4.3R-2 1.1—Background 1.2—Scope

Chapter 2—Notation, p. ITG-4.3R-4 Chapter 3—Definitions, p. ITG-4.3R-7 Chapter 4—Design for flexural and axial loads using equivalent rectangular stress block, p. ITG-4.3R-7 4.1—Parameters of equivalent rectangular stress block 4.2—Stress intensity factor α1 4.3—Stress block depth parameter β1 4.4—Stress block area α1 4.5—Limiting strain εcu 4.6—Axial strength of high-strength concrete columns 4.7—Comparison of different proposals for rectangular stress block 4.8—Recommendations

Chapter 5—Confinement requirements for beams and columns, p. ITG-4.3R-19 5.1—Constitutive models for confined concrete 5.2—Previous research and general observations 5.3—Equations to determine amount of confinement reinforcement required in columns

ACI ITG-4.3R-07 was published and became effective August 2007. Copyright © 2007, American Concrete Institute. All 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 retri eval system or device, unless permission in writing is obtained from the copyright proprietors.

ITG-4.3R-1

ITG-4.3R-2

ACI COMMITTEE REPORT

5.4—Definition of limiting drift ratio on basis of expected drift demand 5.5—Use of high-yield-strength reinforcement for confinement 5.6—Maximum hoop spacing requirements for columns 5.7—Confinement requirements for high-strength concrete beams 5.8—Maximum hoop spacing requirements for highstrength concrete beams 5.9—Recommendations

Chapter 6—Shear strength of reinforced concrete flexural members, p. ITG-4.3R-35 6.1—Shear strength of flexural members without shear reinforcement 6.2—Effect of compressive strength on inclined cracking load of flexural members 6.3—Effect of compressive strength on flexural members with intermediate to high amounts of transverse reinforcement 6.4—Shear strength of members with low shear spandepth ratios 6.5—Calculation of shear strength of members subjected to seismic loading 6.6—Use of high-strength transverse reinforcement 6.7—Recommendations

Chapter 7—Development length/splices, p. ITG-4.3R-44 7.1—Design equations for development length of bars in high-strength concrete 7.2—Design equations for development length of hooked bars in high-strength concrete 7.3—Recommendations

Chapter 8—Design of beam-column joints, p. ITG-4.3R-48 8.1—Confinement requirements for beam-column joints 8.2—Shear strength of exterior joints 8.3—Shear strength of interior joints 8.4—Effect of transverse reinforcement on joint shear strength 8.5—Development length requirements for beam-column joints 8.6—Recommendations

Chapter 9—Design of structural walls, p. ITG-4.3R-51 9.1—Boundary element requirements 9.2—Shear strength of walls with low aspect ratios 9.3—Minimum tensile reinforcement requirements in walls 9.4—Recommendations

Chapter 10—List of proposed modifications to ACI 318-05, p. ITG-4.3R-53 10.1—Proposed modifications to equivalent rectangular stress block 10.2—Proposed modifications related to confinement of potential plastic hinge regions

10.3—Proposed modifications related to bond and development of reinforcement 10.4—Proposed modifications related to strut-and-tie models

Acknowledgments, p. ITG-4.3R-56 Chapter 11—Cited references, p. ITG-4.3R-56 CHAPTER 1—INTRODUCTION 1.1—Background The origin of ACI Innovation Task Group (ITG) 4, HighStrength Concrete for Seismic Applications, can be traced back to the International Conference of Building Officials (ICBO) (now International Code Council [ICC]) Evaluation Report ER-5536, “Seismic Design Utilizing High-Strength Concrete” (ICBO 2001). Evaluation Reports (ER) are issued by Evaluation Service subsidiaries of model code groups. An ER essentially states that although a particular method, process, or product is not specifically addressed by a particular edition of a certain model code, it is in compliance with the requirements of that particular edition of that model code. ER-5536 (ICBO 2001), first issued in April 2001, was generated by Englekirk Systems Development Inc. for the seismic design of moment-resisting frame elements using high-strength concrete. High-strength concrete was defined as “normalweight concrete with a design compressive strength greater than 6000 psi (41 MPa) and up to a maximum of 12,000 psi (83 MPa).” It was based on research carried out at the University of Southern California and the University of California at San Diego to support building construction in Southern California using concrete with compressive strengths greater than 6000 psi (41 MPa). The Portland Cement Association performed a review * of ER-5536 and brought up several concerns that focused on inconsistencies between the evaluation report and existing industry documents in two primary areas: material and structural. Despite those concerns, it was evident that the evaluation report had been created because quality assurance and design provisions were needed by local jurisdictions, such as the City of Los Angeles, to allow the use of high-strength concrete without undue restrictions. ACI has assumed a proactive role in the development of such provisions with the goal of creating a document that can be adopted nationwide. ACI considered its own Committee 363, High Strength Concrete, to be the best choice to address the materials and quality aspects of the document, while ACI Subcommittee 318-H, Structural Concrete Building Code—Seismic Provisions, was considered the best choice to address the seismic detailing aspects. Because 318-H is a subcommittee of a code-writing body, the development of a technical document of this kind is not part of its intended mission. In addition, producing a document through a technical committee can be a lengthy process. Based on these limitations, a request was made to form an ITG that would have the advantage of following a shorter timeline to completion. In *

Unpublished report available from PCA, Skokie, Ill., Aug. 2001.

STRUCTURAL DESIGN AND DETAILING FOR HIGH-STRENGTH CONCRETE IN SEISMIC APPLICATIONS

response to the request, the Technical Activities Committee (TAC) of ACI approved the formation of ITG 4 and established its mission. The mission was to develop an ACI document that addressed the application of high-strength concrete in structures located in areas of moderate and high seismicity. The document was intended to cover structural design, material properties, construction procedures, and quality-control measures. It was to contain language in a format that allowed building officials to approve the use of highstrength concrete in projects being constructed under the provisions of ACI 301-05, “Specifications for Structural Concrete,” and ACI 318, “Building Code Requirements for Structural Concrete.” The concept of “moderate to high seismic applications,” stated in the mission of the document, dates back to when U.S. seismic codes divided the country into seismic zones. These seismic zones were defined as regions in which seismic ground motion on rock, corresponding to a certain probability of occurrence, remained within certain ranges. Present-day seismic codes (ASCE/SEI 2006) follow a different approach to characterizing a seismic hazard. Given that public safety is a primary code objective, and that not all buildings in a given seismic zone are equally crucial to public safety, a new mechanism for triggering seismic design requirements and restrictions, called the seismic performance category (SPC), was developed. The SPC classification includes not only the seismicity at the site, but also the occupancy of the structure. Recognizing that building performance during a seismic event depends not only on the severity of bedrock acceleration, but also on the type of soil that a structure is founded on, seismic design criteria in more recent seismic codes are based on seismic design categories (SDC). The SDC is a function of location, building occupancy, and soil type. The TAC Technology Transfer Committee (TTTC)-established mission of ITG 4 was interpreted to mean that the Task Group was to address the application of high-strength concrete in structures that are: • Located in Seismic Zones 2, 3, or 4 of the “Uniform Building Code” (ICBO 1997); or • Assigned to SDC C, D, or E of “The BOCA National Building Code” (BOCA 1993 and subsequent editions) or the “Standard Building Code” (SBCCI 1994); or • SDC C, D, E, or F of the “International Building Code” (IBC 2003) or the National Fire Protection Association (NFPA) NFPA 5000 “Building Construction and Safety Code” (2003). SPC or SDC C is also referred to as the “intermediate” category. Similarly, SPC D and E or SDC D, E, and F are referred to as “high” categories. The terminology “moderate to high seismic applications,” however, is used throughout this document.

1.2—Scope This document addresses the material and design considerations when using normalweight concretes having specified compressive strengths of 6000 psi (41 MPa) or greater in structures designed for moderate to high seismic applications.

ITG-4.3R-3

Irrespective of seismic zone, SPC, or SDC, this document is also applicable to normalweight high-strength concrete in intermediate or special moment frames and intermediate or special structural walls as defined in ACI 318-05 (ACI Committee 318 2005). The term “high-strength concrete,” as defined by ACI 363R-92 (ACI Committee 363 1992), refers to concrete having a specified compressive strength for design of 6000 psi (41 MPa) or greater. The 6000 psi (41 MPa) threshold that was chosen for this document is similar to that adopted by ACI Committee 363. Even though high-strength concrete is defined based on a threshold compressive strength, the concept of high strength is relative. The limit at which concrete is considered to be high strength depends largely on the location in which it is being used. In some regions, structures are routinely designed with concrete having specified compressive strengths of 12,000 psi (83 MPa) or higher, whereas in other regions, concrete with a much lower specified compressive strength is considered high strength. Essentially, the strength threshold at which concrete is considered high strength depends on regional factors, such as the characteristics and availability of raw materials, production capabilities, testing capabilities, and experience of the ready mixed concrete supplier. ITG-4 produced three documents: ITG-4.1 is a reference specification that can be cited in the project specifications; ITG-4.2R addresses materials and quality considerations th at are the basis for the ITG-4.1 specification; and ITG-4.3R, this document, addresses structural design and detailing. Certain modifications of ACI 318 requirements are proposed in Chapter 10 of ITG-4.3R. From a materials perspective, there are few differences between the properties of high-strength concrete used in seismic applications and those of high-strength concrete used in nonseismic applications; therefore, the information presented in ITG-4.1 and ITG-4.2R is generally applicable to all high-strength concrete. When special considerations are warranted due to seismic applications, they are addressed specifically. Unlike ITG-4.1 and ITG-4.2R, most of the material contained in ITG-4.3R is specific to seismic applications of high-strength concrete structural members. The information in Chapters 4 through 9 of this document is presented in a report format. Chapter 10 contains suggested modifications to design and detailing requirements in ACI 318-05. Some topics, such as compressive stress block and confinement of beam-columns, are more developed than others because there is significantly more literature available on these topics. For all topics, an attempt was made to be as thorough as possible in summarizing the most relevant information pertaining to the design of members with high-strength concrete. For topics with limited information in the literature, however, recommendations were made with the intent of preventing potentially unsafe design.

ITG-4.3R-4


CHAPTER 2—NOTATION Ab,max = Acc

Ach

Acv

=

=

=

Ag

=

Ash

=

Asp

=

Ast

=

Asv

=

Aswb

=

Asww

=

Ate

=

Atr

=

Av

=

Aw

=

av

=

b bc

= =

bw

=

c

=

c′

=

cross-sectional area of largest bar being developed or spliced, in. 2 (mm2) cross-sectional area of structural member measured center-to-center of transverse reinforcement, in. 2 (mm2) cross-sectional area of structural member measured out-to-out of transverse reinforcement, in.2 (mm2) gross area of concrete section bounded by web thickness and length of section in direction of shear force considered, in. 2 (mm2) gross area of concrete section, in. 2 (mm2). For hollow section, Ag is area of concrete only and does not include area of void(s) total cross-sectional area of transverse reinforcement (including crossties) within spacing s and perpendicular to dimension bc , in.2 (mm2) cross-sectional area of transverse reinforcement crossing potential plane of splitting of bars being developed or spliced, in. 2 (mm2) total area of nonprestressed longitudinal reinforcement (bars or steel shapes), in. 2 (mm2) total area of vertical reinforcement in structural wall, in.2 (mm2) total area of vertical reinforcement in boundary element of structural wall, in. 2 (mm2) total area of vertical reinforcement in web of structural wall, excluding the boundary elements, in. 2 (mm2) sum of areas of tie legs used to provide lateral support against buckling for longitudinal bars of column, in.2 (mm2) total cross-sectional area of all transverse reinforcement within spacing s that crosses potential plane of splitting through reinforcement being developed, in. 2 (mm2) area of shear reinforcement with spacing s, in.2 (mm2) gross cross-sectional area of structural wall, in.2 (mm2) shear span, equal to distance from center of concentrated load to either: a) face of support for continuous or cantilever members; or b) center of support for simply supported members, in. (mm) width of compression face of member, in. (mm) cross-sectional dimension of column core measured center-to-center of outer legs of transverse reinforcement comprising area Ash, in. (mm) web width or diameter of circular section, in. (mm) distance from extreme compression fiber to neutral axis, in. (mm) cmin + d b /2 = spacing or cover dimension, in. (mm)

c1

=

c2

=

cb

=

cc ccb

= =

cmax cmin

= =

c p cs

= =

csfw

=

csi cso

= =

DRlim d

= =

d b

=

d s

=

E

=

EE p

=

E s

=

f c′

=

f co ′

=

f p f pc

= =

f s

=

f t,l

=

f t,t

=

dimension of rectangular or equivalent rectangular column, capital, or bracket measured in direction of span for which moments are being determined, in. (mm) dimension of rectangular or equivalent rectangular column, capital, or bracket measured in direction perpendicular to c1, in. (mm) smaller of: a) distance from center of bar or wire to nearest concrete surface; or b) one-half center-to-center spacing of bars or wires being developed, in. (mm) clear cover of reinforcement, in. (mm) least distance from surface or reinforcement to tension face, in. (mm) maximum of c cb and cs , in. (mm) minimum cover used in expressions for bond strength of bars not confined by transverse reinforcement. Smaller of ccb and cs, in. (mm) ρvr · f yt / f c′ = volumetric confinement index minimum of cso and (csi + 0.25) in. [(csi + 6.35) mm], in. (mm) flexural stress index for structural wall that represents measure of ratio of neutral axis depth to length of wall, in. (mm) one-half of clear spacing between bars, in. (mm) clear side concrete cover for reinforcing bar, in. (mm) (∆lim / hcol ) = limiting drift ratio distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in. (mm) nominal diameter of bar, wire, or prestressing strand, in. (mm) nominal diameter of bar used as transverse reinforcement, in. (mm) load effects of earthquake or related internal moments and forces M exp] × 100 = parameter used [( M calc – M exp)/ to characterize accuracy of nominal moment strength of column modulus of elasticity of reinforcement and structural steel, psi (MPa) specified compressive strength of concrete, psi (MPa) in-place strength of unconfined concrete in columns, psi (MPa) (often assumed as 0.85 f c′ ) P / Ag f c′ = axial load ratio P / Ach f c′ = axial load ratio based on area of confined core calculated tensile stress in reinforcement at service loads, psi (MPa) stress imposed on concrete by compression field associated with reinforcement oriented in direction parallel to flexural reinforcement located at edge of compression field, psi (MPa) stress imposed on concrete by compression field associated with reinforcement oriented in


f u

=

f yl

=

f yt f yt,l

f yt,t

h′′

= =

=

=

ha hcol hw

= = =

h x

=

j

=

K tr

=

K tr ′

=

k 1

=

k 2

=

k 3

=

k cc

=

k d

=

k j

=

k s

=

lb

=

ld

=

ldh

=

direction perpendicular to flexural reinforcement located at edge of compression field, psi (MPa) maximum tensile stress that can be developed in bar with 90-degree hook, psi (MPa) specified yield strength of longitudinal reinforcement, psi (MPa) specified yield strength of transverse reinforcement, psi (MPa) specified yield strength of transverse reinforcement oriented parallel to flexural reinforcement located at edge of uniform compression field, psi (MPa) specified yield strength of transverse reinforcement oriented perpendicular to flexural reinforcement located at edge of uniform compression field, psi (MPa) core dimension perpendicular to transverse reinforcement providing confinement measured to outside of hoops, in. (mm) tie depth, in. (mm) clear column height, in. (mm) height of entire wall from base to top or height of segment of wall considered, in. (mm) maximum center-to-center horizontal spacing of crossties or hoop legs on all faces of column, in. (mm) ratio of internal lever arm to effective depth of beam ( Atr f yt /1500sn) = transverse reinforcement index (refer to ACI 318-05, Section 12.2.3) (0.5t d Atr / sn) f c′ 1/2 = transverse reinforcement index for Committee 408 development length expression, in. (mm) ratio of average to maximum stress in compression zone of flexural member ratio of distance from extreme compression fiber to location of compression reaction to distance from extreme compression fiber to location of neutral axis in flexural member ratio of maximum stress in compression zone of flexural member to cylinder strength cover factor in calculation of development length of hooked bars development length factor in calculation of development length of hooked bars development length and lever arm factor in calculation of development length of hooked bars transverse reinforcement bar diameter factor for calculation of development length of hooked bars dimension of loading plate or support in axial direction of member, in. (mm) development length in tension of deformed bar, deformed wire, plain or deformed welded wire reinforcement, or pretensioned strand, in. (mm) development length in tension of deformed bar or deformed wire with standard hook,

lo

=

lw

=

M

=

M exp

=

M ncol

=

m

=

n

=

n L P Po s

= = = =

so

=

T b

=

T s

=

t d V

= =

V a

=

V all V c

= =

V n V s

= =

V t,l

=

V t,t

=

vc,all wst

= = =

α1

ITG-4.3R-5

measured from critical section to outside end of hook, in. (mm) length, measured from joint face along axis of structural member, over which special transverse reinforcement must be provided, in. (mm) length of entire wall or length of segment of wall considered in direction of shear force, in. (mm) maximum unfactored moment due to service loads, including P-∆ effects, in.-lb (N-mm) measured flexural strength of column, in.-lb (N-mm) nominal flexural strength of column, in.-lb (N-mm) f yl /0.85 f c′ = ratio of nominal yield strength of longitudinal reinforcement to nominal strength of concrete in column number of bars being spliced or developed in plane of splitting number of legs of reinforcement in hoops and ties unfactored axial load, lb (N) nominal axial strength at zero eccentricity, lb (N) center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, prestressing tendons, wires, or anchors, in. (mm) center-to-center spacing of transverse reinforcement within length lo, in. (mm) total bond force of developed or spliced bar, lb (N) steel contribution to total bond force, additional bond strength provided by transverse steel, lb (N) term representing effect of bar size on T s maximum unfactored shear force at service loads, including P-∆ effects, lb (N) nominal shear strength provided by strut spanning between load point and support in reinforced concrete members with shear spandepth ratios below 2.5, lb (N) allowable shear force under service loads, lb (N) nominal shear strength provided by the concrete, lb (N) nominal shear strength, lb (N) nominal shear strength provided by shear reinforcement, lb (N) nominal shear strength provided by uniform compression field associated with transverse reinforcement oriented parallel to flexural reinforcement located at edge of compression field, lb (N) nominal shear strength provided by uniform compression field associated with transverse reinforcement oriented perpendicular to flexural reinforcement located at edge of compression field, lb (N) allowable shear stress in concrete strut width, in. (mm) factor relating magnitude of uniform stress in equivalent rectangular compressive stress

ITG-4.3R-6

αc

=

αl

=

αsh

=

αst

=

αt

=

β1

=

β fc

=

βnl,strut

=

βnl,truss

=

βs

=

βsc

=

βta

=

βαt χ1

=

=

∆lim

=

∆ yield

=

δu ε1 εcu

= = =

εlim

=

εo εs ε y

= = =


block to specified compressive strength of concrete coefficient defining relative contribution of concrete to nominal wall shear strength angle between struts and flexural reinforcement for a compression field associated with transverse reinforcement oriented in direction parallel to flexural reinforcement 1 ≤ 4/[( M / Vd ) +1] ≤ 2 = factor to account for effect of shear span-depth ratio on allowable shear stress carried by concrete smallest angle between strut and ties that it intersects at its nodes angle between struts and flexural reinforcement for compression field associated with transverse reinforcement oriented in direction perpendicular to flexural reinforcement factor relating depth of equivalent rectangular compressive stress block to neutral axis depth factor to account for effect of concrete compressive strength on effective compressive strength of concrete in strut factor to account for effect of repeated load reversals into nonlinear range of response on effective compressive strength of concrete in strut factor to account for effect of repeated load reversals into nonlinear range of response on shear strength associated with compression field factor to account for effect of cracking and confining reinforcement on effective compressive strength of concrete in strut factor to account for effect of load reversals, concrete compressive strength, confining reinforcement, and cracking on effective compressive strength of concrete in strut factor to account for effect of interaction between truss and arch mechanisms on effective compressive strength of concrete in strut factor to account for effect of angle of inclination of strut αs on effective compressive strength of concrete in strut ratio of mean concrete compressive stress corresponding to maximum axial load resisted by concentrically loaded column to specified compressive strength of concrete lateral drift corresponding to 20% reduction in lateral resistance, in. (mm) lateral drift corresponding to yielding of longitudinal reinforcement, in. (mm) design displacement, in. (mm) principal tensile strain in strut maximum strain at extreme compression fiber at onset of crushing of concrete concrete strain at extreme compression fiber corresponding to limit state being considered strain in concrete when it reaches peak stress strain demand on reinforcement strain in reinforcement at yield

φ φlim φu

=

strength reduction factor

=

limiting curvature of reinforced concrete wall

=

curvature at limit state of reinforced concrete section

φ y

=

curvature at yielding of flexural reinforcement of reinforced concrete section

γvj λ p

=

joint shear coefficient

=

factor to account for effect of axial load ratio on strength of compression field subjected to repeated load reversals into nonlinear range of response

µ∆ θ p

=

(∆lim / ∆ yield ) = displacement ductility ratio

=

expected rotation in plastic hinge region of flexural member, radians

ρarea

=

ratio of area of distributed transverse reinforcement Ash to gross area of concrete perpendicular to that reinforcement in members with rectilinear and circular transverse reinforcement

ρl

=

ratio of area of distributed longitudinal reinforcement to gross concrete area perpendicular to that reinforcement

ρs

=

ratio of volume of spiral reinforcement to total volume of core confined by spiral (measured out-to-out of spirals)

ρt

=

ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement

ρtc

=

Ash / bcs = ratio of area of distributed transverse reinforcement Ash to area of core perpendicular to that transverse reinforcement

ρt,l

=

ratio of area of distributed reinforcement oriented in direction parallel to flexural reinforcement of compression field to gross concrete area perpendicular to that reinforcement

ρt,t

=

ratio of area of distributed reinforcement oriented in direction perpendicular to flexural reinforcement of compression field to gross concrete area perpendicular to that reinforcement

ρvol

=

ratio of volume of rectilinear or circular transverse reinforcement to volume of core confined by that transverse reinforcement

ρvr

=

ratio of volume of rectilinear transverse reinforcement to volume of core confined by that transverse reinforcement

ρwt

=

ratio of total area of vertical reinforcement to gross area of structural wall

ωc

=

0.1(cmax / cmin) + 0.9 ≤ 1.25 = factor to account for ratio of maximum to minimum cover on development length of straight bar

ψe

=

factor used to modify development length based on reinforcement coating

ψs

=

factor used to modify development length based on reinforcement size

ψt

=

factor used to modify development length based on reinforcement location


CHAPTER 3—DEFINITIONS area transverse reinforcement ratio —ratio of the area of transverse reinforcement crossed by a plane perpendicular to the legs of the transverse reinforcement to the area of reinforced concrete along that plane. axial load ratio—ratio of axial load to the product of compressive strength of concrete and the gross area of concrete cross section. confinement index—product of transverse reinforcement ratio (either by area or by volume) and the yield strength of the transverse reinforcement, divided by the compressive strength of concrete. curvature ductility ratio —ratio of mean curvature at failure in the plastic hinge length to curvature at the onset of section yielding. In the case of reinforced concrete columns, the majority of researchers referenced in this document define failure as a 20% reduction in lateral load resistance. displacement ductility ratio—ratio of displacement at failure to displacement at the onset of member yielding. In the case of reinforced concrete columns, the majority of researchers referenced in this document define failure as a 20% reduction in lateral load resistance. ductility—ability of a reinforced concrete member to maintain its strength when subjected to repeated load reversals beyond the linear range of response. interstory drift—relative lateral displacement between two adjacent stories of a building imposed by the design earthquake. interstory drift ratio—ratio of interstory drift to story height. killed steel—steel made by completely removing or tying up the oxygen in the liquid steel through the addition of elements such as aluminum or silicon before the ingot solidifies, with the objective of achieving maximum uniformity in the steel. limiting drift—drift corresponding to a 20% reduction in lateral load resistance of a reinforced concrete member subjected to load reversals with increasing maximum displacements. limiting drift ratio—ratio of limiting drift to column height. limiting strain—maximum strain at the extreme concrete compression fiber of a flexural member at the onset of concrete crushing, εcu. volumetric transverse reinforcement ratio —ratio of the volume of transverse reinforcement confining the concrete core of a potential plastic hinge region to the volume of concrete inside the confined core.

CHAPTER 4—DESIGN FOR FLEXURAL AND AXIAL LOADS USING EQUIVALENT RECTANGULAR STRESS BLOCK It is common practice for structures assigned to a high Seismic Design Category (SDC) to proportion the majority of the structural elements of the lateral force-resisting system so that the axial load demand remains below the balanced axial load. For these elements, variations in the shape of the stress block related to the compressive strength of the concrete do not have a significant effect on the calculated

ITG-4.3R-7

strength. There are instances, however, in which it is difficult for engineers to avoid proportioning columns with high axial load demands, such as lower-story columns in tall buildings, lower-story columns in narrow moment-resisting frames, and columns supporting the ends of discontinuous walls. For these elements, the shape of the stress block may have a significant effect on the estimated strength. The stress block for members with high-strength concrete is also a concern in moderate seismic applications. In these cases, structures are proportioned for seismic events that impose lower force and deformation demands than high seismic applications, allowing the use of more slender columns. The accuracy of the stress block is of concern in earthquake-resistant design because overestimating the flexural strength of columns leads to overestimating the ratios of column-to-beam moment strengths, which increases the probability of hinging in the columns due to the development of a strong beam-weak column mechanism. Although the stress-strain characteristics of high-strength concrete are different from those of normal-strength concrete, there is no well-defined compressive strength boundary between the two; there is instead a gradual change with increasing concrete strengths (ACI Innovation Task Group 4 2006). The ascending branch of the stress-strain relationship is steeper for higher-strength concretes, indicating higher elastic modulus. It changes from approximately a second-order parabola for concretes within the normalstrength range to almost a straight line as the strength approaches 18,000 psi (124 MPa), which may be considered as the limit for high-strength concrete made with ordinary limestone aggregates. The strain at peak concrete stress, εo, increases with strength as well, varying approximately between 0.0015 and 0.0025 for 3000 to 15,000 psi (21 and 103 MPa) concrete, respectively. Failure becomes more sudden and brittle as the concrete strength increases and unloading beyond the peak becomes more rapid. In summary, concrete becomes more rigid and more brittle with increasing strength. Several researchers developed constitutive models for the stress-strain relationship of concrete that are applicable to high-strength concrete with proper adjustments to the governing parameters (Popovics 1973; Yong et al. 1988; Hsu and Hsu 1994; Azizinamini et al. 1994; Cusson and Paultre 1995). Expressions applicable specifically to highstrength concrete have also been developed (Martinez et al. 1984; Fafitis and Shah 1985; Bjerkeli et al. 1990; Muguruma and Watanabe 1990; Li 1994). Members subjected to uniform compression attain their maximum strength when concrete reaches a strain level corresponding to peak stress, εo. Under a strain gradient, maximum strength is attained at an extreme compressive fiber strain higher than that at peak stress, εlim (Hognestad 1951). This value changes with the geometric shape of the compression zone, and may also vary significantly with concrete strength and confinement. After the limiting strain has been established, the sectional strength can be computed by evaluating internal forces, including the compressive force in the concrete. The magnitude of the compressive force in the concrete can be established by relying on the

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Fig. 4.1—Parameters for rectangular stress block.

assumption that plane sections remain plane after bending and by calculating the stresses corresponding to the strains in the compression zone from the stress-strain relationship. Because it is cumbersome to use a nonlinear stress-strain relationship, ACI 318-05 provides an equivalent stress block for ease in design calculations. This stress block is derived such that both the area under the actual nonlinear stress distribution (force) and the centroid of this area (point of application of force) correspond to those of the stress block as closely as possible. The stress block adopted by ACI 318-05 is of rectangular geometry. Other equivalent stress blocks with various different shapes, such as triangular and trapezoidal, have been proposed in the literature. A historical review of this topic has been presented by Hognestad (1951).

4.1—Parameters of equivalent rectangular stress block The column design provisions of ACI 318-05 are based on an extensive column investigation conducted jointly by the University of Illinois, Lehigh University, and ACI. The initial results of the study were published in 1931 (Slater and Lyse 1931a,b), with a more comprehensive follow-up report in 1934 (Richart and Brown 1934). Subsequently, Hognestad (1951) conducted a large number of column tests and developed the parameters for a rectangular stress block. Figure 4.1 shows the parameters that define the equivalent rectangular stress block according to ACI 318-05. A parabolic stress distribution, shown in Fig. 4.1(b), results in values of k 2 = 0.375 (β1 = 0.75) and k 1 = 0.67 (α1 = 0.9k 3). A linear stress distribution yields values of k 2 = 0.333 (β1 = 0.667) and k 1 = 0.50 (α1 = 0.75k 3). ACI 318-05 stipulates that the average stress factor α1 is not sensitive to compressive strength and remains constant at 0.85, while the β1 factor decreases from 0.85 (k 1k 3 = 0.723) for a compressive strength of 4000 psi (28 MPa) to 0.65 (k 1k 3 = 0.553) for a compressive strength of 8000 psi (55 MPa). According to ACI 318-05, the strain at the extreme compression fiber in the concrete at the onset of crushing is 0.003 (Fig. 4.1(a)). Fasching and French (1998) presented a summary of several proposals for modifying the parameters of the equivalent

Fig. 4.2—Variation of k 2 with concrete strength (Ozbakkaloglu and Saatcioglu 2004).

rectangular stress block for high-strength concrete. They reported average values of k 2 = 0.381 (β1 = 0.762) and k 1k 3 = 0.647 (α1 = 0.849) from tests of C-shaped specimens (column specimens in which axial load and bending are induced by applying a load eccentrically at both ends) by several researchers, in which compressive strengths varied from 8400 to 14,400 psi (58 to 99 MPa). The aforementioned values are very close to those corresponding to a parabolic distribution. Specimens with higher strengths tested by Ibrahim and MacGregor (1994, 1996a), with concrete compressive strengths ranging between 17,600 and 18,600 psi (121 to 128 MPa), had values of k 2 = 0.347 (β1 = 0.694) and k 1k 3 = 0.524 (α1 = 0.755), close to those corresponding to a linear distribution. Ozbakkaloglu and Saatcioglu (2004) summarized the variation of experimentally obtained values for k 2 and the product k 1k 3 with concrete compressive strength. They also presented a comparison with various design expressions, including those of ACI 318-05 and CSA A23.3-94 (Canadian Standards Association 1994). These are shown in Fig. 4.2 and 4.3 and indicate a gradual reduction in k 2 and k 1k 3 with increasing concrete strength.


While the product of the terms k 1 and k 3 is often used as a single parameter in the formulation of an equivalent rectangular stress block, researchers in the past identified the values for k 3 separately. The parameter k 3 represents the ratio of the in-place strength of concrete in a structural member to the compressive strength measured using standard cylinder tests. Saatcioglu et al. (1998) reported values of the k 3 factor for high-strength concrete measured by several researchers for unconfined concrete members subjected to concentric loading. Two 10 in. (250 mm) square columns with compressive strengths of 11,700 and 17,600 psi (81 and 121 MPa), tested by Saatcioglu and Razvi (1998), had k 3 factors of 0.89 and 0.92, respectively. The average value reported by Cusson and Paultre (1994) was 0.88 for columns with compressive strengths of 14,500 psi (100 MPa). Tests by Yong et al. (1988) indicated values of 0.87 and 0.97 for compressive strengths of 12,100 and 13,600 psi (83 and 94 MPa), respectively. Sun and Sakino (1994) obtained values of 0.93 and 0.91 for compressive strengths of 7500 and 19,000 psi (52 and 1 31 MPa), respectively. Saatcioglu and Razvi (1998) indicated that similar values of k 3 were obtained under eccentric loading. Other tests performed to measure the value of k 3 include those by Ibrahim and MacGregor (1994, 1996b), Kaar et al. (1977), Schade (1992), and Swartz et al. (1985). The aforementioned series of tests resulted in average k 3 values of 0.91, 1.00, 0.93, and 0.98, respectively. Ibrahim and MacGregor (1994, 1996b) reported mean k 3 values of 0.932 for specimens with concrete compressive strengths between 8400 and 14,400 psi (58 and 99 MPa), and 0.919 for specimens with higher compressive strengths ranging between 17,600 and 18,600 psi (121 and 128 MPa).

4.2—Stress intensity factor α1 According to Fasching and French (1998), experimental results show that the nominal strength of beams calculated using the stress intensity factor α1 of ACI 318-05 is conservative for high-strength concrete. Data reported by Kaar et al. (1977) had a mean value of α1 = 1.0, and the data reported by Swartz et al. (1985) had a mean value of α1 = 0.96. Ibrahim and MacGregor (1994,1996a) conducted extensive tests of concentrically and eccentrically loaded high-strength concrete columns and developed an expression for α1. They found lower stress intensity factors in concentrically loaded columns, which resulted in the following expression for the stress intensity factor

α1

0.00862 f c′ = 0.85 – -----------------------1000

α1

≥ 0.725

= 0.85 – 0.00125 f c′

≥ 0.725

( f c′ in psi)

(4-1)

( f c′ in MPa)

The equation by Ibrahim and MacGregor was used as the basis for the Canadian Standard CSA A23.3-94 (Canadian Standards Association 1994), where the value of the stress intensity factor is

Fig. 4.3—Variation of k 1k 3 with (Ozbakkaloglu and Saatcioglu 2004).

