ITG43r_07 Report on Structural Design and

ACI ITG-4.3R-07

Reported by ACI Innovation Task Group 4and Other Contributors

Report on Structural Design andDetailing for High-Strength Concrete inModerate to High Seismic Applications

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

Second PrintingDecember 2008

ISBN 978-0-87031-254-0

American Concrete Institute®

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ITG-4.3R-1

ACI Committee Reports, Guides, Standard Practices, andCommentaries are intended for guidance in planning,designing, executing, and inspecting construction. Thisdocument is intended for the use of individuals who arecompetent to evaluate the significance and limitations of itscontent and recommendations and who will acceptresponsibility for the application of the material it contains.The American Concrete Institute disclaims any and allresponsibility for the stated principles. The Institute shall notbe liable for any loss or damage arising therefrom.

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

ITG 4.3R-07, “Report on Structural Design and Detailing forHigh-Strength Concrete in Moderate to High Seismic Applica-tions,” presents a literature review on seismic design using high-strength concrete and provides recommendations for codechanges based on the tests reported in this literature. Forexample, column confinement recommendations are made onthe basis that a target design story drift ratio is 2.5%.

ACI 318, “Building Code Requirements for StructuralConcrete,” governs for the design and construction of buildingsand is applicable for designs using high-strength concrete inmoderate to high seismic applications. ITG 4.3R-07 does notsupersede ACI 318.

Users of ITG 4.3R-07 should not infer that the recommendationsit contains are future ACI 318 Code requirements.

Issued: December 18, 2008.

Report on Structural Design and Detailing forHigh-Strength Concrete in Moderate to

High Seismic ApplicationsReported by ACI Innovation Task Group 4 and Other Contributors

ACI ITG-4.3R-07

ACI ITG-4.3R presents a literature review on seismic design using high-strength concrete. The document is organized in chapters addressing thestructural design of columns, beams, beam-column joints, and structuralwalls made with high-strength concrete, and focuses on aspects most relevantfor seismic design. Each chapter concludes with a series of recommendedmodifications to ACI 318-05 based on the findings of the literature review.

The recommendations include proposals for the modification of the equiva-lent rectangular stress block, equations to calculate the axial strength ofcolumns subjected to concentric loading, column confinement requirements,

limits on the specified yield strength of confinement reinforcement, strutfactors, and provisions for the development of straight bars and hooks.

An accompanying standard, ITG-4.1, is written in mandatory languagein a format that can be adopted by local jurisdictions, and will allow buildingofficials to approve the use of high-strength concrete on projects that arebeing constructed under the provisions of ACI 301, “Specifications forStructural Concrete,” and ACI 318, “Building Code Requirements forStructural Concrete.”

ITG 4 has also developed another nonmandatory language document:ITG-4.2R. It addresses materials and quality considerations and is thesupporting document for ITG-4.1.

Keywords: bond; confinement; drift; flexure; high-strength concrete; high-yield-strength reinforcement; seismic application; shear; stress block; strut-and-tie.

CONTENTSChapter 1—Introduction, p. ITG-4.3R-2

1.1—Background1.2—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 block4.2—Stress intensity factor α14.3—Stress block depth parameter β14.4—Stress block area α1

Joseph M. Bracci D. Kirk Harman Adolfo Matamoros

Michael A. Caldarone Daniel C. Jansen Andrew W. Taylor

Other contributors

Dominic J. Kelly Andres Lepage Henry G. Russell

ACI Innovation Task Group 4

S. K. GhoshChair

ITG-4.3R-2 ACI COMMITTEE REPORT

4.5—Limiting strain εcu4.6—Axial strength of high-strength concrete columns4.7—Comparison of different proposals for rectangular

stress block4.8—Recommendations

Chapter 5—Confinement requirements for beams and columns, p. ITG-4.3R-19

5.1—Constitutive models for confined concrete5.2—Previous research and general observations5.3—Equations to determine amount of confinement

reinforcement required in columns5.4—Definition of limiting drift ratio on basis of expected

drift demand5.5—Use of high-yield-strength reinforcement for

confinement5.6—Maximum hoop spacing requirements for columns5.7—Confinement requirements for high-strength concrete

beams5.8—Maximum hoop spacing requirements for high-

strength concrete beams5.9—Recommendations

Chapter 6—Shear strength of reinforced concrete flexural members, p. ITG-4.3R-35

6.1—Shear strength of flexural members without shearreinforcement

6.2—Effect of compressive strength on inclined crackingload of flexural members

6.3—Effect of compressive strength on flexural memberswith intermediate to high amounts of transversereinforcement

6.4—Shear strength of members with low shear span-depth ratios

6.5—Calculation of shear strength of members subjectedto seismic loading

6.6—Use of high-strength transverse reinforcement6.7—Recommendations

Chapter 7—Development length/splices,p. ITG-4.3R-44

7.1—Design equations for development length of bars inhigh-strength concrete

7.2—Design equations for development length of hookedbars 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 joints8.2—Shear strength of exterior joints8.3—Shear strength of interior joints8.4—Effect of transverse reinforcement on joint shear

strength8.5—Development length requirements for beam-column

joints8.6—Recommendations

Chapter 9—Design of structural walls, p. ITG-4.3R-519.1—Boundary element requirements9.2—Shear strength of walls with low aspect ratios9.3—Minimum tensile reinforcement requirements in walls9.4—Recommendations

Chapter 10—List of proposed modifications toACI 318-05, p. ITG-4.3R-53

10.1—Proposed modifications to equivalent rectangularstress block

10.2—Proposed modifications related to confinement ofpotential plastic hinge regions

10.3—Proposed modifications related to bond and develop-ment of reinforcement

10.4—Proposed modifications related to strut-and-tiemodels

Acknowledgments, p. ITG-4.3R-56

Chapter 11—Cited references, p. ITG-4.3R-56

CHAPTER 1—INTRODUCTION1.1—Background

The origin of ACI Innovation Task Group (ITG) 4, High-Strength Concrete for Seismic Applications, can be tracedback to the International Conference of Building Officials(ICBO) (now International Code Council [ICC]) EvaluationReport ER-5536, “Seismic Design Utilizing High-StrengthConcrete” (ICBO 2001). Evaluation Reports (ER) are issuedby Evaluation Service subsidiaries of model code groups. AnER essentially states that although a particular method,process, or product is not specifically addressed by a particularedition of a certain model code, it is in compliance with therequirements of that particular edition of that model code.

ER-5536 (ICBO 2001), first issued in April 2001, wasgenerated by Englekirk Systems Development Inc. for theseismic design of moment-resisting frame elements usinghigh-strength concrete. High-strength concrete was definedas “normalweight concrete with a design compressivestrength greater than 6000 psi (41 MPa) and up to amaximum of 12,000 psi (83 MPa).” It was based on researchcarried out at the University of Southern California and theUniversity of California at San Diego to support buildingconstruction in Southern California using concrete withcompressive strengths greater than 6000 psi (41 MPa).

The Portland Cement Association performed a review* ofER-5536 and brought up several concerns that focused oninconsistencies between the evaluation report and existingindustry documents in two primary areas: material andstructural. Despite those concerns, it was evident that theevaluation report had been created because quality assuranceand design provisions were needed by local jurisdictions, suchas the City of Los Angeles, to allow the use of high-strengthconcrete without undue restrictions. ACI has assumed aproactive role in the development of such provisions with thegoal of creating a document that can be adopted nationwide.

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

STRUCTURAL DESIGN AND DETAILING FOR HIGH-STRENGTH CONCRETE IN SEISMIC APPLICATIONS ITG-4.3R-3

ACI considered its own Committee 363, High StrengthConcrete, to be the best choice to address the materials andquality aspects of the document, while ACI Subcommittee318-H, Structural Concrete Building Code—SeismicProvisions, was considered the best choice to address theseismic detailing aspects. Because 318-H is a subcommitteeof a code-writing body, the development of a technicaldocument of this kind is not part of its intended mission. Inaddition, producing a document through a technicalcommittee can be a lengthy process. Based on these limita-tions, a request was made to form an ITG that would have theadvantage of following a shorter timeline to completion. Inresponse to the request, the Technical Activities Committee(TAC) of ACI approved the formation of ITG 4 and estab-lished its mission. The mission was to develop an ACI docu-ment that addressed the application of high-strength concretein structures located in areas of moderate and high seismicity.The document was intended to cover structural design, mate-rial properties, construction procedures, and quality-controlmeasures. It was to contain language in a format that allowedbuilding officials to approve the use of high-strength concretein 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 whenU.S. seismic codes divided the country into seismic zones.These seismic zones were defined as regions in whichseismic ground motion on rock, corresponding to a certainprobability of occurrence, remained within certain ranges.Present-day seismic codes (ASCE/SEI 2006) follow adifferent approach to characterizing a seismic hazard. Giventhat public safety is a primary code objective, and that not allbuildings in a given seismic zone are equally crucial topublic safety, a new mechanism for triggering seismicdesign requirements and restrictions, called the seismicperformance category (SPC), was developed. The SPCclassification includes not only the seismicity at the site, butalso the occupancy of the structure.

Recognizing that building performance during a seismicevent 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 arebased on seismic design categories (SDC). The SDC is afunction of location, building occupancy, and soil type.The TAC Technology Transfer Committee (TTTC)-estab-lished mission of ITG 4 was interpreted to mean that theTask Group was to address the application of high-strengthconcrete 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 SafetyCode” (2003).

SPC or SDC C is also referred to as the “intermediate”category. Similarly, SPC D and E or SDC D, E, and F arereferred to as “high” categories. The terminology “moderateto high seismic applications,” however, is used throughoutthis document.

1.2—ScopeThis document addresses the material and design consider-

ations when using normalweight concretes having specifiedcompressive strengths of 6000 psi (41 MPa) or greater instructures designed for moderate to high seismic applications.Irrespective of seismic zone, SPC, or SDC, this document isalso applicable to normalweight high-strength concrete inintermediate or special moment frames and intermediate orspecial structural walls as defined in ACI 318-05 (ACICommittee 318 2005).

The term “high-strength concrete,” as defined by ACI 363R-92(ACI Committee 363 1992), refers to concrete having a spec-ified compressive strength for design of 6000 psi (41 MPa) orgreater. The 6000 psi (41 MPa) threshold that was chosen forthis document is similar to that adopted by ACI Committee 363.

Even though high-strength concrete is defined based on athreshold compressive strength, the concept of high strengthis relative. The limit at which concrete is considered to behigh strength depends largely on the location in which it isbeing used. In some regions, structures are routinely designedwith concrete having specified compressive strengths of12,000 psi (83 MPa) or higher, whereas in other regions,concrete with a much lower specified compressive strength isconsidered high strength. Essentially, the strength thresholdat which concrete is considered high strength depends onregional factors, such as the characteristics and availabilityof raw materials, production capabilities, testing capabilities,and experience of the ready mixed concrete supplier.

ITG-4 produced three documents: ITG-4.1 is a referencespecification that can be cited in the project specifications;ITG-4.2R addresses materials and quality considerations thatare the basis for the ITG-4.1 specification; and ITG-4.3R, thisdocument, addresses structural design and detailing. Certainmodifications of ACI 318 requirements are proposed inChapter 10 of ITG-4.3R.

From a materials perspective, there are few differencesbetween the properties of high-strength concrete used inseismic applications and those of high-strength concreteused in nonseismic applications; therefore, the informationpresented in ITG-4.1 and ITG-4.2R is generally applicable toall high-strength concrete. When special considerations arewarranted due to seismic applications, they are addressedspecifically. Unlike ITG-4.1 and ITG-4.2R, most of thematerial contained in ITG-4.3R is specific to seismicapplications of high-strength concrete structural members.

The information in Chapters 4 through 9 of this documentis presented in a report format. Chapter 10 containssuggested modifications to design and detailing requirementsin ACI 318-05.

Some topics, such as compressive stress block andconfinement of beam-columns, are more developed than othersbecause there is significantly more literature available on these


topics. For all topics, an attempt was made to be as thorough aspossible in summarizing the most relevant informationpertaining to the design of members with high-strengthconcrete. For topics with limited information in the litera-ture, however, recommendations were made with the intentof preventing potentially unsafe design.