α1

0.01 f c′ = 0.85 – --------------1000

α1

≥ 0.67

= 0.85 – 0.0015 f c′

≥ 0.67

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concrete

strength

( f c′ in psi)

(4-2)

( f c′ in MPa)

Park et al. (1998) described the background considerations of the NZS 3101:1995 design provisions (Standards Association of New Zealand 1995) regarding the shape of the equivalent rectangular stress block, which is very similar to that used in ACI 318-05. As stated previously, for a linear stress distribution, the equivalent rectangular stress block has values of k 2 = 0.333 (β1 = 0.667) and k 1 = 0.5 (α1 = 0.75k 3). The following expression for the stress factor is used in the New Zealand Standard, which is close to that corresponding to a linear stress distribution for high-strength concrete

α1 = 0.85, for f c′ ≤ 8000 psi (55 MPa)

(4-3)

0.0275 ( f c′ – 8000 ) α1 = 0.85 – -----------------------------------≥ 0.75 for f c′ > 8000 ( f c′ in psi)

(4-4)

1000

α1 = 0.85 – 0.004( f c′ – 55) ≥ 0.75 for f c′ > 55( f c′ in MPa) Azizinamini et al. (1994) investigated columns subjected to axial load and flexure, and observed that the ACI 318-05 equivalent stress block resulted in conservative estimates of strength for columns with normal-strength concrete, while it overestimated the strength of columns with high-strength concrete. Based on this observation, they recommended maintaining the value of α1 = 0.85 for f c′ ≤ 10,000 psi (69 MPa) and changing it for f c′ > 10,000 psi (69 MPa) using the following expression 0.50 ( f c′ – 10,000 ) ---------------- ≥ 0.60 for f c′ > 10,000 ( f c′ in psi) α1 = 0.85 – ---------------------------1000

(4-5)

α1 = 0.85 – 0.00725( f c′ – 69) ≥ 0.60 for f c′ > 69 ( f c′ in MPa) Bae and Bayrak (2003) developed a proposal based on stress-strain relationships for high-strength concrete. The

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A similar conclusion was derived by Ibrahim and MacGregor (1994), who proposed the following expression for β1

β1

0.0172 f ′ = 0.95 – -------------------c-1000

β1

≥ 0.70

= 0.95 – 0.0025 f c′

≥ 0.70

( f c′ in psi)

(4-8)

( f c′ in MPa)

The previous equation served as the basis for and is very similar to the equation adopted in CSA A23.3-94 (Canadian Standards Association 1994)

β1 Fig. 4.4—Comparison of proposed expressions for stress intensity factor α 1.

stress intensity factor α1 was derived by finding the total area underneath the theoretical stress-strain curve. According to Bae and Bayrak (2003)

α1 = 0.85 – 2.75 × 10 –5( f c′ – 10,000), 0.67 ≤ α1 ≤ 0.85 ( f c′ in psi) (4-6) α1 = 0.85 – 0.004( f c′ – 70), 0.67 ≤ α1 ≤ 0.85 ( f c′ in MPa) Ozbakkaloglu and Saatcioglu (2004) developed a rectangular stress block for high-strength and normal-strength concretes based on a large volume of experimental data and an analytical stress-strain relationship. They suggested varying α1 with concrete compressive strength to reflect the chan ge in the shape of the stress-strain relationship. Accordingly

α1 = 0.85 – ( f c′ – 4000) × 10 –5,

0.72 ≤ α1 ≤ 0.85 ( f c′ in psi)

(4-7)

α1 = 0.85 – 0.0014( f c′ – 30), 0.72 ≤ α1 ≤ 0.85 ( f c′ in MPa) A comparison of the ACI 318-05 stress intensity factor α1 and the aforementioned recommended changes for the stress intensity factor is shown in Fig. 4.4.

4.3—Stress block depth parameter β1

The parameter β1 defines the ratio of the depth of the equivalent rectangular stress block to that of the neutral axis. For a constant value of the stress intensity factor α1, the effect of assuming a theoretical value of β1 smaller than the actual value is that the calculated lever arm is increased, resulting in unconservative estimates of the moment strength. Fasching and French (1998) evaluated the ACI 318-95 expression (same as in ACI 318-05) for factor β1 using experimental results reported by Ibrahim and MacGregor (1994), Kaar et al. (1977), and Swartz et al. (1985). Fasching and French concluded that the ACI 318 expression for β1 underestimated the experimentally observed values in the data set used for the evaluation.

0.0172 f ′ = 0.97 – -------------------c-1000

β1

≥ 0.67

= 0.97 – 0.0025 f c′

≥ 0.67

( f c′ in psi)

(4-9)

( f c′ in MPa)

The stress block depth parameter recommended by Park (1998), and subsequently adopted in NZS 3101:1995 design provisions (Standards Association of New Zealand 1995), has the same definition as the depth parameter β1 in ACI 318-05. Similarly, Azizinamini et al. (1994) recommended no change to the definition of β1 used in ACI 318-05. In effect, these authors implied that changing the location of the equivalent force C c (Fig. 4.1) relative to the extreme compression fiber has a negligible effect on the nominal moment strength because the term (1/2) β1c is small in comparison to the moment arm jd = (d – [1/2]β1c). In columns with small eccentricities, the precision of β1 will have a more significant influence on the moment arm and, consequently, on the nominal moment strength. The overall effect of reducing the stress intensity factor α1 while maintaining the parameter β1 similar to that in ACI 318-05 is that a larger neutral axis depth is calculated for a given amount of reinforcement and axial load, reducing the lever arm and the nominal moment strength of the section. Bae and Bayrak (2003) suggested the following expression for the parameter β1 by finding the location of the compression resultant for the theoretical stress-strain curve

β1 = 0.85 – 2.75 × 10 –5( f c′ – 4000), 0.67 ≤ β1 ≤ 0.85 ( f c′ in psi) (4-10) β1 = 0.85 – 0.004( f c′ – 30), 0.67 ≤ β1 ≤ 0.85 ( f c′ in MPa) Ozbakkaloglu and Saatcioglu (2004) recommended a gradual change in β1 starting at 4000 psi (28 MPa) to reflect the variation in internal lever arm with the changing shape of the stress-strain relationship of concrete. Their recommended relationship for β1 is

β1 = 0.85 – 1.3 × 10 –5( f c′ – 4000), 0.67 ≤ β1 ≤ 0.85 ( f c′ in psi) (4-11) β1 = 0.85 – 0.020( f c′ – 30), 0.67 ≤ β1 ≤ 0.85 ( f c′ in MPa)


ITG-4.3R-11

Fig. 4.5—Comparison of proposed expressions for stress block depth factor β 1.

A comparison of the ACI 318-05 stress block depth parameter β1 and the aforementioned recommended changes to the depth parameter are shown in Fig. 4.5.

4.4—Stress block area α1β1

The product α1β1 is an indication of the area of the stress block. Fasching and French (1998), using the data from Ibrahim and MacGregor (1994), Kaar et al. (1977), and Swartz et al. (1985), showed that the product α1β1 decreased with increasing compressive strength. The decrease was approximately linear from a value of 0.75 for 6000 psi (41 MPa) to 0.5 for 18,000 psi (124 MPa). The provisions in ACI 318-05 include a steeper descent in the product α1β1 from 4000 to 8000 psi (28 to 55 MPa) than results from stress block parameters proposed by several authors for high-strength concrete (Bae and Bayrak 2003; Ibrahim and MacGregor 1997; Ozbakkaloglu and Saatcioglu 2004). Fasching and French (1998) indicated that the steeper descent in the product α1β1 resulted in underestimating the area of the compression block for specimens with concrete compressive strengths up to 14,000 psi (97 MPa), and overestimating the area of the compression block for specimens with concrete compressive strengths of 18,000 psi (124 MPa). For concrete compressive strengths on the order of 18,000 psi (124 MPa), the inferred values of the coefficients α1 and β1 were similar to those corresponding to a linear stress distribution.

4.5—Limiting strain εcu The limiting strain at the extreme compression fiber at the onset of concrete crushing , εcu, is a significant parameter for calculating the nominal moment strength of columns because it defines the strains throughout the cross section, particularly the strains in the longitudinal reinforcement. Calculated strains have a direct effect on the calculated stresses in the longitudinal reinforcement and also on the magnitude of the strength reduction factor φ. ACI 318-05 indicates that the magnitude of the strain at the extreme compression fiber εcu is independent of compressive

Fig. 4.6—Cover spalling strains for high-strength concrete columns (Bae and Bayrak 2003).

strength, and should be taken as 0.003. The majority of design provisions and proposals presented (Ibrahim and MacGregor 1994; Standards Association of New Zealand 1995; Azizinamini et al. 1994; Ozbakkaloglu and Saatcioglu 2004) adopt the same limiting strain of 0.003 as ACI 318-05, whereas CSA A23.3-94 adopts a limiting strain of 0.0035. Fasching and French (1998) indicated that past research on the magnitude of εcu for high-strength concrete resulted in mixed conclusions, with some researchers indicating that the limiting strain increases with compressive strength, and others indicating that it decreases. A review of test data by Fasching and French showed that the limiting strain was more sensitive to the type of aggregate than the concrete compressive strength, with limiting strains ranging between 0.002 and 0.005 for compressive strengths greater than 8000 psi (55 MPa). Average values for each type of aggregate were all above 0.003, and the average for all types of aggregate was 0.0033. Bae and Bayrak (2003) suggested adopting a lower value of εcu due to observed spalling at lower strains in highly confined high-strength concrete columns (Fig. 4.6). They proposed using a limiting strain of 0.0025 for concrete compressive strengths greater than 8000 psi (55 MPa), and 0.003 for lower compressive strengths.

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Fig. 4.7—Variation of ultimate strain with concrete strength according to various design codes and authors.

Ozbakkaloglu and Saatcioglu (2004) reported that, while the crushing strain under uniform compression, εo, increases with increasing concrete strength, the crushing strain under strain gradient, εcu , decreases with increasing concrete strength because of the brittleness of high-strength concretes. Based on moment-curvature analyses of columns under different levels of axial compression, the researchers concluded that εcu varied between 0.0036 and 0.0027 for 4000 to 18,000 psi (28 and 124 MPa) concretes, respectively. This is shown in Fig. 4.7. The same researchers, however, also concluded that the variation in εcu did not appreciably affect sectional strength calculations, and hence recommended the use of a constant average value of εcu = 0.003 for members under strain gradient.

4.6—Axial strength of high-strength concrete columns The design expression used in ACI 318-05 to calculate the strength of concentrically loaded columns, similar in form to Eq. (4-12), is based on an extensive column investigation that was conducted jointly by the University of Illinois (Richart and Brown 1934), Lehigh University (Slater and Lyse 1931a,b), and ACI. One of the main conclusions of this research was that it was possible to express the strength of columns subjected to concentric loading in a simple form, consisting of contributions from: 1) concrete at peak stress; and 2) longitudinal steel at yield Po = 0.85 f c′ ( Ag – Ast ) + Ast f y

(4-12)

The concrete contribution is based on the in-place strength and the net area of concrete, including the cover. The inplace strength of concrete is assumed to be 85% of the cylinder strength. The reduction in strength is attributed to the differences in size, shape, and concrete casting practice between a standard cylinder and an actual column. This ratio of in-place strength to cylinder strength, defined as the coefficient k 3 in Section 4.1, is one of the parameters necessary to define the rectangular stress block. Experimental data are available for in-place strength of high-strength concrete, as

Fig. 4.8—Instability of cover concrete under concentric compression (Saatcioglu and Razvi 1998). The bottom photograph shows section of the cover that spalled off during the tests.

indicated in Section 4.1. Researchers found that the coefficient k 3 for high-strength concrete varied between 0.87 and 0.97 based on concentrically tested columns (Yong et al. 1988; Sun and Sakino 1993; Cusson and Paultre 1994; Saatcioglu a nd Razvi 1998). A similar variation was obtained from column tests under eccentric loading (Kaar et al. 1977; Swartz et al. 1985; Schade 1992; Ibrahim and MacGregor 1994,1996b). Having reviewed the previous experimental data, Ozbakkaloglu and Saatcioglu (2004) concluded that k 3 = 0.9 provides a reasonable estimate for the ratio of concrete strength in a structural member to that determined by standard cylinder tests. In spite of the favorable in-place strength of high-strength concrete, experimentally recorded column strengths have been shown to be below the computed values based on Eq. (4-12) unless the columns are confined by properly designed transverse reinforcement. The strain data recorded by Saatcioglu and Razvi (1998) during their tests of highstrength concrete columns indicated that premature spalling of cover concrete occurred in most columns before the development of strains associated with concrete crushing. This observation, combined with visual observations of cover spalling during tests, as shown in Fig. 4.8, suggests that the cover concrete in high-strength concrete columns suffers stability failure rather than crushing.


Saatcioglu and Razvi (1998) hypothesized that the presence of closely spaced longitudinal and transverse steel, forming a mesh of reinforcement, produced a natural plane of separation between the cover and the core. The separation along this plane was triggered by high compressive stresses associated with high-strength concrete as well as the differences in mechanical properties of core and cover concretes (Richart et al. 1929; Roy and Sozen 1963). Columns tested by Rangan et al. (1991) and some of the columns tested by Yong et al. (1988) contained widely spaced transverse reinforcement of low volumetric ratio, without a sufficient mesh of reinforcement to separate the cover from the core. These columns were able to develop unconfined column strengths Po calculated using Eq. (4-12). Columns tested by Itakura and Yagenji (1992) without any cover consistently showed higher strengths than those computed on the basis of gross cross-sectional area and unconfined concrete because they did not suffer strength loss due to cover spalling. Columns that were sufficiently confined to offset the effects of cover spalling consistently developed higher strengths than Po. The group that contained an insufficient volumetric ratio of closely spaced transverse reinforcement, however, could not sustain strengths computed on the basis of total cross-sectional area and unconfined concrete strength. According to Saatcioglu and Razvi (1998), given the unfavorable circumstances described previously, the premature spalling of cover concrete could lead to reduced strength of concentrically loaded high-strength concrete columns relative to those predicted by Eq. (4-12). The effect of premature cover spalling was introduced into Eq. (4-12) by Ozbakkaloglu and Saatcioglu (2004) through a coefficient k 4 by defining the in-place strength of concrete as k 3k 4 f c′ instead of k 3 f c′ , where k 3 = 0.85. Figure 4.9 shows the variation of the product k 3k 4 with concrete strength obtained from a large volume of test data. The test data also included moderately confined columns for which high values of the product were obtained. The strength loss associated with cover spalling is a function of the area of unconfined cover concrete. For this reason, this effect can be quantified in Ag) of the terms of the ratio of core area to gross area ( Ac / column. As this ratio decreases (cover thickness increases), the strength loss increases. Figure 4.10 illustrates the variation Ag ratio. The product of the product k 3k 4 with respect to the Ac / k 3k 4 in Figure 4.10 indicates the degree of premature loss of strength in high-strength concrete columns as a function of Ag ratio. This premaconcrete compressive strength and the Ac / ture spalling effect can be quite significant in small-scale test columns with thin covers (Ozbakkaloglu and Saatcioglu 2004). Because the stability of the cover improves as the cover thickness increases, columns with thick covers are less likely to be susceptible to premature spalling than those with thin covers. Given the difficulties associated with testing largescale columns with very high concrete compressive strengths under concentric compression, there is a paucity of experimental results for large-scale high-strength concrete columns with thick concrete covers. For this reason, it was suggested by Ozbakkaloglu and Saatcioglu (2004) that, until more data become available, the ratio Ac / Ag should not be

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Fig. 4.9—Variation of k 3k 4 with concrete compressive strength (Ozbakkaloglu and Saatcioglu 2004).

Fig. 4.10—Variation of k 3k 4 with core-to-gross area ratio (Ozbakkaloglu and Saatcioglu 2004).

taken less than 0.6, irrespective of its actual value, in assessing the premature cover spalling effect. The test data in Fig. 4.9 and 4.10 were further examined after removing confined column data and grouping them on the basis of concrete strength (Ozbakkaloglu and Saatcioglu 2004). A regression analysis was conducted to find an expression for the coefficient k 4. The researchers suggested the following expressions for computing concentric axial strength of high-strength concrete columns Po = k 3k 4 f c′ ( Ag – Ast ) + Ast f y

(4-13)

k 3 = 0.90

(4-14)

A k 4 = γc + (1 – γc) -----c A g A c ---- A g

≥ 0.6

≤ 0.95

(4-15)

(4-16)

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γc = 1.1 –

f c′ ---------------20,000

γc = 1.1 –

≤ 0.8 ( f c′ in psi)

f ′ -----c---138

(4-17)

≤ 0.8 ( f c′ in MPa)

The product k 3k 4 can be as low as 0.61 for 18,000 psi Ag = 0.6, which is 28% below (124 MPa) concrete and Ac / the 0.85 value suggested by ACI 318-05 for normal-strength concrete columns, as reproduced in Eq. (4-12). Instead of detailed computation of the coefficient k 4, as outlined previously, a conservative, but simple, approach was recommended for convenience in design by Ozbakkaloglu and Saatcioglu (2004). They suggested that the product k 3k 4 be taken as 0.85 for f c′ of up to 6000 psi (41 MPa), and be reduced by 0.017 for every 1000 psi (6.9 MPa) increase over 6000 psi (41 MPa), up to 18,000 psi (124 MPa). The researchers identified the premature cover spalling as a phenomenon that is prevalent in concentrically loaded highstrength concrete columns. For columns subjected to bending and axial load, Ozbakkaloglu and Saatcioglu (2004) indicated that the critical compression side of the cover would deform toward the core concrete, which would restrain the cover against buckling. Park et al. (1998) indicated that the axial strength of columns subjected to compression is Po = χ1 f c′ ( Ag – Ast ) + f y Ast

(4-18)

They pointed out that the k 3 values that have been measured under concentric compression are greater than the value of χ1 in the NZS 3101:1995 provisions (Standards Association of New Zealand 1995) and, as a result, the nominal axial strength calculated using that standard is conservative. Azizinamini et al. (1994) proposed calculating the axial strength of columns in the same manner as NZS 3101:1995 by using Eq. (4-18). The premature spalling of cover concrete was recognized by CSA A23.3-94 (Canadian Standards Association 1994), and Eq. (4-18) was adopted with the stress intensity factor χ1 decreasing as a function of concrete strength, reducing to 0.67 for 18,000 psi (124 MPa) concrete.

4.7—Comparison of different proposals for rectangular stress block Fasching and French (1998) carried out a comparison between the measured flexural strengths of beam members and those calculated according to different stress block proposals for high-strength concrete. They found a slightly higher level of conservatism for the stress block proposals for high-strength concrete that they evaluated compared with the stress block defined in ACI 318-05. The New Zealand and Canadian proposals resulted in nearly identical average ratios of experimental-to-calculated strengths of 1.25, while the stress block of ACI 318-05 resulted in an average ratio of 1.21. Because the depth of the compression zone in beams is small compared with the depth of the member, it was

Fig. 4.11—Comparison of stress block parameters α 1 and β 1 inferred from experimental results and various expressions proposed for high-strength concrete (Bae and Bayrak 2003).

anticipated that the proposed modifications to the stress block would have a small effect on the nominal moment strength of beams. Fasching and French (1998) recommended that the stress block should be modified to avoid unconservative estimates of column strength. Bae and Bayrak (2003) compared the measured strengths of 224 columns with the strengths calculated using the ACI 318-05 rectangular stress block and other stress blocks outlined in this review (Fig. 4.11 and 4.12). Figure 4.11 shows the variation of the factors α1 and β1, and the product α1β1 proposed by several investigators with respect to concrete compressive strength. To estimate the accuracy of moment and axial strengths, Bae and Bayrak (2003) developed two different error indicators. They defined the error based on the experimental axial force EE p as the ratio of the difference between the nominal and experimental moment strengths to experimental moment strength (Fig. 4.12). EE p is calculated as M – M ex p EE p = ------ncol ------------------------- M ex p

× 100

(4-19)

A negative EE p value implies that the calculated strength was below the measured value, and consequently, the estimate was conservative. The second error indicator was based on the experimental eccentricity (Bae and Bayrak 2003). Based on both error indicators, Bae and Bayrak concluded that estimates using the equivalent rectangular stress block of ACI 318-05 became increasingly unconservative with increasing compressive strength, particularly with concrete strengths exceeding 10,000 psi (69 MPa). The stress blocks proposed by Ibrahim and MacGregor (1997), Park et al. (1998), Standards Association of New Zealand (1995), and Bae and Bayrak (2003) all produced


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Fig. 4.12—Error parameter EEp in estimates of column strength (Bae and Bayrak 2003).

similar levels of conservatism for all levels of concrete strength. The model proposed by Azizinamini et al. (1994) increasingly underestimated the column strengths for concrete compressive strengths beyond 13,000 psi (90 MPa). Bae and Bayrak noted that the data they used lacked a significant number of test results with high axial loads (small eccentricities). When axial loads are high, the different models provide significantly different predictions. They also noted that in seismic applications, the concern is not with high axial loads, but with relatively low axial loads (high eccentricities). Ozbakkaloglu and Saatcioglu (2004) compared column interaction diagrams based on the rectangular stress blocks of ACI 318-05, CSA A23.3-94, and those proposed by Ibrahim and MacGregor (1997) and Ozbakkaloglu and Saatcioglu (2004). The comparisons, shown in Fig. 4.13, indicate that the interaction diagrams generated by the equivalent rectangular stress block of ACI 318-05 and that proposed by

Ozbakkaloglu and Saatcioglu are identical for columns with a concrete compressive strength of 4000 psi (28 MPa), whereas the equivalent rectangular stress blocks recommended by CSA A23.3 and Ibrahim and MacGregor produce slightly lower estimates of strength than ACI 318-05. As concrete strength increased, Ozbakkaloglu and Saatcioglu concluded that the ACI 318-05 stress block lead to overestimating column strengths obtained from test results. Ozbakkaloglu and Saatcioglu indicated that the magnitude of the overestimation was very significant for a column with a concrete compressive strength of 17,400 psi (120 MPa). For this same column, the rectangular stress blocks proposed by Ibrahim and MacGregor and Ozbakkaloglu and Saatcioglu produced similar interaction diagrams, and the CSA A23.3 stress block resulted in a more conservative estimate of strength. The fact that the results obtained using the rectangular stress block in CSA A23.3 were consistently more conservative was attributed to the use of a lower stress intensity factor α1.

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Fig. 4.13—Comparison of interaction diagrams for columns with different concrete strengths (Ozbakkaloglu and Saatcioglu 2004) (Ac /A g = 0.7 ; ρ = 1.33%; b = h = 11.81 in. [300 mm]).

Ozbakkaloglu and Saatcioglu (2004) also provided comparisons of interaction diagrams drawn on the basis of their proposed stress block and that of ACI 318-02 (ACI Committee 318 2002) (which is the same used in ACI 318-05) for columns tested by Lloyd and Rangan (1996), Ibrahim and MacGregor (1994, 1997), and Foster and Attard (1997), under different levels of end eccentricity (Fig. 4.14). They concluded that the stress block of ACI 318-05 overestimated column axial and moment strengths, resulting in unsafe strength values for columns with concrete strengths in excess of 10,000 psi (69 MPa), whereas their proposed stress block (Ozbakkaloglu and Saatcioglu 2004) provided very good agreement with experimental strength values. A parametric study was carried out as part of this report to provide further insight into the differences among various

Fig. 4.14—Comparison of computed interaction diagrams with test data (Ozbakkaloglu and Saatcioglu 2004).


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Table 4.1—Summary of parameters α1 and β1 defining different rectangular stress blocks investigated in parametric study Concrete compressive strength, psi (MPa)

4000 (28)

6000 (41)

8000 (55)

10,000 (69)

12,000 (83)

15,000 (103)

α1

β1

α1

β1

α1

β1

α1

β1

α1

β1

α1

β1

ACI 318-05

0.85

0.85

0.85

0.75

0.85

0.65

0.85

0.65

0.85

0.65

0.85

0.65

Ibrahim and MacGregor (1997)

0.82

0.88

0.80

0.85

0.78

0.81

0.76

0.78

0.75

0.74

0.73

0.70

Equivalent rectangular stress block parameter

Park et al. (1998)

0.85

0.85

0.85

0.75

0.85

0.65

0.80

0.65

0.75

0.65

0.75

0.65

Aziznamini et al. (1994)

0.85

0.85

0.85

0.75

0.85

0.65

0.85

0.65

0.75

0.65

0.60

0.65

proposals. Column interaction diagrams were calculated, with and without strength reduction factors φ, to compare the ACI 318-05 stress block with the proposals by Ibrahim and MacGregor (1997), Park et al. (1998), and Azizinamini et al. (1994). The column cross section that was analyzed is shown in Fig. 4.15, with the bending moment about the Y-Y axis. The column was analyzed for steel ratios of 1 and 2.5% and for concrete compressive strengths of 4000, 6000, 8000, 10,000, 12,000, and 15,000 psi (28, 41, 55, 69, 83, and 103 MPa). The stress block parameters for the compared models are given in Table 4.1, and the results of the parametric study are given in Fig. 4.16. From Fig. 4.16 and Table 4.1, it can be seen that for concr ete compressive strengths of 4000, 6000, and 8000 psi (28, 41, and 55 MPa), the only model that resulted in estimates of strength that were noticeably different from those obtained with the ACI 318-05 stress block was that proposed by Ibrahim and MacGregor (1997). The Ibrahim and MacGregor (1997) model resulted in progressively smaller estimates of nominal strength as concrete compressive strength increased, which indicates that their model was the most conservative in this range. For a concrete compressive strength of 10,000 psi (69 MPa), the ACI 318-05 stress block and that proposed by Azizinamini et al. (1994) produced similar results, whereas the proposals by Ibrahim and MacGregor (1997) and Park et al. (1998) produced more conservative estimates of strength. For a concrete compressive strength of 12,000 psi (83 MPa), the models by Park et al. and Azizinamini et al. have identical stress block parameters. Consequently, strength estimates obtained with these two models were identical, and approximately the same as the nominal strength calculated using the model by Ibrahim and MacGregor. Finally, for a concrete compressive strength of 15,000 psi (103 MPa), the models by Ibrahim and MacGregor and Park et al. yielded similar results, and were slightly more conservative than the equivalent rectangular stress block of ACI 318-05. The model by Azizinamini et al. (1994) resulted in significantly lower estimates of strength than the other models.

4.8—Recommendations It is apparent from a review of the available literature that when the equivalent rectangular stress block of ACI 318-05 is used for members with axial loads above that corresponding to balanced failure and high-strength concrete, the ratio of nominal-to-experimental column strength decreases as the axial load increases. Experimental results (Fig. 4.12(a)) indicate that the nominal moment and axial strengths of

Fig. 4.15—Column cross section used in parametric study.

columns calculated with the ACI 318-05 stress block may be unconservative for compressive strengths greater than approximately 12,000 psi (83 MPa). Two consequences of overestimating the flexural strengths of columns are that the shear demand on the column calculated on the basis of the probable flexural strength is overestimated and that the ratio of column-to-beam moment strengths is overestimated. Overestimating the shear demand is conservative because it leads to a higher amount of transverse reinforcement. Conversely, overestimating the ratio of column-to-beam moment strengths has a negative effect because it increases the probability of hinging in the columns. ACI 318-05 requires a minimum ratio of column-to-beam moment strengths of 1.2. Overestimating column flexural strength decreases that ratio, and may even result in a strong beam-weak column mechanism. Because experimental results showed that the equivalent rectangular stress block of ACI 318-05 is appropriate for normal-strength concrete, a recommendation was developed focusing on columns with compressive strengths greater than 8000 psi (55 MPa). This was done by suggesting a stress block with a variable stress intensity factor α1 for concrete compressive strengths greater than 8000 psi (55 MPa). Accordingly, in inch-pound units, it is recommended that: “factor α1 shall be taken as 0.85 for concrete strengths f c′ up to and including 8000 psi. For strengths above 8000 psi, α1 shall be reduced continuously at a rate of 0.015 for each 1000 psi of strength in excess of 8000 psi, but α1 shall not be taken less than 0.70.” In SI units, the recommendation is that:

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Fig. 4.16—Column strength interaction diagrams comparing different stress blocks.

the proposed stress block with those proposed by others, as well as with the results of sample tests on columns using concrete strengths of up to 18,000 psi (124 MPa). The strength intensity factor α1 is also recommended to calculate the strength of columns subjected to concentric loading. The similarities in the values of α1 and the coefficient that defines the in-place strength of concrete in columns under concentric compression χ1 makes it possible to use the same value in computing column concentric strength Po for convenience in design. The recommendations translate into Eq. (4-20) and (4-21) for spirally reinforced and tied columns, respectively Fig. 4.17—Comparisons of column interaction diagrams and test data (f c′ = 10,440 psi [72 MPa], 7.8 x 11.8 in. (200 x 300 mm), ρ = 1.3%, Ac /Ag = 0.6).

“factor α1 shall be taken as 0.85 for concrete strengths f c′ up to and including 55 MPa. For strengths above 55 MPa, α1 shall be reduced continuously at a rate of 0.0022 for each 6.9 MPa of strength in excess of 55 MPa, but α1 shall not be taken less than 0.70.” A number of revisions to ACI 318-05 are proposed in Chapter 10 of this document. The parameter β1, which defines the depth of the stress block, was not changed. Figures 4.17 to 4.20 show the correlation of

φPn,max = 0.85φ[ χ1 f c′ ( Ag – Ast ) + f y Ast ]

(4-20)

φPn,max = 0.80φ[χ1 f c′ ( Ag – Ast ) + f y Ast ]

(4-21)

Accordingly, in inch-pound units, it is recommended that: “factor χ1 shall be taken as 0.85 for concrete strengths f c′ up to and including 8000 psi. For strengths above 8000 psi, χ1 shall be reduced continuously at a rate of 0.015 for each 1000 psi of strength in excess of 8000 psi, but χ1 shall not be taken less than 0.70.” In SI units, the recommendation is that: “factor χ1 shall be taken as 0.85 for concrete strengths f c′ up to and including 55 MPa. For strengths above 55 MPa, χ1


ITG-4.3R-19

parameters in ACI 318-05 result in unconservative estimates of strength for columns with normal-strength concrete. For this reason, the stress block parameters proposed by the committee were selected so that there would be no change in the stress block parameters of ACI 318-05 for columns with normal-strength concrete.

CHAPTER 5—CONFINEMENT REQUIREMENTS FOR BEAMS AND COLUMNS

Fig. 4.18—Comparison of column interaction diagrams and test data (f c′ = 14,000 psi [97 MPa], 6.9 x 6.9 in. (175 x 175 mm), ρ = 1.3%, Ac /Ag = 0.84).

The increased strength and enhanced performance of highstrength concrete are advantageous features for structural applications. The increasing brittleness of concrete with higher compressive strength is a major concern for seismic applications, however, where toughness under repeated load reversals is of paramount importance. For this reason, proper confinement of concrete is essential for the safe use of highstrength concrete in moderate to high seismic applications. This chapter addresses concrete confinement for beam and column elements. In Chapter 21 of ACI 318-05, which includes seismic design provisions, columns are defined as members with an axial load ratio ( Pu / f c′ Ag) greater than 0.1. The same definition is adopted throughout this document to differentiate between beams and columns. Constitutive models for confined concrete, salient features of previous research, and design recommendations are provided in the following sections.

5.1—Constitutive models for confined concrete Fig. 4.19—Comparison of column interaction diagrams and test data (f c′ = 18,270 psi [126 MPa], 7.9 x 11.8 in. (200 x 300 mm), ρ = 1.3%, Ac /Ag = 0.60).

Fig. 4.20—Observed stress intensity factors for concentrically loaded columns.

shall be reduced continuously at a rate of 0.0022 for each MPa of strength in excess of 55 MPa, but χ1 shall not be taken less than 0.70.” Figure 4.20 provides a comparison of the aforementioned recommendations with experimental data and the nominal strengths calculated using the provisions in ACI 318-05. The proposed parameters α1, β1, and χ1 were selected based on what was deemed an acceptable level of conservatism in the judgment of the committee. Another factor considered by the committee in selecting the aforementioned parameters was that there is no experimental evidence to suggest that the

Several researchers have indicated that constitutive models developed for normal-strength concrete do not offer a good representation of the behavior of high-strength concrete, especially in the case of columns, where the characteristics of the constitutive model have the highest impact on the calculated response. Therefore, previously developed constitutive models have been modified to reflect the differences in behavior, and a number of additional analytical models have been developed specifically for high-strength concrete. Ahmad and Shah (1982), Martinez et al. (1984), and Fafitis and Shah (1985) were among the first to develop models for high-strength confined concrete based on tests of spirally reinforced small cylinders. These models incorporate the effect of confinement through a lateral confining pressure that develops under hoop tension. The models were shown to produce good correlations with tests of spirally confined circular cylinders for concrete strengths of up to 12,000 psi (83 MPa). Yong et al. (1988) developed a model based on small-scale square column tests with concrete strengths ranging between 12,000 and 13,600 psi (83 and 94 MPa). Their approach was similar to that originally proposed by Sargin et al. (1971) for normal-strength concrete. Azizinamini et al. (1994) subsequently modified the model on the basis of large-scale column tests under reversed cyclic loading. Bjerkeli et al. (1990) proposed a generalized model for normalweight and lightweight aggregate confined concretes with compressive strengths of up to 13,000 and 10,000 psi (90 and 69 MPa), respectively. Their model is applicable to elements with circular, square, and rectangular section geometry.

ITG-4.3R-20


A number of confinement models were developed in Japan based on experimental results from the New RC project (Mugurama and Watanabe 1990; Mugurama et al. 1991, 1993; Nagashima et al. 1992). Cusson and Paultre (1994) proposed a model based on tests of large-scale high-strength concrete columns. Their model uses the effectively confined core area concept that was originally proposed by Sheikh and Uzumeri (1982) and modified by Mander et al. (1988). These researchers later improved their model by introducing an iterative procedure to compute the strain in transverse confinement reinforcement (Cusson and Paultre 1995). Li (1994) developed a constitutive model for confined concrete that covered a wide range of concrete compressive strengths between 4000 and 19,000 psi (28 and 131 MPa). The model was quite comprehensive and elaborate, incorporating several parameters to reflect the effects of confinement. Razvi and Saatcioglu (1999) developed a generalized confinement model on the basis of the equivalent uniform lateral pressure concept that they proposed earlier for confinement of normal-strength concrete (Saatcioglu and Razvi 1992). The model covers a wide range of concrete compressive strengths between 3000 and 19,000 psi (21 and 131 MPa), and incorporates the effects of different reinforcement geometry and arrangement while also incorporating the effect of high-strength transverse reinforcement.

5.2—Previous research and general observations One of the most challenging aspects about interpreting results from beam and column studies found in the literature is that there are differences among the loading protocols, loading configurations, scale, and failure criteria used by different researchers. These differences are such that P-∆ effects, reported shear strengths, and drifts at failure are not directly comparable in some instances (Brachmann et al. 2004a,b). In spite of these differences, there are some wellestablished common trends that have been observed about the behavior of beams and columns with high-strength concrete. The ductile behavior of high-strength concrete beams is well documented in several experimental studies found in the literature. Based on a series of beam tests conducted at Cornell University, Nilson (1985) observed that although the ultimate compressive strain was smaller for high-strength concrete, section and member displacement ductilities were larger than in normal-strength concrete elements. Nilson also observed that spiral reinforcement was less effective in highstrength concrete columns subjected to axial compression, resulting in a smaller displacement ductility. A study on the flexural ductility of high-strength concrete beams (Shin et al. 1990) indicated that ductility ratios increased with concrete strength for specimens with similar amounts of longitudinal and transverse reinforcement. This was observed for both monotonic and cyclic loading. Several researchers (Xiao and Yun 1998; Azizinamini et al. 1994; Matamoros and Sozen 2003) have shown, based on tests of columns subjected to cyclic loading under constant axial load, that drift ratios exceeding 3% can be reached with detailing conforming to the existing provisions in Chapter 21

of ACI 318-05 if the axial load demand on the columns is below 0.2 f c′ Ag (approximately 1/2 of the balanced axial load). Even at these low levels of axial load, Matamoros and Sozen (2003) observed that the degradation of the confined core, as indicated by the strain demand in the lateral reinforcement, increased more rapidly with drift for higher values of axial load. Xiao and Martirossyan (1998) and Matamoros and Sozen (2003) observed a similar trend with increasing compressive strength. A study on the properties of high-strength concrete members (Bjerkeli et al. 1990) concluded that properly confined columns can have ductile behavior and sustain large axial strains. The variables of the study were the compressive strength of the concrete, with values of 9400, 13,800, and 16,700 psi (65, 95, and 115 MPa), and the shape of the specimen, with circular and rectangular sectional shapes included. Concrete compressive strengths reported in this study were measured using 4 in. (102 mm) cubes. Smallscale specimens (6 x 6 in. [152 x 152 mm] rectangular columns and 6 in. [152 mm] diameter circular columns) were subjected to eccentrically applied monotonic loading. Both the effectiveness of confinement and the ultimate strain under concentric loading decreased with increases in concrete strength. According to the authors, specimens with a volumetric transverse reinforcement ratio (defined as the ratio of the volume of transverse reinforcement to the core volume confined by the transverse reinforcement) ρvr of 1.1% resulted in inadequate ductility, while the behavior of specimens with ρvr of 3.1% was satisfactory. Circular columns with transverse reinforcement in the form of spirals showed larger values of maximum stress and strain at peak stress than rectangular columns with similar volumetric ratios of hoop reinforcement. The difference between the two increased with the amount of transverse reinforcement. In the set of specimens with ρvr of 1.1%, the ratio of strain at peak stress for the confined case to strain at peak stress for the unconfined case was approximately 1.1 for the rectangular column with hoops and 1.25 for the circular column with spiral reinforcement. The ratio of peak stress for the confined case to peak stress for the unconfined case was approximately 0.85 for the rectangular column with hoops and 0.9 for the circular column with spiral reinforcement. In the set of specimens with ρvr of 3.1%, the ratio of strain at peak stress for the confined case to strain at peak stress for the unconfined case was approximately 1.9 for the rectangular column with hoops and 3.5 for the circular column with spiral reinforcement. The ratio of peak stress for the confined case to peak stress for the unconfined case was approximately 1.05 for the rectangular column with hoops and 1.55 for the circular column with spiral reinforcement. Razvi and Saatcioglu (1994) conducted an investigation on the strength and deformability of high-strength concrete columns based on the results of 250 tests by various researchers. They concluded that the volume of reinforcement required for proper confinement of high-strength columns may be reduced with the use of high-strength steel as transverse reinforcement, particularly for high axial loads. They indicated that the use of high-strength steel did not improve


behavior when low axial loads were present. They also observed that column deformability decreased with increasing axial compression. A specimen tested under axial tension showed improved deformability compared with specimens loaded in compression. Saatcioglu et al. (1998) reviewed the effect of confinement on concentrically loaded columns tested by several different investigators. They concluded that the strength of confined concrete increased with the amount of confinement independently of unconfined compressive strength. They also observed that for a similar percent increase in strength, higher confinement pressure is required for high-strength concrete than for normal-strength concrete. They indicated that values for the confinement index (defined as the product of the volumetric transverse reinforcement ratio and the yield strength of the transverse reinforcement divided by the compressive strength of the concrete) recommended in the literature to ensure ductile behavior under concentric loading ranged between 0.15 and 0.30. The distribution and spacing of the transverse reinforcement is another important parameter that affects behavior. Although high-strength reinforcement may be used to decrease the volumetric transverse reinforcement ratio, the effectiveness of the confining reinforcement decreases as spacing increases. Saatcioglu et al. (1998) indicated that the yield strength of the transverse reinforcement may not be reached for columns in which the volumetric reinforcement ratio, the axial load, or both, is low. Kato et al. (1998) reviewed tes ts carried out in Japan on 91 square columns and 59 circular columns under concentric loading. The compressive strength of the concrete in the specimens ranged between 4000 and 19,000 psi (28 and 131 MPa), while the yield strength of the transverse reinforcement ranged between 25,000 and 198,000 psi (172 and 1365 MPa). Their conclusions were similar to those by Saatcioglu et al. (1998). They indicated that the maximum stress increase in the columns was independent of the compressive strength and proportional to the strength of the transverse reinforcement. An upper limit of 100,000 psi (690 MPa) on the strength of the transverse reinforcement was suggested because calculations using the concrete models derived from the tests suggested that the reinforcement might not be effective beyond that point. In addition, they concluded that increasing the spacing of the transverse reinforcement by using high-strength reinforcement increased the probability of failure due to buckling of the longitudinal reinforcement. Saatcioglu and Razvi (1998) tested 26 large-scale highstrength concrete columns with a square cross section under concentric compression. The concrete compressive strength used varied between 8700 and 17,400 psi (60 and 120 MPa). The researchers investigated the effects of various confinement parameters, including the use of high-grade transverse reinforcement. It was concluded that the lateral pressure required to confine high-strength concrete columns can be achieved by using high-strength transverse reinforcement. It was cautioned, however, that this may not be achieved unless a sufficiently high volumetric ratio of transverse reinforcement is used. The researchers further reported premature spalling of cover concrete under concentric loading that was observed

ITG-4.3R-21

before reaching the crushing strength of unconfined concrete. This was attributed to the stability failure of the cover shell under high compressive stresses when a mesh of reinforcement, consisting of longitudinal bars and closely spaced transverse reinforcement, separated the cover from the core. Similar conclusions were obtained by Razvi and Saatcioglu (1999), who tested 21 large-scale, circular, highstrength concrete columns under concentric compression. Lipien and Saatcioglu (1997) and Saatcioglu and Baingo (1999) reported test results of large-scale square and circular columns, respectively, under constant axial compression and incrementally increasing lateral deformation reversals. The level of axial compression varied between 22 and 43% of the column strength under concentric loading Po , and the concrete strength varied between approximately 9000 and 14,000 psi (62 and 97 MPa). The researchers reported that a minimum of 5% drift capacity can be attained in circular columns if the volumetric ratio of spiral reinforcement is at least equal to f 0.17 f c′ / yt and the limit on the yield strength of transverse reinforcement is increased to 145,000 psi (1000 MPa). The same requirements produced approximately 8% lateral drift when the level of axial compression was reduced from 0.43 Po to 0.22Po. It was further concluded that individual circular ties, with 90-degree hooks well anchored into the core concrete, performed as well as continuous spiral reinforcement having the same material properties. Similar observations were made for square columns with overlapping hoops and crossties. Sheikh et al. (1994) tested four 12 in. (305 mm) square columns with concrete strengths of approximately 8000 psi (55 MPa) under constant axial compression and lateral moment reversals. The level of axial compression ranged between 0.59Po and 0.62Po. Sheikh et al. (1994) reported displacement ductility ratios (at a 20% reduction in lateral resistance) for the high-strength concrete columns ranging between 2.0 and 5.4 for specimens with volumetric confinement indexes ranging between 0.16 and 0.36. The corresponding curvature ductility ratios ranged between 5 and 17. It was concluded that the required amount of confinement reinforcement was proportional to concrete strength. The improvement in column ductility appeared to be proportional to the amount of confinement steel. Azizinamini et al. (1993, 1994) tested nine 12 in. (305 mm) square columns under 0.20 Po, 0.30Po, and 0.40Po. The specimens consisted of a central stub representing the joint region of a frame, with two columns extending outward. Lateral loads were applied at the center of the stub while the columns were subjected to a constant axial load. The transverse reinforcement had yield strengths of 60 and 120 ksi (414 and 827 MPa), with volumetric confinement indexes ranging between 0.13 and 0.37. The concrete compressive strengths ranged between 3800 and 15,000 psi (26 and 103 MPa). Azizinamini et al. (1994) reported that the maximum drift ratios, defined by the authors as the maximum drift ratio at which test columns were capable of withstanding two complete cycles of horizontal displacement, ranged between 3.0 and 5.1%. The test data indicated that an increase in concrete strength did not necessarily result in reductions in the column displacement ductility ratio. Reducing the

ITG-4.3R-22


spacing of the ties, however, resulted in larger ductility ratios. When comparing the behavior of specimens with similar amounts of transverse reinforcement and different yield strengths, Azizinamini et al. (1994) concluded that increasing the yield strength of the transverse reinforcement had no significant effect on the maximum drift ratio. They also expressed concern that, because of buckling of the longitudinal reinforcement, increasing the spacing between hoops while increasing the yield strength of the transverse reinforcement to achieve a similar confinement index would not be fully effective. Test results from two specimens with 1-5/8 and 2-5/8 in. (41 and 67 mm) hoop spacing and transverse reinforcement yield strengths of 71 and 109 ksi (490 and 752 MPa), respectively, showed that the specimen with the closer hoop spacing and lower yield strength had a higher maximum drift ratio (3.3%) than the specimen with the higher yield strength and larger stirrup spacing (2.4%). They attributed the difference in behavior to premature buckling of the longitudinal reinforcement observed in the specimen with the larger stirrup spacing. Thomsen and Wallace (1994) tested twelve 6 in. (152 mm) square column specimens with a concrete compressive strength of approximately 12,000 psi (83 MPa). The specimens consisted of cantilever columns with a foundation block that was anchored to the reaction floor. The axial and lateral loads loads were applied at the free end of the cantilever. Test variables were the spacing and configuration of the transverse reinforcement, the yield strength of the transverse reinforcement (115 and 185 ksi [793 and 1276 MPa]), and the axial load ratio (0, 0.1, and 0.2). Measurements indicated that the longitudinal reinforcement started to yield at a drift ratio of 1%. Shear and flexural strengths deteriorated at drift ratios exceeding 2%, and severe damage occurred at drift ratios higher than 4%. The longitudinal reinforcement buckled in specimens with axial load ratios of 0.2 and at drift ratios greater than 4%. The main conclusion of the study by Thomsen and Wallace was that high-strength reinforcement may be used effectively to confine high-strength concrete. A significant amount of experimental data from columns f c′ Ag exceeding 0.3 is available with axial load ratios f p = P / from an extensive study on the behavior of concrete members with high-strength materials sponsored by the Ministry of Construction in Japan (Aoyama et al. 1990). Because the maximum number of stories in high-rise buildings is limited by concrete strength, Japanese engineers believe that strengths higher than 6000 psi (41 MPa) would be essential to the construction of buildings taller than 30 stories. Tests conducted in Japan focused on columns subjected to axial load ratios above 0.3 (Aoyama et al. 1990; Sakaguchi et al. 1990; Muguruma and Watanabe 1990; Sugano et al. 1990; Kimura et al. 1995; Hibi et al. 1991). These tests showed a strong correlation among axial load, amount of confinement, and the drift capacity (drift limit) of columns. A large amount of transverse reinforcement was required to obtain ductile behavior in columns subjected to axial loads greater than the balanced load. Japanese researchers addressed this problem by incorporating high-strength steel as transverse reinforcement.

Sakaguchi et al. (1990) reported test results from eight high-strength concrete columns with compressive strengths of 11,200 and 13,600 psi (77 and 94 MPa) and a shear spandepth ratio of 1.1. The specimens consisted of columns with rigid blocks at the top and bottom. The bottom block was attached to the reaction floor, while the top block was used to apply the lateral and vertical loads. The column specimens were deformed in double curvature. All specimens had transverse reinforcement with a yield strength of 200,000 psi (1379 MPa). The variables of the study were the amount of transverse reinforcement, with volumetric confinement indexes ranging between 0 and 0.27, and the axial load ratio, which was set to 0, 0.2, or 0.4. The majority of the columns were tested with an axial load ratio of 0.4. Because the main thrust of the study was to investigate the shear strength of the columns, no limiting drift values were reported. Sakaguchi et al. (1990) concluded that in specimens with very light amounts of transverse reinforcement, a shear slip failure occurred soon after the formation of an inclined crack. In specimens with intermediate and high amounts of transverse reinforcement, shear strength increased with the amount of reinforcement. They indicated that a relatively high amount of transverse reinforcement was needed to maintain ductile behavior after the formation of inclined cracks in light of the low shear span-depth ratio. Muguruma and Watanabe (1990) tested eight specimens, varying the transverse reinforcement yield strength between 48,000 and 115,000 psi (331 and 793 MPa) while maintaining a constant volumetric ratio ρvr of 1.6%. The specimens consisted of a central stub with two columns extending outward. The lateral load was applied at the center of the stub, deforming the specimens in single curvature, while the axial load was maintained constant. Four tests were conducted on specimens with a concrete compressive strength of 12,400 psi (85 MPa) at axial load ratios f p of 0.4 and 0.6. For these specimens, the limiting drift ratio, defined as the drift ratio attained without a significant loss in strength, ranged between 1.5 and 10%. There was a strong correlation among the limiting drift ratio, axial load, and the yield strength of the transverse reinforcement. The limiting drift ratio decreased as the axial load ratio increased. Increasing the yield strength of the transverse reinforcement had the opposite effect. The limiting drift ratio increased by a factor as high as 3 when the yield strength of the transverse reinforcement was increased from 48,000 to 115,000 psi (331 and 793 MPa). The two specimens with a volumetric f c′ ) of 0.06 had confinement index c p (defined as ρvr f yt / limiting drift ratios of 6.0% for f p = 0.4 and 1.5% for f p = 0.63. When the volumetric reinforcement index was increased to 0.15 through the use of high-strength transverse reinforcement, the limiting drift ratio increased to over 10% for f p = 0.4 and 4.5% for f p = 0.63. The remaining four specimens had a concrete compressive strength of 16,800 psi (116 MPa) and were tested at axial load ratios of 0.25 and 0.41. Limiting drift ratios for these specimens varied between 3.0 and 8.5%. A volumetric confinement index of 0.05 was sufficient to attain a limiting drift ratio of 3.0% for an axial load ratio of 0.41. The authors concluded it was possible to achieve a high ductility ratio in columns with

STRUCTURA STRUCTURAL L DESIGN AND DETAILING DETAILING FOR HIGH-STREN HIGH-STRENGTH GTH CONCRETE CONCRETE IN SEISMIC APPLICAT APPLICATIONS IONS

high-strength concrete through the use of high-strength transverse reinforcement. A research program, motivated by the need to use highstrength materials in high-rise structures, was carried out in Tokyo. It comprised a first series of eight column te sts and 10 beam tests (Sugano et al. 1990), and a second series of five column tests (Kimura et al. 1995). The specimens each consisted of a column with rigid blocks blocks at the top and bottom. The specimens specimens were deformed in double curvature while the axial load was maintained constant. The first test series showed excellent behavior for column specimens with an axial load ratio of 0.3, which achieved limiting drift ratios of 4%. The limiting drift ratio increased in proportion to the yield strength of the transverse reinforcement normalized by the concrete compressive strength. The authors suggested a minimum confinement index of 0.10 to achieve limiting drift ratios of 2% at an axial load ratio of 0.6. The beams that were tested had span-depth ratios of 1.5, concrete compressive strengths ranging from 5800 to 12,000 psi (40 to 83 MPa), longitudinal longitudinal reinforcement ratios of 1.9 and 2.9%, transverse reinforcement with yield strengths of 44.3, 114.6, and 197 ksi (305, 790, and 1358 MPa), and confinement indexes ranging from 0.08 to 0.36. Beams with high confinement indexes (above 0.15) had limiting drift ratios above 5%; the limiting drift ratio was not very sensitive to the amount of transverse reinforcement or concrete compressive strength. The second series in the study concluded that the ductility of high-strength concrete columns was strongly affected by both the level of axial compression and the yield strength of the transverse reinforcement. The authors stated that the yield strength of the transverse reinforcement normalized by the compressive strength of the concrete was an appropriate index to evaluate ductility. A series of five tests at the University of Tokyo focused on column behavior after flexural yielding (Hibi et al. 1991). The specimens each consisted of a column with rigid blocks at the top and bottom. The specimens were deformed in double curvature while the axial load was maintained constant. The columns had axial load ratios of 0.30 and 0.45, and a shear span-depth ratio of 1.5. The amount and the strength of the transverse reinforcement were varied, while the quantity ρt f yt was maintained approximately constant. The tests showed a strong correlation between toughness and axial load. The behavior of specimens with an axial load ratio of 0.3 was very ductile, achieving limiting drift ratios exceeding 4%. Specimens with higher axial loads failed in shear, with limiting drift ratios on the order of 3.5%. At drift ratios below 2%, the University of Tokyo tests indicated that the shear component of the lateral deflection within the plastic hinge region was similar for all specimens, regardless of axial load. It must be pointed out, however, that none of the specimens reached yielding of the transverse reinforcement, thus limiting the degradation of the confined core within the plastic hinge region. All of these test results showed that beams and columns made with high-strength concrete can be used safely in seismic design for a wide range of axial loads, provided that an adequate amount of transverse reinforcement is provided to confine the core concrete.

ITG-4.3RITG-4.3R-23 23

5.3—Equations to determine amount of confinement reinforcement required in columns Section 21.4.4 of ACI 318-05 specifies the minimum amount of transverse reinforcement for confining the core concrete and providing lateral support to the longitudinal reinforcement in columns subjected to cyclic loading. Equation (21-2) in ACI 318-05 specifies the minimum volumetric ratio of spiral or circular hoop reinforcement for circular columns as f / ρs = 0.12 f c′ / yt

ACI 318 Eq. (21-2)

For rectangular columns, the minimum amount of reinforcement required by ACI 318-05 is given by Eq. (21-3) and (21-4) f ′ A Ash = 0.3sbc ---c--  ------g- – 1  f yt  A ch

ACI 318 Eq. (21-3)

f ′ Ash = 0.09sbc ---c- f yt

ACI 318 Eq. (21-4)

ACI 318-05, Eq. (21-3), controls when the ratio of gross area Ag to area of the confined core Ach is greater than 1.3. As a result, ACI 318-05, Eq. (21-3), is likely to control for small columns. These requirements were developed to ensure that the strength of the confined core would be sufficient to compensate for the loss in axial strength that occurs when the concrete in the exterior shell of the column spalls off. ACI 318-05, Eq. (21-2) and (21-4), imply that the confining stress provided by rectangular hoops is less effective than that provided by a similar volume of spiral reinforcement. A comparison between the volumetric reinforcement ratio required to confine a similar volume of concrete in a circular column with spiral reinforcement, according to ACI 318-05, Eq. (21-2), and a rectangular column with rectangular hoops, according to Eq. (21-4), indicates that spiral reinforcement is considered to be approximately 50% more effective than hoop reinforcement. The commentary in ACI 318-05 indicates that, although the strength and ductility of columns are affected by the amount of axial load, the axial loads and deformation demands during an earthquake are not known with sufficient accuracy to justify the calculation of the amount of transverse reinforcement as a function of these parameters. Experimental results (Matamoros and Sozen 2003) have shown that the amount of transverse reinforcement required by ACI 318-05, Eq. (21-2) to (21-4), will result in limiting drift ratios exceeding 3% for concrete compressive strengths up to 10,000 psi (69 MPa) and axial load ratios below 0.2 f c′ Ag. The main concerns about ACI 318-05, Eq. (21-2) to (21-4), are whether they provide sufficient transverse reinforcement to properly confine high-strength columns with axial loads greater than the balanced failure load, and that they require excessive amounts of transverse reinforcement for members with lower axial load, leading to congestion of reinforcement and concrete placement problems. Another concern, brought to attention by Bayrak and Sheikh (1998),

ITG-4.3R-24


is that in the case of high-strength concrete members, the amount of transverse reinforcement required for proper confinement will create a plane of weakness that may lead to loss of the shell of the column before an axial strain of 0.003 is attained. Confinement provisions in the New Zealand concrete design standard NZS 3101:1995 recognize the effect of axial load on column behavior. In potential plastic hinge regions, when hoop reinforcement is used, the design standard requires that the total area of transverse bars Ash in each of the transverse directions within spacing s should not be less than that given by the following three equations Ash -------- = sh ″

1.3 – ρ l m A g f c′ P  ----------------------------- ----- -------------- 3.3  A ch f yt φ f c′ A g

(5-1)

∑ Ate

(5-2)

A sh =

The area of a tie leg Ate required to tie the longitudinal bars reliant on it is defined as Ast f yl A te = 10 -----------s f yt

Ast in in. 2, s in ( A in in.)

1 Ast f yl s A te = ------ -------------------16 f yt 100

(5-3)

Ast in mm2, s in mm) ( A

where

ρl

Ast / Ag = longitudinal reinforcement ratio; Ast total total area area of nonpr nonprest estress ressed ed longi longitudi tudinal nal reinforcereinforcement (bars or shapes); m = f yl /0.85 f c′ ; Ag = gros grosss area area of of conc concre rete te sect sectio ion; n; Ach = cross-s cross-sect ection ional al area area of stru structu ctural ral memb member er measu measured red out-to-out out-to-out of the transverse reinforcement; s = center center-to -to-ce -cente nterr spac spacing ing of hoop hoop sets sets;; h′′ = core core dime dimensi nsion on perpendi perpendicula cularr to to trans transver verse se reinforcement providing confinement measured to outside of hoops; f = specif specified ied yield yield stren strength gth of longi longitud tudina inall reinfor reinforcece yl ment; = specif specified ied yield yield stre strengt ngth h of transv transvers ersee reinfor reinforcece f yt ment; f c′ = specif specified ied comp compres ressiv sivee streng strength th of of concre concrete; te; P = unfactored axial load; φ = streng strength th reduc reductio tion n factor factor,, define defined d in this this case case as as 0.85 if plastic hinging can occur, or 1.0 otherwise; Σ Ate = sum of area areass of legs legs requir required ed to to tie tie the the longit longitudinal udinal bars; and areas of of longit longitudi udinal nal bars bars tied tied to to the hoop hoop Σ Ab = sum of areas for lateral support. The following limits apply

= =

Ag / Ach ≤ 1. 1 .2

(5-4)

0 .4 ρlm ≤ 0.

(5-5)

f 116,000 psi (800 MPa) yt ≤ 11

(5-6)

f c′

≤ 10 10,000 psi (69 MPa)

(5-7)

For rectangular-shaped transverse reinforcement, the center-to-center spacing in potential plastic hinge regions should not exceed the smaller of 1/4 of the smaller dimension of the cross section, or six longitudinal bar diameters. The spacing between adjacent hoop legs or crossties should not exceed 8 in. (203 mm), or 1/4 of the dimension of the section parallel to the direction of the spacing. The previous equations were based on the results of theoretical cyclic moment-curvature analyses (Park et al. 1998) for compressive strengths up to 5800 psi (40 MPa). According to Park et al., analyses by Li (1994) showed that the equations can be projected to columns with concrete compressive strengths up to 14,500 psi (100 MPa) provided that the maximum value of yield strength of the transverse reinforcement used in the calculations is limited to 116,000 psi (800 MPa). Li and Park (2004) carried out a parametric study to verify whether the provisions for confining reinforcement in ACI 318-05 and NZS 3101:1995 were applicable to high-strength concrete columns. They investigated the effect of several parameters on the available strength and curvature ductility of plastic hinge regions of columns. The parameters investigated by Li and Park were concrete compressive strength, axial load level, yield strength of the transverse reinforcement, volumetric ratio of the transverse reinforcement, percentage of longitudinal reinforcement, and ratio of the area of the confined core to the total area of the cross section. They performed a series of cyclic moment-curvature analyses based on stress-strain relationships previously derived for high-strength concrete to develop a set of design equations relating the amount of transverse reinforcement to the curvature ductility ratio. Li and Park (2004) found that concrete compressive strength and the ratio of the area of confined core to area of the cross section had a considerable influence on the quantity of confining reinforcement needed to achieve a given ductility ratio. They also found that the required amount of transverse reinforcement needed to achieve a given curvature ductility ratio increased significantly as the axial load ratio increased, and that the amount of transverse reinforcement increased as the percentage of longitudinal reinforcement increased. They adopted a curvature ductility ratio of 20 as indicative of adequate column toughness. They stated that a curvature ductility ratio of 20 was likely to result in displacement ductility ratios for the overall structure on the order of 4 to 6. They also suggested a curvature ductility ratio of at least 10 for frames where limited ductility would be sufficient. Li and Park (2004) found that the expressions in ACI 318-05 produced columns with adequate toughness for low levels of axial load, but were unconservative for high levels of axial load. Within the data set used in their study, there were four


high-strength concrete columns with rectilinear normalstrength reinforcement ( f yt < 72,500 psi [ f yt < 500 MPa]) that contained 200, 138, 180, and 167% of the confining transverse reinforcement required by ACI 318-05. These columns achieved curvature ductility ratios of 17, 14, 21, and 14, respectively—all below or very close to the limit of 20 that they suggested as a performance criterion. It was concluded by Li and Park (2004) that the amount of confining reinforcement required by ACI 318-05 was inadequate to achieve curvature ductility ratios of 10 under high axial loads. Li and Park proposed the following expression for the amount of confinement needed for columns with rectilinear normal-yield-strength ( f yt < 72,500 psi [ f yt < 500 MPa]) reinforcement A sh A ( φ u ⁄ φ y – 33 ρ l m + 22 ) f c′ P u ------- = ------g-- --------------------------------------------------------- --------------sb c A ch f yt φ f c′ A g η

η = 91 –

( f c′ in psi)

(5-15)

and

η = 91 – 0.1 f c′

( f c′ in MPa)

For columns confined by circular high-yield-strength reinforcement, they proposed A sh A ( φ u ⁄ φ y – 55 ρ l m + 25 ) f c′ P u ------- = ------g-- --------------------------------------------------------- --------------79 sb c A ch f yt φ f c′ A g

(5-16)

In Eq. (5-8) to (5-16), the following limitations apply

ρi 0.85 f c′

(5-8)

-------------------- f yt

where

η = 117 when f c′ < 10,000 psi (70 MPa)

f c′ ----------1450

ITG-4.3R-25

A g ------- A ch

(5-9)

≤ 0.4

(5-17)

≤ 1.5

(5-18)

and the specified yield strength f yt is limited to

and f c′  η =  ------------

648.6

2

f yt ≤ 130,500 psi (900 MPa)

f c′ – ---------+ 539.4 when f c′≥ 10,000 ( f c′ in 15.2

psi)

(5-10)

η = 0.05( f c′ )2 – 9.54 f c′ + 539.4 when f c′ ≥ 70( f c′ in MPa) For columns confined by circular normal-yield-strength steel, they proposed the following A sh ------- = sb c

A ( φ u ⁄ φ y – 33 ρ l m + 22 ) f c ′ P u ---------------------- ----- ----------- – 0.006 κ ------g- ------------------------------ A ch f yt φ f c ′ A g 111

(5-11)

where

κ = 1.1 when f c′ < 11,600 psi (80 MPa)

(5-12)

κ = 1.0 when f c′ ≥ 11,600 psi (80 MPa)

(5-13)

and

According to Li and Park (2004), the proposed equations estimated, with reasonable accuracy, the curvature ductility ratio of 56 high-strength concrete columns reported in the literature. Due to the emphasis placed on performance-based design, more recent studies focus on quantifying the relationship between limiting drift (or ductility ratio), axial load, and the amount of confinement. Saatcioglu and Razvi (2002) developed a procedure to estimate the amount of transverse reinforcement needed to sustain a given drift demand in columns subjected to cyclic loading. Their procedure was derived based on nonlinear static analyses, using a computer program that incorporated analytical models for concrete confinement, steel strain-hardening, bar buckling, formation and progression of plastic hinging, and anchorage slip. They indicated that their computer program was verified extensively against a large volume of column test data. They proposed the following expression for the transverse reinforcement area ratio ρtc needed to attain a given limiting drift ratio under a specified level of axial load

For columns confined by rectilinear high-yield-strength reinforcement ( f yt ≥ 72,500 psi [ f yt ≥ 500 MPa]), they proposed the following Ash A ( φ u ⁄ φ y – 30 ρ l m + 22 ) f c′ P u ------- = ------g-- --------------------------------------------------------- --------------sb c A ch f yt φ f c′ A g η

where

(5-19)

ρtc

f ′ A g 1 P = 14 ---c--  ------- – 1 ----------- ----- δ  k Po f yt  A ch

(5-20)

ve

where (5-14) 2

bc k ve = 0.15 ------sh x

(5-21)

ITG-4.3R-26


Pu is the maximum axial compressive force that can possibly be applied on the column during a strong earthquake. This quantity may be computed as the factored axial load calculated in accordance with ACI 318-05, or the axial force associated with the formation of probable moment resistances at the ends of the framing beams dictated by capacity design requirements. The capacity reduction factor may be taken as 0.9 to reflect the improved ductility in the column due to effects of confinement.

Saatcioglu and Razvi (2002), based on a comparison of their proposed equations with those in ACI 318-05 (Fig. 5.1), concluded that ACI 318-05 provisions result in overly conservative requirements for spiral columns and some rectangular columns subjected to low levels of axial loads. Fig. 5.1—Comparison of confinement steel requirements to proposal by Saatcioglu and Razvi (2002). P ----- ≥ 0.2 Po Ag -------- – 1 A ch

(5-22)

≥ 0.3

(5-23)

The transverse area ratio ρtc in each cross-sectional direction is computed as the ratio of total transverse steel in each direction divided by the concrete area defined by core dimension bc times the vertical spacing of the transverse reinforcement s. The core dimension is defined as the center-to-center dimension of the perimeter tie, hoop, or spiral perpendicular to the confinement reinforcement under consideration. In Eq. (5-21), bc / s is the ratio of core dimension to vertical spacing of the transverse reinforcement, and bc / h x is the ratio of core dimension to the center-to-center distance between laterally supported longitudinal reinforcement. The coefficient k ve reflects the efficiency of reinforcement arrangement as a function of the spacing of the transverse reinforcement along the column height and the distance between laterally supported longitudinal bars. A value k ve = 1.0 represents the most efficient arrangement of closely spaced circular hoops with anchored hooks and spirals. The P / Po ratio defines the level of axial load relative to column concentric capacity Po, and δ defines the drift ratio as relative column displacement divided by column height. Ag and Ach are cross-sectional areas based on gross sectional dimensions and core dimensions, respectively. Saatcioglu and Razvi (2002) indicated that because the story drift ratio is limited to 2.0 to 2.5% by current building codes, Eq. (5-20) can be simplified for use in high seismic applications by assuming a permissible drift ratio of 2.5% and replacing the ratio P / Po by Pu / φPo in Eq. (5-20) and (5-22). This results in Eq. (5-24) with the limits specified as in Eq. (5-22) and (5-23)

ρtc

f ′ A g 1 P = 0.35 ---c--  ------- – 1 ----------- ----  f yt Ach k P 0 ve

(5-24)

They also concluded that ACI 318-05 requirements can be unsafe when the axial load level is above approximately 40% of the column strength under concentric loading Po , particularly for columns with inefficient arrangements of transverse reinforcement. Saatcioglu and Razvi (2002) pointed out that, unlike their proposed equations, the New Zealand specification does not include an efficiency parameter for the arrangement of transverse reinforcement, resulting in overly conservative designs for columns with superior arrangements of reinforcement. Brachmann et al. (2004a,b) reviewed test results from 184 rectangular columns subjected to shear reversals under constant axial load with axial load ratios ranging from 0 to 0.7. The database used by Brachmann et al. included tests carried out in Japan with high-strength concrete and high axial load ratios. The equation proposed by Brachmann et al. was derived by analyzing the effect of confinement on the limiting drift ratio of members without axial load. The effect of the axial load ratio on the effectiveness of confinement was determined by grouping test results according to the level of axial load and comparing the estimated drift ratio with that of members without axial load. This is illustrated in Fig. 5.2, which shows that increasing the level of axial load results in a decrease of the limiting drift ratio. Brachmann et al. (2004b) proposed the following relationship between drift limit, axial load, and amount of confinement, as an alternative to Eq. (21-4) of ACI 318-05

ρtr

=

ζ DR li m  2 f c′  --------------------- 1 – 1.1 f p f -- yt

(5-25)

where the value for the coefficient ζ is given in Table 5.1. The term ρtr refers to the transverse reinforcement ratio, which may be expressed in terms of the volumetric or area transverse reinforcement ratio, depending on the value of ζ. Brachman et al. (2004b) recommended modifying Eq. (5-25) by replacing the axial load ratio f p by the core axial load ratio f pc to assure adequate confinement of the core for columns with thick cover

ρ tr

=

ζ DR li m  2 f c′  ------------------------ 1 – 0.8 f pc f -- yt

(5-26)


ITG-4.3R-27

Table 5.1—Values of coefficient ζ for proposed design Eq. (5-25) and (5-26) Transverse reinforcement ratio ρtr

Coefficient ζ, circular sections

Coefficient ζ, square and rectangular sections

ρvr ρt

10

12

6

8

Table 5.2—Values of coefficient γ for Eq. (5-27) Transverse Coefficient γ, Type of seismic reinforcement Coefficient γ, square and rectangular ratio ρtr application circular columns columns Moderate

High

ρvr ρt ρvr ρt

0.15

0.18

0.09

0.12

0.25

0.30

0.15

0.20

Fig. 5.2—Effect of axial load on column limiting drift ratio (Brachmann et al. 2004a).

f c′ Ach. The previous equations were calibrated where f pc = P / so that the probability of overestimating the limiting drift in a column with the amount of transverse reinforcement provided in accordance with the previous equations would be 15% (one standard deviation from the mean). A comparison of measured and calculated limiting drift ratios is presented in Fig. 5.3. Because the equation relates the amount of confinement to the limiting drift ratio of a column, it can be used by designers seeking different levels of performance or expected drift demands. Recommendations for design for different levels of seismic applications can be derived by specifying suitable values for the limiting drift ratio. According to Brachmann et al. (2004a), yielding of the specimens occurred at a drift ratio of approximately 1%. Consequently, the difference between the specified limiting drift ratio and a drift ratio of 1% is an indication of the capability of a column to deform in the inelastic range of response without significant loss in lateral resistance. Prescriptive confinement requirements for regions of moderate and high seismic applications can be established by conservatively assuming limiting drift ratios of 1.5 and 2.5%. The resulting design expression for the two different definitions of the transverse reinforcement ratio is

ρtr

=

γ  2 f ---c-′ ---------------------- 1 – 0.8 f pc f yt

(5-27)

where the values of γ are given in Table 5.2. Equation (5-27) requires the same amount of transverse reinforcement as ACI 318-05, Eq. (21-4), in rectangular columns of special moment frames with a core axial load ratio f pc of 0.4. In the case of circular columns, the same amount of transverse reinforcement is required at a core axial load ratio f pc of 0.35. For a rectangular column with two symmetric layers of reinforcement, an axial load ratio of 0.4 corresponds approximately to the balanced failure condition. The study by Brachmann et al. (2004a and b) was based on data from rectangular columns. Equations (21-2) and (21-4) of ACI 318-05 imply that the effectiveness of rectangular hoops is approximately 2/3 that of spiral reinforcement.