CHAPTER 2—NOTATIONAb,max = cross-sectional area of largest bar being

developed or spliced, in.2 (mm2)Acc = cross-sectional area of structural member

measured center-to-center of transversereinforcement, in.2 (mm2)

Ach = cross-sectional area of structural membermeasured out-to-out of transverse reinforcement,in.2 (mm2)

Acv = gross area of concrete section bounded by webthickness and length of section in direction ofshear force considered, in.2 (mm2)

Ag = gross area of concrete section, in.2 (mm2). Forhollow section, Ag is area of concrete only anddoes not include area of void(s)

Ash = total cross-sectional area of transverse reinforce-ment (including crossties) within spacing s andperpendicular to dimension bc, in.2 (mm2)

Asp = cross-sectional area of transverse reinforce-ment crossing potential plane of splitting ofbars being developed or spliced, in.2 (mm2)

Ast = total area of nonprestressed longitudinalreinforcement (bars or steel shapes), in.2 (mm2)

Asv = total area of vertical reinforcement in structuralwall, in.2 (mm2)

Aswb = total area of vertical reinforcement in boundaryelement of structural wall, in.2 (mm2)

Asww = total area of vertical reinforcement in web ofstructural wall, excluding the boundaryelements, in. 2 (mm2)

Ate = sum of areas of tie legs used to provide lateralsupport against buckling for longitudinal barsof column, in.2 (mm2)

Atr = total cross-sectional area of all transversereinforcement within spacing s that crossespotential plane of splitting through reinforcementbeing developed, in.2 (mm2)

Av = area of shear reinforcement with spacing s, in.2

(mm2)Aw = gross cross-sectional area of structural wall,

in.2 (mm2)av = shear span, equal to distance from center of

concentrated load to either: a) face of support forcontinuous or cantilever members; or b) center ofsupport for simply supported members, in.(mm)

b = width of compression face of member, in. (mm)bc = cross-sectional dimension of column core

measured center-to-center of outer legs oftransverse reinforcement comprising area Ash,in. (mm)

bw = web width or diameter of circular section, in.(mm)

c = distance from extreme compression fiber toneutral axis, in. (mm)

c′ = cmin + db /2 = spacing or cover dimension, in.(mm)

c1 = dimension of rectangular or equivalent rectan-gular column, capital, or bracket measured indirection of span for which moments are beingdetermined, in. (mm)

c2 = dimension of rectangular or equivalent rectan-gular column, capital, or bracket measured indirection perpendicular to c1, in. (mm)

cb = smaller of: a) distance from center of bar orwire to nearest concrete surface; or b) one-halfcenter-to-center spacing of bars or wires beingdeveloped, in. (mm)

cc = clear cover of reinforcement, in. (mm)ccb = least distance from surface or reinforcement to

tension face, in. (mm)cmax = maximum of ccb and cs , in. (mm)cmin = minimum cover used in expressions for bond

strength of bars not confined by transversereinforcement. Smaller of ccb and cs, in. (mm)

cp = ρvr · fyt /fc′ = volumetric confinement indexcs = minimum of cso and (csi + 0.25) in. [(csi + 6.35)

mm], in. (mm)csfw = flexural stress index for structural wall that

represents measure of ratio of neutral axisdepth to length of wall, in. (mm)

csi = one-half of clear spacing between bars, in. (mm)cso = clear side concrete cover for reinforcing bar,

in. (mm)DRlim = (Δlim /hcol) = limiting drift ratiod = distance from extreme compression fiber to

centroid of longitudinal tension reinforcement,in. (mm)

db = nominal diameter of bar, wire, or prestressingstrand, in. (mm)

ds = nominal diameter of bar used as transversereinforcement, in. (mm)

E = load effects of earthquake or related internalmoments and forces

EEp = [(Mcalc – Mexp)/Mexp] × 100 = parameter usedto characterize accuracy of nominal momentstrength of column

Es = modulus of elasticity of reinforcement andstructural steel, psi (MPa)

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

fco′ = in-place strength of unconfined concrete incolumns, psi (MPa) (often assumed as 0.85fc′ )

fp = P/Ag fc′ = axial load ratiofpc = P/Ach fc′ = axial load ratio based on area of

confined corefs = calculated tensile stress in reinforcement at

service loads, psi (MPa)


ft,l = stress imposed on concrete by compressionfield associated with reinforcement oriented indirection parallel to flexural reinforcementlocated at edge of compression field, psi (MPa)

ft,t = stress imposed on concrete by compressionfield associated with reinforcement oriented indirection perpendicular to flexural reinforcementlocated at edge of compression field, psi (MPa)

fu = maximum tensile stress that can be developedin bar with 90-degree hook, psi (MPa)

fyl = specified yield strength of longitudinal reinforce-ment, psi (MPa)

fyt = specified yield strength of transverse reinforce-ment, psi (MPa)

fyt,l = specified yield strength of transverse reinforce-ment oriented parallel to flexural reinforcementlocated at edge of uniform compression field,psi (MPa)

fyt,t = specified yield strength of transverse reinforce-ment oriented perpendicular to flexuralreinforcement located at edge of uniformcompression field, psi (MPa)

h′′ = core dimension perpendicular to transversereinforcement providing confinement measuredto outside of hoops, in. (mm)

ha = tie depth, in. (mm)hcol = clear column height, in. (mm)hw = height of entire wall from base to top or height

of segment of wall considered, in. (mm)hx = maximum center-to-center horizontal spacing

of crossties or hoop legs on all faces of column,in. (mm)

j = ratio of internal lever arm to effective depth ofbeam

Ktr = (Atr fyt/1500sn) = transverse reinforcementindex (refer to ACI 318-05, Section 12.2.3)

Ktr′ = (0.5tdAtr/sn)fc′1/2 = transverse reinforcement

index for Committee 408 development lengthexpression, in. (mm)

k1 = ratio of average to maximum stress incompression zone of flexural member

k2 = ratio of distance from extreme compressionfiber to location of compression reaction todistance from extreme compression fiber tolocation of neutral axis in flexural member

k3 = ratio of maximum stress in compression zoneof flexural member to cylinder strength

kcc = cover factor in calculation of developmentlength of hooked bars

kd = development length factor in calculation ofdevelopment length of hooked bars

kj = development length and lever arm factor in calcu-lation of development length of hooked bars

ks = transverse reinforcement bar diameter factorfor calculation of development length of hookedbars

lb = dimension of loading plate or support in axialdirection of member, in. (mm)

ld = development length in tension of deformed bar,deformed wire, plain or deformed welded wirereinforcement, or pretensioned strand, in. (mm)

ldh = development length in tension of deformedbar or deformed wire with standard hook,measured from critical section to outside end ofhook, in. (mm)

lo = length, measured from joint face along axis ofstructural member, over which special transversereinforcement must be provided, in. (mm)

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

M = maximum unfactored moment due to serviceloads, including P-Δ effects, in.-lb (N-mm)

Mexp = measured flexural strength of column, in.-lb(N-mm)

Mncol = nominal flexural strength of column, in.-lb(N-mm)

m = fyl /0.85fc′ = ratio of nominal yield strength oflongitudinal reinforcement to nominal strengthof concrete in column

n = number of bars being spliced or developed inplane of splitting

nL = number of legs of reinforcement in hoops and tiesP = unfactored axial load, lb (N)Po = nominal axial strength at zero eccentricity, lb (N)s = center-to-center spacing of items, such as longi-

tudinal reinforcement, transverse reinforcement,prestressing tendons, wires, or anchors, in. (mm)

so = center-to-center spacing of transverse reinforce-ment within length lo, in. (mm)

Tb = total bond force of developed or spliced bar,lb (N)

Ts = steel contribution to total bond force, additionalbond strength provided by transverse steel, lb (N)

td = term representing effect of bar size on TsV = maximum unfactored shear force at service

loads, including P-Δ effects, lb (N)Va = nominal shear strength provided by strut

spanning between load point and support inreinforced concrete members with shear span-depth ratios below 2.5, lb (N)

Vall = allowable shear force under service loads, lb (N)Vc = nominal shear strength provided by the concrete,

lb (N)Vn = nominal shear strength, lb (N)Vs = nominal shear strength provided by shear

reinforcement, lb (N)Vt,l = nominal shear strength provided by uniform

compression field associated with transversereinforcement oriented parallel to flexuralreinforcement located at edge of compressionfield, lb (N)

Vt,t = nominal shear strength provided by uniformcompression field associated with transversereinforcement oriented perpendicular to flexuralreinforcement located at edge of compressionfield, lb (N)


vc,all = allowable shear stress in concretewst = strut width, in. (mm)α1 = factor relating magnitude of uniform stress in

equivalent rectangular compressive stress blockto specified compressive strength of concrete

αc = coefficient defining relative contribution ofconcrete to nominal wall shear strength

αl = angle between struts and flexural reinforcementfor a compression field associated withtransverse reinforcement oriented in directionparallel to flexural reinforcement

αsh = 1 ≤ 4/[(M/Vd) +1] ≤ 2 = factor to account foreffect of shear span-depth ratio on allowableshear stress carried by concrete

αst = smallest angle between strut and ties that itintersects at its nodes

αt = angle between struts and flexural reinforcementfor compression field associated with transversereinforcement oriented in direction perpendicularto flexural reinforcement

β1 = factor relating depth of equivalent rectangularcompressive stress block to neutral axis depth

βfc = factor to account for effect of concretecompressive strength on effective compressivestrength of concrete in strut

βnl,strut = factor to account for effect of repeated loadreversals into nonlinear range of response oneffective compressive strength of concrete in strut

βnl,truss = factor to account for effect of repeated loadreversals into nonlinear range of response onshear strength associated with compression field

βs = factor to account for effect of cracking andconfining reinforcement on effectivecompressive strength of concrete in strut

βsc = factor to account for effect of load reversals,concrete compressive strength, confiningreinforcement, and cracking on effectivecompressive strength of concrete in strut

βta = factor to account for effect of interactionbetween truss and arch mechanisms on effectivecompressive strength of concrete in strut

βαt = factor to account for effect of angle of inclinationof strut αs on effective compressive strength ofconcrete in strut

χ1 = ratio of mean concrete compressive stresscorresponding to maximum axial load resistedby concentrically loaded column to specifiedcompressive strength of concrete

Δlim = lateral drift corresponding to 20% reduction inlateral resistance, in. (mm)

Δyield = lateral drift corresponding to yielding oflongitudinal reinforcement, in. (mm)

δu = design displacement, in. (mm)ε1 = principal tensile strain in strutεcu = maximum strain at extreme compression fiber

at onset of crushing of concreteεlim = concrete strain at extreme compression fiber

corresponding to limit state being considered

εo = strain in concrete when it reaches peak stressεs = strain demand on reinforcementεy = strain in reinforcement at yieldφ = strength reduction factorφlim = limiting curvature of reinforced concrete wallφu = curvature at limit state of reinforced concrete

sectionφy = curvature at yielding of flexural reinforcement

of reinforced concrete sectionγvj = joint shear coefficientλp = factor to account for effect of axial load ratio

on strength of compression field subjected torepeated load reversals into nonlinear range ofresponse

μΔ = (Δlim /Δyield) = displacement ductility ratioθp = expected rotation in plastic hinge region of

flexural member, radiansρarea = ratio of area of distributed transverse reinforce-

ment Ash to gross area of concrete perpendicularto that reinforcement in members with rectilinearand circular transverse reinforcement

ρl = ratio of area of distributed longitudinal reinforce-ment to gross concrete area perpendicular tothat reinforcement

ρs = ratio of volume of spiral reinforcement to totalvolume of core confined by spiral (measuredout-to-out of spirals)

ρt = ratio of area of distributed transverse reinforce-ment to gross concrete area perpendicular tothat reinforcement

ρtc = Ash/bcs = ratio of area of distributed transversereinforcement Ash to area of core perpendicularto that transverse reinforcement

ρt,l = ratio of area of distributed reinforcementoriented in direction parallel to flexural reinforce-ment of compression field to gross concrete areaperpendicular to that reinforcement

ρt,t = ratio of area of distributed reinforcementoriented in direction perpendicular to flexuralreinforcement of compression field to grossconcrete area perpendicular to that reinforcement

ρvol = ratio of volume of rectilinear or circulartransverse reinforcement to volume of coreconfined by that transverse reinforcement

ρvr = ratio of volume of rectilinear transversereinforcement to volume of core confined bythat transverse reinforcement

ρwt = ratio of total area of vertical reinforcement togross area of structural wall

ωc = 0.1(cmax/cmin) + 0.9 ≤ 1.25 = factor to accountfor ratio of maximum to minimum cover ondevelopment length of straight bar

ψe = factor used to modify development lengthbased on reinforcement coating

ψs = factor used to modify development lengthbased on reinforcement size

ψt = factor used to modify development lengthbased on reinforcement location


CHAPTER 3—DEFINITIONSarea transverse reinforcement ratio—ratio of the area

of transverse reinforcement crossed by a plane perpendicularto the legs of the transverse reinforcement to the area ofreinforced concrete along that plane.

axial load ratio—ratio of axial load to the product ofcompressive strength of concrete and the gross area ofconcrete cross section.

confinement index—product of transverse reinforcementratio (either by area or by volume) and the yield strength ofthe transverse reinforcement, divided by the compressivestrength of concrete.

curvature ductility ratio—ratio of mean curvature atfailure in the plastic hinge length to curvature at the onset ofsection yielding. In the case of reinforced concrete columns,the majority of researchers referenced in this documentdefine failure as a 20% reduction in lateral load resistance.

displacement ductility ratio—ratio of displacement atfailure to displacement at the onset of member yielding. Inthe case of reinforced concrete columns, the majority ofresearchers referenced in this document define failure as a20% reduction in lateral load resistance.

ductility—ability of a reinforced concrete member tomaintain its strength when subjected to repeated load reversalsbeyond the linear range of response.

interstory drift—relative lateral displacement betweentwo adjacent stories of a building imposed by the designearthquake.

interstory drift ratio—ratio of interstory drift to storyheight.

killed steel—steel made by completely removing or tyingup the oxygen in the liquid steel through the addition ofelements such as aluminum or silicon before the ingotsolidifies, with the objective of achieving maximum uniformityin the steel.

limiting drift—drift corresponding to a 20% reduction inlateral load resistance of a reinforced concrete member subjectedto load reversals with increasing maximum displacements.

limiting drift ratio—ratio of limiting drift to columnheight.

limiting strain—maximum strain at the extreme concretecompression fiber of a flexural member at the onset ofconcrete crushing, εcu.

volumetric transverse reinforcement ratio—ratio of thevolume of transverse reinforcement confining the concretecore of a potential plastic hinge region to the volume ofconcrete inside the confined core.

CHAPTER 4—DESIGN FOR FLEXURALAND AXIAL LOADS USING EQUIVALENT

RECTANGULAR STRESS BLOCKIt is common practice for structures assigned to a high

Seismic Design Category (SDC) to proportion the majorityof the structural elements of the lateral force-resisting systemso that the axial load demand remains below the balancedaxial load. For these elements, variations in the shape of thestress block related to the compressive strength of theconcrete do not have a significant effect on the calculated

strength. There are instances, however, in which it is difficultfor engineers to avoid proportioning columns with high axialload 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. Forthese elements, the shape of the stress block may have asignificant effect on the estimated strength. The stress blockfor members with high-strength concrete is also a concern inmoderate seismic applications. In these cases, structures areproportioned for seismic events that impose lower force anddeformation demands than high seismic applications, allowingthe use of more slender columns.

The accuracy of the stress block is of concern in earth-quake-resistant design because overestimating the flexuralstrength of columns leads to overestimating the ratios ofcolumn-to-beam moment strengths, which increases theprobability of hinging in the columns due to the developmentof a strong beam-weak column mechanism.

Although the stress-strain characteristics of high-strengthconcrete are different from those of normal-strengthconcrete, there is no well-defined compressive strengthboundary between the two; there is instead a gradual changewith increasing concrete strengths (ACI Innovation TaskGroup 4 2006). The ascending branch of the stress-strainrelationship is steeper for higher-strength concretes, indicatinghigher elastic modulus. It changes from approximately asecond-order parabola for concretes within the normal-strength range to almost a straight line as the strengthapproaches 18,000 psi (124 MPa), which may be consideredas the limit for high-strength concrete made with ordinarylimestone aggregates. The strain at peak concrete stress, εo,increases with strength as well, varying approximatelybetween 0.0015 and 0.0025 for 3000 to 15,000 psi (21 and103 MPa) concrete, respectively. Failure becomes more suddenand brittle as the concrete strength increases and unloadingbeyond the peak becomes more rapid. In summary, concretebecomes more rigid and more brittle with increasing strength.

Several researchers developed constitutive models for thestress-strain relationship of concrete that are applicable tohigh-strength concrete with proper adjustments to thegoverning parameters (Popovics 1973; Yong et al. 1988;Hsu and Hsu 1994; Azizinamini et al. 1994; Cusson andPaultre 1995). Expressions applicable specifically to high-strength concrete have also been developed (Martinez et al.1984; Fafitis and Shah 1985; Bjerkeli et al. 1990; Mugurumaand Watanabe 1990; Li 1994).

Members subjected to uniform compression attain theirmaximum strength when concrete reaches a strain levelcorresponding to peak stress, εo. Under a strain gradient,maximum strength is attained at an extreme compressivefiber strain higher than that at peak stress, εlim (Hognestad1951). This value changes with the geometric shape of thecompression zone, and may also vary significantly withconcrete strength and confinement. After the limiting strainhas been established, the sectional strength can be computedby evaluating internal forces, including the compressiveforce in the concrete. The magnitude of the compressiveforce in the concrete can be established by relying on the


assumption that plane sections remain plane after bendingand by calculating the stresses corresponding to the strains inthe compression zone from the stress-strain relationship.Because it is cumbersome to use a nonlinear stress-strainrelationship, ACI 318-05 provides an equivalent stress blockfor ease in design calculations. This stress block is derivedsuch that both the area under the actual nonlinear stressdistribution (force) and the centroid of this area (point ofapplication of force) correspond to those of the stress blockas closely as possible. The stress block adopted by ACI 318-05is of rectangular geometry. Other equivalent stress blockswith various different shapes, such as triangular and trape-zoidal, have been proposed in the literature. A historicalreview of this topic has been presented by Hognestad (1951).

4.1—Parameters of equivalent rectangularstress block

The column design provisions of ACI 318-05 are based onan extensive column investigation conducted jointly by theUniversity of Illinois, Lehigh University, and ACI. Theinitial results of the study were published in 1931 (Slater andLyse 1931a,b), with a more comprehensive follow-up reportin 1934 (Richart and Brown 1934). Subsequently,Hognestad (1951) conducted a large number of column testsand developed the parameters for a rectangular stress block.

Figure 4.1 shows the parameters that define the equivalentrectangular stress block according to ACI 318-05. A parabolicstress distribution, shown in Fig. 4.1(b), results in values ofk2 = 0.375 (β1 = 0.75) and k1 = 0.67 (α1 = 0.9k3). A linearstress distribution yields values of k2 = 0.333 (β1 = 0.667)and k1 = 0.50 (α1 = 0.75k3). ACI 318-05 stipulates that theaverage stress factor α1 is not sensitive to compressive strengthand remains constant at 0.85, while the β1 factor decreasesfrom 0.85 (k1k3 = 0.723) for a compressive strength of 4000psi (28 MPa) to 0.65 (k1k3 = 0.553) for a compressivestrength of 8000 psi (55 MPa). According to ACI 318-05, thestrain at the extreme compression fiber in the concrete at theonset of crushing is 0.003 (Fig. 4.1(a)).

Fasching and French (1998) presented a summary ofseveral proposals for modifying the parameters of the equivalent

rectangular stress block for high-strength concrete. Theyreported average values of k2 = 0.381 (β1 = 0.762) and k1k3= 0.647 (α1 = 0.849) from tests of C-shaped specimens(column specimens in which axial load and bending areinduced by applying a load eccentrically at both ends) byseveral researchers, in which compressive strengths variedfrom 8400 to 14,400 psi (58 to 99 MPa). The aforementionedvalues are very close to those corresponding to a parabolicdistribution. Specimens with higher strengths tested byIbrahim and MacGregor (1994, 1996a), with concretecompressive strengths ranging between 17,600 and 18,600 psi(121 to 128 MPa), had values of k2 = 0.347 (β1 = 0.694) andk1k3 = 0.524 (α1 = 0.755), close to those corresponding to alinear distribution. Ozbakkaloglu and Saatcioglu (2004)summarized the variation of experimentally obtained valuesfor k2 and the product k1k3 with concrete compressivestrength. They also presented a comparison with variousdesign expressions, including those of ACI 318-05 and CSAA23.3-94 (Canadian Standards Association 1994). These areshown in Fig. 4.2 and 4.3 and indicate a gradual reduction ink2 and k1k3 with increasing concrete strength.

Fig. 4.1—Parameters for rectangular stress block.

Fig. 4.2—Variation of k2 with concrete strength (Ozbakkalogluand Saatcioglu 2004).


While the product of the terms k1 and k3 is often used as asingle parameter in the formulation of an equivalent rectan-gular stress block, researchers in the past identified thevalues for k3 separately. The parameter k3 represents theratio of the in-place strength of concrete in a structuralmember to the compressive strength measured using standardcylinder tests. Saatcioglu et al. (1998) reported values of thek3 factor for high-strength concrete measured by severalresearchers for unconfined concrete members subjected toconcentric loading. Two 10 in. (250 mm) square columnswith compressive strengths of 11,700 and 17,600 psi (81 and121 MPa), tested by Saatcioglu and Razvi (1998), had k3factors of 0.89 and 0.92, respectively. The average valuereported by Cusson and Paultre (1994) was 0.88 for columnswith compressive strengths of 14,500 psi (100 MPa). Tests byYong et al. (1988) indicated values of 0.87 and 0.97 forcompressive strengths of 12,100 and 13,600 psi (83 and94 MPa), respectively. Sun and Sakino (1994) obtainedvalues of 0.93 and 0.91 for compressive strengths of 7500and 19,000 psi (52 and 131 MPa), respectively. Saatciogluand Razvi (1998) indicated that similar values of k3 wereobtained under eccentric loading.

Other tests performed to measure the value of k3 includethose by Ibrahim and MacGregor (1994, 1996b), Kaar et al.(1977), Schade (1992), and Swartz et al. (1985). The afore-mentioned series of tests resulted in average k3 values of0.91, 1.00, 0.93, and 0.98, respectively. Ibrahim andMacGregor (1994, 1996b) reported mean k3 values of 0.932for specimens with concrete compressive strengths between8400 and 14,400 psi (58 and 99 MPa), and 0.919 for speci-mens with higher compressive strengths ranging between17,600 and 18,600 psi (121 and 128 MPa).

4.2—Stress intensity factor α1According to Fasching and French (1998), experimental

results show that the nominal strength of beams calculatedusing the stress intensity factor α1 of ACI 318-05 is conser-vative for high-strength concrete. Data reported by Kaar etal. (1977) had a mean value of α1 = 1.0, and the data reportedby Swartz et al. (1985) had a mean value of α1 = 0.96.

Ibrahim and MacGregor (1994,1996a) conducted extensivetests of concentrically and eccentrically loaded high-strengthconcrete columns and developed an expression for α1. Theyfound lower stress intensity factors in concentrically loadedcolumns, which resulted in the following expression for thestress intensity factor

( fc′ in psi) (4-1)

( fc′ in MPa)

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

α1 0.850.00862fc′

1000------------------------- 0.725≥–=

α1 0.85 0.00125fc′ 0.725≥–=

( fc′ in psi) (4-2)

( fc′ in MPa)

Park et al. (1998) described the background considerationsof the NZS 3101:1995 design provisions (Standards Associ-ation of New Zealand 1995) regarding the shape of theequivalent rectangular stress block, which is very similar tothat used in ACI 318-05. As stated previously, for a linearstress distribution, the equivalent rectangular stress block hasvalues of k2 = 0.333 (β1 = 0.667) and k1 = 0.5 (α1 = 0.75k3). Thefollowing expression for the stress factor is used in the NewZealand Standard, which is close to that corresponding to alinear stress distribution for high-strength concrete

α1 = 0.85, for fc′ ≤ 8000 psi (55 MPa) (4-3)

α1 = 0.85 – ≥ 0.75 for fc′ > 8000 (fc′ in psi) (4-4)

α1 = 0.85 – 0.004( fc′ – 55) ≥ 0.75 for fc′ > 55( fc′ in MPa)

Azizinamini et al. (1994) investigated columns subjectedto axial load and flexure, and observed that the ACI 318-05equivalent stress block resulted in conservative estimates ofstrength for columns with normal-strength concrete, while itoverestimated the strength of columns with high-strengthconcrete. Based on this observation, they recommendedmaintaining the value of α1 = 0.85 for fc′ ≤ 10,000 psi (69 MPa)and changing it for fc′ > 10,000 psi (69 MPa) using thefollowing expression

α1 = 0.85 – ≥ 0.60 for fc′ > 10,000 (fc′ in psi) (4-5)

α1 = 0.85 – 0.00725(fc′ – 69) ≥ 0.60 for fc′ > 69 (fc′ in MPa)

Bae and Bayrak (2003) developed a proposal based onstress-strain relationships for high-strength concrete. The

α1 0.850.01fc′1000

---------------- 0.67≥–=

α1 0.85 0.0015fc′ 0.67≥–=

0.0275 fc′ 8000–( )

1000------------------------------------

0.50 fc′ 10,000–( )

1000--------------------------------------------

Fig. 4.3—Variation of k1k3 with concrete strength(Ozbakkaloglu and Saatcioglu 2004).


stress intensity factor α1 was derived by finding the total areaunderneath the theoretical stress-strain curve. According toBae and Bayrak (2003)

α1 = 0.85 – 2.75 × 10–5( fc′ – 10,000), 0.67 ≤ α1 ≤ 0.85 ( fc′ in psi) (4-6)

α1 = 0.85 – 0.004( fc′ – 70), 0.67 ≤ α1 ≤ 0.85 ( fc′ in MPa)

Ozbakkaloglu and Saatcioglu (2004) developed a rectan-gular stress block for high-strength and normal-strengthconcretes based on a large volume of experimental data and ananalytical stress-strain relationship. They suggested varyingα1 with concrete compressive strength to reflect the change inthe shape of the stress-strain relationship. Accordingly

α1 = 0.85 – ( fc′ – 4000) × 10–5, 0.72 ≤ α1 ≤ 0.85 (fc′ in psi) (4-7)

α1 = 0.85 – 0.0014( fc′ – 30), 0.72 ≤ α1 ≤ 0.85 ( fc′ in MPa)

A comparison of the ACI 318-05 stress intensity factor α1and the aforementioned recommended changes for the stressintensity factor is shown in Fig. 4.4.

4.3—Stress block depth parameter β1The 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, theeffect of assuming a theoretical value of β1 smaller than theactual value is that the calculated lever arm is increased,resulting in unconservative estimates of the moment strength.

Fasching and French (1998) evaluated the ACI 318-95expression (same as in ACI 318-05) for factor β1 usingexperimental results reported by Ibrahim and MacGregor(1994), Kaar et al. (1977), and Swartz et al. (1985). Faschingand French concluded that the ACI 318 expression for β1underestimated the experimentally observed values in thedata set used for the evaluation.

A similar conclusion was derived by Ibrahim andMacGregor (1994), who proposed the following expressionfor β1

( fc′ in psi) (4-8)

( fc′ in MPa)

The previous equation served as the basis for and is verysimilar to the equation adopted in CSA A23.3-94 (CanadianStandards Association 1994)

( fc′ in psi) (4-9)

( fc′ in MPa)

The stress block depth parameter recommended by Park(1998), and subsequently adopted in NZS 3101:1995 designprovisions (Standards Association of New Zealand 1995),has the same definition as the depth parameter β1 in ACI318-05. Similarly, Azizinamini et al. (1994) recommendedno change to the definition of β1 used in ACI 318-05. Ineffect, these authors implied that changing the location of theequivalent force Cc (Fig. 4.1) relative to the extremecompression fiber has a negligible effect on the nominalmoment strength because the term (1/2)β1c is small incomparison to the moment arm jd = (d – [1/2]β1c). Incolumns with small eccentricities, the precision of β1 willhave a more significant influence on the moment arm and,consequently, on the nominal moment strength. The overalleffect of reducing the stress intensity factor α1 whilemaintaining the parameter β1 similar to that in ACI 318-05is that a larger neutral axis depth is calculated for a givenamount of reinforcement and axial load, reducing the leverarm and the nominal moment strength of the section.