Fig. 5.3—Measured and calculated limiting drift ratio limit versus volumetric confinement index cp = ρ vpf yt /f c′ according to Eq. (5-26).

Brachmann et al. (2004b) based their recommendation for circular columns on a similar assumption. Test data in the study by Brachmann et al. (2004a,b) had compressive strengths ranging from 3000 to 17,000 psi (21 to 117 MPa); uniform factors of safety for columns were obtained throughout the range of compressive strengths.

5.4—Definition of limiting drift ratio on basis of expected drift demand The seismic design provisions in ASCE/SEI 7-05 (ASCE/ SEI 2006) require in Section 12.12 that beams and columns of moment-resisting frames be proportioned for stiffness so that the interstory drift demand generated by the design earthquake forces is limited to 2.0% of story height for standard-occupancy buildings (Seismic Occupancy Category III). The design earthquake is defined in Section 11.4.4 of ASCE/SEI 7-05 as that with a seismic demand equal to 2/3 of the seismic demand corresponding to the maximum considered earthquake (MCE), which has a 2% probability of being exceeded in a period of 50 years. There is a probability that the drift demands experienced during the life cycle of a standard occupancy structure may exceed the 2% limit established in ASCE/SEI 7-05.

ITG-4.3R-28


Drift demand can be greater than that computed in accordance with Sections 12.8.6 and 12.9.2 of ASCE/SEI 7-05 because of the drift computation procedure that is implemented in ASCE/SEI 7-05. The most frequently used drift computation procedure in ASCE/SEI 7-05 (Section 12.8.6) involves an elastic analysis of the building structure using design-level earthquake forces. The design-level earthquake forces specified in Section 12.8.3 of ASCE/SEI 7-05 are obtained from an elastic design response spectrum that produces a seismic response coefficient C s (Section 12.8.1), which is inversely proportional to the response modification factor R. Because proportioning the strength of the structure on the basis of reduced earthquake forces does not reduce the drift demands (Shimazaki and Sozen 1984; Shimazaki 1988; Lepage 1997; Browning 2001; Matamoros et al. 2003), the reduced displacement demands computed based on the forces specified in Section 12.8 of ASCE/SEI 7-05, with the inclusion of the coefficient R must be adjusted to obtain reasonable estimates of the displacement demands caused by the design earthquake. This is accomplished in Sections 12.8.6 and 12.9.2 of ASCE/SEI 7-05 through the use of the deflection amplification factor C d . Current values of R and C d specified in Table 12.2-1 of ASCE/SEI 7-05 for special reinforced concrete moment-resisting frames are 8 and 5.5, respectively. There is a significant body of research based on nonlinear analyses of reinforced concrete frames and physical tests of small-scale specimens in earthquake simulators showing that these two factors are approximately equal for special reinforced concrete moment-resisting frames if the stiffnesses of the frames used in the linear analysis are calculated on the basis of cracked section properties (Shibata and Sozen 1976; Shimazaki and Sozen 1984; Lepage 1997; Browning 2001; Matamoros et al. 2004). Consequently, drift demands in special moment-resisting frames calculated using the R and C d factors specified in Table 12.2-1 of ASCE/SEI 7-05 may underestimate the drift demand associated with the design earthquake by as much as 45%. Also, as hinges form in columns, the nonlinear response tends to concentrate drift demands in the stories between plastic hinges in columns rather than distributing them evenly over the height of a building, as an elastic analysis would indicate. In special reinforced concrete moment frames, however, the strong column-weak beam provision guards against plastic hinges within columns from being close to one another, that is, plastic mechanisms over only a few stories, where large drifts are concentrated. One of the criteria that must be considered in establishing a limiting drift for the purpose of determining the amount of confinement in columns is the performance objective outlined by design codes. The general goals of the code provisions, though not specifically stated, are to provide life safety in the design-level earthquake and collapse prevention for the MCE (BSSC 2004). The amount of confinement is primarily determined by the need for providing life safety in the design earthquake while considering collapse prevention in the MCE. The drift demand from the MCE may be as high as 50% greater than the drift demand from the design-level earthquake.

The most common failure criterion adopted by researchers investigating the relationship between column performance and the amount of transverse reinforcement used to confine the concrete has been the point in the hysteresis curve corresponding to a 20% reduction in the maximum lateral load that was measured. If the performance of a frame expected in the MCE is considered, the amount of confinement must be adequate to achieve collapse prevention at drift demands approximately 50% greater than the 2% interstory drift limit established in Section 12.12 of ASCE/SEI 7-05. Experimental results from columns tested to axial load failure at the University of California (Lynn 2001; Sezen 2002) show that specimens with significantly less transverse reinforcement than that specified by the proposals summarized in Section 5.3 were able to sustain drift demands before axial load failure exceeding 3.5% of the story height. It must be noted, however, that all columns tested by Lynn (2001) and Sezen (2002) were made with normal-strength concrete and that there were no references found addressing the axial load failure of columns with high-strength concrete.

5.5—Use of high-yield-strength reinforcement for confinement Because the amount of confinement required in columns is proportional to the compressive strength of the concrete, congestion problems arise in potential plastic hinge regions of columns with high-strength concrete, particularly in the beam-column joints. Conversely, the amount of required confinement reinforcement is inversely proportional to the yield strength of the reinforcement, which presents the possibility of decreasing the volume of transverse reinforcement, thereby relieving congestion. Several studies done at the University of Ottawa have investigated the use of high-strength reinforcement for the confinement of high-strength concrete columns (Saatcioglu and Razvi 1998; Razvi and Saatcioglu 1999; Lipien and Saatcioglu 1997; Saatcioglu and Baingo 1999; Saatcioglu and Razvi 2002). The researchers tested a total of 66 nearly full-size circular and square columns, with concrete strengths ranging between 8700 and 18,000 psi (60 and 124 MPa), under either monotonically increasing concentric compression or a constant compression accompanied by incrementally increasing lateral deformation reversals. Three different grades of transverse reinforcement were used, with yield strengths of 60,000, 83,000, and 145,000 psi (414, 572, and 1000 MPa). The researchers concluded that, given the right combination of parameters, transverse reinforcement with yield strengths up to 145,000 psi (1000 MPa) can be effective in confining high-strength concrete columns, increasing the column lateral drift ratio up to a minimum of 5% in heavily loaded columns (0.43 Po) and 8% in lightly loaded columns (0.22Po). The researchers focused on finding how much of the additional strength available in transverse reinforcement with higher nominal yield strengths could be mobilized by a relatively brittle material like high-strength concrete before significant strength degradation. They observed that the effectiveness of transverse reinforcement increased with confinement efficiency, the volumetric ratio of steel, and the


level of axial compression. The efficiency of confinement is improved by selecting a superior reinforcement arrangement, either in the form of circular hoops or spirals, where hoop tension results in uniform confinement pressure, or by selecting well-distributed longitudinal reinforcement laterally supported by perimeter and overlapping hoops, crossties, or both. According to the researchers, a square column with 12 longitudinal bars in which each bar is supported by the corner of a hoop or the hook of a crosstie provides an example of a superior arrangement, while a square column with four corner bars tied by perimeter hoops exemplifies a poor reinforcement arrangement for rectilinear reinforcement. Similarly, the spacing of transverse reinforcement along the column height affects the efficiency of confinement quite significantly. It was shown that a spacing of 1/4 of the smaller cross-sectional dimension was adequate to provide sufficient confinement efficiency, with reductions in efficiency occurring as the spacing approached 1/2 of the smaller cross-sectional dimension. The confinement efficiency was quantified empirically by Razvi and Saatcioglu (1999). Accordingly, the confinement efficiency parameter k ve equals 1.0 for closely spaced circular hoops or spirals, and can be computed by Eq. (5-24) for rectilinear reinforcement. Tests of columns under concentric compression indicated that square columns with 12,000 to 18,000 psi (83 to 124 MPa) concrete and confinement efficiency parameter k ve ≥ 0.5 experienced yielding of transverse reinforcement with yield strength of 145 ksi (1000 MPa) when the volumetric ratio of reinforcement was approximately 2%. Circular columns with similar properties required a smaller volumetric ratio of 1.3% to trigger the yielding of 145 ksi (1000 MPa) reinforcement when spiral reinforcement ( k ve = 1.0) was used. The yielding of high-strength transverse reinforcement was recorded at or immediately after column strength, often just before the onset of significant strength degradation. The following expression was suggested by Razvi and Saatcioglu (1999) for the computation of transverse steel stress at or shortly after the attainment of strength under concentric compression

 k ρ tc  f s = E s  0.0025 + 0.213 ----ve ----------  f co ′  

≤ f yt

(5-28)

′ is where ρtc is the area ratio of transverse reinforcement ; f co the in-place strength of unconfined concrete in the column in psi (often taken as 0.85 f c′ ); and E s is the modulus of elasticity of reinforcing steel. According to Razvi and Saatcioglu (2002), the upper limit on the yield strength of steel may be taken as 200,000 psi (1379 MPa) because this was the maximum yield strength of transverse reinforcement used (Nagashima et al. 1992) in the high-strength concrete column tests evaluated. The level of axial load was found to be another parameter that affects the effectiveness of high-strength transverse reinforcement for columns subjected to lateral loading (Saatcioglu and Baingo 1999). Spirals with 145 ksi (1000 MPa) yield strength developed their tensile strength in columns

ITG-4.3R-29

with 18,000 psi (124 MPa) concrete before significant strength decay, when the level of axial load was 0.43 Po. When the level of axial compression dropped to 0.22 Po, the stress in spirals did not exceed approximately 110,000 psi (758 MPa). Steel with 90 ksi (621 MPa) yield strength was effective in all columns tested. Saatcioglu and Razvi (2002) recommended a limit of 110 ksi (758 MPa) on the yield strength of transverse reinforcement for confinement design when column axial compression is at least 20% of its strength under concentric loading, and 90 ksi (621 MPa) otherwise. Otani et al. (1998) and Otani (1995) described the use of high-strength reinforcement in the seismic design guidelines for high-rise reinforced concrete buildings in Japan. According to Otani (1995), high yield strength is normally attained by heat treatment of hot-rolled, chemically controlled killed steel. The chemical composition of the reinforcing steel must be carefully controlled to develop large elongations at fracture, especially when welding is used to splice closed hoops and stirrups. Shear reinforcement is provided in the form of rectangular hoops and stirrups with 135-degree hooks, circular or rectangular spirals, supplementary ties with 135- or 90-degree hooks, or welded closed hoops and stirrups. The yield strength is defined by the 0.2% permanent offset. The fracture strain is measured over a gauge length of eight times the nominal bar diameter, and must not be less than 0.05 at any region of the bar, including sections where bars have been connected through welding. Four types of high-yield-strength bars were developed in Japan as part of the New RC project for use as transverse reinforcement, with yield strengths ranging from 99,000 to 185,000 psi (683 to 1276 MPa). These are: 1) UHY685; 2) KSS785; 3) SPR785; and 4) SBPD1275/1420 steel bars. Grade 685 steel bars—Mechanical characteristics of UHY685 reinforcement (Hokuetsu Metal Co. 1990) are: a) minimum yield strength of 99,000 psi (683 MPa); b) minimum tensile strength of 128,000 psi (883 MPa); and c) minimum fracture strain of 0.10. The nominal diameters of these bars are 0.35, 0.39, 0.50, and 0.63 in. (9.00, 9.53, 12.7, and 15.9 mm), which give nominal cross-sectional areas of 0.10, 0.11, 0.20, and 0.31 in.2 (63.6, 71.3, 126.7, and 198.6 mm2), respectively (Otani 1995). According to Otani et al. (1998), a second type of Grade 685 reinforcement (USD685B) was developed for use as longitudinal reinforcement in plastic hinge regions. The yield strength of USD685B reinforcement must range between 99,000 and 110,000 psi (683 and 758 MPa), and the ratio of yield strength to tensile strength must be less than or equal to 0.8. This type of reinforcement must have a strain of at least 0.014 at the upper-bound yield stress of 110,000 psi (758 MPa) to ensure an adequate yield plateau. KSS785 steel bars—Mechanical characteristics of KSS785 reinforcement (Kobe Steel Ltd. 1989; Sumitomo Electrical Industries Ltd. 1989; Sumitomo Metal Industries Ltd. 1989) are: a) minimum yield strength of 114,000 psi (786 MPa); b) minimum tensile strength of 135,000 psi (931 MPa); and c) minimum fracture strain of 0.08. Nominal diameters of these bars are 0.24, 0.31, 0.38, and 0.50 in. (6.35, 7.94, 9.53, and

ITG-4.3R-30


Fig. 5.4—Ratio of measured to calculated limiting drift ratio versus yield strength of the transverse reinforcement according to Eq. (5-26). (Note: Yield strength of transverse reinforcement was limited to 120,000 psi [827 MPa] in the calculation of the limiting drift ratio regardless of the actual yield strength.)

12.7 mm), which give nominal cross-sectional areas of 0.05, 0.08, 0.11, and 0.20 in.2 (31.7, 49.5, 71.3, and 126.7 mm2). SPR785 steel bars—Mechanical characteristics of SPR785 reinforcement (Tokyo Steel Co. 1994) are: a) minimum yield strength of 114,000 psi (786 MPa); b) minimum tensile strength of 135,000 psi (931 MPa); and c) minimum fracture strain of 0.10. Nominal diameters of these bars are 0.38, 0.50, and 0.63 in. (9.53, 12.7, and 15.9 mm), which give nominal cross-sectional areas of 0.11, 0.20, and 0.31 in. 2 (71.3, 126.7, and 198.6 mm2), respectively. SBPD1275/1420 steel bars—Two producers (Neutren Co. Ltd. 1985; Kawasake Steel Techno-wire Co. 1990) manufacture Type D SBPD(N/L) 1275/1420 bars conforming to the requirements of the Japanese Standards Association (1994) JIS G 3137, “Small Size-Deformed Steel Bars for Prestressed Concrete,” which requires: a) a minimum yield strength of 185,000 psi (1276 MPa); b) a minimum tensile strength of 206,000 psi (1420 MPa); and c) a minimum fracture strain of 0.05. The JIS G 3137 specification was instituted following the establishment of ISO 6934 (1991) (Steel for the Prestressing of Concrete; Part 3: Quenched and Tempered Wire; and Part 5: Hot-Rolled Steel Bars with or without Subsequent Processing), but the JIS requires more rigorous control of the chemical composition of the steel. Furthermore, the amount of impurities in SBPD1275/1420 high-strength shear reinforcement is controlled more rigorously than required by the JIS G 3137 specification. The minimum strain at fracture is set to 0.07 because the bars are normally bent either 90 or 135 degrees at the corners and ends. Nominal bar diameters available are 0.25, 0.28, 0.35, 0.42, and 0.50 in. (6.4, 7.1, 9.0, 10.7, and 12.7 mm), which correspond to nominal cross-sectional areas of 0.05, 0.06, 0.10, 0.14, and 0.19 in.2 (30, 40, 64, 90, and 125 mm2), respectively. Otani et al. (1998) described the guidelines for the design of high-rise structures using high-strength materials developed as part of the research initiative sponsored by the

Ministry of Construction in Japan (Japan Institute of Construction Engineering 1993). According to Otani et al. (1998), these seismic design guidelines limit the yield strength of the longitudinal reinforcement to 102,000 psi (703 MPa) and the concrete compressive strength to 8700 psi (60 MPa). The maximum yield strength of the transverse reinforcement allowed by the document is 189,000 psi (1303 MPa). The database used in the study by Brachmann et al. (2004a,b) had specimens with transverse reinforcement yield strengths ranging between 37,000 and 183,000 psi (255 and 1262 MPa), and volumetric transverse reinforcement ratios ranging from 0.17 to 6.64%. Because specimens with transverse reinforcement with yield strengths of 180,000 psi (1241 MPa) had significantly lower test/calculated ratios, they recommended establishing an upper limit of 120,000 psi (827 MPa) on the yield strength of the transverse reinforcement. The ratio of measured to calculated limiting drift ratio according to the equation proposed by Brachmann et al. (2004b) versus the yield strength of the transverse reinforcemen t is shown in Fig. 5.4, where the yield strength of transverse reinforcement was limited to 120,000 psi (827 MPa) in the calculation of the limiting drift ratio regardless of the actual yield strength. The broken line in Fig. 5.4 represents a linear regression between the ratio of measured to calculated drift (computed limiting the yield strength of the reinforcement to 120,000 psi [827 MPa]) and the actual yield strength of the reinforcement. The suggestion by Brachmann et al. (2004a,b) to limit the yield strength of the transverse reinforcement to 120,000 psi (827 MPa) is consistent with the observations by Saatcioglu et al. (1998) and Kato et al. (1998) that the effective confining pressure decreases and the probability of buckling of the longitudinal reinforcement increases with increasing hoop spacing. Similarly, the NZS 3101 design provision establishes an upper limit of 116,000 psi (800 MPa) for the nominal yield strength of the transverse reinforcement.

5.6—Maximum hoop spacing requirements for columns Section 21.4.4.2 of ACI 318-05 allows a maximum spacing of transverse reinforcement in regions of potential plastic hinging of 1/4 of the minimum member dimension, six times the diameter of the longitudinal reinforcement, and 4 in. (102 mm). The 4 in. (102 mm) spacing requirement may be increased linearly up to 6 in. (152 mm) as the spacing of crossties or legs of overlapping hoops decreases from 14 to 8 in. (356 to 203 mm). The ICBO ER-5536 document (2001) suggests that the maximum spacing of hoops within plastic hinge regions should be 5 in. (127 mm). The rationale for this provision stems from the fact that in the experimental research used as the basis for the aforementioned document (C4 Committee 2000), satisfactory behavior was observed in specimens with a maximum hoop spacing of 6 in. (152 mm). Englekirk and Pourzanjani indicate in the C 4 report (2000), however, that test results by Azizinamini et al. (1994) contradict this observation. In specimens with an axial load ratio of 0.2 and concrete compressive strength of approximately 14,500 psi (100 MPa), Azizinamini et al. observed that the


mode of failure changed from yielding of the transverse reinforcement to buckling of the longitudinal reinforcement as the hoop spacing was increased from 1.62 in. (41 mm) (which represents a hoop spacing of d /6.6, 2.2 longitudinal bar diameters, and 4.32 transverse bar diameters) to 2.62 in. (67 mm) (which represents a hoop spacing of d /4.1, 3.5 longitudinal bar diameters, and seven transverse bar diameters), and the strength of the transverse reinforcement from 60,000 to 120,000 psi (414 to 827 MPa). The database used by Brachmann et al. (2004a,b) had columns with hoop spacing ranging between 1 and 17 in. (25 to 432 mm). When specimens with concrete compressive strengths of 5000 psi (34 MPa) or above only were considered, however, the majority of the data had a maximum hoop spacing below 4 in. (102 mm). The data do not show a decrease in the factor of safety with increased spacing, and two specimens with hoop spacings of approximately 10 in. (254 mm) showed adequate performance. On this limited basis, there seems to be no conclusive experimental evidence justifying the reduction in maximum hoop spacing from 6 to 5 in. (152 to 127 mm), although the paucity of experimental data with maximum hoop spacing above 4 in. (102 mm) is a concern.

5.7—Confinement requirements for high-strength concrete beams The only confinement requirements for concrete in plastic hinge regions of beams established in ACI 318-05 are in terms of the maximum spacing allowed between hoops. Unlike in the case of ACI 318-05, Eq. (21-2) to (21-4), for columns, there are no equations that set the minimum amount of transverse reinforcement that must be used in beams. Such a lack of requirement is of some concern for high-strength concrete beams because test results previously summarized show that the limiting drift ratio of beams is proportional to the volumetric confinement index c p (Fig. 5.5). The data in Fig. 5.5 indicate that to maintain a level of deformability, the product of ρvr f yt must increase with the concrete compressive strength. Ghosh and Saatcioglu (1994) summarized test results from high-strength concrete beams under monotonic and cyclic loading by several researchers. Based on tests by Fajardo and Pastor (Pastor et al. 1984) under monotonic loading, they concluded that the addition of lateral tie steel increases the displacement ductility of beams provided that the volumetric confinement index is greater than 0.11. The definition of the volumetric confinement index used by Ghosh and Saatcioglu, however, included the effects of the compression reinforcement f c p = (ρvr + ρ′) -- yt -- f c′

(5-29)

A volumetric confinement index of 0.11, calculated as defined in Eq. (5-29), corresponded to a displacement ductility of approximately 3. For beams with volumetric confinement indexes below 0.11, increasing the volumetric confinement index in the plastic hinge region resulted in small increases in displacement ductility. In cases where the

ITG-4.3R-31

Fig. 5.5—Limiting drift ratio versus confinement index cp for beam specimens in database used by Brachmann et al. (2004a).

volumetric confinement index exceeded 0.11, increasing the volumetric confinement index resulted in significant increases in displacement ductility. Ghosh and Saatcioglu (1994) attributed the low deformability of the beams with lower amounts of transverse reinforcement to the lack of confinement of the concrete in the compression zone. Brachmann et al. (2004a) proposed an equation for the minimum amount of transverse reinforcement for adequate confinement of reinforced concrete beams based on experimental results. For members without axial load, the minimum amount of confining reinforcement is given by

ρvr

f ′ 2 f ′ = ( 12 DR li m ) ----c- ≥ 0.12 ---c- f yt f yt

(5-30)

Equation (5-30) was calibrated so that the probability of overestimating the limiting drift in a beam with the amount of transverse reinforcement provided in accordance to Eq. (5-30) would be 15% for the data set used (one standard deviation from the mean). Figure 5.5 shows the measured limiting drift ratios and those calculated with Eq. (5-30) for 62 specimens with f p ≤ 0.1, and concrete compressive strengths ranging from 3000 to 15,000 psi (21 to 103 MPa). The average ratio of measured to calculated drift was 1.6, with a coefficient of variation of 0.26. Based on the sample of 62 specimens considered, the probability of underestimating the limiting drift of beam elements with Eq. (5-30) was approximately 10%. Equation (5-30) requires a higher amount of transverse reinforcement for high-strength concrete beams than that calculated using the current ACI 318-05 approach of proportioning the transverse reinforcement to resist, in most practical circumstances, 100% of the shear demand (ACI 318-05, Section 21.3.4.2). A comparison based on assumptions of a span length to beam depth ratio of 10, an effective depth equal to 90% of the beam height, a width-height ratio of the core equal to 2, and a limiting drift ratio of 2% indicates that the amount of reinforcement would increase by a factor of

ITG-4.3R-32


approximately 0.2 f c′ / ρl f yl , where ρl is the longitudinal reinforcement ratio and f yl is the yield strength of the longitudinal reinforcement. The difference is most significant for lightly reinforced beams. For beams with normal-strength concrete, the amount of transverse reinforcement would be approximately the same as required by the current code, while in the case of beams with high-strength concrete, the amount of transverse reinforcement would increase by as much as a factor of 4. Before a code change is implemented, such an increase in the amount of transverse reinforcement should be justified on the basis of experimental evidence showing inadequate performance of high-strength concrete beams under cyclic loading. Experimental research on column collapse indicates that vertical load-carrying capacity is lost soon after the lateral load-carrying capacity has degraded to zero (Yoshimura and Nakamura 2002; Elwood and Moehle 2005), and that the lateral drift at axial failure decreases with axial load. Elwood (2002) and Elwood and Moehle (2005) developed a model consistent with the observation from experimental research that the drift ratio at axial failure is inversely proportional to the axial load demand. From this research, it follows that the risk of catastrophic failure at drifts slightly higher than the limiting drift ratio (defined as that corresponding to a 20% reduction in strength) decreases as the amount of axial load on the member decreases. For this reason, it is reasonable to adopt a lower margin of safety for proportioning the amount of transverse reinforcement needed to reach a target limiting drift ratio in beams than in columns. Brachmann et al. (2004a) provided expressions with various probabilities of overestimating the limiting drift ratio. The expression corresponding to the mean response (such that the probability of overestimating the limiting drift ratio in a beam with the amount of transverse reinforcement provided in accordance to Eq. (5-31) would be 50%) is given by

ρvr

f ′ 2 f ′ = ( 8 DR li m ) ----c- ≥ 0.12 ----c f yt f yt

(5-31)

Because the volume of transverse reinforcement required by Eq. (5-31) is 44% of that required by Eq. (5-30), the amount of transverse reinforcement required in beams is closer to that calculated using the approach in ACI 318-05. A comparison based on assumptions of a span length to beam depth ratio of 10, an effective depth equal to 90% of the beam height, a width-height ratio of the core equal to 2, and a limiting drift ratio of 2% indicates that the amount of reinforcement would increase by a factor of approximately 0.09 f c′ / ρl f yl where ρl is the longitudinal reinforcement ratio and f yl is the yield strength of the longitudinal reinforcement. In this case, the amount of transverse reinforcement required by Eq. (5-31) in lightly reinforced beams ( ρl = 0.01) would range between approximately 1/2 the amount currently required by ACI 318-05 for beams with normal-strength concrete and two times the amount calculated using ACI 318-05 for beams with high-strength concrete.

5.8—Maximum hoop spacing requirements for high-strength concrete beams According to Section 21.3.3.2 of ACI 318-05, the maximum hoop spacing in flexural members of special moment frames must not exceed d /4, eight times the diameter of the smallest longitudinal bar, 24 times the diameter of the hoop bars, and 12 in. (305 mm). A similar spacing requirement is established in Section 21.12.4.2 of ACI 318-05 for beams of intermediate moment frames. Although the upper limit for the hoop spacing is 12 in. (305 mm), it is important to note that the requirements related to bar size and d /4 are likely to result in significantly smaller upper limits on spacing. Consequently, the 12 in. (305 mm) spacing limit is not the controlling criterion for most practical cases. For instance, a cross section with an effective depth of 24 in. (610 mm), No. 7 longitudinal bars, and No. 3 hoops would have a maximum hoop spacing of 6 in. (152 mm), significantly lower than the nominal 12 in. (305 mm) limit established by ACI 318-05. The ICBO ER-5536 document (2001) proposed an upper limit of 5 in. (127 mm) for the stirrup spacing in beams, which implies a significant reduction from the 12 in. (305 mm) limit currently adopted in ACI 318-05. The paucity of experimental results from beams with hoop spacing larger than 4 in. (102 mm) is a concern in determining whether the reduction from 12 to 5 in. (305 to 127 mm) is justified. The high-strength concrete beams tested by Pastor et al. (1984) that provided the basis for the study by Ghosh and Saatcioglu (1994) had stirrup spacing ranging from 3 to 12 in. (76 to 305 mm). The width of the test region ranged between 6.56 and 7.38 in. (167 to 187 mm), and the depth was approximately 12 in. (305 mm). Beams with a hoop spacing of 12 in. (305 mm) exhibited the worst performance, with ductility ratios on the order of 2 or 3. All beams with a stirrup spacing of 6 in. (152 mm) or less exhibited displacement ductilities higher than 4. This observation raises concerns about the 12 in. (305 mm) spacing limit adopted by ACI 318-05 particularly because these beams were not subjected to the deterioration of the core that would occur under load reversals. The conclusions by Ghosh and Saatcioglu (1994) about the effects of confinement also seem to indicate that there is no compelling reason to have different procedures to determine the amounts of confinement in beams and columns.

5.9—Recommendations There are several recommendations deemed necessary for proper confinement of sections with high-strength concrete. Research by Brachman et al. (2004a,b), and Saatcioglu and Razvi (2002) has indicated that the current provisions for confinement in ACI 318-05, even though the effect of axial load is neglected, result in sufficient amounts of confinement to achieve limiting drift ratios of at least 2% in most cases. The main disadvantage of the current provisions is that the safety afforded is not uniform for all columns, and the amount of transverse reinforcement required in members with lower levels of axial load is overly conservative. Although excessive conservatism does not pose a safety concern, it creates significant congestion problems that hinder the use of high-strength concrete.