Bae and Bayrak (2003) suggested the following expressionfor the parameter β1 by finding the location of the compressionresultant for the theoretical stress-strain curve

β1 = 0.85 – 2.75 × 10–5(fc′ – 4000), 0.67 ≤ β1 ≤ 0.85 (fc′ in psi) (4-10)

β1 = 0.85 – 0.004(fc′ – 30), 0.67 ≤ β1 ≤ 0.85 (fc′ in MPa)

Ozbakkaloglu and Saatcioglu (2004) recommended agradual change in β1 starting at 4000 psi (28 MPa) to reflectthe variation in internal lever arm with the changing shape ofthe stress-strain relationship of concrete. Their recommendedrelationship for β1 is

β1 = 0.85 – 1.3 × 10–5(fc′ – 4000), 0.67 ≤ β1 ≤ 0.85 (fc′ in psi) (4-11)

β1 = 0.85 – 0.020(fc′ – 30), 0.67 ≤ β1 ≤ 0.85 (fc′ in MPa)

β1 0.950.0172fc′

1000---------------------- 0.70≥–=

β1 0.95 0.0025fc′ 0.70≥–=

β1 0.970.0172fc′

1000---------------------- 0.67≥–=

β1 0.97 0.0025fc′ 0.67≥–=

Fig. 4.4—Comparison of proposed expressions for stressintensity factor α1.


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

4.4—Stress block area α1β1The product α1β1 is an indication of the area of the stress

block. Fasching and French (1998), using the data fromIbrahim and MacGregor (1994), Kaar et al. (1977), andSwartz et al. (1985), showed that the product α1β1 decreasedwith increasing compressive strength. The decrease wasapproximately linear from a value of 0.75 for 6000 psi(41 MPa) to 0.5 for 18,000 psi (124 MPa). The provisions inACI 318-05 include a steeper descent in the product α1β1from 4000 to 8000 psi (28 to 55 MPa) than results from stressblock parameters proposed by several authors for high-strengthconcrete (Bae and Bayrak 2003; Ibrahim and MacGregor1997; Ozbakkaloglu and Saatcioglu 2004). Fasching andFrench (1998) indicated that the steeper descent in theproduct α1β1 resulted in underestimating the area of thecompression block for specimens with concrete compressivestrengths up to 14,000 psi (97 MPa), and overestimating thearea of the compression block for specimens with concretecompressive strengths of 18,000 psi (124 MPa). For concretecompressive strengths on the order of 18,000 psi (124 MPa),the inferred values of the coefficients α1 and β1 were similarto those corresponding to a linear stress distribution.

4.5—Limiting strain εcuThe limiting strain at the extreme compression fiber at the

onset of concrete crushing, εcu, is a significant parameter forcalculating the nominal moment strength of columnsbecause it defines the strains throughout the cross section,particularly the strains in the longitudinal reinforcement.Calculated strains have a direct effect on the calculatedstresses in the longitudinal reinforcement and also on themagnitude of the strength reduction factor φ. ACI 318-05indicates that the magnitude of the strain at the extremecompression fiber εcu is independent of compressive

strength, and should be taken as 0.003. The majority ofdesign provisions and proposals presented (Ibrahim andMacGregor 1994; Standards Association of New Zealand1995; Azizinamini et al. 1994; Ozbakkaloglu and Saatcioglu2004) 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 onthe magnitude of εcu for high-strength concrete resulted inmixed conclusions, with some researchers indicating that thelimiting strain increases with compressive strength, and othersindicating that it decreases. A review of test data by Faschingand French showed that the limiting strain was more sensi-tive to the type of aggregate than the concrete compressivestrength, with limiting strains ranging between 0.002 and0.005 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 valueof εcu due to observed spalling at lower strains in highlyconfined high-strength concrete columns (Fig. 4.6). Theyproposed using a limiting strain of 0.0025 for concretecompressive strengths greater than 8000 psi (55 MPa), and0.003 for lower compressive strengths.

Fig. 4.5—Comparison of proposed expressions for stressblock depth factor β1.

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


Ozbakkaloglu and Saatcioglu (2004) reported that, whilethe crushing strain under uniform compression, εo, increaseswith increasing concrete strength, the crushing strain understrain gradient, εcu, decreases with increasing concretestrength because of the brittleness of high-strength concretes.

Based on moment-curvature analyses of columns underdifferent levels of axial compression, the researchersconcluded that εcu varied between 0.0036 and 0.0027 for4000 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 appreciablyaffect sectional strength calculations, and hence recommendedthe use of a constant average value of εcu = 0.003 formembers under strain gradient.

4.6—Axial strength of high-strengthconcrete columns

The design expression used in ACI 318-05 to calculate thestrength of concentrically loaded columns, similar in form toEq. (4-12), is based on an extensive column investigationthat was conducted jointly by the University of Illinois(Richart and Brown 1934), Lehigh University (Slater andLyse 1931a,b), and ACI. One of the main conclusions of thisresearch was that it was possible to express the strength ofcolumns subjected to concentric loading in a simple form,consisting of contributions from: 1) concrete at peak stress;and 2) longitudinal steel at yield

Po = 0.85fc′ (Ag – Ast) + Ast fy (4-12)

The concrete contribution is based on the in-place strengthand the net area of concrete, including the cover. The in-place strength of concrete is assumed to be 85% of thecylinder strength. The reduction in strength is attributed tothe differences in size, shape, and concrete casting practicebetween a standard cylinder and an actual column. This ratioof in-place strength to cylinder strength, defined as the coef-ficient k3 in Section 4.1, is one of the parameters necessaryto define the rectangular stress block. Experimental data areavailable for in-place strength of high-strength concrete, as

indicated in Section 4.1. Researchers found that the coefficientk3 for high-strength concrete varied between 0.87 and 0.97based on concentrically tested columns (Yong et al. 1988;Sun and Sakino 1993; Cusson and Paultre 1994; Saatcioglu andRazvi 1998). A similar variation was obtained from columntests 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 k3 = 0.9provides a reasonable estimate for the ratio of concretestrength in a structural member to that determined by standardcylinder tests.

In spite of the favorable in-place strength of high-strengthconcrete, experimentally recorded column strengths have beenshown to be below the computed values based on Eq. (4-12)unless the columns are confined by properly designedtransverse reinforcement. The strain data recorded bySaatcioglu and Razvi (1998) during their tests of high-strength concrete columns indicated that premature spallingof cover concrete occurred in most columns before thedevelopment of strains associated with concrete crushing.This observation, combined with visual observations ofcover spalling during tests, as shown in Fig. 4.8, suggeststhat the cover concrete in high-strength concrete columnssuffers stability failure rather than crushing.

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

Fig. 4.8—Instability of cover concrete under concentriccompression (Saatcioglu and Razvi 1998). The bottomphotograph shows section of the cover that spalled offduring the tests.


Saatcioglu and Razvi (1998) hypothesized that the presenceof closely spaced longitudinal and transverse steel, forminga mesh of reinforcement, produced a natural plane of separationbetween the cover and the core. The separation along thisplane was triggered by high compressive stresses associatedwith high-strength concrete as well as the differences inmechanical properties of core and cover concretes (Richartet al. 1929; Roy and Sozen 1963). Columns tested by Ranganet al. (1991) and some of the columns tested by Yong et al.(1988) contained widely spaced transverse reinforcement oflow volumetric ratio, without a sufficient mesh of reinforcementto separate the cover from the core. These columns were ableto develop unconfined column strengths Po calculated usingEq. (4-12). Columns tested by Itakura and Yagenji (1992)without any cover consistently showed higher strengths thanthose computed on the basis of gross cross-sectional area andunconfined concrete because they did not suffer strength lossdue to cover spalling. Columns that were sufficientlyconfined to offset the effects of cover spalling consistentlydeveloped higher strengths than Po. The group thatcontained an insufficient volumetric ratio of closely spacedtransverse reinforcement, however, could not sustainstrengths computed on the basis of total cross-sectional areaand unconfined concrete strength.

According to Saatcioglu and Razvi (1998), given theunfavorable circumstances described previously, the prematurespalling of cover concrete could lead to reduced strength ofconcentrically loaded high-strength concrete columns relativeto those predicted by Eq. (4-12). The effect of prematurecover spalling was introduced into Eq. (4-12) byOzbakkaloglu and Saatcioglu (2004) through a coefficient k4by defining the in-place strength of concrete as k3k4 fc′instead of k3 fc′ , where k3 = 0.85. Figure 4.9 shows thevariation of the product k3k4 with concrete strength obtainedfrom a large volume of test data. The test data also includedmoderately confined columns for which high values of theproduct were obtained. The strength loss associated withcover spalling is a function of the area of unconfined coverconcrete. For this reason, this effect can be quantified interms of the ratio of core area to gross area (Ac /Ag) of thecolumn. As this ratio decreases (cover thickness increases),the strength loss increases. Figure 4.10 illustrates the variationof the product k3k4 with respect to the Ac/Ag ratio. The productk3k4 in Figure 4.10 indicates the degree of premature loss ofstrength in high-strength concrete columns as a function ofconcrete compressive strength and the Ac/Ag ratio. This prema-ture spalling effect can be quite significant in small-scale testcolumns with thin covers (Ozbakkaloglu and Saatcioglu 2004).

Because the stability of the cover improves as the coverthickness increases, columns with thick covers are less likelyto be susceptible to premature spalling than those with thincovers. Given the difficulties associated with testing large-scale columns with very high concrete compressivestrengths under concentric compression, there is a paucity ofexperimental results for large-scale high-strength concretecolumns with thick concrete covers. For this reason, it wassuggested by Ozbakkaloglu and Saatcioglu (2004) that, untilmore data become available, the ratio Ac/Ag should not be

taken less than 0.6, irrespective of its actual value, inassessing the premature cover spalling effect.

The test data in Fig. 4.9 and 4.10 were further examinedafter removing confined column data and grouping them onthe basis of concrete strength (Ozbakkaloglu and Saatcioglu2004). A regression analysis was conducted to find anexpression for the coefficient k4. The researchers suggestedthe following expressions for computing concentric axialstrength of high-strength concrete columns

Po = k3k4 fc′ (Ag – Ast) + Ast fy (4-13)

k3 = 0.90 (4-14)

k4 = γc + (1 – γc) ≤ 0.95 (4-15)

≥ 0.6 (4-16)

Ac

Ag

-----

Ac

Ag

-----

Fig. 4.9—Variation of k3k4 with concrete compressivestrength (Ozbakkaloglu and Saatcioglu 2004).

Fig. 4.10—Variation of k3k4 with core-to-gross area ratio(Ozbakkaloglu and Saatcioglu 2004).


γc = 1.1 – ≤ 0.8 ( fc′ in psi) (4-17)

γc = 1.1 – ≤ 0.8 (fc′ in MPa)

The product k3k4 can be as low as 0.61 for 18,000 psi(124 MPa) concrete and Ac /Ag = 0.6, which is 28% belowthe 0.85 value suggested by ACI 318-05 for normal-strengthconcrete columns, as reproduced in Eq. (4-12). Instead ofdetailed computation of the coefficient k4, as outlinedpreviously, a conservative, but simple, approach wasrecommended for convenience in design by Ozbakkalogluand Saatcioglu (2004). They suggested that the product k3k4be taken as 0.85 for fc′ of up to 6000 psi (41 MPa), and bereduced by 0.017 for every 1000 psi (6.9 MPa) increase over6000 psi (41 MPa), up to 18,000 psi (124 MPa). Theresearchers identified the premature cover spalling as aphenomenon that is prevalent in concentrically loaded high-strength concrete columns. For columns subjected to bendingand axial load, Ozbakkaloglu and Saatcioglu (2004) indicatedthat the critical compression side of the cover would deformtoward the core concrete, which would restrain the coveragainst buckling.

Park et al. (1998) indicated that the axial strength ofcolumns subjected to compression is

Po = χ1fc′ (Ag – Ast) + fyAst (4-18)

They pointed out that the k3 values that have beenmeasured under concentric compression are greater than thevalue of χ1 in the NZS 3101:1995 provisions (StandardsAssociation of New Zealand 1995) and, as a result, thenominal axial strength calculated using that standard isconservative. Azizinamini et al. (1994) proposed calculatingthe axial strength of columns in the same manner as NZS3101:1995 by using Eq. (4-18). The premature spalling ofcover concrete was recognized by CSA A23.3-94 (Cana-dian Standards Association 1994), and Eq. (4-18) wasadopted with the stress intensity factor χ1 decreasing as afunction of concrete strength, reducing to 0.67 for 18,000 psi(124 MPa) concrete.

4.7—Comparison of different proposalsfor rectangular stress block

Fasching and French (1998) carried out a comparisonbetween the measured flexural strengths of beam membersand those calculated according to different stress blockproposals for high-strength concrete. They found a slightlyhigher level of conservatism for the stress block proposalsfor high-strength concrete that they evaluated compared withthe stress block defined in ACI 318-05. The New Zealandand Canadian proposals resulted in nearly identical averageratios of experimental-to-calculated strengths of 1.25, whilethe stress block of ACI 318-05 resulted in an average ratio of1.21. Because the depth of the compression zone in beams issmall compared with the depth of the member, it was

fc′20,000----------------

fc′138---------

anticipated that the proposed modifications to the stressblock would have a small effect on the nominal momentstrength of beams. Fasching and French (1998) recommendedthat the stress block should be modified to avoid uncon-servative estimates of column strength.

Bae and Bayrak (2003) compared the measured strengthsof 224 columns with the strengths calculated using the ACI318-05 rectangular stress block and other stress blocksoutlined in this review (Fig. 4.11 and 4.12). Figure 4.11shows the variation of the factors α1 and β1, and the productα1β1 proposed by several investigators with respect toconcrete 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 forceEEp as the ratio of the difference between the nominal andexperimental moment strengths to experimental momentstrength (Fig. 4.12). EEp is calculated as

(4-19)

A negative EEp value implies that the calculated strengthwas below the measured value, and consequently, the estimatewas conservative.

The second error indicator was based on the experimentaleccentricity (Bae and Bayrak 2003). Based on both errorindicators, Bae and Bayrak concluded that estimates usingthe equivalent rectangular stress block of ACI 318-05became increasingly unconservative with increasingcompressive strength, particularly with concrete strengthsexceeding 10,000 psi (69 MPa).

The stress blocks proposed by Ibrahim and MacGregor(1997), Park et al. (1998), Standards Association of NewZealand (1995), and Bae and Bayrak (2003) all produced

EEpMncol Mexp–

Mexp

--------------------------------- 100×=

Fig. 4.11—Comparison of stress block parameters α1 andβ1 inferred from experimental results and various expressionsproposed for high-strength concrete (Bae and Bayrak 2003).


similar levels of conservatism for all levels of concrete strength.The model proposed by Azizinamini et al. (1994) increasinglyunderestimated the column strengths for concrete compressivestrengths beyond 13,000 psi (90 MPa). Bae and Bayrak notedthat the data they used lacked a significant number of testresults with high axial loads (small eccentricities). Whenaxial loads are high, the different models provide significantlydifferent predictions. They also noted that in seismicapplications, the concern is not with high axial loads, butwith relatively low axial loads (high eccentricities).

Ozbakkaloglu and Saatcioglu (2004) compared columninteraction diagrams based on the rectangular stress blocksof ACI 318-05, CSA A23.3-94, and those proposed byIbrahim and MacGregor (1997) and Ozbakkaloglu andSaatcioglu (2004).

The comparisons, shown in Fig. 4.13, indicate that theinteraction diagrams generated by the equivalent rectangularstress block of ACI 318-05 and that proposed by

Ozbakkaloglu and Saatcioglu are identical for columns witha concrete compressive strength of 4000 psi (28 MPa), whereasthe equivalent rectangular stress blocks recommended byCSA A23.3 and Ibrahim and MacGregor produce slightlylower estimates of strength than ACI 318-05. As concretestrength increased, Ozbakkaloglu and Saatcioglu concludedthat the ACI 318-05 stress block lead to overestimatingcolumn strengths obtained from test results. Ozbakkalogluand Saatcioglu indicated that the magnitude of the overestima-tion was very significant for a column with a concretecompressive strength of 17,400 psi (120 MPa). For this samecolumn, the rectangular stress blocks proposed by Ibrahimand MacGregor and Ozbakkaloglu and Saatcioglu producedsimilar interaction diagrams, and the CSA A23.3 stress blockresulted in a more conservative estimate of strength. The factthat the results obtained using the rectangular stress block inCSA A23.3 were consistently more conservative was attributedto the use of a lower stress intensity factor α1.

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


Ozbakkaloglu and Saatcioglu (2004) also providedcomparisons of interaction diagrams drawn on the basis oftheir proposed stress block and that of ACI 318-02 (ACICommittee 318 2002) (which is the same used in ACI 318-05)for columns tested by Lloyd and Rangan (1996), Ibrahim andMacGregor (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 over-estimated column axial and moment strengths, resulting inunsafe strength values for columns with concrete strengths inexcess of 10,000 psi (69 MPa), whereas their proposed stressblock (Ozbakkaloglu and Saatcioglu 2004) provided verygood agreement with experimental strength values.

A parametric study was carried out as part of this report toprovide further insight into the differences among various

Fig. 4.13—Comparison of interaction diagrams for columnswith different concrete strengths (Ozbakkaloglu andSaatcioglu 2004) (Ac /Ag = 0.7; ρ = 1.33%; b = h =11.81 in. [300 mm]).

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


proposals. Column interaction diagrams were calculated,with and without strength reduction factors φ, to compare theACI 318-05 stress block with the proposals by Ibrahim andMacGregor (1997), Park et al. (1998), and Azizinamini et al.(1994). The column cross section that was analyzed is shownin Fig. 4.15, with the bending moment about the Y-Y axis.The column was analyzed for steel ratios of 1 and 2.5% andfor concrete compressive strengths of 4000, 6000, 8000,10,000, 12,000, and 15,000 psi (28, 41, 55, 69, 83, and 103MPa). The stress block parameters for the compared modelsare given in Table 4.1, and the results of the parametric studyare given in Fig. 4.16.

From Fig. 4.16 and Table 4.1, it can be seen that for concretecompressive strengths of 4000, 6000, and 8000 psi (28, 41,and 55 MPa), the only model that resulted in estimates ofstrength that were noticeably different from those obtainedwith the ACI 318-05 stress block was that proposed byIbrahim and MacGregor (1997).

The Ibrahim and MacGregor (1997) model resulted inprogressively smaller estimates of nominal strength asconcrete compressive strength increased, which indicatesthat their model was the most conservative in this range. Fora concrete compressive strength of 10,000 psi (69 MPa), theACI 318-05 stress block and that proposed by Azizinaminiet al. (1994) produced similar results, whereas the proposalsby Ibrahim and MacGregor (1997) and Park et al. (1998)produced more conservative estimates of strength. For aconcrete compressive strength of 12,000 psi (83 MPa), themodels by Park et al. and Azizinamini et al. have identicalstress block parameters. Consequently, strength estimatesobtained with these two models were identical, and approx-imately the same as the nominal strength calculated using themodel by Ibrahim and MacGregor. Finally, for a concretecompressive strength of 15,000 psi (103 MPa), the modelsby Ibrahim and MacGregor and Park et al. yielded similarresults, and were slightly more conservative than theequivalent rectangular stress block of ACI 318-05. Themodel by Azizinamini et al. (1994) resulted in significantlylower estimates of strength than the other models.

4.8—RecommendationsIt is apparent from a review of the available literature that

when the equivalent rectangular stress block of ACI 318-05is used for members with axial loads above that corre-sponding to balanced failure and high-strength concrete, theratio of nominal-to-experimental column strength decreasesas the axial load increases. Experimental results (Fig. 4.12(a))indicate that the nominal moment and axial strengths of

columns calculated with the ACI 318-05 stress block may beunconservative for compressive strengths greater thanapproximately 12,000 psi (83 MPa).

Two consequences of overestimating the flexuralstrengths of columns are that the shear demand on thecolumn calculated on the basis of the probable flexural strengthis overestimated and that the ratio of column-to-beammoment strengths is overestimated. Overestimating theshear demand is conservative because it leads to a higheramount of transverse reinforcement. Conversely, overesti-mating the ratio of column-to-beam moment strengths has anegative effect because it increases the probability of hinging inthe columns. ACI 318-05 requires a minimum ratio ofcolumn-to-beam moment strengths of 1.2. Overestimatingcolumn flexural strength decreases that ratio, and may evenresult in a strong beam-weak column mechanism.

Because experimental results showed that the equivalentrectangular stress block of ACI 318-05 is appropriate fornormal-strength concrete, a recommendation was developedfocusing on columns with compressive strengths greaterthan 8000 psi (55 MPa). This was done by suggesting a stressblock with a variable stress intensity factor α1 for concretecompressive 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 fc′ upto and including 8000 psi. For strengths above 8000 psi, α1shall be reduced continuously at a rate of 0.015 for each 1000psi of strength in excess of 8000 psi, but α1 shall not be takenless than 0.70.” In SI units, the recommendation is that:

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

Table 4.1—Summary of parameters α1 and β1 defining different rectangular stress blocks investigated in parametric studyConcrete compressive strength, psi (MPa) 4000 (28) 6000 (41) 8000 (55) 10,000 (69) 12,000 (83) 15,000 (103)

Equivalent rectangular stress block parameter 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

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


“factor α1 shall be taken as 0.85 for concrete strengths fc′ upto and including 55 MPa. For strengths above 55 MPa, α1shall be reduced continuously at a rate of 0.0022 for each6.9 MPa of strength in excess of 55 MPa, but α1 shall not betaken less than 0.70.”

A number of revisions to ACI 318-05 are proposed inChapter 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

the proposed stress block with those proposed by others, aswell as with the results of sample tests on columns usingconcrete strengths of up to 18,000 psi (124 MPa).

The strength intensity factor α1 is also recommended tocalculate the strength of columns subjected to concentricloading. The similarities in the values of α1 and the coefficientthat defines the in-place strength of concrete in columnsunder concentric compression χ1 makes it possible to use thesame value in computing column concentric strength Po forconvenience in design. The recommendations translate intoEq. (4-20) and (4-21) for spirally reinforced and tiedcolumns, respectively

φPn,max = 0.85φ[χ1 fc′ (Ag – Ast) + fyAst] (4-20)

φPn,max = 0.80φ[χ1fc′ (Ag – Ast) + fyAst] (4-21)

Accordingly, in inch-pound units, it is recommended that:“factor χ1 shall be taken as 0.85 for concrete strengths fc′ upto and including 8000 psi. For strengths above 8000 psi, χ1shall be reduced continuously at a rate of 0.015 for each 1000 psiof strength in excess of 8000 psi, but χ1 shall not be takenless than 0.70.” In SI units, the recommendation is that:“factor χ1 shall be taken as 0.85 for concrete strengths fc′ upto and including 55 MPa. For strengths above 55 MPa, χ1

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

Fig. 4.17—Comparisons of column interaction diagramsand test data (fc′ = 10,440 psi [72 MPa], 7.8 x 11.8 in. (200x 300 mm), ρ = 1.3%, Ac/Ag = 0.6).


shall be reduced continuously at a rate of 0.0022 for eachMPa of strength in excess of 55 MPa, but χ1 shall not betaken less than 0.70.”

Figure 4.20 provides a comparison of the aforementionedrecommendations with experimental data and the nominalstrengths calculated using the provisions in ACI 318-05. Theproposed parameters α1, β1, and χ1 were selected based onwhat was deemed an acceptable level of conservatism in thejudgment of the committee. Another factor considered by thecommittee in selecting the aforementioned parameters wasthat there is no experimental evidence to suggest that the

parameters in ACI 318-05 result in unconservative estimatesof strength for columns with normal-strength concrete. Forthis reason, the stress block parameters proposed by thecommittee were selected so that there would be no change inthe stress block parameters of ACI 318-05 for columns withnormal-strength concrete.

CHAPTER 5—CONFINEMENT REQUIREMENTS FOR BEAMS AND COLUMNS

The increased strength and enhanced performance of high-strength concrete are advantageous features for structuralapplications. The increasing brittleness of concrete withhigher compressive strength is a major concern for seismicapplications, however, where toughness under repeated loadreversals is of paramount importance. For this reason, properconfinement of concrete is essential for the safe use of high-strength concrete in moderate to high seismic applications.

This chapter addresses concrete confinement for beam andcolumn elements. In Chapter 21 of ACI 318-05, whichincludes seismic design provisions, columns are defined asmembers with an axial load ratio (Pu/ fc′ Ag) greater than 0.1.The same definition is adopted throughout this document todifferentiate between beams and columns. Constitutivemodels for confined concrete, salient features of previousresearch, and design recommendations are provided in thefollowing sections.

5.1—Constitutive models for confined concreteSeveral researchers have indicated that constitutive models

developed for normal-strength concrete do not offer a goodrepresentation of the behavior of high-strength concrete,especially in the case of columns, where the characteristics ofthe constitutive model have the highest impact on the calculatedresponse. Therefore, previously developed constitutivemodels have been modified to reflect the differences inbehavior, and a number of additional analytical models havebeen developed specifically for high-strength concrete.

Ahmad and Shah (1982), Martinez et al. (1984), andFafitis and Shah (1985) were among the first to developmodels for high-strength confined concrete based on tests ofspirally reinforced small cylinders. These models incorporatethe effect of confinement through a lateral confining pressurethat develops under hoop tension. The models were shown toproduce good correlations with tests of spirally confinedcircular cylinders for concrete strengths of up to 12,000 psi(83 MPa).

Yong et al. (1988) developed a model based on small-scalesquare column tests with concrete strengths ranging between12,000 and 13,600 psi (83 and 94 MPa). Their approach wassimilar to that originally proposed by Sargin et al. (1971) fornormal-strength concrete. Azizinamini et al. (1994) subse-quently modified the model on the basis of large-scalecolumn tests under reversed cyclic loading.

Bjerkeli et al. (1990) proposed a generalized model fornormalweight and lightweight aggregate confined concreteswith compressive strengths of up to 13,000 and 10,000 psi (90and 69 MPa), respectively. Their model is applicable to elementswith circular, square, and rectangular section geometry.

Fig. 4.18—Comparison of column interaction diagrams andtest data (fc′ = 14,000 psi [97 MPa], 6.9 x 6.9 in. (175 x175 mm), ρ = 1.3%, Ac/Ag = 0.84).

Fig. 4.19—Comparison of column interaction diagrams andtest data (fc′ = 18,270 psi [126 MPa], 7.9 x 11.8 in. (200 x300 mm), ρ = 1.3%, Ac/Ag = 0.60).

Fig. 4.20—Observed stress intensity factors for concentricallyloaded columns.