Experimental research shows that a viable alternative to reduce congestion in plastic hinge regions is the use of highstrength transverse reinforcement. There is consensus among researchers that there should be an upper limit to the nominal yield strength of the transverse reinforcement used for confinement purposes of approximately 120 ksi (827 MPa). The experimental data that were reviewed did not substantiate the need to reduce the maximum hoop spacing in beams or columns. Although there was a greater concern in the case of beams because the upper limit for hoop spacing established by ACI 318-05 is 12 in. (305 mm), a closer review shows that spacing limits in terms of the diameter of the longitudinal and transverse reinforcement should be adequate to prevent buckling of the longitudinal reinforcement. Research results and experimental evidence indicate that the amount of confinement afforded by the current spacing limits should be sufficient to achieve drift ratios (approximately similar to the rotation of the plastic hinge in units of radians) on the order of 0.02 without catastrophic failure. For these reasons, it was deemed unnecessary to introduce confinement requirements for beams with high-strength concrete. The following recommended modifications to ACI 318-05, presented in greater detail in Chapter 10 of this document, are made for adequate confinement of high-strength concrete columns in special moment frames (SMF). The basis for the proposed equations is the approach by Saatcioglu and Razvi (2002), with some minor conservative modifications to simplify their use. In inch-pound units: • The use of transverse reinforcement with a specified yield strength of up to 120,000 psi shall be allowed to meet the confinement requirements for high-strength concrete columns. The yield strength of the reinforcement can be measured by the offset method of ASTM A 370 using 0.2% permanent offset. • Transverse reinforcement required as follows in (a) through (c) shall be provided unless a larger amount is required by ACI 318-05, Sections 21.4.3.2 or 21.4.5: (a)The area ratio of transverse reinforcement shall not be less than that required by Eq. (5-32)

ρt =

f ′ A g 1 Pu 0.35 ---c--  ------- – 1 ----------- ---------- k Ag f c′ f yt  Ach

ITG-4.3R-33

columns with circular geometry shall be in the form of spirals or hoops, for which k ve = 1.0. Reinforcement for columns with rectangular geometry shall be provided in the form of single or overlapping hoops. Crossties of the same bar size and spacing as the hoops shall be permitted. Each end of the crosstie shall engage a peripheral longitudinal reinforcing bar. Consecutive crossties shall be alternated end for end along the longitudinal reinforcement. The parameter k ve for rectangular hoop reinforcement shall be determined by Eq. (5-35) 0.15 b k ve = ---------------c ≤ 1.0 sh x

(5-35)

(c)If the thickness of the concrete outside the confining transverse reinforcement exceeds 4 in., additional transverse reinforcement shall be provided at a spacing not exceeding 12 in. Concrete cover on the additional reinforcement shall not exceed 4 in. In SI units: • The use of transverse reinforcement with a specified yield strength of up to 830 MPa should be allowed to meet the confinement requirements for high-strength concrete columns. The yield strength of the reinforcement can be measured by the offset method of ASTM A 370 using 0.2% permanent offset. • Transverse reinforcement required as follows in (a) through (c) shall be provided unless a larger amount is required by ACI 318M-05, Sections 21.4.3.2 or 21.4.5: (a)The area ratio of transverse reinforcement shall not be less than that required by Eq. (5-36)

ρt =

f ′ A g 1 Pu 0.35 ---c--  ------- – 1 ----------- ----------  f yt A ch k A g f c′

(5-36)

ve

where A g -------- – 1 ≥ 0.3 A ch

(5-32)

ve

(5-37)

and

where A g -------- – 1 ≥ 0.3 A ch

(5-33)

and Pu ---------- A g f c′

≥ 0.2

(5-34)

(b)Transverse reinforcement shall have either circular or rectangular geometry. Reinforcement for

Pu ---------- A g f c′

≥ 0.2

(5-38)

(b)Transverse reinforcement shall have either circular or rectangular geometry. Reinforcement for columns with circular geometry shall be in the form of spirals or hoops, for which k ve =1.0. Reinforcement for columns with rectangular geometry shall be provided in the form of single or overlapping hoops. Crossties of the same bar size and spacing as the hoops shall be permitted. Each end

ITG-4.3R-34


of the crosstie shall engage a peripheral longitudinal reinforcing bar. Consecutive crossties shall be alternated end for end along the longitudinal reinforcement. The parameter k ve for rectangular hoop reinforcement shall be determined by Eq. (5-39). 0.15 b k ve = ---------------c ≤ 1.0 sh x

(5-39)

(c)If the thickness of the concrete outside the confining transverse reinforcement exceeds 100 mm, additional transverse reinforcement shall be provided at a spacing not exceeding 300 mm. Concrete cover on the additional reinforcement shall not exceed 100 mm. The term h x is defined as the maximum horizontal spacing of hoop or crosstie legs perpendicular to bc , in. Section 21.12.3 of ACI 318-05 requires that the design shear strength φV n of beams and columns of intermediate moment frames be no less than: a) the sum of the shear associated with development of nominal moment strengths of the member at each restrained end of the clear span and the shear calculated for factored gravity loads; and b) the maximum shear obtained from design load combinations that include E , with E assumed to be twice that prescribed by the governing code for earthquake-resistant design. If the dimensions of a column are maintained constant, the ratio of axial load demand to balanced failure load decreases as concrete compressive strength in the column increases. Under the current design provisions in Section 21.12.3 of ACI 318-05, the amount of transverse reinforcement increases with the nominal flexural strength of columns, which decreases as the ratio of axial load to balanced load decreases (assuming that the column is not compression controlled). For this reason, it is possible that the amount of transverse reinforcement required by the aforementioned provision be similar or even less for columns with highstrength concrete than it is for columns with similar dimensions made with normal-strength concrete. This is inconsistent with the conclusions from the literature review presented in Sections 5.2 and 5.3 of this report, which indicate that the amount of confinement needed for ductile behavior in columns increases with increasing concrete compressive strength. To prevent the sudden failure of columns with highstrength concrete in intermediate moment frames (IMF), it is recommended that a minimum amount of confinement reinforcement be added to the provisions in the code. The confinement reinforcement requirement for IMF columns in ITG-4.3R is based on a design expression developed by Saatcioglu and Razvi (2002), and modified by ACI ITG 4 to facilitate its use for design. One of the key assumptions adopted by ACI ITG-4 in deriving this requirement is that a 20% reduction in lateral strength at a drift ratio of 1.5% corresponds to a tolerable level of damage for intermediate moment frames. This criterion is related to the level of damage deemed reasonable for this type of a lateral-forceresisting system, and should not be interpreted to mean that

intermediate moment frames must be proportioned so that drift ratios are kept below 1.5%. This assumption is consistent with the fact that the R factor for the IMF traditionally has been set by building codes to approximately 60 to 75% of that for a SMF. For example, according to ASCE 7-05, the R factor for an IMF is 5, while that for a SMF is 8. If the R factor is taken as a measure of the ductility demands (including inherent overstrength) and it is assumed that the maximum nonlinear displacement is approximately equal to the maximum displacement of a linear system (Shimazaki 1988; Lepage 1997; Browning 2001) (implying that C d ≈ R), the difference in R factors implies that the SMF is expected to experience nearly 8/5 (or 1.6 times) as much plastic rotation demands as the IMF. Lower plastic rotation demands imply lower strain demands on the concrete and a reduction in the amount of confinement reinforcement required. This reduction is indirectly recognized in these recommendations by using 1.5% drift ratio instead of 2.5% when deriving the requirements for confinement reinforcement for the IMF. To further simplify the calculation, a value of k ve = 0.5 is adopted for columns with rectilinear transverse reinforcement. Considering that a value of k ve = 1.0 is used in columns with spiral reinforcement, this assumption implies that the rectilinear confining reinforcement arrangement being used is 71% as effective as that of spiral reinforcement. The following changes to ACI 318-05 are recommended for columns of IMFs. In inch-pound units: • The use of transverse reinforcement with a specified yield strength of up to 120,000 psi shall be allowed to meet the confinement requirements for high-strength concrete columns. The yield strength of the reinforcement can be measured by the offset method of ASTM A 370 using 0.2% permanent offset; • For columns with concrete compressive strength greater than 8000 psi and rectilinear transverse reinforcement, the area ratio of transverse reinforcement shall not be less than that required by Eq. (5-40)

ρc

f ′ A g Pu = 0.3 ---c--  ------- – 1 ---------- Ag f c′ f yt  A ch

(5-40)

where Ag -------- – 1 ≥ 0.3 A ch

(5-41)

and Pu ---------- A g f c′

•

≥ 0.2

(5-42)

For columns with concrete compressive strength greater than 8000 psi and transverse reinforcement in the form of circular hoops or spirals, the area ratio of transverse reinforcement shall not be less than that required by Eq. (5-43)


ρc

f ′ A g Pu = 0.2 ----c-  ------- – 1 ---------- Ag f c′ f yt  Ach

≥ 0.2

(5-51)

CHAPTER 6—SHEAR STRENGTH OF REINFORCED CONCRETE FLEXURAL MEMBERS

where A g -------- – 1 ≥ 0.3 A ch

(5-44)

and Pu ---------- A g f c′

≥ 0.2

(5-45)

In SI units: • The use of transverse reinforcement with a specified yield strength of up to 830 MPa should be allowed to meet the confinement requirements for high-strength concrete columns. The yield strength of the reinforcement can be measured by the offset method of ASTM A 370 using 0.2% permanent offset; • For columns with concrete compressive strength greater than 55 MPa and rectilinear transverse reinforcement, the area ratio of transverse reinforcement shall not be less than that required by the following equation

ρc

f ′ A g Pu = 0.3 ---c--  ------- – 1 ---------- Ag f c′ f yt  Ach

(5-46)

where A g -------- – 1 ≥ 0.3 A ch

(5-47)

In flexural members made with high-strength concrete, the strength of the paste is similar to or higher than that of the aggregates. As a result, cracks tend to propagate through the aggregates and have a smoother surface than in normalstrength concrete (ACI Committee 363 1992). A smoother crack surface reduces the effect of aggregate interlock on shear strength, which theoretically implies a reduction in the concrete component of the total shear strength. The effect of compressive strength on the shear force carried by the transverse reinforcement can be analyzed using a variable angle truss model (Fig. 6.1). The equilibrium equations for a variable angle truss model with a uniform compression field (Joint ACI-ASCE Committee 445 1998) indicate that the average shear stress carried by the truss mechanism is given by V A v f s j 1 v s = -------s-- = ----------------------b w d b w s tan α t

Pu ---------- A g f c′

≥ 0.2

(5-48)

For columns with concrete compressive strength greater than 55 MPa and transverse reinforcement in the form of circular hoops or spirals, the area ratio of transverse reinforcement shall not be less than that required by the following equation

ρc

f ′ A g Pu = 0.2 ---c--  ------- – 1 ---------- Ag f c′ f yt  Ach

(6-1)

where j is the ratio of internal lever arm (the distance between the tension force in the reinforcement and the compression force carried by the concrete) to the effective depth, and αt is the angle of inclination of the compressive strut. Equation (6-1) shows that if all other parameters in a beam remain constant, the shear stress carried by the truss mechanism increases as the angle of inclination of the strut αt decreases. The same model indicates that the compressive stress in the struts of the compression field f c is given by

c

and

•

Pu ---------- A g f c′

(5-43)

ITG-4.3R-35

vs = --------------------------cos α t sin α t

(6-2)

The average compressive stress acting on the struts increases as the average shear stress vs increases and the angle of inclination of the struts αt decreases. These two equations show that, on the basis of a variable angle truss model, it should be expected that if concrete strength increases, a truss mechanism with a shallower angle of inclination of the struts can be developed due to the higher

(5-49)

where A g -------- – 1 ≥ 0.3 A ch

and

(5-50) Fig. 6.1—Variable angle truss model with uniform compression field.

ITG-4.3R-36


Fig. 6.2—Effect of different parameters on test/estimate ratios for shear strength using ACI 318-05 Eq. (11-3). Data set compiled by Reineck et al. (2003). (Note: The calculated ACI shear strengths did not consider the limit of 100 psi (8.3 MPa) on the term f c′ . The dashed line in each figure represents linear regression best fit of the data.)

capacity of the struts. Equation (6-1) shows that a reduction in the strut angle leads to an increase in the shear force carried by the reinforcement, increasing the effectiveness of the transverse reinforcement. After inclined cracking occurs, the force carried by the concrete is expected to decrease with increasing compressive strength due to reduced aggregate interlock. The opposite occurs with the force carried by the reinforcement through the truss mechanism, which is expected to increase due to the higher strength of the concrete in the struts of the w eb. Consequently, one of the most significant concerns in calculating the shear strength of members with high-strength concrete is preventing the sudden failure of members with relatively small amounts of transverse reinforcement, for which the maximum shear force that can be carried by the truss mechanism is similar to or smaller than the shear force corresponding to inclined cracking. In members with high amounts of transverse reinforcement, theory suggests that the reduction in the shear force carried by the concrete is offset by an increase in the effectiveness of the transverse reinforcement.

6.1—Shear strength of flexural members without shear reinforcement Figures 6.2 and 6.3 show the effects of different parameters on the test/calculated ratio obtained with Eq. (11-3) and (11-5) of ACI 318-05 for nonprestressed beams without transverse reinforcement V c = 2 f c′ b w d V c = 0.17 f c′ b w d

( f c′ in psi) ( f c′ in MPa)

ACI 318 Eq. (11-3)

V c = V c =

 1.9 

 0.16 

V d f c′ + 2500 ρ w -----u---- b w d ≥ 3.5 f c′ b w d ( f c′ in psi ) M u 

ACI 318 Eq. (11-5)

V d f c′ + 17.2 ρ w -----u---- b w d ≥ 0.29 f c′ bw d ( f c′ in MPa ) M u 

Test results presented in Fig. 6.2 and 6.3 are from the database of shear tests developed by Reineck et al. (2003). Although the figures indicate that there is no bias with respect to the compressive strength of concrete, they show a significant problem for members with light amounts of longitudinal reinforcement. Collins and Kuchma (1999), Nilson (1994), Ahmad et al. (1986), and Ahmad and Lue (1987) point out that this problem is of most significance for lightly reinforced slender beams with high-strength concrete. Figures 6.2 and 6.3 also show that the shear strength of members without transverse reinforcement may be affected by the effective depth of the member (Joint ACI-ASCE Committee 445 1998). Although there is considerable debate about the proper model to quantify the effect of size (Joint ACI-ASCE Committee 445 1998), Collins et al. (1993) stated that tests of high-strength concrete beams conducted by Kuchma et al. (1997) showed that this effect is not significant if longitudinal reinforcement is distributed throughout the depth of the member. The report by Joint ACI-ASCE Committee 445 (1998) summarizes several equations that have been proposed to more accurately reflect the effects of compressive strength, longitudinal reinforcement ratio, and effective depth on shear strength of members without transverse reinforcement.


ITG-4.3R-37

Fig. 6.3—Effect of different parameters on test/estimate ratios for shear strength using ACI 318-05 Eq. (11-5). Data set compiled by Reineck et al. (2003). (Note: The calculated ACI shear strengths did not consider the limit of 100 psi (8.3 MPa) on the term f c′ . The dashed line in each figure represents linear regression best fit of the data.)

In seismic design, most flexural members are required to have transverse reinforcement and thus the effect of size is not a significant concern. Members in which transverse reinforcement is not used are primarily slabs and footings, and it is unlikely that such members with large effective depths and high-strength concrete would be used in high seismic applications.

6.2—Effect of compressive strength on inclined cracking load of flexural members ACI 318-89 (ACI Committee 318 1989) placed an upper limit of 100 psi (8.3 MPa) on the term f c′ for calculating the shear strength of reinforced concrete beams, joists, and slabs. This upper limit was based on experimental results (Mphonde and Frantz 1984; Elzanaty et al. 1986), which indicated that the ratio of measured to calculated inclined cracking load in beams increased with the compressive strength of concrete at a lower rate than indicated by Eq. (11-3) or (11-5) of ACI 318-89. Similar behavior was observed in a study on the shear strength of high-strength concrete beams without transverse reinforcement by Thorenfeldt and Drangsholt (1990). The inclined cracking load remained almost constant in spite of an increase in compressive strength from 11,300 to 14,200 psi (78 to 98 MPa). These and other test results raised concerns about the shear strength of high-strength concrete flexural members with small amounts of transverse reinforcement. ACI 318-89 allowed the limit of 100 psi (8.3 MPa) on the term f c′ to be exceeded if transverse reinforcement sufficient to carry a

nominal shear stress of 50 psi (0.34 MPa), multiplied by the factor f c′ /5000 ≤ 3, f c′ in psi ( f c′ /35 ≤ 3 [ f c′ in MPa]), was provided to prevent sudden shear failures at the onset of inclined cracking. The use of the factor f c′ /5000 ≤ 3 resulted in a step-wise increase in the amount of transverse reinforcement with compressive strength, requiring that the product of the transverse reinforcement ratio and the yield strength of the transverse reinforcement ( ρt f yt ) be at least 50 psi (0.34 MPa) for concrete compressive strengths below 10,000 psi (69 MPa), and double that amount ( ρt f yt = 100 psi [0.69 MPa]) for concrete compressive strengths slightly higher than 10,000 psi (69 MPa). The amount of transverse reinforcement increased linearly with compressive strength up to a maximum ρt f yt of 150 psi (1.03 MPa) for a concrete compressive strength of 15,000 psi (103 MPa). Experimental results by Roller and Russell (1990) showed that the amount of transverse reinforcement that resulted in a nominal shear stress of 150 psi (1.03 MPa) was barely sufficient to ensure a safe estimate of strength using the ACI 318-89 equation for shear strength (Fig. 6.4). Based on experimental results by several authors (Johnson and Ramirez 1989; Ozcebe et al. 1999; Hofbeck et al. 1969; Mattock et al. 1976; Walraven et al. 1987; Roller and Russell 1990), a new form of ACI 318, Eq. (11-13), was introduced in ACI 318-02 to estimate the minimum amount of transverse reinforcement in beams, with the goals of increasing the safety of the estimates and eliminating the steep increase that occurred at a concrete compressive strength of 10,000 psi (69 MPa). The minimum amount of transverse reinforcement is given by

ITG-4.3R-38


As observed in Fig. 6.4, the ratio of measured to nominal shear strength of the beams with 10,500 psi (72 MPa) concrete in the study by Roller and Russell (1990) was not very sensitive to the nominal strength provided by the transverse reinforcement, while the opposite was true for the beams with 18,200 psi (125 MPa) concrete. While providing vs = 50 psi (0.34 MPa) resulted in an adequate estimate of strength for beams with a concrete compressive strength of 10,500 psi (72 MPa), the same amount resulted in an unconservative estimate of strength for the beams with concrete compressive strengths of 17,400 and 18,200 psi (120 and 125 MPa). In both cases, tests showed that a minimum vs of approximately 150 psi (1.03 MPa) would have been necessary to obtain a strength above the nominal value given by Eq. (11-5) of ACI 318-83.

Fig. 6.4—Ratio of measured to nominal strength versus calculated shear strength provided by truss mechanism for beams with high-strength concrete tested by Roller and Russell (1990).

b s A v, min = 0.75 f c′ ----w--- f yt Av, min

b s = 0.062 f c′ ----w--- f yt

( f c ′ in psi) ACI 318 Eq. (11-13) ( f c ′ in MPa)

6.3—Effect of compressive strength on flexural members with intermediate to high amounts of transverse reinforcement The 10 beams tested by Roller and Russell (1990) included three different groups, with concrete compressive strengths of 10,500, 17,400, and 18,200 psi (72, 120, and 125 MPa). There were five beams with compressive strengths of 17,400 psi (120 MPa), for which the design shear stress vs (equal to the product of the transverse reinforcement ratio ρt and the yield strength of the hoops f yt ) carried by the truss mechanism ranged from 0.3 f c′ to 8.9 f c′ (psi) (0.025 f c′ to 0.74 f c′ [MPa]). The beam with the lightest amount of transverse reinforcement ( vs = 0.3 f c′ (psi) [vs = 0.025 f c′ (MPa)]) had a shear strength below the nominal value calculated according to the provisions of ACI 318-83 (ACI Committee 318 1983). The remaining four beams (Fig. 6.4), with compressive strengths of 17,400 psi (120 MPa), had measured shear strengths above the nominal values V n calculated using ACI 318, Eq. (11-6) ( V c term), and ACI 318, Eq. (11-17) (V s term), of the ACI 318-83. Although for these four beams the ratio of measured to nominal strength decreased with the amount of transverse reinforcement, the tests were within the range allowed by ACI 318, which places an upper limit of vs = 8 f c′ (psi) (vs = 0.66 f c′ [MPa]), on the nominal shear strength attributed to the truss mechanism. The two remaining series of tests, with compressive strengths of 10,500 and 18,200 psi (72 and 125 MPa), were primarily aimed at determining the minimum amount of transverse reinforcement needed to prevent sudden failures after inclined cracking.

6.4—Shear strength of members with low shear span-depth ratios A series of tests was conducted in Japan to investigate the shear strength of high-strength concrete members (Sakaguchi et al. 1990). The series included six beams with shear span-depth ratios ranging between 1 and 1.14, and different amounts of transverse reinforcement. The purpose of the tests was to determine the inclined cracking load and ultimate shear strength of the beams. Concrete compressive strength was maintained constant at approximately 13,000 psi (90 MPa). The principal variable was the product ρt f yt , where ρt is the transverse reinforcement ratio defined as ρt = Av / bws and f yt is the yield strength of the transverse reinforcement. According to the truss model adopted in ACI 318-05, the product ρ t f yt represents the average shear stress carried by the reinforcement in slender beams ( ρt f yt = vs = V s / bwd ), that, in the tests by Sakaguchi et al. (1990) ranged from 0 to 1150 psi (7.9 MPa). In beams with ρt f yt lower than 260 psi f c′ = 2%), inclined cracking propagated (1.8 MPa) (ρt f / yt rapidly, leading to a sudden shear failure. In specimens with ρt f yt of 725 and 1145 psi (5 and 7.9 MPa) ( ρt f yt / f c′ higher than 5.5%), both the shear and longitudinal reinforcement yielded before failure at a load considerably exceeding the inclined cracking strength. The conclusions from the study by Sakaguchi et al. (1990), based on tests of deep beams, differ from those by Roller and Russell (1990). Sakaguchi et al. focused on the amount of transverse reinforcement needed to preclude failure at the onset of inclined cracking and achieve yielding of the transverse reinforcement before failure. They found that for beams with a compressive strength of approximately 13,000 psi (90 MPa), the amount of transverse reinforcement needed to develop a truss mechanism and prevent sudden failure after inclined cracking was approximately vs = ρt f yt = 260 psi (1.8 MPa) (5.2 times 50 psi), which corresponds to 2.3 f c′ (psi) (0.19 f c′ [MPa]) significantly higher than the ρt f yt = 0.75 f c′ (psi) (0.06 f c′ [MPa]) required by ACI 318-05 for flexural members. The study by Sakaguchi et al. (1990) raises concerns about the behavior of members with low shear span-depth ratios subjected to cyclic loading. ACI 318-05 requires that such members be proportioned using nonlinear analysis or in


accordance with Appendix A of the Code, which outlines provisions for the use of strut-and-tie models. Strut-and-tie models are a methodology for member design that can be applied to different types of structural members, including deep beams and structural walls. Although Chapter 6 of this document addresses shear design and Chapter 8 addresses the design of structural walls, some of the reference material presented in this chapter about the behavior and design of members with low shear span-depth ratios is based on studies of deep beams and walls. Such material is included in this chapter only when it is relevant to the topic of strut-and-tie models. Little reference material is available on the use of strutand-tie models for the seismic design of deep beams made with high-strength concrete. The Architectural Institute of Japan (AIJ) seismic design guideline (1994) includes a design procedure for beams that is based on the superposition of two different strut-and-tie models. The AIJ model is inconsistent with the provisions in Appendix A of ACI 318-05. The AIJ procedure includes two reduction factors applied to the compressive strength of the concrete struts that Appendix A of ACI 318-05 does not include. The first factor was originally proposed by N ielsen (1999) and was developed based on test results from beams with uniform stress fields subjected to monotonic loading. It is a function of the compressive strength of the concrete, and it decreases linearly as the compressive strength increases f ′ = 0.7 – --------c-------29,000

βs βs

f c′ = 0.7 – -------200

( f c ′ in psi) (6-3) ( f c ′ in MPa)

The second factor is a function of the amount of rotation θ p expected in a plastic hinge region of a flexural member. It is given by

βsc = (1 – 15θ p)βs ≥ 0.25βs

βs βs

9 = --------3 f ′ c 1.7 = --------3 f ′ c

ITG-4.3R-39

( f c ′ in psi) (6-5) ( f c ′ in MPa)

Von Ramin and Matamoros (2004, 2006) defined the strut strength as the product of factors related to the compressive strength of the concrete ( β fc), the angle of inclination of the strut (βαt ), and, in the case of members in which the strut interacts with a truss mechanism, an additional factor ( βta). The strut factor is defined as

βs = β fcβαt βta

(6-6)

The work by Von Ramin and Matamoros (2004, 2006) on members with low shear span-depth ratios was calibrated using experimental data from deep beams and structural walls with concrete compressive strengths ranging from 2200 to 20,300 psi (15 to 140 MPa). Von Ramin developed a base expression for the strut factor using experimental results from elements subjected to monotonic loading. The effect of load reversals was later introduced by comparing the base factors for the monotonic loading case to reduced values of strength of columns and walls subjected to repeated load reversals into the nonlinear range of response. Following this methodology, Von Ramin and Matamoros (2004, 2006) proposed the following expressions for the compressive strength factor

β fc = 0.85 – f c′ ⁄ 36,200 ≥ 0.5 β fc = 0.85 – 0.004 f c′ ≥ 0.5

( f c ′ in psi) ( f c ′ in MPa)

(6-7)

They proposed the following expression for the strut angle factor in members without transverse reinforcement

β α t =

1 ---------------------------------3 1 + 0.1cot α st

(6-8)

(6-4) and in members with transverse reinforcement

Aoyama (1993) carried out a comparison of measured and calculated shear strengths for beams and columns subjected to cyclic loading following the procedure in the 1988 Japanese design guideline. He concluded that the method in the Japanese guideline resulted in accurate estimates of the reduced shear strength of both beams and columns subjected to cyclic loading with various shear span-depth ratios. He indicated, however, that the method did not perform well for members with high-strength concrete. Further research at Kyoto University showed that the performance of the method was improved by adopting the strut factor proposed in the draft of the CEB-FIP model code (Comité Euro-International du Béton 1988), which is proportional to the reciprocal of the cubic root of the compressive strength of concrete (Watanabe and Kabeyasawa 1998)

βα t =

4.6 -----------------------------------------5 6.5 + 0.13cot α st

(6-9)

where αst is the angle of inclination of the strut with the main longitudinal tie (Fig. 6.5), that in the case of structural walls, is oriented in the vertical direction. Von Ramin and Matamoros (2006) indicated that the angle of inclination of the main strut in members with low shear span-depth ratios may be approximated as cotαst = av / d

(6-10)

For members with low shear span depth-ratios in which a truss mechanism is superimposed on a strut (Fig. 6.5), Von

ITG-4.3R-40


A similar approach was proposed by Watanabe and Ichinose (1991), and implemented in the seismic design guidelines of the Architectural Institute of Japan (1994). Von Ramin and Matamoros (2004, 2006) suggested the following limits for the angle of inclination of the struts of the compression fields cotαl ≤ 2cosαst

(Fig. 6.5(a))

(6-14)

(Fig. 6.5(b))

(6-15)

and Fig. 6.5—Strut and compression field angles for structural walls as defined by Von Ramin and Matamoros (2006).

Ramin and Matamoros (2004, 2006) indicated that the strength of the strut must be reduced to reflect interaction with the tie. Von Ramin and Matamoros (2004, 2006) proposed the following expression for the interaction factor

βta

(βs f c′ – f t, t ) (β s f c′ – f t, l ) = -------------------------------------------------------(βs f c′ ) 2 – f t, t f t, l

cot

α

st cotαt ≤ --------------2

They also suggested a lower limit of 30 degrees for both angles. The strength provided by the two orthogonal truss mechanisms is given by

(6-11)

2 V t,l = ρt,l f yt,l b · a · tan αl

(Fig. 6.5(a))

(6-16)

V t,t = ρt,t f yt,t b · jd · tanαt

(Fig. 6.5(a))

(6-17)

and

where f t,l and f t,t are the stresses imposed on the concrete by the compression fields associated with reinforcement oriented in directions parallel to and perpendicular to the main longitudinal tie. These stresses are calculated based on the assumption of a uniform compression field (Von Ramin and Matamoros 2006) as

The nominal shear strength of members with low shear span-depth ratios is calculated as V n + V a + V t,t + V t,l

t, t

ρt, t f yt , t = ---------------2 sin α t

(6-12)

(6-18)

where V a is the component of the shear strength resulting from arch-action. The term V a was defined on the basis of the strength of a strut spanning from load point to support as

and

ρt, l f yt , l

t, l

= ---------------2 cos α l

V a = βs f c′ wst bsinαst

(6-19)

(6-13)

where ρt,t is the transverse reinforcement ratio for the transverse reinforcement oriented perpendicular to the main longitudinal tie, f yt,t is the specified yield strength of the transverse reinforcement oriented perpendicular to the main longitudinal tie, ρt,l is the transverse reinforcement ratio for the transverse reinforcement oriented in the direction parallel to the main longitudinal tie, f yt,l is the specified yield strength of the reinforcement oriented parallel to the main longitudinal tie, αt is the angle between the main longitudinal tie (which is oriented in the vertical direction in the case of structural walls) and the struts of the compression field induced by the transverse reinforcement oriented perpendicular to the main longitudinal tie (Fig. 6.5), and αl is the angle between the main longitudinal tie and the struts of the compression field induced by the transverse reinforcement oriented parallel to the main longitudinal tie. Equation (6-11) originates from a lower bound plasticity solution of a strut-and-tie model proposed by Nielsen (1999).

where wst is the strut width, and b is the width of the structural member. Based on the geometric configuration of the node, the width of the strut w is given by wst = hacosαst lbsinαst

(6-20)

with ha = 2cb = twice the cover of the longitudinal reinforcement and lb is the dimension of the loading plate or support in the axial direction of the member. In the case of squat walls in which designers include the strength provided by the transverse reinforcement, contrary to expectations, Eq. (6-11) will result in a significant reduction in the calculated strength of the strut. In structural walls with those characteristics, the amount of transverse reinforcement needed to avoid a reduction in shear strength after inclined cracking is very large. A larger nominal shear strength may be obtained by neglecting the effect of the transverse reinforcement in the calculation of the strength of the wall, which is consistent with the behavior observed in tests. In those cases, although the amount of transverse reinforcement does not


affect the nominal shear strength, a minimum amount of reinforcement should be provided as dictated by ACI 318-05. Von Ramin and Matamoros (2004, 2006) indicated that, for walls with well-confined boundary elements, Eq. (6-18) resulted in conservative estimates of strength, and that a better estimate of the shear strength is obtained by adding the shear strength of the boundary element, calculated as if it were a compression member. Based on test results from columns and beams subjected to load reversals, Von Ramin and Matamoros (2004) suggested the following expression for the reduction in the strength of the strut as a result of repeated load reversals into the nonlinear range of response

β n l, s tr ut =

8 DR li m 1 – ----------------------------------------( ρt f yt ⁄ f c ′ ) + 0.01

(6-21)

The strut factor in members subjected to repeated load reversals into the nonlinear range of response is given by

βsc = βnl,strut βs

(6-22)

Von Ramin and Matamoros (2004) indicated that the strength of the truss mechanism should be reduced as well by the following factor

βn l, t ru ss

1 = ----------------------------------------------λ p 1 + 1.5 ⋅ DR li m ⋅ 6

(6-23)

where

λ p = 1 + 2 · (P / Ag f c′ )0.35

(6-24)

Warwick and Foster (1993) also noted the effect of compressive strength and shear span-depth ratio on the strut factor. They proposed the following strut factor expression for concrete compressive strengths ranging between 2900 and 14,500 psi (20 and 100 MPa) f c′ a a 2 = 1.25 – ---------------– 0.72  -----v + 0.18  -----v ( f c′ in psi)  d   d  72,500 (6-25) 2 f c′ a a v v βs = 1.25 – --------- – 0.72  ----- + 0.18  ----- ( f c′ in MPa) d d 500

βs

The CSA Standard adopts a strut factor that considers the strain compatibility of the struts and the strain softening of the diagonally cracked concrete. The expression for the strut factor is

βs

1 = ---------------------------0.8 + 170 ε 1

(6-26)

ITG-4.3R-41

where ε1 is the principal tensile strain in the strut. Based on strain compatibility, the principal tensile strain is expressed as a function of the strain in the tie εs as

ε1 = εs + (εs + 0.002)/tan2αst

(6-27)

The strain in the tie εs is usually taken as the yield strain of the reinforcement ε y. A modification of Eq. (6-26) was later proposed by Vecchio et al. (1994) for high-strength concrete with compressive strength ranging up to 10,400 psi (72 MPa)

βs

1 = -----------------------------

ε 0.9 + 0.27 ----1 ε0

(6-28)

6.5—Calculation of shear strength of members subjected to seismic loading Current provisions in Section 21.3.4 of ACI 318-05 for proportioning the amount of transverse reinforcement in beams (flexural members) of special moment frames require that the design shear force be calculated on the basis of opposing probable flexural strengths at the joint faces and the factored tributary gravity load along the span. The shear strength must be calculated according to the procedures outlined in Chapter 11 of ACI 318-05, which were calibrated based on tests of members subjected to monotonic loading. The effect of repeated shear reversals is accounted for in that the term related to the contribution of the concrete, V c , must be neglected if the earthquake-induced shear is 1/2 or more of the design shear force and the axial force is less than Ag f c′ /20. Additional requirements for the amount of transverse reinforcement are given in Section 21.3.3 of ACI 318-05, which limits the maximum hoop spacing to the smallest of d /4, eight times the diameter of the smallest longitudinal bar, 24 times the diameter of the hoop bar, and 12 in. (305 mm). A similar two-tier approach is used to determine the amount of transverse reinforcement in columns (members subjected to bending and axial load) of special moment frames. The shear demand must be calculated on the basis of the probable moment strengths at the joints and the amount of reinforcement required for shear strength must be calculated in accordance with Chapter 11 of ACI 318-05. As in the case of beams, the term related to the contribution of the concrete, V c , must be neglected if the earthquake-induced shear is 1/2 or more of the design shear force and the axial force is less than Ag f c′ /20. For the majority of practical design cases, the term V c does not have to be neglected in columns because the axial force is not less than Ag f c′ /20. Moreover, the shear strength of a column increases as the compressive axial load on it increases. In addition, designers must verify that the amount of transverse reinforcement provided is greater than that required by Eq. (21-3) or (21-4) of ACI 318-05. These two equations specify the amount of transverse reinforcement for adequate confinement of the column core under cyclic loading. The latter criterion controls for most practical situations.

ITG-4.3R-42


6.6—Use of high-strength transverse reinforcement The use of high-strength transverse reinforcement is advantageous for column confinement. This topic is addressed in detail in Chapter 5 of this report. Section 11.5.2 of ACI 318-05 limits the yield strength of shear reinforcement to a maximum of 60,000 psi (414 MPa), which is increased to 80,000 psi (552 MPa) in the case of welded deformed wire reinforcement. It is stated in the commentary to the code that this provision is intended to limit the width of inclined cracks at service-load levels. Otani (1995) described the approach followed by the Japanese code for shear design using high-yield-strength transverse reinforcement. The objective of the Japanese Standard is to limit the width of shear cracks under long-term loads to an acceptable value, particularly in the case of columns, and to provide a safe estimate of strength (5% failure ratio on the basis of 1200 test data) for short-term loads. In the case of beams subjected to long-term loading, the maximum allowable shear force is given by V all = bj[αshvc,all + 0.5 f yt (ρt – 0.002)]

(6-29)

For columns subjected to long-term loading, the allowable shear force is given by V all = bj αsh f yt

(6-30)

In the case of beams under short-term service loads, the allowable shear force is given by V all = bj[αshvc,all + 0.5 f yt (ρt – 0.001)]

(6-31)

For columns subjected to short-term service loads, the allowable shear force is given by V all = bj[vc,all + 0.5 f yt (ρt – 0.001)]

(6-32)

where

αsh = 1 ≤ where vc, all M

= =

V

=

b j

= =

d

=

ρt

=

4 ------------------------ M ⁄ Vd + 1

≤ 2

(6-33)

allowable shear stress in concrete; maximum moment in the member due to service loads; maximum shear force in the member due to service loads (at the same location as M ); width of compression face of member; ratio of internal lever arm to effective depth of beam (under bending, j = 7/8d ); distance from extreme compression fiber to centroid of longitudinal tension reinforcement; and ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to

that reinforcement (the nominal value of ρt has an upper limit of 0.006 for long-term loads and 0.008 for short-term loads). The allowable shear stress in the concrete is given by the minimum of f c′ /30 and 70 + f c′ /100 (psi) ( f c′ /30 and 0.5 + f c′ /100 [MPa]) for normalweight concrete under long-term loading. For short-term loading, the allowable stress is increased by a factor of 1.5. For lightweight-aggregate concrete, a reduction factor of 0.9 must be applied. The maximum allowable tensile stress in the shear reinforcement is limited by the Japanese Design Standard to 28,500 psi (197 MPa) under long-term loads and 85,400 psi (589 MPa) under short-term loads. The reasons for establishing an upper limit on the allowable tensile stress include: 1) serviceability concerns; and 2) experimental evidence from beams with high-strength transverse reinforcement tested in Japan showing that yielding of the transverse reinforcement was not reached at shear failure.