A number of confinement models were developed in Japanbased 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 ontests of large-scale high-strength concrete columns. Theirmodel uses the effectively confined core area concept thatwas originally proposed by Sheikh and Uzumeri (1982) andmodified by Mander et al. (1988). These researchers laterimproved their model by introducing an iterative procedureto compute the strain in transverse confinement reinforcement(Cusson and Paultre 1995).

Li (1994) developed a constitutive model for confinedconcrete that covered a wide range of concrete compressivestrengths between 4000 and 19,000 psi (28 and 131 MPa).The model was quite comprehensive and elaborate, incorpo-rating several parameters to reflect the effects of confinement.

Razvi and Saatcioglu (1999) developed a generalizedconfinement model on the basis of the equivalent uniformlateral pressure concept that they proposed earlier forconfinement of normal-strength concrete (Saatcioglu andRazvi 1992). The model covers a wide range of concretecompressive strengths between 3000 and 19,000 psi (21 and131 MPa), and incorporates the effects of different reinforce-ment geometry and arrangement while also incorporating theeffect of high-strength transverse reinforcement.

5.2—Previous research and general observationsOne of the most challenging aspects about interpreting

results from beam and column studies found in the literatureis that there are differences among the loading protocols,loading configurations, scale, and failure criteria used bydifferent researchers. These differences are such that P-Δeffects, reported shear strengths, and drifts at failure are notdirectly comparable in some instances (Brachmann et al.2004a,b). In spite of these differences, there are some well-established common trends that have been observed about thebehavior of beams and columns with high-strength concrete.

The ductile behavior of high-strength concrete beams iswell documented in several experimental studies found inthe literature. Based on a series of beam tests conducted atCornell University, Nilson (1985) observed that although theultimate compressive strain was smaller for high-strengthconcrete, section and member displacement ductilities werelarger than in normal-strength concrete elements. Nilson alsoobserved that spiral reinforcement was less effective in high-strength concrete columns subjected to axial compression,resulting in a smaller displacement ductility.

A study on the flexural ductility of high-strength concretebeams (Shin et al. 1990) indicated that ductility ratiosincreased with concrete strength for specimens with similaramounts of longitudinal and transverse reinforcement. Thiswas observed for both monotonic and cyclic loading.

Several researchers (Xiao and Yun 1998; Azizinamini etal. 1994; Matamoros and Sozen 2003) have shown, based ontests of columns subjected to cyclic loading under constantaxial load, that drift ratios exceeding 3% can be reached withdetailing conforming to the existing provisions in Chapter 21

of ACI 318-05 if the axial load demand on the columns isbelow 0.2fc′ Ag (approximately 1/2 of the balanced axialload). Even at these low levels of axial load, Matamoros andSozen (2003) observed that the degradation of the confinedcore, as indicated by the strain demand in the lateral reinforce-ment, increased more rapidly with drift for higher values ofaxial load. Xiao and Martirossyan (1998) and Matamorosand Sozen (2003) observed a similar trend with increasingcompressive strength.

A study on the properties of high-strength concretemembers (Bjerkeli et al. 1990) concluded that properlyconfined columns can have ductile behavior and sustainlarge axial strains. The variables of the study were thecompressive strength of the concrete, with values of 9400,13,800, and 16,700 psi (65, 95, and 115 MPa), and the shapeof the specimen, with circular and rectangular sectionalshapes included. Concrete compressive strengths reported inthis study were measured using 4 in. (102 mm) cubes. Small-scale specimens (6 x 6 in. [152 x 152 mm] rectangularcolumns and 6 in. [152 mm] diameter circular columns) weresubjected to eccentrically applied monotonic loading. Boththe effectiveness of confinement and the ultimate strainunder concentric loading decreased with increases inconcrete strength. According to the authors, specimens witha volumetric transverse reinforcement ratio (defined as theratio of the volume of transverse reinforcement to the corevolume confined by the transverse reinforcement) ρvr of1.1% resulted in inadequate ductility, while the behavior ofspecimens with ρvr of 3.1% was satisfactory. Circularcolumns with transverse reinforcement in the form of spiralsshowed larger values of maximum stress and strain at peakstress than rectangular columns with similar volumetricratios of hoop reinforcement. The difference between thetwo increased with the amount of transverse reinforcement.In the set of specimens with ρvr of 1.1%, the ratio of strain atpeak stress for the confined case to strain at peak stress forthe unconfined case was approximately 1.1 for the rectangularcolumn with hoops and 1.25 for the circular column withspiral reinforcement. The ratio of peak stress for the confinedcase to peak stress for the unconfined case was approxi-mately 0.85 for the rectangular column with hoops and 0.9for the circular column with spiral reinforcement. In the setof specimens with ρvr of 3.1%, the ratio of strain at peakstress for the confined case to strain at peak stress for theunconfined case was approximately 1.9 for the rectangularcolumn with hoops and 3.5 for the circular column withspiral reinforcement. The ratio of peak stress for the confinedcase to peak stress for the unconfined case was approximately1.05 for the rectangular column with hoops and 1.55 for thecircular column with spiral reinforcement.

Razvi and Saatcioglu (1994) conducted an investigationon the strength and deformability of high-strength concretecolumns based on the results of 250 tests by variousresearchers. They concluded that the volume of reinforcementrequired for proper confinement of high-strength columnsmay be reduced with the use of high-strength steel as transversereinforcement, particularly for high axial loads. They indicatedthat the use of high-strength steel did not improve


behavior when low axial loads were present. They alsoobserved that column deformability decreased withincreasing axial compression. A specimen tested underaxial tension showed improved deformability comparedwith specimens loaded in compression.

Saatcioglu et al. (1998) reviewed the effect of confinementon concentrically loaded columns tested by several differentinvestigators. They concluded that the strength of confinedconcrete increased with the amount of confinement indepen-dently of unconfined compressive strength. They alsoobserved that for a similar percent increase in strength,higher confinement pressure is required for high-strengthconcrete than for normal-strength concrete. They indicatedthat values for the confinement index (defined as the productof the volumetric transverse reinforcement ratio and theyield strength of the transverse reinforcement divided by thecompressive strength of the concrete) recommended in theliterature to ensure ductile behavior under concentric loadingranged between 0.15 and 0.30. The distribution and spacingof the transverse reinforcement is another important parameterthat affects behavior. Although high-strength reinforcementmay be used to decrease the volumetric transverse reinforcementratio, the effectiveness of the confining reinforcementdecreases as spacing increases. Saatcioglu et al. (1998)indicated that the yield strength of the transverse reinforcementmay not be reached for columns in which the volumetricreinforcement ratio, the axial load, or both, is low.

Kato et al. (1998) reviewed tests carried out in Japan on91 square columns and 59 circular columns under concentricloading. The compressive strength of the concrete in thespecimens ranged between 4000 and 19,000 psi (28 and131 MPa), while the yield strength of the transverse reinforce-ment ranged between 25,000 and 198,000 psi (172 and1365 MPa). Their conclusions were similar to those bySaatcioglu et al. (1998). They indicated that the maximumstress increase in the columns was independent of thecompressive strength and proportional to the strength of thetransverse reinforcement. An upper limit of 100,000 psi(690 MPa) on the strength of the transverse reinforcementwas suggested because calculations using the concrete modelsderived from the tests suggested that the reinforcement mightnot be effective beyond that point. In addition, they concludedthat increasing the spacing of the transverse reinforcement byusing high-strength reinforcement increased the probability offailure due to buckling of the longitudinal reinforcement.

Saatcioglu and Razvi (1998) tested 26 large-scale high-strength concrete columns with a square cross section underconcentric compression. The concrete compressive strengthused varied between 8700 and 17,400 psi (60 and 120 MPa).The researchers investigated the effects of various confinementparameters, including the use of high-grade transversereinforcement. It was concluded that the lateral pressurerequired to confine high-strength concrete columns can beachieved by using high-strength transverse reinforcement. Itwas cautioned, however, that this may not be achieved unlessa sufficiently high volumetric ratio of transverse reinforcementis used. The researchers further reported premature spallingof cover concrete under concentric loading that was observed

before reaching the crushing strength of unconfinedconcrete. This was attributed to the stability failure of thecover shell under high compressive stresses when a mesh ofreinforcement, consisting of longitudinal bars and closelyspaced transverse reinforcement, separated the cover fromthe core. Similar conclusions were obtained by Razvi andSaatcioglu (1999), who tested 21 large-scale, circular, high-strength concrete columns under concentric compression.

Lipien and Saatcioglu (1997) and Saatcioglu and Baingo(1999) reported test results of large-scale square and circularcolumns, respectively, under constant axial compression andincrementally increasing lateral deformation reversals. Thelevel of axial compression varied between 22 and 43% of thecolumn strength under concentric loading Po, and the concretestrength varied between approximately 9000 and 14,000 psi(62 and 97 MPa). The researchers reported that a minimumof 5% drift capacity can be attained in circular columns if thevolumetric ratio of spiral reinforcement is at least equal to0.17fc′ /fyt and the limit on the yield strength of transversereinforcement is increased to 145,000 psi (1000 MPa). The samerequirements produced approximately 8% lateral drift whenthe level of axial compression was reduced from 0.43Po to0.22Po. 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 havingthe same material properties. Similar observations were madefor square columns with overlapping hoops and crossties.

Sheikh et al. (1994) tested four 12 in. (305 mm) squarecolumns with concrete strengths of approximately 8000 psi(55 MPa) under constant axial compression and lateralmoment reversals. The level of axial compression rangedbetween 0.59Po and 0.62Po. Sheikh et al. (1994) reporteddisplacement ductility ratios (at a 20% reduction in lateralresistance) for the high-strength concrete columns rangingbetween 2.0 and 5.4 for specimens with volumetricconfinement indexes ranging between 0.16 and 0.36. Thecorresponding curvature ductility ratios ranged between 5and 17. It was concluded that the required amount ofconfinement reinforcement was proportional to concretestrength. The improvement in column ductility appeared to beproportional to the amount of confinement steel.

Azizinamini et al. (1993, 1994) tested nine 12 in. (305 mm)square columns under 0.20Po, 0.30Po, and 0.40Po. Thespecimens consisted of a central stub representing the jointregion of a frame, with two columns extending outward.Lateral loads were applied at the center of the stub while thecolumns were subjected to a constant axial load. The transversereinforcement had yield strengths of 60 and 120 ksi (414 and827 MPa), with volumetric confinement indexes rangingbetween 0.13 and 0.37. The concrete compressive strengthsranged between 3800 and 15,000 psi (26 and 103 MPa).Azizinamini et al. (1994) reported that the maximum driftratios, defined by the authors as the maximum drift ratio atwhich test columns were capable of withstanding twocomplete cycles of horizontal displacement, ranged between3.0 and 5.1%. The test data indicated that an increase inconcrete strength did not necessarily result in reductions inthe column displacement ductility ratio. Reducing the


spacing of the ties, however, resulted in larger ductilityratios. When comparing the behavior of specimens withsimilar amounts of transverse reinforcement and differentyield strengths, Azizinamini et al. (1994) concluded thatincreasing the yield strength of the transverse reinforcementhad no significant effect on the maximum drift ratio. Theyalso expressed concern that, because of buckling of thelongitudinal reinforcement, increasing the spacing betweenhoops while increasing the yield strength of the transversereinforcement to achieve a similar confinement index wouldnot be fully effective. Test results from two specimens with1-5/8 and 2-5/8 in. (41 and 67 mm) hoop spacing and transversereinforcement yield strengths of 71 and 109 ksi (490 and752 MPa), respectively, showed that the specimen with thecloser hoop spacing and lower yield strength had a highermaximum drift ratio (3.3%) than the specimen with thehigher yield strength and larger stirrup spacing (2.4%). Theyattributed the difference in behavior to premature bucklingof the longitudinal reinforcement observed in the specimenwith the larger stirrup spacing.

Thomsen and Wallace (1994) tested twelve 6 in. (152 mm)square column specimens with a concrete compressivestrength of approximately 12,000 psi (83 MPa). The specimensconsisted of cantilever columns with a foundation block thatwas anchored to the reaction floor. The axial and lateral loadswere applied at the free end of the cantilever. Test variableswere the spacing and configuration of the transverse reinforce-ment, the yield strength of the transverse reinforcement (115and 185 ksi [793 and 1276 MPa]), and the axial load ratio (0,0.1, and 0.2). Measurements indicated that the longitudinalreinforcement started to yield at a drift ratio of 1%. Shear andflexural strengths deteriorated at drift ratios exceeding 2%,and severe damage occurred at drift ratios higher than 4%.The longitudinal reinforcement buckled in specimens withaxial load ratios of 0.2 and at drift ratios greater than 4%. Themain conclusion of the study by Thomsen and Wallace wasthat high-strength reinforcement may be used effectively toconfine high-strength concrete.

A significant amount of experimental data from columnswith axial load ratios fp = P/fc′ Ag exceeding 0.3 is availablefrom an extensive study on the behavior of concretemembers with high-strength materials sponsored by theMinistry of Construction in Japan (Aoyama et al. 1990).Because the maximum number of stories in high-rise buildingsis limited by concrete strength, Japanese engineers believethat strengths higher than 6000 psi (41 MPa) would be essentialto the construction of buildings taller than 30 stories.

Tests conducted in Japan focused on columns subjected toaxial load ratios above 0.3 (Aoyama et al. 1990; Sakaguchiet al. 1990; Muguruma and Watanabe 1990; Sugano et al.1990; Kimura et al. 1995; Hibi et al. 1991). These testsshowed a strong correlation among axial load, amount ofconfinement, and the drift capacity (drift limit) of columns.A large amount of transverse reinforcement was required toobtain ductile behavior in columns subjected to axial loadsgreater than the balanced load. Japanese researchersaddressed this problem by incorporating high-strength steelas transverse reinforcement.