6.7—Recommendations Based on the body of research that was reviewed, there are no specific recommendations deemed necessary for the design of slender high-strength concrete members for shear. The modification to Eq. (11-13) of ACI 318-05 to make the minimum amount of reinforcement a function of the compressive strength of concrete provides an adequate solution to prevent sudden shear failures after inclined cracking in members with light amounts of transverse reinforcement. A study by Sakaguchi et al. (1990) raises concerns about the behavior of members with low shear span-depth ratios subjected to cyclic loading. There is evidence (Sakaguchi et al. 1990; Kabeyasawa and Hiraishi 1998; Von Ramin and Matamoros 2004, 2006) that the application of the strut factors specified in Appendix A of ACI 318-05 to the design of high-strength concrete members may be unconservative because these factors were calibrated based on test results of elements loaded monotonically to failure. In elements subjected to load reversals, concrete may alternate between states of tension and compression due to changes in the direction of loading. If the element remains in the elastic range of response, the width of the cracks that form while concrete is subjected to tensile strains is not large enough to cause severe damage, and the use of strut factors derived for the monotonic loading case is acceptable. This type of behavior was observed in tests of deep beams subjected to load reversals conducted by Uribe and Alcocer (2001) in which failure took place prior to significant inelastic deformations in the flexural reinforcement (peak recorded strains in the flexural reinforcement at failure were on the order of 1%). When elements undergo excursions into the inelastic range of response, crack widths are significantly larger than those observed in the linear range of response due to larger deformations associated with yielding of the reinforcement. If concrete is not properly confined, this type of behavior leads to rapid degradation of strength. Furthermore, in some instances, the compression force may not be sufficient to fully close cracks formed while concrete and reinforcement


were subjected to tension. These effects may result in reduced strength for concrete in the struts, or may render struts ineffective due to changes in the load path in the element. To address the aforementioned problems caused by load reversals into the inelastic range of response, several proposals in the literature suggest that it is necessary to adjust strut factors for monotonic loading when using them for seismic design. Uribe and Alcocer (2001) indicated that procedures for seismic design using strut-and-tie models should account for the reduction in strength of the concrete in the struts as well as potential reductions in bond strength due to load reversals. They also suggested that proper detailing should include the use of closely spaced hoops to limit the width of the cracks under tension, and to provide confinement to concrete in the struts. Expressions for the reduction in strength with inelastic deformations are presented in the Japanese Design Code (AIJ 1994) and by Von Ramin and Matamoros (2006). In the Japanese Design Code (AIJ 1994), the capacity of struts is reduced as a function of the plastic rotation, while in the proposal developed by Von Ramin and Matamoros (2006), the reduction in strength is a function of deformation demand, amount of confining reinforcement, and the axial stress on the element. Because the strut factors in Appendix A of ACI 318-05 do not account for the effects of load reversals, the committee recommends that they only be used to proportion elements intended to remain elastic for the design earthquake. Specific recommendations for the design of members with low shear span-depth ratios using strut-and-tie models are presented in the following. In the case of bottle-shaped struts, a recommendation is made based on the strut factors suggested by Von Ramin and Matamoros (2004, 2006). These factors were calibrated using deep beams and walls, and adjusted to account for the 0.85 factor included in Eq. (A-3) of Appendix A of ACI 318-05:

βs = β fcβαt ≤ 0.6

(6-34)

where

β fc = 1 – f c′ /30,000 ≥ 0.6

( f c′ in psi)

β fc = 1 – 0.005 f c′ ≥ 0.6 βα t =

1 ---------------------------------3 1 + 0.1cot α st

(6-35)

( f c′ in MPa)

(6-36)

where αst is the angle of inclination of the strut with respect to the main tie. In the case of members subjected to point loads with single struts running between the load and reaction points, the angle of inclination of the strut may be approximated as

cos

αst

a = -----v d

(6-37)

ITG-4.3R-43

Fig. 6.6—Comparison between strut factors proposed and that in Appendix A for ACI 318-05 for bottle-shaped struts without transverse reinforcement.

A comparison between the proposed strut factor and that corresponding to bottle-shaped struts in Appendix A of ACI 318-05 is presented in Fig. 6.6. As shown in Fig. 6.6, when the angle of inclination of the strut is 35 degrees, the proposed strut factor becomes equal to that in ACI 318-05 at a concrete compressive strength of approximately 7000 psi (48 MPa). For struts with uniform cross-sectional area over their length, the stress conditions are very similar to those in the compression zone of members subjected to flexure and axial load. For this reason, it is recommended that the strut factor be similar to the α1 factor defined of Section 4.8 of this report, adjusted for the 0.85 factor in ACI 318, Eq. (A-3). In inch-pound units, it is recommended that: “for struts with uniform cross-sectional area over their length, the factor βs shall be taken as 1.0 for concrete strengths f c′ up to and including 8000 psi. For strengths above 8000 psi, βs shall be reduced continuously at a rate of 0.02 for each 1000 psi of strength in excess of 8000 psi, but βs shall not be taken less than 0.80.” In SI units, the recommendation is that: “for struts with uniform cross-sectional area over their length, the factor βs shall be taken as 1.0 for concrete strengths f c′ up to and including 55 MPa. For strengths above 55 MPa, βs shall be reduced continuously at a rate of 0.003 for each MPa of strength in excess of 55 MPa, but βs shall not be taken less than 0.80.” Because research on the effect of repeated load reversals into the nonlinear range of response on strut factors is at an early stage, it is recommended that the use of strut-and-tie models be limited to design of members where significant degradation of strength under load reversals into the nonlinear range is not expected to take place. Recommendations about the amount of transverse reinforcement needed for proper confinement of the concrete under nonlinear deformations are addressed in Chapter 5 of this report.

ITG-4.3R-44


CHAPTER 7—DEVELOPMENT LENGTH/SPLICES According to ACI 318-05, the development length of deformed bars or deformed wires in tension may be calculated according to the following requirements. For cases in which: 1) the clear spacing of the bars being developed or spliced is not less than d b, the cover is not less than d b, and the stirrups or ties throughout ld or the splice length are not less than the code minimum; or 2) the clear spacing of the bars being developed or spliced is not less than 2 d b and the cover is not less than d b l f ψ ψ λ ----d - = -- y----t ----e--- for No. 6 and smaller bars ( f c′ and f y in psi) d b 25 f c′ l 12 f ψ ψ λ ----d - = -------- y--------t -----e---- for No. 6 and smaller bars ( f c′ and f y in MPa) d b 25 f c′ l f y ψt ψ e λ ----d - = ------------------- for No. 7 and larger bars ( f c′ and f y in psi) d b 20 f c′ l 3 f ψ ψ λ ----d - = ---- y----t ---e--- for No. 7 and larger bars ( f c′ and f y in MPa) d b 5 f c′

(7-1)

(7-2)

For cases not meeting the aforementioned spacing, cover, and confinement criteria l 3 f ψ ψ λ ----d - = ---- y-----t ---e---- for No. 6 and smaller bars ( f c′ and f y in psi) d b 50 f c′ l 18 f ψ ψ λ ----d - = -------- y--------t -----e---- for No. 6 and smaller bars ( f c′ and f y in MPa) d b 25 f c′ l 3 f ψ ψ λ ----d - = ----- y---------t ------e--- for No. 7 and larger bars ( f c′ and f y in psi) d b 40 f c′ l 9 f ψ ψ λ ----d - = ----- y------t ---e--- for No. 7 and larger bars ( f c′ and f y in MPa) d b 10 f c′

(7-3)

(7-4)

Alternatively, the development length of deformed bars or deformed wires in tension may be calculated with a more complex equation: ACI 318 Eq. (12-1) l 3 f ψ t ψ e ψ s λ ----d - = ------ ----- y---- ---------------------- ( f c′ and f y in psi) 40 f c′  c b + K tr  d b --------- --------d  b l 9 f y ψ t ψe ψ s λ ----d - = ------ ------------------------------- ( f c′ and f y in MPa) d b 10 f c′  c b + K tr  --------- --------d  b

ACI 318 Eq. (12-1)

in which the term ( cb + K tr )/ d b ≤ 2.5. The development length calculated with any of the previous formulas must be not less than 12 in. (305 mm). Due to a lack of test data on bars embedded in highstrength concrete, ACI 318-05 places an upper limit of 100 psi (8.3 MPa) on the term f c′ in the previous equations. This limit does not allow designers to take advantage of any increase in bond strength associated with increases in concrete compressive strength beyond 10,000 psi (69 MPa). Research on bond of reinforcement in high-strength concrete has shown that there is a significant difference between the behavior of members with and without transverse

reinforcement in the splice region (McCabe 1998; Zuo and Darwin 2000; Azizinamini et al. 1993). In high-strength concrete members without transverse reinforcement, there is a greater tendency for the cracks to propagate through the aggregate, resulting in smoother failure surfaces than those found in normal-strength concrete (McCabe 1998). When the critical failure stress is reached, there is only limited redistribution of stresses and, as a result, failure tends to be more sudden and brittle in nature than in normal-strength concrete. Zuo and Darwin (2000) observed brittle failures in high-strength concrete without significant damage to the concrete at the interface between the bar and the concrete. Azizinamini et al. (1999b) also indicated that the strength of specimens without transverse reinforcement cannot be estimated with much accuracy because there are significant variations in measured strength for similar specimens. McCabe (1998) stated that in members without tran sverse reinforcement, the maximum stress before splitting failure is related to the fracture properties of the concrete, and not solely to the compressive strength. Because the fracture energy does not increase proportionally to the square root of the compressive strength, design expressions based on the square root function may be unconservative for compressive strengths greater than 10,000 psi (69 MPa) (McCabe 1998). Zuo and Darwin (2000) proposed a relationship between bond force and compressive strength to the 1/4 power based on a statistical study of monotonic tests of beams without transverse reinforcement and with concrete compressive strengths up to 16,000 psi (110 MPa). It has also been suggested that the lower water-cementitious material ratios of high-strength concrete result in less bleeding and sedimentation, which makes the top bar effect less significant than in normal-strength concrete (Fujii et al. 1998; Azizinamini et al. 1999b).

7.1—Design equations for development length of bars in high-strength concrete Design equations applicable to high-strength concrete have been proposed in ACI 408R-03, based on the statistical analysis by Zuo and Darwin (2000). It is proposed in the ACI Committee 408 report that Eq. (12-1) of ACI 318-05 be replaced by the following y  --- f --- – 2210 ω ψt ψ e λ  f ---- ′ 1 ⁄ 4

l c ----d - = ------------------------------------------------------- ( f c′ and f y in psi) d b c ′ω + K tr ′ 70  ----------------------- d b  f y  --42 ----– 2210 ω ψt ψ e λ 1 ⁄ 4  f --- ′

(7-5)

l c ----d - = ------------------------------------------------------- ( f c′ and f y in MPa) d b c ′ω + K tr ′  70 ------------------------  d b 

where c′ = cmin + 0.5d b

(7-6)


c

ma x + 0.9 ≤ 1.25 ω = 0.1 ----------

c mi n

′

K tr ′ = (0.5t d Atr / sn) f c (t d in inches, Atr in in.2, and f c′ in psi)

ITG-4.3R-45

(7-7)

relationship between the amount of transverse reinforcement and the total bond force is given by

(7-8)

A 1 ⁄ 4 T b =  2177 t d ----sp --- + 66 f c′ (T b in lb, t d in in., Asp in in.2, and f c′ in   n

psi)

(7-13)

′

K tr ′ = (6.25t d Atr / sn) f c (t d in mm, Atr in mm2, and f c′ in MPa)

t d = 0.78d b + 0.22

(d b in inches)

t d = 0.03d b + 0.22

(d b in mm)

(7-9)

and

′ )/ d b ≤ 4.0 (c′ω + K tr

(7-10)

The simplified expressions provided in Section 12.2.2 of ACI 318-05 are proposed to be replaced by the following: for cases in which 1) the clear spacing of the bars being developed or spliced is not less than d b, the cover is not less than d b, and ′ / db ≥ 0.5; the stirrups or ties throughout ld provide a value of K tr or 2) the clear spacing of the bars being developed or spliced is not less 2d b, and the cover is not less than d b l ----d - = d b

y  -------- f   105-- f ----′--1-- ⁄ ---4 – 20 ψt ψ e λ

( f c′ and f y in psi)

c

l 0.4 f y  ----d - =  -------1--- f ′ ⁄ 4 – 20  ψ t ψ e λ ( f c′ and f y in MPa) d b c

(7-11)

For cases not meeting the aforementioned spacing, cover, and confinement criteria l ----d - = d b

 ------- f --- y------- – 30 ψ t ψ e λ  70 f ′ 1 ⁄ 4 

( f c′ and f y in psi)

c

0.6 f y l  ----d - =  -------1--- f ′ ⁄ 4 – 30  ψ t ψ e λ ( f c′ and f y in MPa) d b c

(7-12)

The use of transverse reinforcement significantly changes behavior (Azizinamini et al. 1999b), because the confinement provided by the transverse reinforcement restrains the development of splitting cracks. Furthermore, the behavior becomes significantly more ductile. Zuo and Darwin (2000) showed the significant effect of transverse reinforcement on bond strength. Their study showed that the best fit between bond force and compressive strength for members with transverse reinforcement was obtained for a power coefficient of 3/4 compared with a coefficient of 1/4 for members without transverse reinforcement. An alternative design procedure was proposed by Azizinamini et al. (1999a). Rather than introducing new design equations, the procedure relies on a minimum amount of transverse reinforcement over the splice region to take advantage of the concrete compressive strength and improve the ductility of the splices (Azizinamini et al. 1999a). The approach proposed by Azizinamini et al. is based on an analysis of test results by Darwin et al. (1996), which concluded that the

t d A sp 2  1 ⁄ 4 T b =  ------- 500- ---n---- + 1 f c′ (T b in kN, t d in mm, Asp in mm , and f c′ in MPa)

where T b is the bond force, Asp is the cross-sectional area of transverse reinforcement crossing the potential plane of splitting along the length of splice, n is the number of bars being spliced, and f c′ is the specified compressive strength. This equation was used to estimate the amount of transverse reinforcement required to achieve an increase in bond strength proportional to the square root of the compressive strength. For test data with a concrete compressive strength of 15,000 psi (103 MPa), the amount of transverse reinforcement needed to obtain a safe estimate of the development length of a No. 8 (No. 25) bar with the ACI 318 equations was approximately Asp = 0.5nAb,max

(7-14)

where n is the number of bars being spliced. A linear adjustment was proposed to estimate the amount of transverse reinforcement required for members with concrete compressive strengths other than 15,000 psi (103 MPa) and higher than 10,000 psi (69 MPa) A sp = 0.5 nA b, ma x( f c′ ⁄ 15,000 ), f c′ A sp =

≥ 10,000 ( f c′ in psi) 0.5 nA b, ma x( f c′ ⁄ 100 ), f c′ ≥ 69 ( f c′ in MPa)

(7-15)

Equation (7-15) was calibrated on the basis of experiments with concrete compressive strengths of up to 16,000 psi (110 MPa). Additional requirements are that the maximum spacing of stirrups in the longitudinal direction not exceed 12 in. (305 mm), a minimum of three stirrups be used through the length of the splice, and that the bar size for the stirrups be at least No. 3 (No. 10). The proposal by Azizinamini et al. (1999a) requires that the development length be calculated using the equations in Sections 12.2.2 or 12.2.3 of ACI 318-05 assuming a value of K tr = 0. Because the current restriction in the code applies to concrete compressive strengths greater than 10,000 psi (69 MPa), the amount of transverse reinforcement proposed previously would be required when the compressive strength exceeds that threshold. The main advantage of the procedure proposed by Azizinamini et al. (1999a) is that it does not require adopting new equations for development length. There may, however, be additional cost if additional transverse reinforcement is required.

7.2—Design equations for development length of hooked bars in high-strength concrete There is little experimental data on the behavior of hooked bars in high-strength concrete. Fujii et al. (1998) summarized

ITG-4.3R-46


research on hooked bars in exterior joints carried out in Japan as part of the research program on high-strength materials. Compressive strength of concrete in the specimens tested as part of the study ranged from 5800 to 17,400 psi (40 to 120 MPa). All specimens in the testing program failed due to splitting of the side cover (cover to the side of the bar). Fujii et al. (1998) indicated that bond force was proportional to the cubic root of the compressive strength rather than the square root of f c′ . Increasing side cover led to increases in strength up to a cover of six bar diameters. The maximum stress developed in specimens with closely spaced bars (bar spacings ranging between two and 15 bar diameters) was approximately 75% of that observed in bars spaced farther apart than 30 bar diameters. The maximum stress increased in proportion to the development length up to a development length of 16 bar diameters, after which the observed increase in maximum stress was negligible. The maximum bar stress also increased proportionally to the ratio of development length to the lever arm between the tension and the compression resultants in the beam. Finally, the maximum stress in the bar was found to increase with the amount of transverse reinforcement. The increase was proportional to the ratio Asp f yt / s, where Asp is the cross-sectional area of transverse reinforcement crossing the potential splitting plane, f yt is the yield strength of the transverse reinforcement, and s is the spacing. The increase was approximately linear, with a maximum of 40% for an Asp f yt / s ratio of 3350 lb/in. (0.59 kN/mm). Fujii et al. (1998) proposed the following expression for the maximum tensile stress that can be developed in a bar with 90-degree hook

nominal diameter of the anchored bar; development length in tension of deformed bar or deformed wire with standard hook, measured from critical section to outside end of hook; = ratio of internal lever arm to effective depth of j the beam section at the column face; and d s = nominal diameter of bar used as transverse reinforcement (positioned at the hook). The configuration of the hook must satisfy the requirements of ACI 318-05.

7.3—Recommendations

(7-20)

clear cover of reinforcement (side cover in this case) to the outermost anchored bar;

In inch-pound units: Lap splices of flexural reinforcement shall be permitted only if hoop or spiral reinforcement is provided over the lap length. When the value of f c′ exceeds 100 psi, ld shall be

(7-16)

0.4 f u = 200k cc k j k d k s( f c′ ) ( f u and f c′ in MPa)

where k cc is the cover factor, k j and k d are development length factors, and k s is the transverse reinforcement factor. The factors are as follows 0.1 c k cc = 0.43 + ---------d b 0.5 l dh k j = 0.8 + ------------- jd

(1 ≤ k j ≤ 4)

l dh k d = 0.038 ----- + 0.54 d b

≤ 1.0

(7-17)

(7-18)

(7-19)

2

0.46 d k s = 0.7 + ----------------s 2 d b

=

= =

Research in bond and development of reinforcement (McCabe 1998) indicates that design expressions based on the square root of the compressive strength of the concrete may be unconservative for compressive strengths greater than 10,000 psi (69 MPa). Research by Azizinamini et al. (1993, 1999b) and Zuo and Darwin (2000) showed that the two main alternatives to correcting this problem were to increase the development length or to add transverse reinforcement. The main advantage of the latter approach is that it improves the behavior of the spliced or developed bars because failure is significantly more ductile. This is particularly advantageous in seismic design. Zuo and Darwin (2000) proposed a relationship between bond force and compressive strength to the 1/4 power based on a statistical study of monotonic tests of beams without transverse reinforcement and with concrete compressive strengths up to 16,000 psi (110 MPa). Their study concluded that the best fit between bond force and compressive strength for members with transverse reinforcement was obtained for compressive strength raised to the power of 3/4, compared with the compressive strength raised to the power of 1/4 for members without transverse reinforcement. Because ductile behavior is preferable in earthquake-resistant design, it was decided that the use of transverse reinforcement would be the preferable of the two alternatives. Therefore, the recommendation by Azizinamini et al. (1999a) was adopted as the basis for the proposed addition to Chapter 21 of ACI 318-05. Consistent with the approach adopted in ACI 318-05, the design recommendation adopted by the committee did not include any limitations to its applicability related to use of epoxy coating. It is important to note, however, that the recommendation by Azizinamini et al. (1999a) was based primarily on test results from uncoated bar splices in elements with concrete compressive strength of up to 16,000 psi (110 MPa). At the time the recommendation was adopted by the committee, there was a paucity of experimental results from splices of epoxy-coated bars with transverse reinforcement in elements with high-strength concrete, and from uncoated and epoxy-coated bars terminated using standard hooks in high-strength concrete. The proposed recommendation is stated in the following:

0.4 f u = 4000k cc k j k d k s( f c′ ) ( f u and f c′ in psi)

where cc

d b ldh

≤ 1.0


ITG-4.3R-47

calculated from either 12.2.2 or 12.2.3 with K tr = 0, and transverse reinforcement crossing the potential plane of splitting shall be provided over the tension splice length with a minimum total cross-sectional area Asp given by ACI 318, Eq. (21-AA). Asp = 0.5nAb,max ( f c′ /15,000)

ACI 318 Eq. (21-AA)

where n is the number of bars or wires being spliced along the plane of splitting. Maximum spacing of the transverse reinforcement enclosing the lapped bars shall not exceed d /4 or 4 in., and the minimum hoop or spiral bar size shall be No. 3. Lap splices shall not be used (a) within joints; (b) within a distance of twice the member depth from the face of the joint; and (c) where analysis indicates flexural yielding is caused by inelastic lateral displacements of the frame. In SI units: Lap splices of flexural reinforcement shall be permitted only if hoop or spiral reinforcement is provided over the lap length. When the value of f c′ exceeds 25/3 MPa, ld shall be calculated from either 12.2.2 or 12.2.3 with K tr = 0, and transverse reinforcement crossing the potential plane of splitting shall be provided over the tension splice length with a minimum total cross-sectional area Asp as given by ACI 318M, Eq. (21-AA). Asp = 0.5nAb,max ( f c′ /100)

ACI 318M Eq. (21-AA)

where n is the number of bars or wires being spliced along the plane of splitting. Maximum spacing of the transverse reinforcement enclosing the lapped bars shall not exceed d /4 or 100 mm, and the minimum hoop or spiral bar size shall be No. 10. Lap splices shall not be used (a) within the joints; (b) within a distance of twice the member depth from the face of the joint; and (c) where analysis indicates flexural yielding is caused by inelastic lateral displacements of the frame. Conclusions from Zuo and Darwin (2000) for splices are consistent with those by Fujii et al. (1998) for hooked bars. Fujii et al. (1998) summarized research on hooked bars in exterior joints carried out in Japan as part of the research program on high-strength materials. Concrete compressive strengths of the specimens tested as part of the study ranged from 5800 to 17,400 psi (40 to 120 MPa). All specimens in the testing program failed due to splitting of the side cover (cover to the side of the bar). Fujii et al. concluded that bond force was proportional to the cubic root of the compressive strength rather than the square root of f c′ . It is a concern that the current equation for the development length of hooked bars in tension of ACI 318-05 (Eq. (21-6))

Fig. 7.1—Proposed modification for development length of hooks.

may result in unconservative estimates for compressive strengths above 10,000 psi (69 MPa). While the term f c′ has an upper limit of 100 psi (8.3 MPa) in Chapter 12 of ACI 318-05, there is no such limit on Chapter 21. Given that no literature was found evaluating the use of the current ACI provisions for the development length of hooked bars in members with high-strength concrete, a modification to Eq. (21-6) of ACI 318-05 is proposed in this report to reduce the likelihood of unconservative estimates. The proposed modification is as follows: In inch-pound units: 21.5.4.1 The development length ldh for a bar with a standard 90-degree hook in normalweight aggregate concrete shall not be less than the largest of 8 d b, 6 in., or the lengths required by ACI 318 Eq. (21-6) and (21-BB) f y d b ldh = ---------------65 f c′ f y d b ldh = --------------------------1 ⁄ 4 650 ( f c′ )

ACI 318 Eq. (21-6)

ACI 318 Eq. (21-BB)

for bar sizes No. 3 through 11. In SI units: 21.5.4.1 The development length ldh for a bar with a standard 90 degree hook in normalweight aggregate concrete shall not be less than the largest of 8 d b, 150 mm, or the lengths required by ACI 318M Eq. (21-6) and (21-BB)

12 f y d b ldh = ---------------65 f c′ 42 f y d b ldh = --------------------------1 ⁄ 4 650 ( f c′ ) for bar sizes No. 10 through 36.

(ACI Eq. (21-6))

ACI 318M Eq. (21-BB)

ITG-4.3R-48


Fig. 7.2—Percentage change in ldh according to proposed modification for development length of hooks.

The proposed modification results in the same development lengths as given by ACI 318-05 (Fig. 7.1) for concrete compressive strengths up to 10,000 psi (69 MPa). For strengths greater than 10,000 psi (69 MPa), the development length of a hooked bar ldh increases in proportion to the fourth root of the compressive strength, resulting in an increase in development length (Fig. 7.2) that varies from 0 at 10,000 psi (69 MPa) to approximately 20% at 20,000 psi (138 MPa).

CHAPTER 8—DESIGN OF BEAM-COLUMN JOINTS The provisions for the design of joints in ACI 318-05 require that the horizontal shear stress in the joint be compared with the nominal shear strength (Fig. 8.1), which is calculated as V n = γvj f c′ A j V n = γvj f c′ A j

( f c′ in psi)

(8-1)

( f c′ in MPa) (add factor 1/12 in equation)

where A j is the effective cross-sectional area within a joint in a plane parallel to the plane of reinforcement generating shear in the joint, and γvj is a constant equal to 20, 15, or 12 for joints confined on all four faces (typically interior joints), joints confined on three faces or two opposite faces (typically exterior joints), and all other (typically corner) joints, respectively. A column face is considered confined if a beam frames into it and the beam is wide enough to cover 3/4 of the column face. The horizontal shear force in the joint must be calculated based on the assumption that the stress in the flexural tensile reinforcement of the beams framing into the joint is 1.25 f y (Fig. 8.1).

8.1—Confinement requirements for beam-column joints For special moment-resisting frames, ACI 318-05 requires the same amount of transverse hoop reinforcement as that

Fig. 8.1—Joint shear stress.

required in potential plastic hinge regions of columns, unless the joint is confined by structural members on all four sides. For rectangular columns, the amount of transverse reinforcement through the joint must be at least A g f c′ f ′ Ash = 0.3  ------- – 1 sb c ---- ≥ 0.09 sb c ---c- Ach  f yt f yt

(8-2)

Vertical spacing of transverse reinforcement within the length l o, near the top and bottom of columns, may not exceed 1/4 of the minimum column dimension, six times the diameter of column longitudinal bars, and the longitudinal spacing so. These criteria result in hoop spacing generally in the range of 4 to 6 in. (102 and 152 mm). This requirement is similar to that included in the design provisions developed by Joint ACI-ASCE Committee 352 (2002). In the case of joints that are confined by structural members framing into all four sides of the joint, with each member having a width of at least 3/4 of the column width, Section 21.5.2.2 of ACI 318-05 requires a minimum of 1/2 the amount of reinforcement in Eq. (8-2), and a maximum hoop spacing of 6 in. (152 mm). The aforementioned requirements apply to joints of special moment frames only. There are no specific code requirements for joints of frames that are not part of the


lateral force-resisting system of a building assigned to Seismic Category D or higher. Such joints and joints of intermediate moment frames must comply with Section 7.10.4 of ACI 318-05 in the case of spirally reinforced columns, and Section 7.10.5 in the case of tied columns. Section 7.10.5.2 requires that vertical spacing of ties shall not exceed 16 longitudinal bar diameters, 48 tie bar or wire diameters, or the least dimension of the compression member. Section 7.10.5.4 requires that ties complying with the aforementioned limitation must be provided at no more than 1/2 of a tie spacing below the lowest horizontal reinforcement in slab or drop panel above. It also requires that ties must be located vertically not more than 1/2 of a tie spacing above the top of footing or slab in any story. Where beams or brackets frame from four directions into a column, termination of ties not more than 3 in. (76 mm) below the lowest reinforcement in the shallowest of such beams or brackets is permitted. Section 7.10.4.6 requires that spirals in a spirally reinforced column must extend from the top of the footing or slab to the level of the lowest horizontal reinforcement in members supported above. Section 7.10.4.7 requires that where beams or brackets do not frame into all sides of a column, ties must extend above termination of the spiral to the bottom of the slab or drop panel. No maximum spacing for such ties is specified. Within the regions of potential plastic hinging at the ends of columns of intermediate moment frames, nonspiral transverse reinforcement must be in the form of hoops and must be provided at a spacing not to exceed: a) eight times the diameter of the smallest longitudinal bar; b) 24 times the diameter of the hoop bar; c) 1/2 of the smallest crosssectional dimension of column; and d) 12 in. (305 mm). The only requirement concerning transverse joint reinforcement, however, is in Section 21.12.5.5, which requires such reinforcement to conform to Section 11.11.2. That section requires transverse reinforcement having a minimum cross f f sectional area equal to 0.75 f c′ c2s / yt ≥ 50 c2s / yt (0.063 for f c′ in MPa) to be provided over a depth not less than that of the deepest framing member. Ghosh et al. (1995) recommended that the column end transverse reinforcement, as required by Section 21.12.5.2, be continued through joints of intermediate moment frames, irrespective of whether they are confined or unconfined.

8.2—Shear strength of exterior joints Saqan and Kreger (1998) evaluated test results from 26 beam-column connections tested in Japan and the U.S. with concrete compressive strengths ranging from 6000 to 15,500 psi (41 to 107 MPa). The maximum joint shear was calculated based on the story shears in the specimens at drift ratios of 2%. In the case of exterior joints, only two of the 22 specimens considered by Saqan and Kreger (1998) had shear strengths less than those calculated per ACI 318-05. Saqan and Kreger (1998) attributed the lower strengths observed in the two specimens to high bond stresses that degraded the shear strength of the joints prematurely. The ratios of column

ITG-4.3R-49

depth to beam bar diameter in these two tests were 13.6 and 15.7, below the limit of 20 specified by the design provisions of ACI 318-05 and Joint ACI-ASCE Committee 352 (2002). The average ratio of measured to calculated strength was 1.31 for the entire group of exterior joint tests, and the average joint shear coefficient γvj was 20.8 compared with the value of 15 given in ACI 318-05 and the design provisions of Committee 352. Of the 22 specimens evaluated, the majority did not comply with the code requirements for exterior connections, namely that there should be a minimum of two beams on opposite sides of the column with widths of at least 75% of the column width. The strict interpretation of this requirement would have led to classifying the specimens as corner connections and adopting a shear coefficient γvj of 12. Noguchi et al. (1998) presented an overview of experimental research on connections in Japan. The total number of specimens with concrete compressive strength over 8700 psi (60 MPa) was 110, with 76 simulating interior connections, and 28 specimens simulating exterior joints without transverse beams. Noguchi et al. (1998) concluded that the provisions for calculating joint shear strength in ACI 318-89 (same as those in ACI 318-05) provided conservative results for the tests carried out in Japan. The mean value of the joint shear strength measured experimentally was approximately proportional to the compressive strength raised to the power 0.72. The ACI provisions, which assume that joint shear strength increases with the square root of the compressive strength, resulted in a safe lower-bound estimate of strength.

8.3—Shear strength of interior joints Saqan and Kreger (1998) had only four test results from specimens simulating interior joints. All specimens sustained joint shear strengths higher than the nominal values calculated according to ACI 318-05, despite having lower amounts of transverse reinforcement than dictated by ACI 318-05 and the design provisions of Committee 352, and despite not meeting the requirement that beams extend over at least 75% of the width of all column faces. They concluded that on the limited basis of these four tests, the design provisions for joint shear strength in ACI 318-05 and those proposed by Committee 352 provided safe estimates of strength for concrete compressive strengths of up to 15,000 psi (103 MPa). The evaluation of test results by Noguchi et al. (1998) also led to the conclusion that the ACI design provisions yielded conservative estimates of strength for concrete compressive strengths up to 17,400 psi (120 MPa).

8.4—Effect of transverse reinforcement on joint shear strength The amount of transverse reinforcement in the exterior joint specimens reviewed by Saqan and Kreger (1998) ranged from 0.07 to 2.02 times the amount required by ACI 318-05. They found no discernible correlation between joint shear strength or mode of failure and the amount of transverse reinforcement. Of the 22 specimens evaluated by Saqan and Kreger, only five had an amount of transverse

ITG-4.3R-50


reinforcement higher than required by ACI 318-05. The remaining specimens had an average amount of reinforcement that was 47% of the minimum required, and had joint shear strengths that were 42% higher than the calculated nominal strength. Based on this, Saqan and Kreger indicated that the amount of transverse reinforcement in the joint could be reduced for joints with high-strength concrete, although the effect of axial load should be assessed before such a reduction is put in place. Noguchi et al. (1998) concluded that transverse reinforcement was marginally effective in increasing joint shear strength, and that the effect of transverse reinforcement on joint shear strength was not sensitive to concrete compressive strength. They also found that the effect of transverse reinforcement was slightly more significant for exterior joints than for interior joints. Although experimental results showed that beam-column joints with low amounts of transverse reinforcement were able to attain shear strengths comparable with those of wellreinforced joints, one important additional consideration is that the same cannot be concluded about the toughness of the joints. The term “toughness” in this case refers to how sustainable the peak shear strength was upon further load reversals up to similar or greater joint distortions (Joint ACIASCE Committee 352 2002). Noguchi et al. (1998) concluded that the plastic deformation capacity and the ductility of joints were enhanced by transverse reinforcement in a manner consistent with the behavior of joints with normal-strength concrete.