Sakaguchi et al. (1990) reported test results from eighthigh-strength concrete columns with compressive strengthsof 11,200 and 13,600 psi (77 and 94 MPa) and a shear span-depth ratio of 1.1. The specimens consisted of columns withrigid blocks at the top and bottom. The bottom block wasattached to the reaction floor, while the top block was usedto apply the lateral and vertical loads. The column specimenswere deformed in double curvature. All specimens had trans-verse reinforcement with a yield strength of 200,000 psi(1379 MPa). The variables of the study were the amount oftransverse reinforcement, with volumetric confinementindexes 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 weretested with an axial load ratio of 0.4. Because the main thrust ofthe 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 trans-verse reinforcement, a shear slip failure occurred soon after theformation of an inclined crack. In specimens with intermediateand high amounts of transverse reinforcement, shear strengthincreased with the amount of reinforcement. They indicated thata relatively high amount of transverse reinforcement wasneeded to maintain ductile behavior after the formation ofinclined cracks in light of the low shear span-depth ratio.

Muguruma and Watanabe (1990) tested eight specimens,varying the transverse reinforcement yield strength between48,000 and 115,000 psi (331 and 793 MPa) while maintaininga constant volumetric ratio ρvr of 1.6%. The specimensconsisted of a central stub with two columns extendingoutward. The lateral load was applied at the center of thestub, deforming the specimens in single curvature, while theaxial load was maintained constant. Four tests wereconducted on specimens with a concrete compressivestrength of 12,400 psi (85 MPa) at axial load ratios fp of 0.4and 0.6. For these specimens, the limiting drift ratio, definedas the drift ratio attained without a significant loss instrength, ranged between 1.5 and 10%. There was a strongcorrelation among the limiting drift ratio, axial load, and theyield strength of the transverse reinforcement. The limitingdrift ratio decreased as the axial load ratio increased.Increasing the yield strength of the transverse reinforcementhad the opposite effect. The limiting drift ratio increased bya factor as high as 3 when the yield strength of the transversereinforcement was increased from 48,000 to 115,000 psi(331 and 793 MPa). The two specimens with a volumetricconfinement index cp (defined as ρvr fyt /fc′ ) of 0.06 hadlimiting drift ratios of 6.0% for fp = 0.4 and 1.5% for fp =0.63. When the volumetric reinforcement index wasincreased to 0.15 through the use of high-strength transversereinforcement, the limiting drift ratio increased to over 10%for fp = 0.4 and 4.5% for fp = 0.63. The remaining four spec-imens had a concrete compressive strength of 16,800 psi(116 MPa) and were tested at axial load ratios of 0.25 and0.41. Limiting drift ratios for these specimens variedbetween 3.0 and 8.5%. A volumetric confinement index of0.05 was sufficient to attain a limiting drift ratio of 3.0% foran axial load ratio of 0.41. The authors concluded it waspossible to achieve a high ductility ratio in columns with


high-strength concrete through the use of high-strengthtransverse reinforcement.

A research program, motivated by the need to use high-strength materials in high-rise structures, was carried out inTokyo. It comprised a first series of eight column tests and10 beam tests (Sugano et al. 1990), and a second series of fivecolumn tests (Kimura et al. 1995). The specimens eachconsisted of a column with rigid blocks at the top and bottom.The specimens were deformed in double curvature while theaxial load was maintained constant. The first test series showedexcellent behavior for column specimens with an axial loadratio of 0.3, which achieved limiting drift ratios of 4%. Thelimiting drift ratio increased in proportion to the yield strengthof the transverse reinforcement normalized by the concretecompressive strength. The authors suggested a minimumconfinement index of 0.10 to achieve limiting drift ratios of2% at an axial load ratio of 0.6. The beams that were testedhad span-depth ratios of 1.5, concrete compressive strengthsranging from 5800 to 12,000 psi (40 to 83 MPa), longitudinalreinforcement ratios of 1.9 and 2.9%, transverse reinforce-ment with yield strengths of 44.3, 114.6, and 197 ksi (305,790, and 1358 MPa), and confinement indexes ranging from0.08 to 0.36. Beams with high confinement indexes (above0.15) had limiting drift ratios above 5%; the limiting drift ratiowas not very sensitive to the amount of transverse reinforce-ment or concrete compressive strength. The second series inthe study concluded that the ductility of high-strength concretecolumns was strongly affected by both the level of axialcompression and the yield strength of the transverse reinforce-ment. The authors stated that the yield strength of the trans-verse reinforcement normalized by the compressive strengthof the concrete was an appropriate index to evaluate ductility.

A series of five tests at the University of Tokyo focused oncolumn behavior after flexural yielding (Hibi et al. 1991).The specimens each consisted of a column with rigid blocksat the top and bottom. The specimens were deformed indouble curvature while the axial load was maintainedconstant. The columns had axial load ratios of 0.30 and 0.45,and a shear span-depth ratio of 1.5. The amount and thestrength of the transverse reinforcement were varied, whilethe quantity ρt fyt was maintained approximately constant.The tests showed a strong correlation between toughness andaxial load. The behavior of specimens with an axial loadratio of 0.3 was very ductile, achieving limiting drift ratiosexceeding 4%. Specimens with higher axial loads failed inshear, with limiting drift ratios on the order of 3.5%. At driftratios below 2%, the University of Tokyo tests indicated thatthe shear component of the lateral deflection within theplastic hinge region was similar for all specimens, regardlessof axial load. It must be pointed out, however, that none ofthe specimens reached yielding of the transverse reinforcement,thus limiting the degradation of the confined core within theplastic hinge region.

All of these test results showed that beams and columnsmade with high-strength concrete can be used safely inseismic design for a wide range of axial loads, provided thatan adequate amount of transverse reinforcement is providedto confine the core concrete.

5.3—Equations to determine amount of confinement reinforcement required in columns

Section 21.4.4 of ACI 318-05 specifies the minimumamount of transverse reinforcement for confining the coreconcrete and providing lateral support to the longitudinalreinforcement in columns subjected to cyclic loading.Equation (21-2) in ACI 318-05 specifies the minimumvolumetric ratio of spiral or circular hoop reinforcement forcircular columns as

ρs = 0.12fc′/fyt ACI 318 Eq. (21-2)

For rectangular columns, the minimum amount of reinforce-ment required by ACI 318-05 is given by Eq. (21-3) and (21-4)

Ash = 0.3sbc ACI 318 Eq. (21-3)

Ash = 0.09sbc ACI 318 Eq. (21-4)

ACI 318-05, Eq. (21-3), controls when the ratio of grossarea 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 forsmall columns. These requirements were developed toensure that the strength of the confined core would be sufficientto compensate for the loss in axial strength that occurs whenthe concrete in the exterior shell of the column spalls off.ACI 318-05, Eq. (21-2) and (21-4), imply that the confiningstress provided by rectangular hoops is less effective thanthat provided by a similar volume of spiral reinforcement. Acomparison between the volumetric reinforcement ratiorequired to confine a similar volume of concrete in a circularcolumn 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 isconsidered to be approximately 50% more effective thanhoop reinforcement. The commentary in ACI 318-05 indicatesthat, although the strength and ductility of columns areaffected by the amount of axial load, the axial loads anddeformation demands during an earthquake are not knownwith sufficient accuracy to justify the calculation of theamount of transverse reinforcement as a function of theseparameters.

Experimental results (Matamoros and Sozen 2003) haveshown that the amount of transverse reinforcement requiredby ACI 318-05, Eq. (21-2) to (21-4), will result in limitingdrift ratios exceeding 3% for concrete compressive strengthsup to 10,000 psi (69 MPa) and axial load ratios below0.2fc′ Ag. The main concerns about ACI 318-05, Eq. (21-2) to(21-4), are whether they provide sufficient transversereinforcement to properly confine high-strength columnswith axial loads greater than the balanced failure load, andthat they require excessive amounts of transverse reinforcementfor members with lower axial load, leading to congestion ofreinforcement and concrete placement problems. Anotherconcern, brought to attention by Bayrak and Sheikh (1998),

fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞

fc′fyt

-----


is that in the case of high-strength concrete members, theamount of transverse reinforcement required for properconfinement will create a plane of weakness that may lead toloss of the shell of the column before an axial strain of 0.003is attained.

Confinement provisions in the New Zealand concretedesign standard NZS 3101:1995 recognize the effect of axialload on column behavior. In potential plastic hinge regions,when hoop reinforcement is used, the design standardrequires that the total area of transverse bars Ash in each ofthe transverse directions within spacing s should not be lessthan that given by the following three equations

(5-1)

(5-2)

The area of a tie leg Ate required to tie the longitudinal barsreliant on it is defined as

(Ast in in.2, s in in.) (5-3)

(Ast in mm2, s in mm)

whereρl = Ast /Ag = longitudinal reinforcement ratio;Ast = total area of nonprestressed longitudinal reinforce-

ment (bars or shapes);m = fyl /0.85fc′ ;Ag = gross area of concrete section;Ach = cross-sectional area of structural member measured

out-to-out of the transverse reinforcement;s = center-to-center spacing of hoop sets;h′′ = core dimension perpendicular to transverse

reinforcement providing confinement measuredto outside of hoops;

fyl = specified yield strength of longitudinal reinforce-ment;

fyt = specified yield strength of transverse reinforce-ment;

fc′ = specified compressive strength of concrete;P = unfactored axial load;φ = strength reduction factor, defined in this case as

0.85 if plastic hinging can occur, or 1.0 otherwise;ΣAte = sum of areas of legs required to tie the longitudinal

bars; andΣAb = sum of areas of longitudinal bars tied to the hoop

for lateral support.The following limits apply

Ag/Ach ≤ 1.2 (5-4)

ρlm ≤ 0.4 (5-5)

fyt ≤ 116,000 psi (800 MPa) (5-6)

fc′ ≤ 10,000 psi (69 MPa) (5-7)

For rectangular-shaped transverse reinforcement, thecenter-to-center spacing in potential plastic hinge regionsshould not exceed the smaller of 1/4 of the smaller dimensionof the cross section, or six longitudinal bar diameters. Thespacing between adjacent hoop legs or crossties should notexceed 8 in. (203 mm), or 1/4 of the dimension of the sectionparallel to the direction of the spacing.

The previous equations were based on the results oftheoretical 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 thatthe equations can be projected to columns with concretecompressive strengths up to 14,500 psi (100 MPa) providedthat the maximum value of yield strength of the transversereinforcement used in the calculations is limited to 116,000 psi(800 MPa).

Li and Park (2004) carried out a parametric study to verifywhether the provisions for confining reinforcement in ACI318-05 and NZS 3101:1995 were applicable to high-strengthconcrete columns. They investigated the effect of severalparameters on the available strength and curvature ductilityof plastic hinge regions of columns. The parameters investi-gated by Li and Park were concrete compressive strength,axial load level, yield strength of the transverse reinforcement,volumetric ratio of the transverse reinforcement, percentage oflongitudinal reinforcement, and ratio of the area of theconfined core to the total area of the cross section. Theyperformed a series of cyclic moment-curvature analysesbased on stress-strain relationships previously derived forhigh-strength concrete to develop a set of design equationsrelating the amount of transverse reinforcement to the curva-ture ductility ratio.

Li and Park (2004) found that concrete compressivestrength and the ratio of the area of confined core to area ofthe cross section had a considerable influence on the quantityof confining reinforcement needed to achieve a givenductility ratio. They also found that the required amount oftransverse reinforcement needed to achieve a given curvatureductility ratio increased significantly as the axial load ratioincreased, and that the amount of transverse reinforcementincreased as the percentage of longitudinal reinforcementincreased. They adopted a curvature ductility ratio of 20 asindicative of adequate column toughness. They stated that acurvature ductility ratio of 20 was likely to result in displacementductility ratios for the overall structure on the order of 4 to 6.They also suggested a curvature ductility ratio of at least 10for frames where limited ductility would be sufficient.

Li and Park (2004) found that the expressions in ACI 318-05produced columns with adequate toughness for low levels ofaxial load, but were unconservative for high levels of axialload. Within the data set used in their study, there were four

Ash

sh″--------

1.3 ρlm–

3.3----------------------⎝ ⎠

⎛ ⎞ Ag

Ach

--------fc′fyt

----- Pφfc′ Ag

---------------=

Ash Ate∑=

Ate 10Ast fyl

fyt

------------s=

Ate116------

Ast fyl

fyt

------------ s100---------=


high-strength concrete columns with rectilinear normal-strength reinforcement ( fyt < 72,500 psi [ fyt < 500 MPa])that contained 200, 138, 180, and 167% of the confining trans-verse reinforcement required by ACI 318-05. These columnsachieved curvature ductility ratios of 17, 14, 21, and 14,respectively—all below or very close to the limit of 20 thatthey suggested as a performance criterion.

It was concluded by Li and Park (2004) that the amount ofconfining reinforcement required by ACI 318-05 wasinadequate to achieve curvature ductility ratios of 10 underhigh axial loads.