8.5—Development length requirements for beam-column joints ACI 318-05 criteria for the design of interior beamcolumn joints in special moment frames subjected to seismic loading include the requirement that the column dimension parallel to the beam reinforcement must be no less than 20 times the diameter of the largest longitudinal bar for normalweight concrete nor 26 times the bar diameter for lightweight concrete. These criteria are based on an evaluation of test results (Zhu and Jirsa 1983) for beam-column joints made with normal-strength concrete subjected to load reversals. Zhu and Jirsa (1983) concluded that the ratios of column width to bar diameter of 20 to 22 were appropriate to avoid bond damage at an interstory drift of 3%. The slip of bars in beam-column joints under load reversals plays an important role in the ability of reinforced concrete frames to resist seismic loading (Durrani and Wight 1982; Zhu and Jirsa 1983; Ciampi et al. 1982). Based on push-pull tests of bars embedded in beam-column joints with normalstrength concrete, Ciampi et al. (1982) found that to limit bond damage under cyclic loading, anchorage lengths between 25 and 30 bar diameters and between 35 and 40 bar diameters were necessary for Grade 40 and 60 (280 and 420 MPa) deformed bars, respectively. The criteria used to define satisfactory performance were: 1) that the bond damage be limited to the end region of the embedment length; 2) that the hysteretic loops of the anchored bar remain stable; and 3) that the strength of the anchorage

continues to increase for slip values larger than the peak values during the previous cycles. The evaluation of test results by Zhu and Jirsa (1983) resulted in the smaller values now used in ACI 318-05. More recent tests, however, support the earlier observations and indicate that the current design criteria will not prevent bond slip, even in the earliest stages of cyclic loading, and that significant bond slip will occur even under more stringent requirements than those in ACI 318-05 (Quintero-Febres and Wight 2001; Joint ACIASCE Committee 352 2002). Development length requirements for beam-column joints differ significantly among the ACI 318-05 (ACI Committee 318 2005), the AIJ Design Guideline (AIJ 1994), and the NZS 3101 (Standards Association of New Zealand 1995). While the minimum column dimension requirement in ACI 318-05 is insensitive to material properties, design provisions in the AIJ Design Guideline (AIJ 1994) and in NZS 3101 establish the ratio of bar diameter to column depth as a function of the square root of the concrete compressive strength and the yield strength of the reinforcement. The philosophy behind this requirement is that bond deterioration can cause significant loss in the capacity of the connection to dissipate energy (pinching behavior). Noguchi et al. (1998), based on the tests of beam-column joints with concrete compressive strengths greater than 8700 psi (60 MPa) carried out in Japan as part of the New RC project, concluded that specimens with high-strength concrete and highstrength reinforcement demonstrated significantly reduced ability to dissipate energy compared with beam-column joints made with normal-strength concrete. They indicated that while specimens that met the Japanese design guideline had adequate behavior, it is not clear if a less stringent requirement such as that of ACI 318-05 would be sufficient for adequate toughness under cyclic loading. They concluded that further evaluation of the Japanese design guideline was needed for high-strength materials.

8.6—Recommendations Because research indicates that the equations for calcul ating the shear strength of joints are conservative for high-strength concrete, no change to the code provisions is recommended. There are significant differences in the provisions for the ratio of column dimension parallel to the beam reinforcement t o the diameter of the largest longitudinal beam bar (which effectively defines the minimum interior column dimension) between ACI 318-05 and both the AIJ Design Guideline (1994) and NZS 3101 (Standards Association of New Zealand 1995). ACI 318-05 requires significantly smaller column dimensions for joints with high-strength concrete. Although there is consensus in the literature that the minimum column dimension specified in ACI 318-05 is not sufficient to prevent slip of the reinforcement, this situation is not specific to high-strength concrete. The main difficulty faced by the ITG was that there were no references found evaluating the minimum column dimension specified in ACI 318-05 when high-strength concrete was used. Although there is experimental evidence from research carried out in Japan that the toughness of joints subjected to repeated load


reversals decreases with increasing compressive strength, the research conducted in Japan was aimed at evaluating the performance of joints proportioned according to the Japanese design provisions. For that reason, no consensus was found on how to modify the ACI 318-05 provisions to account for this effect.

CHAPTER 9—DESIGN OF STRUCTURAL WALLS Seismic design of structural walls is covered in Section 21.7 of ACI 318-05. For walls with low aspect ratios, the primary design consideration is shear strength. According to ACI 318-05, the nominal shear strength of walls is given by V n = Acv(αc f c′ + ρt f y)

ACI 318 Eq. (21-7)

where the coefficient αc = 3.0 for hw / lw ≤ 1.5, 2.0 for hw / lw ≥ 2.0, ( f c′ and f y in psi) where the coefficient αc = 0.25 for hw / lw ≤ 1.5, 0.17 for hw / lw ≥ 2.0, ( f c′ and f y in MPa) and varies linearly in between. The minimum amount of web reinforcement required by the code is ρl = ρt = 0.0025, with a maximum spacing between bars of 18 in. (457 mm). In slender walls, the flexural behavior of the walls is most important. The minimum amount of longitudinal reinforcement is specified to prevent premature failure due to rupture of the reinforcement. The significance of this problem is greater for walls made with high-strength concrete because the depth of the neutral axis decreases and the strain demand in the reinforcement increases with compressive strength. Another mode of failure that the code intends to prevent, or at least postpone, through the use of special boundary elements at the edges of structural walls is crushing of the concrete in the compression zone due to flexural demands. According to ACI 318-05, compression zones shall be reinforced with special boundary elements in areas where lw c ≥ ----------------------------, δ u ⁄ h w ≥ 0.007 600 ( δ u ⁄ h w )

(9-1)

where c corresponds to the largest neutral axis depth calculated for the factored axial force and nominal moment strength, consistent with the design displacement δu , in. These elements allow proper confinement and ductile behavior of the compression zone. Due to the amount of transverse reinforcement required, however, the use of boundary elements significantly increases the cost of the walls.

9.1—Boundary element requirements The equation to determine whether boundary elements are required stems from establishing a limiting strain demand εlim that the wall can sustain without special confinement, such that

ε φli m

c = ----li---m --

(9-2)

ITG-4.3R-51

From research by Wallace and Moehle (1992), the following expression was proposed for the limiting curvature

φlim =

δ 1 ---- 0.0025 ( l w – 0.5 h w ) + 2 -----ulw hw

(9-3)

Because the first term within the square brackets is small compared with the second, it can be conservatively neglected to calculate the depth of the neutral axis lw lw ε c = ----li---m -- = --------------= --------------2 δu φli m δ --------------600 -----uhw εli m hw

(9-4)

The previous expression was derived by assuming a limiting strain of 0.003 and rounding the term 2/0.003 = 667 down to 600. The design expression implemented in ACI 318-05 is thus intended to require special boundary elements if the strain in the extreme compression fiber of a wall exceeds 0.003 for the design drift demand. In the current design procedure, the limiting strain is independent of the concrete compressive strength. A limiting strain of 0.003 has been shown to be a safe limit for normal-strength concrete (Wallace 1998). The main concern in applying this provision to high-strength concrete walls is whether a limiting strain of 0.003 remains a safe value as the concrete compressive strength increases. Wallace (1998) suggests that a similar limiting strain for normal-and high-strength concrete can be adopted, although greater conservatism may be prudent for high-strength concrete given the relatively brittle behavior of unconfined high-strength concrete. As previously stated in Section 4.5, Fasching and French (1998) indicate that opinions about the limiting strain for high-strength concrete are varied. The test data set they compiled had limiting strains ranging from 0.002 and 0.005, with an average value of 0. 0033. Average values for data sets with the same type of aggregate were all above 0.003. Bae and Bayrak (2003) suggested adopting a lower limiting strain due to observed spalling at lower strains in highly confined high-strength concrete columns. They attribute the premature spalling observed in these columns to the existence of a failure plane created by closely spaced hoops. Ozbakkaloglu and Saatcioglu (2004) proposed, on the basis of moment-curvature analyses, that the limiting concrete strain be linearly reduced from 0.0036 for 4000 psi (28 MPa) concrete to 0.0027 for 18,000 psi (124 MPa) concrete. Their analysis consisted of finding the maximum moment resistance and the corresponding extreme compression fiber strain from a series of moment-curvature diagrams. They concluded that although the optimal values of flexural strength were obtained by varying the limiting strain as proposed, the calculated flexural strength was not very sensitive to the limiting strain, and recommended adopting a constant value of 0.003.

ITG-4.3R-52


Saatcioglu and Razvi (1998) observed premature spalling of cover concrete in most of the concentrically loaded columns that they tested, prior to the development of strains associated with concrete crushing. Similar to Bae and Bayrak (2003), they attributed the premature spalling in these columns to a stability failure caused by a failure plane induced by the presence of closely spaced longitudinal and transverse steel. Furthermore, they indicated that this problem was not observed in columns with widely spaced transverse reinforcement tested by Rangan et al. (1991) and Yong et al. (1988).

9.2—Shear strength of walls with low aspect ratios Tests of low-rise walls with high-strength concrete carried out in North America are scarce. Wallace (1998) performed an analysis comparing the strength estimated using the shear design equation in ACI 318-05 with test results of low-rise walls made of high-strength concrete carried out in Japan. The analysis by Wallace showed that the ratio of measured to estimated strength decreased with the ratio ρn f f c′ . The y / f c′ ≥ 0.08 was overstrength of several specimens with ρn f y / estimated using the ACI 318 equation. He carried out a second comparison using a design procedure proposed by Wood (1990). According to Wood, the shear strength of the walls is given by V n = Asv f y /4

10 f c′ Acv ≥ V n ≥ 6 f c′ Acv

(9-5) ( f c′ in psi)

0.83 f c′ Acv ≥ V n ≥ 0.5 f c′ Acv

(9-6)

( f c′ in MPa)

where Asv is the total area of vertical reinforcement, and Acv is the area of the wall bounded by the web thickness and the wall length. Wallace found that for the high-strength walls with different amounts of vertical reinforcement tested in Japan, the equation proposed by Wood provided a uniform ratio of measured to calculated shear strength. The average ratio of measured to calculated strength was 1.76, with a coefficient of variation of 20%. Wallace also showed that for high-strength concrete walls, shear strength was not sensitive to the amount of web reinforcement, and suggested using a shear strength of 9 f c′ Acv (in psi) (0.75 f c′ Acv [in MPa]) as a safe lower bound. Kabeyasawa and Hiraishi (1998) presented a summary of 21 tests on high-strength concrete walls conducted in Japan, with compressive strengths ranging from 8700 to 17,400 psi (60 to 120 MPa). The parameters of the experimental program were the concrete compressive strength, the transverse and longitudinal reinforcement ratios, the axial load, the type of boundary element, and the shear span-depth ratio. Six of the specimens were designed to reach flexural yielding before shear failure. Specimens designed to fail in shear had different amounts of web reinforcement. All shear-critical specimens failed due to crushing of the concrete in the web of the wall.

Specimens with lower amounts of web reinforcement failed after yielding of that reinforcement, and their strength was safely estimated by the Japanese seismic design guideline. In specimens with high amounts of transverse reinforcement, failure occurred due to crushing of the web concrete before yielding of the web reinforcement, and their strength was overestimated by the Japanese design guideline. The Japanese guideline is based on a strut-and-tie approach in which the total strength is the sum of the strength contributions from truss and arch action. The procedure is based on estimating the demand on the concrete placed by the truss mechanism, and whatever capacity is left, if any, is assigned to the direct strut mechanism. Kabeyasawa and Hiraishi (1998) also indicated that although the walls designed to fail in flexure were able to sustain deformations past the yield point of the flexural reinforcement, the energy dissipated, as indicated by the hysteresis loops, was relatively low. They indicated that equivalent damping coefficients for the high-strength concrete walls were on the order of 5 to 8%, while these values for normal-strength walls are considerably higher, on the order of 20%. In addition, the hysteresis loops exhibited pinching behavior.

9.3—Minimum tensile reinforcement requirements in walls Failure of lightly reinforced structural walls may occur, in some instances at relatively low levels of drift, due to fracture of the tensile reinforcement (Wood 1989). A documented case of this type of failure occurred in an eight-story structural wall building that suffered severe damage and fracture of the tensile reinforcement near the base of the structural walls during the 1985 Chilean earthquake (Wood 1989). According to Wood, the damaged walls had calculated tensile strains in the boundary reinforcement that were twice the measured fracture strain of the reinforcement. This problem can be exacerbated by the use of highstrength concrete because the depth of the compression zone needed to equilibrate the force in the tensile reinforcement is considerably less than in walls with normal-strength concrete. Based on results from 37 structural wall tests, Wood proposed two different criteria that may be used to determine the vulnerability of walls to failure due to fracture of the tensile reinforcement. The first criterion uses the calculated steel strain in the extreme layer of reinforcement at the nominal flexural strength of the cross section as an index value. Because there were several walls within the set with calculated steel strains greater than 5% that failed in shear, however, Wood concluded that the calculated steel strain cannot be used as the sole criterion for determining the susceptibility of a wall to fracture of the reinforcement. It was observed that of the subset of 24 walls with a shear stress index greater than 0.75, 20 failed in shear, and of the 13 walls that developed a shear stress index less than 0.75, 12 failed in flexure. The shear stress index was defined by Wood as vmax / vn , where vmax is the maximum shear stress demand on the wall and


vn = 2 f c′ + ρn f y ≤ 8 f c′ (psi)

(9-7)

vn = f c′ /6 + ρn f y ≤ 2 f c′ /3 (MPa)

Within the subset of walls with shear stress indexes below 0.75, Wood observed that 10 of the 12 walls with total vertical reinforcement ratios ρwt less than 1% were susceptible to fracture of the tensile reinforcement. Fracture of the reinforcement was observed in walls with calculated steel strains in the extreme layer of reinforcement as low as 2.5%. A limit of 4% was proposed as a reasonable boundary for identifying walls that are likely to fail due to fracture of the reinforcement. The second criterion is based on the flexural stress index c fsw, which is representative of the ratio of neutral axis depth to wall length, and is given by

ρ wt f yl + P ⁄ A w c fs w = --------------------------------- f c′

(9-8)

where

ρwt

Asw b + A sw w = ---------------------------- A w

(9-9)

where

ρwt

total vertical reinforcement ratio of the wall; gross area of the wall; area of vertical reinforcement in the boundary element of the wall (the participation of the steel in the compression boundary element is ignored in the formulation because it was assumed that the neutral axis depth is small); Asww = total area of vertical reinforcement in the web of the wall, excluding boundary elements; and P = axial load on the wall, with a positive value representing a compressive force. Wood noted that of the 27 specimens in which the main reinforcement did not fracture, 26 had flexural stress indexes greater than 15%, and suggested that structural walls susceptible to fracture of the tensile reinforcement are those with a flexural stress index below 15%. Both of the two requirements proposed by Wood may be interpreted as prescribing a minimum amount of tensile reinforcement in structural walls. Aw Aswb

= = =

9.4—Recommendations The literature survey indicates that design provisions for the detailing of boundary elements in slender walls in ACI 318-05 are adequate for high-strength concrete, and no significant change is necessary. The technical references in which a lower limiting compressive strain was suggested for high-strength concrete columns attributed the need for a lower limiting strain to the existence of a failure plane caused by closely spaced ties, or to an overestimation of the

ITG-4.3R-53

flexural strength. The former is not a concern in the case of end regions of walls without boundary elements, while the latter is not a concern because the limiting strain of the concrete is not likely to have a significant effect on the calculated flexural strength of slender walls. One area of concern is the behavior of walls with very light amounts of longitudinal reinforcement. A simple procedure was proposed by Wood to prevent wall failure due to fracture of the tension reinforcement. In the case of walls with low aspect ratios, the study by Wallace (1998) showed that shear strength equations in ACI 318-05 become less conservative as the amount of transverse reinforcement increases in walls with high-strength concrete. For high amounts of transverse reinforcement, the equation for shear strength in ACI 318-05 was found to be unconservative. One viable option to obtain a uniform level of safety is to adopt the equations proposed by Wood. The main disadvantage of this option is that the level of conservatism was found to be quite large for high-strength concrete. Another alternative is to recommend the use of strut-and-tie models following the recommendations presented in Chapter 6. The study by Wallace indicated that the current ACI procedure was unconservative for several high-strength concrete walls with ρn f f c′ ≥ 0.08. These cases, however, y / are rare in earthquake-resistant construction. This concern may be addressed with an addition to the commentary to ACI 318-05, Section 21.7.4, indicating that the current design equations may yield unconservative estimates of shear strength for high-strength concrete walls with high amounts of transverse reinforcement.

CHAPTER 10—LIST OF PROPOSED MODIFICATIONS TO ACI 318-05 One of the main goals of this report was to present a series of recommendations for the use of high-strength concrete in seismic design. The main purpose of the literature review presented in the previous chapters on structural design was to identify specific sections of ACI 318-05 that should be revised to allow for the use of high-strength concrete in seismic design. Although some of the changes that were proposed were intended to facilitate a smooth transition between normal- and high-strength concrete, the majority of them specifically address structural design using highstrength concrete. The following are specific modifications to ACI 318-05 intended for the safe use of high-strength concrete in seismic design. Section numbers are noted where applicable. SI units are not repeated in this Chapter for clarity. See previous chapters for SI equivalents.

10.1—Proposed modifications to equivalent rectangular stress block The following changes are proposed to the equivalent rectangular stress in ACI 318-05. Changes and additions to Section 2.1— = factor relating magnitude of uniform stress in α1 the equivalent rectangular compressive stress

ITG-4.3R-54


block to specified compressive strength of concrete as defined in 10.2.7.2, Chapter 10. β1 = factor relating depth of equivalent rectangular compressive stress block to neutral axis depth, see 10.2.7.3 10.2.7.4, Chapters 10, 18, Appendix B = factor relating mean concrete compressive χ1 stress at axial load failure of concentrically loaded columns to specified compressive strength of concrete as defined in 10.3.6.4, Chapter 10. Changes to Section 10.2.7 — 10.2.7.1 Concrete stress of 0.85 α1 f c′ shall be assumed uniformly distributed over an equivalent compression zone bounded by edges of the cross section and a straight line located parallel to the neutral axis at a distance a = β1c from the fiber of maximum compressive strain. 10.2.7.2 For f c′ between 2500 and 8000 psi, α1 shall be taken as 0.85. For f c′ above 8000 psi, α1 shall be reduced linearly at a rate of 0.015 for each 1000 psi of strength in excess of 8000 psi, but α1 shall not be taken less than 0.70. 10.2.7.2 10.2.7.3 Distance from the fiber of maximum strain to the neutral axis, c, shall be measured in a direction perpendicular to that axis. 10.2.7.3 10.2.7.4 For f c′ between 2500 and 4000 psi, β1 shall be taken as 0.85. For f c′ above 4000 psi, β1 shall be reduced linearly at a rate of 0.05 for each 1000 psi of strength in excess of 4000 psi, but β1 shall not be taken less than 0.65. Changes to Section 10.3.6 — 10.3.6.1 For nonprestressed members with spiral reinforcement conforming to 7.10.4 or composite members conforming to 10.16, or confined columns conforming to 21.4.4.1 through 21.4.4.3 for the full height of the column

φPn,max = 0.85φ[0.85 f c′ ( Ag – Ast ) + f y Ast ] φPn,max = 0.85φ[χ1 f c′ ( Ag – Ast ) + f y Ast ]

10.2—Proposed modifications related to confinement of potential plastic hinge regions Addition to Section 2.1— k ve = confinement efficiency factor. See Eq. (21-YY) Changes to Section 21.2.5— 21.2.5 Reinforcement in members resisting earthquakeinduced forces—Reinforcement resisting earthquakeinduced flexural and axial forces in frame members and in structural wall boundary elements shall comply with ASTM A 706. ASTM A 615 Grades 40 and 60 (280 and 420 MPa) reinforcement shall be permitted in these members if: (a) The actual yield strength based on mill tests does not exceed f y by more than 18,000 psi (retests shall not exceed this value by more than an additional 3000 psi); and (b) The ratio of the actual tensile strength to the actual yield strength is not less than 1.25 The value of f yt for transverse reinforcement including spiral reinforcement shall not exceed 60,000 psi. The use of transverse reinforcement with a specified yield strength not exceeding 120,000 psi shall be permitted when required to meet the confinement requirements given by Eq. (21-XX). The yield strength of the reinforcement shall be measured by the offset method of ASTM A 370 using 0.2% permanent offset. The requirement of Section 3.5.3.2 shall be inapplicable to such high-strength transverse reinforcement. Replace Section 21.4.4.1 with the following— 21.4.4.1 Transverse reinforcement as required in (a) through (c) shall be provided unless a larger amount is required by 21.4.3.2 or 21.4.5. (a) The area ratio of transverse reinforcement shall not be less than that required by Eq. (21-XX)

ρt =

f ′ A g 1 Pu 0.35 ---c--  ------- – 1 ----------- ---------- k Ag f c′ f yt  A ch

(21-XX)

ve

(10-1) (10-1)

10.3.6.2 For nonprestressed members with tie reinforcement conforming to 7.10.5

φPn,max = 0.80φ[0.85 f c′ ( Ag – Ast ) + f y Ast ]

(10-2)

φPn,max = 0.80φ[χ1 f c′ ( Ag – Ast ) + f y Ast ]

(10-2)

10.3.6.3 For prestressed members, design axial strength φPn shall not be taken greater than 0.85 (for members with spiral reinforcement) or 0.80 (for members with tie reinforcement) of the design axial strength at zero eccentricity φPo calculated assuming concrete stress of χ1 f c′ uniformly distributed across the entire depth of the section. 10.3.6.4 For f c′ between 2500 and 8000 psi, χ1 shall be taken as 0.85. For f c′ above 8000 psi, χ1 shall be reduced linearly at a rate of 0.015 for each 1000 psi of strength in excess of 8000 psi, but χ1 shall not be taken less than 0.70.

where Ag / Ach – 1 ≥ 0.3, and Pu / Ag f c′ ≥ 0.2. (b) Transverse reinforcement shall have either circular or rectangular geometry. Reinforcement for columns with circular geometry shall be in the form of spirals or hoops, for which k ve = 1.0. Reinforcement for columns with rectangular geometry shall be provided in the form of single or overlapping hoops. Crossties of the same bar size and spacing as the hoops shall be permitted. Each end of the crosstie shall engage a peripheral longitudinal reinforcing bar. Consecutive crossties shall be alternated end for end along the longitudinal reinforcement. The parameter k ve for rectangular hoop reinforcement shall be determined by Eq. (21-YY) 0.15 b k ve = ---------------c ≤ 1.0 sh x

(21-YY)

(c) If the thickness of the concrete outside the confining transverse reinforcement exceeds 4 in., additional transverse reinforcement shall be provided at a spacing not exceeding 12 in. Concrete cover on the additional reinforcement shall not exceed 4 in.


Changes to Section 21.12.5— 21.12.5.1 Columns shall be spirally reinforced in accordance with 7.10.4 or shall conform to 21.12.5.2 through 21.12.5.421.12.5.5. Section 21.12.5.521.12.5.6 shall apply to all columns. 21.12.5.2 At both ends of the member, hoops shall be provided at spacing so over a length lo measured from the joint face. Spacing so shall not exceed the smallest of (a), (b), (c), and (d): (a) eight times the diameter of the smallest longitudinal bar enclosed; (b) 24 times the diameter of the hoop bar; (c) 1/2 of the smallest cross-sectional dimension of the frame member; (d) 12 in. length lo shall not be less than the largest of (e), (f), and (g); (e) 1/6 of the clear span of the member; (f) maximum cross-sectional dimension of the member; and (g) 18 in. 21.12.5.3 For members in which the specified concrete compressive strength is greater than 8000 psi, transverse reinforcement as required in (a) and (b) shall be provided at both ends of the member over a length lo measured from the joint face. (a) Members with transverse reinforcement with rectilinear geometry shall not be less than that required by Eq. (21-ZZ)

ρ t =

f ′ A g Pu 0.3 ----c-  ------- – 1 ---------- Ag f c′ f yt  Ach

(21-ZZ)

(b) Members with transverse reinforcement with circular geometry shall not be less than that required by Eq. (21-WW)

ρt =

f ′ Ag Pu 0.2 ---c--  ------- – 1 ---------- Ag f c′ f yt  A ch

(21-WW)

Ach – 1 ≥ 0.3, and Pu / Ag f c′ ≥ 0.2. where Ag / 21.12.5.321.12.5.4 The first hoop shall be located not more than so /2 from the joint face. 21.12.5.421.12.5.5 Outside the length lo, spacing of transverse reinforcement shall conform to 7.10 and 11.5.5.1. 21.12.5.521.12.5.6 Joint transverse reinforcement shall conform to 11.11.2.

10.3—Proposed modifications related to bond and development of reinforcement Additions to Section 2.1— Asp = total cross-sectional area of all transverse reinforcement that is within the splice or development length and that crosses the potential plane of splitting through the reinforcement being spliced or developed, in. 2 Ab,max = cross-sectional area of largest bar being spliced or developed, in.2 Changes to Chapter 21 — 21.3.2.3 Lap splices of flexural reinforcement shall be permitted only if hoop or spiral reinforcement is provided over the lap length. When the value of f c′ exceeds 100 psi, ld shall be calculated using either 12.2.2 or 12.2.3 with K tr = 0, and transverse reinforcement crossing the potential plane of splitting shall be provided over the tension splice length

ITG-4.3R-55

with a minimum total cross-sectional area Asp given by Eq. (21-AA) Asp = 0.5nAb,max ( f c′ /15,000)

(21-AA)

where n is the number of bars or wires being spliced along the plane of splitting. Maximum spacing of the transverse reinforcement enclosing the lapped bars shall not exceed d/ 4 or 4 in., and the minimum hoop or spiral bar size shall be No. 3. Lap splices shall not be used: (a) within the joints; (b) within a distance of twice the member depth from the face of the joint; and (c) where analysis indicates flexural yielding is caused by inelastic lateral displacements of the frame. 21.4.3.2 Mechanical splices shall conform to 21.2.6, and welded splices shall conform to 21.2.7. Lap splices shall be permitted only within the center half of the member length. Lap splices shall be designed as tension lap splices in accordance with 21.3.2.3, and shall be enclosed with transverse reinforcement conforming to 21.4.4.2 and 21.4.4.3 and the maximum spacing of transverse reinforcement in lap splices shall be as given by 21.4.4.2. The transverse reinforcement also shall conform to 21.4.4.3. 21.5.4.1 The development length ldh for a bar with a standard 90-degree hook in normalweight aggregate concrete shall not be less than the largest of 8 d b, 6 in., and the lengths required by Eq. (21-6) and (21-BB) f y d b l dh = ---------------65 f c′

(21-6)

f y d b l dh = ---------------------1 ⁄ 4 650 f c′

(21-BB)

for bar sizes No. 3 through 11. 21.7.2.3 Reinforcement in structural walls shall be developed or spliced for f y in tension in accordance with Chapter 12, except: (a) The effective depth of the member referenced in 12.10.3 shall be permitted to be 0.8 lw for walls; (b) The requirements of 12.11, 12.12, and 12.13 need not be satisfied; (c) At locations where yielding of longitudinal reinforcement is likely to occur as a result of lateral displacements, development lengths of longitudinal reinforcement shall be 1.25 times the values calculated for f y in tension. When the value of f c′ exceeds 100 psi, transverse reinforcement with a minimum total cross-sectional area Asp as given by Eq. (21-AA) shall be provided over the development or splice length; (d) Mechanical splices of reinforcement shall conform to 21.2.6, and welded splices of reinforcement shall conform to 21.2.7; and (e) When the value of f c′ exceeds 100 psi, ld shall be calculated with K tr = 0.

ITG-4.3R-56


21.7.6.6 Mechanical and welded splices of longitudinal reinforcement of boundary elements shall conform to 21.2.6 and 21.2.7. Lap splices shall be designed as tension lap splices in accordance with 21.3.2.3, except that the maximum spacing of transverse reinforcement shall be as given by 21.4.4.2 and the transverse reinforcement shall also conform to 21.4.4.3. Addition to Section 2.1— αst = smallest angle of inclination of a strut with respect to the ties that it intersects in both of its nodes β fc = factor to account for the effect of concrete compressive strength on the effective compressive strength of concrete in a strut = factor to account for the effect of the angle of βαt inclination of the strut αst on the effective compressive strength of concrete in a strut

10.4—Proposed modifications related to strut-and-tie models Changes to Appendix A — A.3.2 The effective compressive strength of the concrete f ce in a strut shall be taken as f ce = 0.85βs f c′

(A-3)

A.3.2.1 For a strut of uniform cross-sectional area over its length βs= 1.0: for f c′ between 2500 and 8000 psi, βs shall be taken as 1.0; for f c′ above 8000 psi, βs shall be reduced linearly at a rate of 0.02 for each 1000 psi of strength in excess of 8000 psi, but βs shall not be taken less than 0.80. A.3.2.2 For struts located such that the width of the midsection of the strut is larger than the width at the nodes (bottle-shaped struts):

(a) with reinforcement satisfying A.3.3, βs = 0.75; and (b) without reinforcement satisfying A.3.3, βs = 0.6 shall be taken as the smaller of: (a) 0.6 λ; and (b) the product of β fcβαt , where β fc = 1 – f c′ /30,000, but β fc shall not be taken less than 0.60.

β α t =

1 ---------------------------------3 1 + 0.1cot α st

and λ is given in 11.7.4.3. In the case of members subjected to point loads with single struts connecting the load and reaction point, the angle of inclination of the strut may be approximated as

cot

αs

a = -----v d

A.3.2.3 For struts in tension members, or the tension flanges of members, βs = 0.40 A.3.2.4 For all other cases, βs = 0.60

Acknowledgments Thanks are due to the Carpenters Contractors Cooperation Committee, Inc., of Los Angeles, Calif., for sponsoring Innov ation Task Group 4 and to Joseph C. Sanders for acting as liaison with that group. The members of ITG 4 are indebted to the following individuals for their review of portions of this document and for their constructive comments: R. J. Frosch, M. E. Kreger, D. A. Kuchma, J. M. LaFave, J. A. Ramirez, J. W. Wallace, and S. L. Wood. O. Bayrak is owed many thanks for his input related to stress block parameters. M. Saatcioglu made numerous contributions related to stress block parameters and column confinement, which are gratefully acknowledged.

CHAPTER 11—CITED REFERENCES Abrams, D. P., 1987, “Influence of Axial Force Variations on Flexural Behavior of Reinforced Concrete Columns,” ACI Structural Journal, V. 84, No. 3, May-June, pp. 246-254. ACI Committee 301, 2005, “Specifications for Structural Concrete (ACI 301-05),” American Concrete Institute, Farmington Hills, Mich., 49 pp. ACI Committee 318, 1983, “Building Code Requirements for Reinforced Concrete (ACI 318-83),” American Concrete Institute, Farmington Hills, Mich., 155 pp. ACI Committee 318, 1989, “Building Code Requirements for Reinforced Concrete (ACI 318-89) and Commentary (318R-89),” American Concrete Institute, Farmington Hills, Mich., 347 pp. ACI Committee 318, 2002, “Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (318R-02),” American Concrete Institute, Farmington Hills, Mich., 443 pp. ACI Committee 318, 2005, “Building C ode Requirements for Structural Concrete (ACI 318-05) and Commentary (318R-05),” American Concrete Institute, Farmington Hills, Mich., 430 pp. ACI Committee 363, 1992, “Report on High-Strength Concrete (ACI 363R-92),” American Concrete Institute, Farmington Hills, Mich., 56 pp. ACI Committee 408, 2003, “Bond and Development of Straight Reinforcing Bars in Tension (ACI 408R-03),” American Concrete Institute, Farmington Hills, Mich., 49 pp. ACI Innovation Task Group 4, 2006, “Materials and Quality Considerations for High-Strength Concrete in Moderate to High Seismic Applications (ITG-4.2R-06),” American Concrete Institute, Farmington Hills, Mich., 26 pp. Ahmad, S. H.; Khaloo, A. R.; and Poveda, A., 1986, “Shear Capacity of Reinforced High-Strength Concrete Beams,” ACI JOURNAL, Proceedings V. 83, No. 2, Mar.Apr., pp. 297-305. Ahmad, S. H., and Lue, D. M., 1987, “Flexure-Shear Interaction of Reinforced High-Strength Concrete Beams,” ACI Structural Journal, V. 84, No. 4, July-Aug., pp. 330-341. Ahmad, S. H., and Shah, S., 1982, “Stress-Strain Curves of Concrete Confined by Spiral Reinforcement,” ACI JOURNAL , Proceedings V. 79, No. 6, Nov.-Dec., pp. 484-490. Aoyama, H., 1993, “Design Philosophy for Shear in Earthquake Resistance in Japan,” Earthquake Resistance


of Reinforced Concrete Structures, A Volume Honoring Hiroyuki Aoyama, University of Tokyo, pp. 407-418. Aoyama, H.; Murota, T.; Hiraishi, H.; and Bessho, S., 1990, “Outline of the Japanese National Project on Advanced Reinforced Concrete Buildings with HighStrength and High-Quality Materials,” Proceedings of the Second International Symposium on High Strength Concrete , SP-121, W. T. Hester, ed., American Concrete Institute, Farmington Hills, Mich., pp. 21-32. Architectural Institute of Japan (AIJ), 1994, “Design for Earthquake Resistant Reinforced Concrete Buildings Based on Ultimate Strength Concept, with Commentary,” 337 pp. ASCE/SEI, 2006, “Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-05),” Structural Engineering Institute, American Society of Civil Engineers, Reston, Va., 424 pp. Azizinamini, A.; Baum Kuska, S.; Brungardt, P.; and Hatfield, E., 1994, “Seismic Behavior of Square HighStrength Concrete Columns,” ACI Structural Journal, V. 91, No. 3, May-June, pp. 336-345. Azizinamini, A.; Darwin, D.; Eligehausen, R.; Pavel, R.; and Ghosh, S. K., 1999a, “Proposed Modifications to ACI 318-95 Tension Development and Lap Splice for HighStrength Concrete,” ACI Structural Journal, V. 96, No. 6, Nov.-Dec., pp. 922-926. Azizinamini, A.; Pavel, R.; Hatfield, E.; and Ghosh, S. K ., 1999b, “Behavior of Lap-Spliced Reinforcing Bars Embedded in High-Strength Concrete,” ACI Structural Journal, V. 96, No. 5, Sept.-Oct., pp. 826-835. Azizinamini, A.; Stark, M.; Roller, J. J.; and Ghosh, S. K., 1993, “Bond Performance of Reinforcing Bars Embedded in High-Strength Concrete,” ACI Structural Journal, V. 90, No. 5, Sept.-Oct., pp. 554-561. Bae, S., and Bayrak, O., 2003, “Stress Block Parameters for High-Strength Concrete Members,” ACI Structural Journal, V. 100, No. 5, Sept.-Oct., pp. 626-636. Bassapa, R. H., and Rangan, B. V., 1995, “Strength of High Strength Concrete Columns under Eccentric Compression,” Research Report No. 2/95, School of Civil Engineering, Curtin University of Technology, Perth, Australia. Bayrak, O., 1999, “Seismic Performance of Rectilinearly Confined High Strength Concrete Columns,” PhD dissertation, University of Toronto, Toronto, Ontario, Canada. Bayrak, O., and Sheikh, S., 1998, “Confinement Reinforcement Design Considerations for Ductile HSC Columns,” Journal of Structural Engineering, V. 124, No. 9, pp. 999-1010. Bjerkeli, L.; Tomaszewicz, A.; and Jensen A. A., 1990, “Deformation Properties and Ductility of High Strength Concrete,” Proceedings, Second International Symposium on High-Strength Concrete, SP-121, W. T. Hester, ed., American Concrete Institute, Farmington Hills, Mich., pp. 215-238. BOCA, 1993, “The BOCA National Building Code,” Building Officials and Code Administrators International, Country Club Hills, Ill. Brachmann, I.; Browning, J.; and Matamoros, A., 2004a, “Drift-Dependent Confinement Requirements for Reinforced Concrete Columns under Cyclic Loading,” ACI Structural Journal, V. 101, No. 5, Sept.-Oct., pp. 669-677.

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Brachmann, I.; Browning, J.; and Matamoros, A., 2004b, “Relationship Between Drift and Confinement in Reinforced Concrete Columns Under Cyclic Loading,” Proceedings, 13th World Conference in Earthquake Engineering, Vancouver, British Columbia, Canada, 15 pp. Browning, J., 2001, “Proportioning of EarthquakeResistant RC Building Structures,” Journal of Structural Engineering, ASCE, V. 127, No. 2, pp. 145-151. BSSC, 2004, “NEHRP Recommended Provisions for New Buildings and Other Structures Part 2: Commentary (FEMA 450),” 2003 Edition, Building Seismic Safety Council, National Institute of Building Sciences, Washington, D.C. C4 Committee, 2000, “High Strength Concrete Research,” Carpenters/Contractors Cooperation Committee, Inc., Los Angeles, Calif. Canadian Standards Association, 1994, “Design of Concrete Structures for Buildings (CAN3-A23.3-94),” Rexdale, Ontario, Canada. Ciampi, V.; Eligehausen, R.; Bertero, V. V.; and Popov, E. P., 1982, “Analytical Model for Deformed Bar Bond Under Generalized Excitations,” UCB/EERC Report No. 82/ 23, Earthquake Engineering Research Center, University of California at Berkeley, Berkeley, Calif. Collins, M., and Kuchma, D., 1999, “How Safe Are Our Large, Lightly Reinforced Concrete Beams, Slabs, and Footings?” ACI Structural Journal, V. 96, No. 4, July-Aug., pp. 482-490. Collins, M. P.; Mitchell, D.; and MacGregor, J. G., 1993, “Structural Design Considerations for High-Strength Concrete,” Concrete International, V. 15, No. 5, May, pp. 27-34. Comité Euro-International du Béton (CEB), 1988, “CEB-FIP Model Code 1990—First Predraft (1988),” Bulletin d’Information No. 190a/190b, Lausanne, Switzerland. Comité Euro-International du Béton (CEB), 1993, “CEB-FIP Model Code 1990,” Bulletin d’Information No. 213/214, Lausanne, Switzerland. Cusson, D., and Paultre, P., 1994, “High-Strength Concrete Columns Confined by Rectangular Ties,” Journal of Structural Engineering, ASCE, V. 120, No. 3, pp. 783-804. Cusson, D., and Paultre, P., 1995, “Stress-Strain Model for Confined High-Strength Concrete,” Journal of Structural Engineering, ASCE, V. 121, No. 3, pp. 468-477. Darwin, D.; Zuo, J.; Tholen, M. L.; and Idun, E. K., 1996, “Development Length Criteria for Conventional and High Relative Rib Area Reinforcing Bars,” ACI Structural Journal, V. 93, No. 3, May-June, pp. 347-359. Durrani, A. J., and Wight, J. K., 1982, “Experimental and Analytical Study of Internal Beam to Column Connections Subjected to Reversed Cyclic Loading,” Report No. UMEE 82R3, Department of Civil Engineering, University of Mich., Ann Arbor, Mich., 275 pp. Elwood, K., 2002, “Shake Table Tests and Analytical Studies on the Gravity Load Collapse of Reinforced Concrete Frames,” PhD dissertation, Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, Calif.

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Elwood, K., and Moehle, J., 2005, “Axial Capacity Model for Shear-Damaged Columns,” ACI Structural Journal, V. 102, No. 4, July-Aug., pp. 578-587. Elzanaty, A. H.; Nilson, A. H.; and Slate, F. O., 1986, “Shear Capacity of Reinforced Concrete Beams Using HighStrength Concrete,” ACI JOURNAL, Proceedings V. 83, No. 2, Mar.-Apr. pp. 290-296. Fafitis, A., and Shah, S. P., 1985, “Lateral Reinforcement for High Strength Concrete Columns,” High Strength Concrete, SP-87, H. G. Russell, ed., American Concrete Institute, Farmington Hills, Mich., pp. 213-232. Fasching, C. J., and French, C. E., 1998, “Effect of HighStrength Concrete (HSC) on Flexural Members,” HighStrength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 137-178. Foster, S. J., and Attard, M. M., 1997, “Experimental Tests on Eccentrically Loaded High-Strength Concrete Columns,” ACI Structural Journal, V. 94, No. 3, May-June, pp. 295-303. Fujii, S.; Noguchi, H.; and Morita, S., 1998, “Bond and Anchorage of Reinforcement in High-Strength Concrete,” High-Strength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 23-43. Ghosh, S. K.; Domel, A. W.; and Fanella, D. A., 1995, Design of Concrete Buildings for Earthquake & Wind Forces, 2nd Edition, Portland Cement Association, Skokie, Ill. Ghosh, S. K., and Saatcioglu, M., 1994, “Ductility and Seismic Behavior,” High Performance Concrete: Properties and Applications, S. P. Shah and S. H. Ahmad, eds., McGraw Hill, 388 pp. Hibi, J.; Mihara, Y.; Otani, S.; and Aoyama H., 1991, “Behavior of Reinforced Concrete Columns Using High Strength Concrete after Flexural Yielding,” Transactions of the Japan Concrete Institute, V. 13, 1991, pp. 395-402. Hofbeck, J. A; Ibrahim, I. O.; and Mattock, A. H., 1969, “Shear Transfer in Reinforced Concrete,” ACI J OURNAL , Proceedings V. 66, No. 2, Feb., pp. 119-128. Hognestad, E., 1951, “A Study of Combined Bending and Axial Load in Reinforced Concrete Members,” Bulletin Series No. 399, University of Illinois Engineering Experiment Station, University of Illinois at Urbana-Champaign, Urbana, Ill., 128 pp. Hognestad, E.; Hanson, N. W.; and McHenry, D., 1955, “Concrete Stress Distribution in Ultimate Strength Design,” ACI JOURNAL , Proceedings V. 52, pp. 455-479. Hokuetsu Metal Co., 1990, “Design and Construction Guidelines for Reinforced Concrete Beams and Columns using High-Strength Shear Reinforcement UHY Hoops.” (in Japanese) Hsu, L. S., and Hsu, C. T., 1994, “Complete Stress-Strain Behavior of High-Strength Concrete Under Compression,” Magazine of Concrete Research, V. 46, No. 169, pp. 301-312. IBC, 2003, “International Building Code 2003,” published in cooperation by BOCA, ICBO, and SBCCI, International Code Council, Falls Church, Va., 632 pp. Ibrahim, H., and MacGregor, J., 1994, “Flexural Behavior of High-Strength Concrete Columns,” Report No. 196,

Department of Civil Engineering, University of Alberta, Edmonton, Alberta, Canada, 197 pp. Ibrahim, H., and MacGregor, J., 1996a, “Tests of Eccentrically Loaded High-Strength Concrete Columns,” ACI Structural Journal, V. 93, No. 5, Sept.-Oct., pp. 585-594. Ibrahim, H., and MacGregor, J., 1996b, “Flexural Behavior of Laterally Reinforced High-Strength Concrete Sections,” ACI Structural Journal, V. 93, No. 6, Nov.-Dec., pp. 674-684. Ibrahim, H., and MacGregor, J., 1997, “Modification of the ACI Rectangular Stress Block for High-Strength Concrete,” ACI Structural Journal, V. 94, No. 1, Jan.-Feb., pp. 40-48. ICBO, 1997, Uniform Building Code, Whittier, Calif. ICBO, 2001, “Seismic Design Utilizing High-Strength Concrete,” ICBO ER-5536, ICBO Evaluation Service Inc., Whittier, Calif., http://www.icces.org/reports/pdf_files/ UBC/5536.pdf ISO, 1991, “Steels for the Reinforcement and Prestressing of Concrete,” Standard 6934-4:1991. Itakura, Y., and Yagenji, A., 1992, “Compressive Test on High-Strength R/C Columns and Their Analysis Based on Energy Concept,” Proceedings of 10th World Conference on Earthquake Engineering, Madrid, Spain, pp. 2599-2602. Japan Institute of Construction Engineering, Design Guidelines Committee, 1993, “New RC Structural Design Guidelines and Commentary,” Annual Report of New RC Project . (in Japanese) Japanese Standards Association, 1994, “Small SizeDeformed Steel Bars for Prestressed Concrete,” JIS G 3137:1994. Johnson, M. K., and Ramirez, J. A., 1989, “Minimum Amount of Shear Reinforcement in High-Strength Concrete Members,” ACI Structural Journal, V. 86, No. 4, July-Aug., pp. 376-382. Joint ACI-ASCE Committee 352, 2002, “Recommendations for Design of Beam-Column Connections in Monolithic Reinforced Concrete Structures (ACI 352R-02),” American Concrete Institute, Farmington Hills, Mich., 40 pp. Joint ACI-ASCE Committee 445, 1998, “Recent Approaches to Shear Design of Structural Concrete,” Journal of Structural Engineering, V. 124, No. 12, pp. 1375-1417. Kaar, P.; Hanson, N.; and Capell, H., 1977, “Stress-Strain Characteristics of High-Strength Concrete,” Report RD051.01D, Portland Cement Association, Skokie, Ill. Kabeyasawa, T., and Hiraishi, H., 1998, “Tests and Analyses of High-Strength Reinforced Concrete Shear Walls in Japan,” High-Strength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 281-310. Kato, D., 1991, “Stress-Strain Behaviors of Square Confined Reinforced Concrete Columns,” Journ al of Structural and Construction Engineering, No. 422, pp. 65-74. Kato, D., and Wakatsuki, K., 1992, “Effects of Hoop Ties on the Stress-Strain Relation of Square Confined R/C Columns,” Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, pp. 645-646. Kato, D.; Watanabe, F.; Nishiyama, M.; and Sato, H., 1998, “Confined Concrete with High-Strength Materials,”


High-Strength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 85-104. Kawasake Steel Techno-wire Co., 1990, “Design and Construction Guidelines of Reinforced Concrete Members using High-Strength Shear Reinforcement River Bon.” (in Japanese) Kimura, H.; Sugano, S.; and Nagashima, T., 1995, “Study of Flexural Strength and Ductility of R/C Columns Using High Strength Concrete,” Takenaka Technical Research Report No. 51, pp. 161-178. Kuchma, D.; Vegh, P.; Simionopoulous, K.; Stannik, B.; and Collins, M. P., 1997, “The Influence of Concrete Strength, Distribution of Longitudinal Reinforcement, and Member Size, on the Shear Strength of Reinforced Concrete Beams,” Bulletin d’Information No. 237, Lausanne Switzerland. Kobe Steel Ltd., 1989, “Design and Construction Guidelines for Reinforced Concrete Beams and Columns using High-Strength Shear Reinforcement D-Hoops.” (in Japanese) Lepage, A., 1997, “A Method for Drift-Control in Earthquake-Resistant Design of Reinforced Concrete Building Structures,” PhD thesis, University of Illinois at UrbanaChampaign, Urbana, Ill. Legeron, F., and Paultre, P., 2000, “Behavior of HighStrength Concrete Columns under Cyclic Flexure and Constant Axial Load,” ACI Structural Journal, V. 97, No. 4, July-Aug., pp. 591-601. Li, B., 1994, “Strength and Ductility of Reinforced Concrete Members and Frames Constructed Using High Strength Concrete,” Research Report 94-5, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Li, B., and Park, R., 2004, “Confining Reinforcement for High-Strength Concrete Columns,” ACI Structural Journal, V. 101, No. 3, May-June, pp. 314-324. Lipien, W., and Saatcioglu, M., 1997, “Tests of Square High-Strength Concrete Columns Under Reversed Cyclic Loading,” Research Report No. OCEERC 97-11, Ottawa Carleton Earthquake Engineering Research Centre, University of Ottawa, Ottawa, Ontario, Canada, 184 pp. Lloyd, N., and Rangan, B., 1996, “Studies on HighStrength Concrete Columns under Eccentric Compression,” ACI Structural Journal, V. 93, No. 6, Nov.-Dec., pp. 631-638. Lynn, A. C., 2001, “Seismic Evaluation of Existing Reinforced Concrete Building Columns,” PhD dissertation, Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, Calif. Mander, J.; Priestley, N.; and Park, R., 1988, “Theoretical Stress-Strain Model for Confined Concrete,” Journal of Structural Engineering, ASCE, V. 114, No. 8, pp. 1804-1826. Martinez, S.; Nilson, A.; and Slate, F., 1984, “Spirally Reinforced High-Strength Concrete Columns,” ACI JOURNAL , Proceedings V. 81, No. 5, Sept.-Oct., pp. 431-442. Matamoros, A.; Browning, J.; and Luft, M., 2003, “Evaluation of Simple Methods for Estimating Drift of Reinforced Concrete Buildings Subjected to Earthquakes,” Earthquake Spectra, V. 19, No. 4, pp. 839-861.

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Matamoros, A.; Garcia, L. E.; Browning, J.; and Lepage, A., 2004, “The Flat-Rate Design Method for Low- and Medium-Rise Reinforced Concrete Structures,” ACI Structural Journal, V. 101, No. 4, July-Aug., pp. 435-446. Matamoros, A., and Sozen, M., 2003, “Drift Limits of High-Strength Concrete Columns Subjected to Load Reversals,” Journal of Structural Engineering, ASCE, V. 129, No. 3, pp. 297-313. Mattock, A. H.; Li, W. K.; and Wang, T. C., 1976, “Shear Transfer in Lightweight Reinforced Concrete,” PCI Journal, V. 21, No. 1, pp. 20-39. McCabe, S., 1998, “Bond and Development of Steel Reinforcement in High-Strength Concrete—An Overview,” High-Strength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 1-21. Mphonde, A. G., and Frantz, G. C., 1984, “Shear Tests of High- and Low-Strength Concrete Beams without Stirrups,” ACI JOURNAL, Proceedings V. 81, No. 4, July-Aug., pp. 350-357. Mugumura, H.; Nishiyama, M.; Watanabe, F.; and Tanaka, H., 1991, “Ductile Behavior of High-Strength Concrete Columns Confined by High-Strength Transverse Reinforcement,” Evaluation and Rehabilitation of Concrete Structures and Innovations in Design, SP-128, V. M. Malhotra, ed., American Concrete Institute, Farmington Hills, Mich., pp. 877-891. Muguruma, H.; Nishiyama, M.; and Watanabe, F., 1993, “Stress-Strain Curve for Concrete with a Wide-Range of Compressive Strength,” Proceedings, Symposium on HighStrength Concrete, Norway, pp. 314-321. Muguruma, H., and Watanabe, F., 1990, “Ductility Improvement of High-Strength Concrete Columns with Lateral Confinement,” Proceedings, Second International Symposium on High-Strength Concrete, SP-121, W. T. Hester, ed., American Concrete Institute, Farmington Hills, Mich., pp. 47-60. Nagashima, T.; Sugano, S.; Kimura, H.; and Ichikawa, A., 1992, “Monotonic Axial Compression Test on Ultra-HighStrength Concrete Tied Columns,” Proceedings, 10th World Conference on Earthquake Engineering, Madrid, Spain, pp. 2983-2988. National Fire Protection Association, 2003, “NFPA 5000—NFPA Building Construction and Safety Code,” Quincy, Mass., 540 pp. Nedderman, H., 1973, “Flexural Stress Distribution in Very High Strength Concrete,” MASc Thesis, Department of Civil Engineering, University of Texas, Arlington, Tex. Neutren Co. Ltd., 1985, “Design Standard Using High Tensile Steel ULBON as Shear Reinforcement in Reinforced Concrete Beams and Columns.” Nielsen, M. P., 1999, “Limit Analysis and Concrete Plasticity,” New Directions in Civil Engineering, 2nd Edition, CRC Press, Boca Raton, Fla., 908 pp. Nilson, A., 1985, “Design Implications of Current Research on High-Strength Concrete,” High-Strength Concrete, SP-87, H. G. Russell, ed., American Concrete Institute, Farmington Hills, Mich., pp. 85-118.

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Nilson, A., 1994, “Structural Members,” High Performance Concrete: Properties and Applications , S. P. Shah and S. H. Ahmad, eds., McGraw-Hill. Nishiyama, M.; Fukushima, I.; Watanabe, F.; and Muguruma, H., 1993, “Axial Loading Tests on High-Strength Concrete Prisms Confined by Ordinary and High-Strength Steel,” Proceedings of the Symposium on High-Strength Concrete, Norway, pp. 322-329. Noguchi, H.; Fujii, S.; and Teraoka, M., 1998, “Shear Strength of Beam-Column Joints with High-Strength Materials,” High-Strength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 329-356. Otani, S., 1995, “Use of High-Strength Lateral Reinforcement in Japanese RC Construction,” Proceedings, Samsung Forum on Tall Buildings, Seoul, Korea. Otani, S.; Teshigawara, M.; Murakami, M.; and Okada, T., 1998, “New RC Design Guidelines for High-Rise Reinforced Concrete Buildings using High-Strength Materials,” HighStrength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 405-417. Ozbakkaloglu, T., and Saatcioglu, M., 2004, “Rectangular Stress Block for High-Strength Concrete,” ACI Structural Journal, V. 101, No. 4, July-Aug., pp. 475-483. Ozcebe, G.; Ersoy, U.; and Tankut, T., 1999, “Evaluation of Minimum Shear Reinforcement Requirements for Higher Strength Concrete,” ACI Structural Journal, V. 96, No. 3, May-June, pp. 361-368. Ozden, S., 1992, “Behavior of High-Strength Concrete under Strain Gradient,” MA thesis, University of Toronto, Toronto, Ontario, Canada. Park, R., 1998, “Design and Behavior of RC Columns Incorporating High-Strength Materials,” Concrete International , V. 20, No. 11, Nov., pp. 55-62. Park, R., and Priestley, M. J. N., 1982, “Ductility of Square-Confined Concrete Columns,” Journal of the Structural Division, ASCE, V. 108, No. 4, pp. 929-950. Park, R.; Tanaka, H.; and Li, B. , 1998, “Flexural Strength and Ductility of High-Strength Concrete Columns,” HighStrength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 237-257. Pastor, J.; Nilson, A.; and Slate, F., 1984, “Behavior of High-Strength Concrete Beams,” Research Report No. 84-3, Department of Structural Engineering, Cornell University, Ithaca, N.Y. Popovics, S., 1973, “Analytical Approach to Complete Stress-Strain Curves,” Cement and Concrete Research , V. 3, No. 5, pp. 583-599. Quintero-Febres, C. G., and Wight, J. K., 2001, “Experimental Study of Reinforced Concrete Interior Wide BeamColumn Connections Subjected to Lateral Loading,” ACI Structural Journal, V. 98, No. 4, July-Aug., pp. 572-582. Rangan, B. V.; Saunders, P.; and Seng, E., 1991, “Design of High-Strength Concrete Columns,” Evaluation and Rehabilitation of Concrete Structures and Innovations in Design,

SP-128, V. M. Malhotra, ed., American Concrete Institute, Farmington Hills, Mich., pp. 851-862. Razvi, S., and Saatcioglu, M., 1994, “Strength and Deformability of Confined High-Strength Concrete Columns,” ACI Structural Journal, V. 91, No. 6, Nov.-Dec., pp. 678-687. Razvi, S., and Saatcioglu, M., 1999, “Circular High-Strength Concrete Columns under Concentric Compression,” ACI Structural Journal, V. 96, No. 5, Sept.-Oct., pp. 817-825. Reineck, K.; Kuchma, D.; Sim, K.; and Marx, S., 2003, “Shear Database for Reinforced Concrete Members without Shear Reinforcement,” ACI Structural Journal, V. 100, No. 2, Mar.-Apr., pp. 240-249. Richart, F. E.; Brandtzaeg, A.; and Brown, R. L., 1929, “The Failure of Plain and Spirally Reinforced Concrete in Compression,” Bulletin No. 190 , University of Illinois Engineering Experiment Station, Urbana, Ill., 74 pp. Richart, F. E., and Brown, R. L., 1934, “An Investigation of Reinforced Concrete Columns,” Bulletin No. 267, University of Illinois Engineering Experiment Station, Urbana, Ill., 91 pp. Roller, J. J., and Russell, H. G., 1990, “Shear Strength of High-Strength Concrete Beams with Web Reinforcement,” ACI Structural Journal, V. 87, No. 2, Mar.-Apr., pp. 191-198. Roy, H. E. H., and Sozen, M. A., 1963, “A Model to Simulate the Response of Concrete to Multi-Axial Loading,” Structural Research Series No. 268, Department of Civil Engineering, University of Illinois. Saatcioglu, M., and Baingo, D., 1999, “Circular HighStrength Concrete Columns Under Simulated Seismic Loading,” Journal of Structural Engineering, ASCE, V. 125, No. 3, pp. 272-280. Saatcioglu, M., and Ozcebe, G., 1989, “Response of Reinforced Concrete Columns to Simulated Seismic Loading,” ACI Structural Journal, V. 86, No. 1, Jan.-Feb., pp. 3-12. Saatcioglu, M., and Razvi, S., 1992, “Strength and Ductility of Confined Concrete,” Journ al of Struc tural Engineering, ASCE, V. 118, No. 6, pp. 1590-1607. Saatcioglu, M., and Razvi, S., 1998, “High-Strength Concrete Columns with Square Sections under Concentric Compression,” Journal of Structural Engineering, ASCE, V. 124, No. 12, pp. 1438-1447. Saatcioglu, M., and Razvi, S., 2002, “Displacement-Based Design of Reinforced Concrete Columns for Confinement,” ACI Structural Journal, V. 99, No. 1, Jan.-Feb., pp. 3-11. Saatcioglu, M., Paultre, P.; and Ghosh, S. K., 1998, “Confinement of High-Strength Concrete,” High-Strength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 105-136. Sakaguchi, N.; Yamanobe, K.; Kitada, Y.; Kawachi, T.; and Koda, S., 1990, “Shear Strength of High-Strength Concrete Members,” Proceedings of the Second International Symposium on High-Strength Concrete, SP-121, W. T. Hester, ed., American Concrete Institute, Farmington Hills, Mich., pp. 155-178. Sakai, Y.; Hibi, J.; Otani, S.; and Aoyama, H., 1990, “Experimental Study of Flexural Behavior of Reinforced


Concrete Columns Using High Strength Concrete,” Transactions of the Japan Concrete Institute, V. 12, pp. 323-330. Saqan, E. I., and Kreger, M. E., 1998, “Evaluation of U.S. Shear Strength Provisions for Design of Beam-Column Connections Constructed with High-Strength Concrete,” High-Strength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 311-328. Sargin, M.; Ghosh, S. K.; and Handa, V., 1971, “Effect of Lateral Reinforcement Upon the Strength and Deformation Properties of Concrete,” Magazine of Con crete Resea rch , V. 23, No. 75-76, pp. 99-110. SBCCI, 1994, “Standard Building Code,” Southern Building Code Congress, Birmingham, Ala. Schade, J. E., 1992, “Flexural Concrete Stress in High Strength Concrete Columns,” MASc thesis, Department of Civil Engineering, University of Calgary, Calgary, Alberta, Canada, 156 pp. Sezen, H., 2002, “Seismic Response and Modeling of Reinforced Concrete Building Columns,” PhD dissertation, Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, Calif. Sheikh, S.; Shah, D.; and Khoury, S., 1994, “Confinement of High-Strength Concrete Columns,” ACI Structural Journal, V. 91, No. 1, Jan.-Feb., pp. 100-111. Sheikh, S. A., and Uzumeri, S. M., 1982, “Analytical Model for Concrete Confinement in Tied Columns,” Journal of Structural Engineering, ASCE, V. 108, No. 5, pp. 2703-2723. Shibata, A., and Sozen, M., 1976, “Substitute-Structure Method for Seismic Design in Reinforced Concrete,” Journal of Structural Divi sion , ASCE, V. 102, No. ST3, pp. 1-18. Shimazaki, K., 1988, “Strong Ground Motion Drift and Base Shear Strength Coefficient for R/C Structures,” Proceedings of the Ninth World Conference on Earthquake Engineering, Tokyo and Kyoto, Japan, pp. 165-170. Shimazaki, K., and Sozen, M., 1984, “Seismic Drift of Reinforced Concrete Structures,” Technical Research Report of Hazama-Gumi Ltd., pp. 145-166. Shin, S. W.; Kamara, M.; and Ghosh, S. K., 1990, “Flexural Ductility, Strength Prediction, and Hysteretic Behavior of Ultra-High-Strength Concrete Members,” Proceedings of the Second International Symposium on High-Strength Concrete, SP-121, W. T. Hester, ed., American Concrete Institute, Farmington Hills, Mich., pp. 239-264. Slater, W., and Lyse, I., 1931a, “Progress Report on Column Tests at Lehigh University,” ACI J OURNAL, Proceedings V. 2, No. 6, June, pp. 677-730. Slater, W., and Lyse, I., 1931b, “Progress Report on Column Tests at Lehigh University,” ACI J OURNAL, Proceedings V. 2, No. 7, July, pp. 791-835. Standards Association of New Zealand, 1995, “Concrete Design Standard, NZS 3101:1995, Part 1” and “Commentary on the Concrete Design Standard, NZS 3101:1995, Part 2,” Wellington, New Zealand. Sugano, S.; Nagashima, T.; Kimura, H.; Tamura, A.; and Ichikawa, A., 1990, “Experimental Studies on Seismic Behavior of Reinforced Concrete Members of High Strength

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Concrete,” Proceedings of the Second International Symposium on High-Strength Concrete, SP-121, W. T. Hester, ed., American Concrete Institute, Farmington Hills, Mich., pp. 61-87. Sumitomo Electrical Industries Ltd., 1989, “Design and Construction Guidelines for Reinforced Concrete Beams and Columns using High-Strength Shear Reinforcement SumiHoops.” (in Japanese) Sumitomo Metal Industries Ltd., 1989, “Design and Construction Guidelines for Reinforced Concrete Beams and Columns using High-Strength Shear Reinforcement D-Hoops.” (in Japanese) Sun, Y. P., and Sakino, K., 1993, “Ductility Improvement of Reinforced Concrete Columns with High-Strength Materials,” Transactions of the Japan Concrete Institute, V. 15, pp. 455-462. Sun, Y. P., and Sakino, K., 1994, “Effect of Confinement of Transverse Reinforcement on the Axial Behavior of Concrete,” Proceedings of the Japan Concrete Institute, V. 16, No. 2, pp. 449-454. Swartz, S.; Nikaeen, A.; Babu, H.; Periyakaruppan, N.; and Refai, T., 1985, “Structural Bending Properties of Higher Strength Concrete,” High Strength Concrete, SP-87, H. G. Russell, ed., American Concrete Institute, Farmington Hills, Mich., 288 pp. Thomsen, J., and Wallace, J., 1994, “Lateral Load Behavior of Reinforced Concrete Columns Constructed Using High-Strength Materials,” ACI Structural Journal, V. 91, No. 5, Sept.-Oct., pp. 605-615. Thorenfeldt, E., and Drangsholt, G., 1990, “Shear Capacity of Reinforced High-Strength Concrete Beams,” Proceedings of the Second International Symposium on High-Strength Concrete, SP-121, W. T. Hester, ed., American Concrete Institute, Farmington Hills, Mich., pp. 129-154. Tokyo Steel Co., 1994, “Design and Construction Guidelines for Reinforced Concrete Beams and Columns using High-Strength Shear Reinforcement SPR785.” (in Japanese) Uribe, C., and Alcocer, S., 2001, “Comportamiento de Vigas Peraltadas Diseñadas con el Modelo de Puntales y Tensores,” Informe Técnico CI/EIG-1012001, Centro Nacional de Prevención de Desastres, México, 248 pp. (in Spanish) Vecchio, F.; Collins, M.; and Aspiotis, J., 1994, “HighStrength Concrete Elements Subjected to Shear,” ACI Structural Journal, V. 91, No. 4, July-Aug., pp. 423-433. Von Ramin, M., and Matamoros, A., 2004, “Shear Strength of Reinforced Concrete Members Subjected to Monotonic and Cyclic Loads,” SM Report No. 72, University of Kansas Center for Research, Inc., Lawrence, Kans., 517 pp. Von Ramin, M., and Matamoros, A. B., 2006, “Shear Strength of Reinforced Concrete Members Subjected to Monotonic Loads,” ACI Structural Journal, V. 103, No. 1, Jan.-Feb., pp. 83-92. Wahidi, S. A., 1995, “Strength and Behavior of Reinforced Concrete Columns Made from High Performance Materials,” PhD dissertation, University of Texas at Austin, Austin, Tex., 299 pp.

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Wallace, J. W., 1998, “Behavior and Design of HighStrength RC Walls,” High-Strength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 259-279. Wallace, J. W., and Moehle, J. P., 1992, “Ductility and Detailing Requirements of Bearing Wall Buildings,” Journ al of Struct ural Engineeri ng , ASCE, V. 118, No. 6, pp. 1625-1644. Walraven, J.; Frenay, J.; and Pruijssers, A., 1987, “Influence of Concrete Strength and Load History on the Shear Friction Capacity of Concrete Members,” PCI Journal, V. 32, No. 1, Jan.-Feb., pp. 66-84. Warwick, W. B., and Foster, S. J., 1993, “Investigation into the Efficiency Factor Used in Non-Flexural Reinforced Concrete Member Design,” UNICIV Report No. R-320, School of Civil Engineering, University of South Wales, Kensington. Watanabe, F., and Ichinose, T., 1991, “Strength and Ductility Design of RC Members Subjected to Combined Bending and Shear,” Preliminary Proceedings, International Workshop on Concrete Shear in Earthquakes, University of Houston, Houston, Tex., pp. IV4-1 to IV4-10. Watanabe, F., and Kabeyasawa, T., 1998, “Shear Strength of RC Members with High-Strength Concrete,” HighStrength Concrete in Seismic Regions, SP-176, C. W. French and M. E. Kreger, eds., American Concrete Institute, Farmington Hills, Mich., pp. 379-396. Watanabe, F., and Muguruma, H., 1988, “Toward the Ductility Design of Concrete Members (Overview of Researches in Kyoto University),” Proceedings of Pacific Concrete Conference, New Zealand, pp. 89-100.

Wood, S. L., 1990, “Shear Strength of Low-Rise Reinforced Concrete Walls,” ACI Structural Journal, V. 87, No. 1, Jan.Feb., pp. 99-107. Wood, S.L., 1989, “Minimum Tensile Reinforcement Requirements in Walls,” ACI Structural Journal, V. 86, No. 5, Sept.-Oct., pp. 582-591. Xiao, Y., and Martirossyan, A., 1998, “Seismic Performance of High-Strength Concrete Columns,” Journal of Structural Engineering, ASCE, V. 124, No. 3, Mar., pp. 241-251. Xiao, Y., and Yun, H., 1998, “Full-Scale Experimental Studies on High-Strength Concrete Short Columns,” Report No. USC-SERP 98/05, University of Southern California, 97 pp. Yong, Y. K.; Nour, M. G.; and Nawy, E. G., 1988, “Behavior of Laterally Confined High-Strength Concrete under Axial Loads,” Journal of Structural Engineering, ASCE, V. 114, No. 2, pp. 332-351. Yoshimura, M., and Nakamura, T., 2002, “Axial Collapse of Reinforced Concrete Short Columns,” Proceedings of the Fourth U.S.-Japan Workshop on Performance-Based Earthquake Engineering Methodology for Reinforced Concrete Building Structures, Toba, Japan, Report No. PEER-2002/21, Pacific Earthquake Engineering Research Center, University of California at Berkeley, Berkeley, Calif., Oct., pp. 187-198. Zhu, S., and Jirsa, J. O., 1983, “A Study of Bond Deterioration in Reinforced Concrete Beam-Column Joints,” PMFSEL Report No. 83-1, Phil M. Ferguson Structural Engineering Laboratory, University of Texas at Austin, Austin, Tex., July, 69 pp. Zuo, J., and Darwin, D., 2000, “Splice Strength of Conventional and High Relative Rib Area Bars in Normal and High-Strength Concrete,” ACI Structural Journal, V. 97, No. 4, July-Aug., pp. 630-641.

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