Li and Park proposed the following expression for theamount of confinement needed for columns with rectilinearnormal-yield-strength ( fyt < 72,500 psi [ fyt < 500 MPa])reinforcement

(5-8)

where

η = 117 when fc′ < 10,000 psi (70 MPa) (5-9)

and

η = when fc′ ≥ 10,000 (fc′ in psi) (5-10)

η = 0.05(fc′ )2 – 9.54fc′ + 539.4 when fc′ ≥ 70(fc′ in MPa)

For columns confined by circular normal-yield-strengthsteel, they proposed the following

(5-11)

where

κ = 1.1 when fc′ < 11,600 psi (80 MPa) (5-12)

and

κ = 1.0 when fc′ ≥ 11,600 psi (80 MPa) (5-13)

For columns confined by rectilinear high-yield-strengthreinforcement ( fyt ≥ 72,500 psi [ fyt ≥ 500 MPa]), theyproposed the following

(5-14)

where

η = 91 – ( fc′ in psi) (5-15)

and

η = 91 – 0.1fc′ ( fc′ in MPa)

For columns confined by circular high-yield-strengthreinforcement, they proposed

(5-16)

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

≤ 0.4 (5-17)

(5-18)

and the specified yield strength fyt is limited to

fyt ≤ 130,500 psi (900 MPa) (5-19)

According to Li and Park (2004), the proposed equationsestimated, with reasonable accuracy, the curvature ductilityratio of 56 high-strength concrete columns reported in theliterature.

Due to the emphasis placed on performance-based design,more recent studies focus on quantifying the relationshipbetween limiting drift (or ductility ratio), axial load, and theamount of confinement. Saatcioglu and Razvi (2002)developed a procedure to estimate the amount of transversereinforcement needed to sustain a given drift demand incolumns subjected to cyclic loading. Their procedure wasderived based on nonlinear static analyses, using a computerprogram that incorporated analytical models for concreteconfinement, steel strain-hardening, bar buckling, formationand progression of plastic hinging, and anchorage slip. Theyindicated that their computer program was verified extensivelyagainst a large volume of column test data. They proposedthe following expression for the transverse reinforcementarea ratio ρtc needed to attain a given limiting drift ratiounder a specified level of axial load

(5-20)

where

(5-21)

(5-22)

Ash

sbc

-------Ag

Ach

--------φu φy 33ρlm 22+–⁄( )

η-----------------------------------------------------

fc′fyt

-----Pu

φfc′ Ag

---------------=

fc′648.6-------------⎝ ⎠

⎛ ⎞2 fc′

15.2----------– 539.4+

Ash

sbc

------- κAg

Ach

-------φu φy 33ρlm 22+–⁄( )

111-----------------------------------------------------

fc ′fyt

-----Pu

φfc ′Ag

--------------- 0.006–=

Ash

sbc

-------Ag

Ach

--------φu φy 30ρlm 22+–⁄( )

η-----------------------------------------------------

fc′fyt

-----Pu

φfc′ Ag

---------------=

fc′1450------------

Ash

sbc

-------Ag

Ach

--------φu φy 55ρlm 25+–⁄( )

79-----------------------------------------------------

fc′fyt

-----Pu

φfc′ Ag

---------------=

ρi0.85fc′fyt

---------------------

Ag

Ach

-------- 1.5≤

ρtc 14fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ 1

kve

----------- PPo

-----δ=

kve 0.15bc

2

shx

-------=

PPo

----- 0.2≥


(5-23)

The transverse area ratio ρtc in each cross-sectional directionis computed as the ratio of total transverse steel in each directiondivided by the concrete area defined by core dimension bctimes the vertical spacing of the transverse reinforcement s.The core dimension is defined as the center-to-centerdimension of the perimeter tie, hoop, or spiral perpendicularto the confinement reinforcement under consideration. InEq. (5-21), bc/s is the ratio of core dimension to verticalspacing of the transverse reinforcement, and bc/hx is the ratioof core dimension to the center-to-center distance betweenlaterally supported longitudinal reinforcement. The coefficientkve reflects the efficiency of reinforcement arrangement as afunction of the spacing of the transverse reinforcement alongthe column height and the distance between laterally supportedlongitudinal bars. A value kve = 1.0 represents the most efficientarrangement of closely spaced circular hoops with anchoredhooks and spirals. The P/Po ratio defines the level of axial loadrelative to column concentric capacity Po, and δ defines the driftratio as relative column displacement divided by column height.Ag and Ach are cross-sectional areas based on gross sectionaldimensions and core dimensions, respectively.

Saatcioglu and Razvi (2002) indicated that because thestory drift ratio is limited to 2.0 to 2.5% by current buildingcodes, Eq. (5-20) can be simplified for use in high seismicapplications 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 inEq. (5-22) and (5-23)

(5-24)

Pu is the maximum axial compressive force that canpossibly be applied on the column during a strong earth-

Ag

Ach

-------- 1 0.3≥–

ρtc 0.35fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ 1

kve

----------- PP0

-----=

quake. This quantity may be computed as the factored axialload calculated in accordance with ACI 318-05, or the axialforce associated with the formation of probable momentresistances at the ends of the framing beams dictated bycapacity design requirements. The capacity reduction factormay be taken as 0.9 to reflect the improved ductility in thecolumn due to effects of confinement.

Saatcioglu and Razvi (2002), based on a comparison oftheir proposed equations with those in ACI 318-05 (Fig. 5.1),concluded that ACI 318-05 provisions result in overlyconservative requirements for spiral columns and somerectangular columns subjected to low levels of axial loads.

They also concluded that ACI 318-05 requirements can beunsafe when the axial load level is above approximately 40% ofthe column strength under concentric loading Po , particularly forcolumns with inefficient arrangements of transverse reinforce-ment. Saatcioglu and Razvi (2002) pointed out that, unlike theirproposed equations, the New Zealand specification does notinclude an efficiency parameter for the arrangement oftransverse reinforcement, resulting in overly conservative designsfor columns with superior arrangements of reinforcement.

Brachmann et al. (2004a,b) reviewed test results from 184rectangular columns subjected to shear reversals underconstant axial load with axial load ratios ranging from 0 to0.7. The database used by Brachmann et al. included testscarried out in Japan with high-strength concrete and highaxial load ratios. The equation proposed by Brachmann et al.was derived by analyzing the effect of confinement on thelimiting drift ratio of members without axial load. The effectof the axial load ratio on the effectiveness of confinementwas determined by grouping test results according to thelevel of axial load and comparing the estimated drift ratiowith that of members without axial load. This is illustrated inFig. 5.2, which shows that increasing the level of axial loadresults in a decrease of the limiting drift ratio. Brachmann etal. (2004b) proposed the following relationship between driftlimit, axial load, and amount of confinement, as an alternativeto Eq. (21-4) of ACI 318-05

(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 areatransverse reinforcement ratio, depending on the value of ζ.

Brachman et al. (2004b) recommended modifying Eq. (5-25)by replacing the axial load ratio fp by the core axial load ratiofpc to assure adequate confinement of the core for columnswith thick cover

(5-26)

where fpc = P/ fc′ Ach. The previous equations were calibratedso that the probability of overestimating the limiting drift ina column with the amount of transverse reinforcement

ρtrζDRlim

1 1.1fp–--------------------⎝ ⎠

⎛ ⎞ 2fc′fyt

-----=

ρtrζDRlim

1 0.8fpc–-----------------------⎝ ⎠

⎛ ⎞ 2fc′fyt

-----=

Fig. 5.1—Comparison of confinement steel requirements toproposal by Saatcioglu and Razvi (2002).


provided in accordance with the previous equations would be15% (one standard deviation from the mean). A comparison ofmeasured and calculated limiting drift ratios is presented inFig. 5.3. Because the equation relates the amount of confinementto the limiting drift ratio of a column, it can be used bydesigners seeking different levels of performance or expecteddrift demands.

Recommendations for design for different levels ofseismic applications can be derived by specifying suitablevalues for the limiting drift ratio. According to Brachmann etal. (2004a), yielding of the specimens occurred at a drift ratioof approximately 1%. Consequently, the difference betweenthe specified limiting drift ratio and a drift ratio of 1% is anindication of the capability of a column to deform in theinelastic range of response without significant loss in lateralresistance. Prescriptive confinement requirements forregions of moderate and high seismic applications can beestablished by conservatively assuming limiting drift ratiosof 1.5 and 2.5%. The resulting design expression for the twodifferent definitions of the transverse reinforcement ratio is

(5-27)

where the values of γ are given in Table 5.2.

Equation (5-27) requires the same amount of transversereinforcement as ACI 318-05, Eq. (21-4), in rectangularcolumns of special moment frames with a core axial loadratio fpc of 0.4. In the case of circular columns, the sameamount of transverse reinforcement is required at a core axialload ratio fpc of 0.35. For a rectangular column with twosymmetric layers of reinforcement, an axial load ratio of 0.4corresponds approximately to the balanced failure condition.

The study by Brachmann et al. (2004a and b) was based ondata from rectangular columns. Equations (21-2) and (21-4)of ACI 318-05 imply that the effectiveness of rectangularhoops is approximately 2/3 that of spiral reinforcement.Brachmann et al. (2004b) based their recommendation forcircular columns on a similar assumption.

ρtrγ

1 0.8fpc–-----------------------⎝ ⎠

⎛ ⎞ 2fc′fyt

-----=

Test data in the study by Brachmann et al. (2004a,b) hadcompressive strengths ranging from 3000 to 17,000 psi (21to 117 MPa); uniform factors of safety for columns wereobtained 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 columnsof moment-resisting frames be proportioned for stiffness sothat the interstory drift demand generated by the designearthquake forces is limited to 2.0% of story height forstandard-occupancy buildings (Seismic Occupancy CategoryIII). The design earthquake is defined in Section 11.4.4 ofASCE/SEI 7-05 as that with a seismic demand equal to 2/3of the seismic demand corresponding to the maximumconsidered earthquake (MCE), which has a 2% probabilityof being exceeded in a period of 50 years. There is a proba-bility that the drift demands experienced during the life cycleof a standard occupancy structure may exceed the 2% limitestablished in ASCE/SEI 7-05.

Drift demand can be greater than that computed in accor-dance with Sections 12.8.6 and 12.9.2 of ASCE/SEI 7-05

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

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

Transversereinforcement ratio ρtr

Coefficient ζ,circular sections

Coefficient ζ, square and rectangular sections

ρvr 10 12

ρt 6 8

Fig. 5.3—Measured and calculated limiting drift ratio limitversus volumetric confinement index cp = ρvpfyt/fc′ accordingto Eq. (5-26).

Table 5.2—Values of coefficient γ for Eq. (5-27)

Type of seismic application

Transversereinforcement

ratio ρtrCoefficient γ,

circular columns

Coefficient γ,square and rectangular

columns

Moderateρvr 0.15 0.18

ρt 0.09 0.12

Highρvr 0.25 0.30

ρt 0.15 0.20


because of the drift computation procedure that is implementedin ASCE/SEI 7-05. The most frequently used drift computationprocedure in ASCE/SEI 7-05 (Section 12.8.6) involves anelastic analysis of the building structure using design-levelearthquake forces. The design-level earthquake forcesspecified in Section 12.8.3 of ASCE/SEI 7-05 are obtainedfrom an elastic design response spectrum that produces aseismic response coefficient Cs (Section 12.8.1), which isinversely proportional to the response modification factor R.

Because proportioning the strength of the structure on thebasis of reduced earthquake forces does not reduce the driftdemands (Shimazaki and Sozen 1984; Shimazaki 1988;Lepage 1997; Browning 2001; Matamoros et al. 2003), thereduced displacement demands computed based on theforces specified in Section 12.8 of ASCE/SEI 7-05, with theinclusion of the coefficient R must be adjusted to obtainreasonable estimates of the displacement demands caused bythe design earthquake. This is accomplished in Sections12.8.6 and 12.9.2 of ASCE/SEI 7-05 through the use of thedeflection amplification factor Cd. Current values of R andCd specified in Table 12.2-1 of ASCE/SEI 7-05 for specialreinforced concrete moment-resisting frames are 8 and 5.5,respectively. There is a significant body of research based onnonlinear analyses of reinforced concrete frames and physicaltests of small-scale specimens in earthquake simulatorsshowing that these two factors are approximately equal forspecial reinforced concrete moment-resisting frames if thestiffnesses of the frames used in the linear analysis arecalculated on the basis of cracked section properties (Shibataand Sozen 1976; Shimazaki and Sozen 1984; Lepage 1997;Browning 2001; Matamoros et al. 2004). Consequently, driftdemands in special moment-resisting frames calculatedusing the R and Cd factors specified in Table 12.2-1 ofASCE/SEI 7-05 may underestimate the drift demand associatedwith the design earthquake by as much as 45%.

Also, as hinges form in columns, the nonlinear responsetends to concentrate drift demands in the stories betweenplastic hinges in columns rather than distributing themevenly over the height of a building, as an elastic analysiswould indicate. In special reinforced concrete momentframes, however, the strong column-weak beam provisionguards against plastic hinges within columns from beingclose to one another, that is, plastic mechanisms over only afew stories, where large drifts are concentrated.

One of the criteria that must be considered in establishinga limiting drift for the purpose of determining the amount ofconfinement in columns is the performance objectiveoutlined by design codes. The general goals of the codeprovisions, though not specifically stated, are to provide lifesafety in the design-level earthquake and collapse preventionfor the MCE (BSSC 2004). The amount of confinement isprimarily determined by the need for providing life safety inthe design earthquake while considering collapse preventionin the MCE. The drift demand from the MCE may be as highas 50% greater than the drift demand from the design-levelearthquake.

The most common failure criterion adopted by researchersinvestigating the relationship between column performance

and the amount of transverse reinforcement used to confinethe concrete has been the point in the hysteresis curvecorresponding to a 20% reduction in the maximum lateralload that was measured. If the performance of a frameexpected in the MCE is considered, the amount of confinementmust be adequate to achieve collapse prevention at driftdemands approximately 50% greater than the 2% interstorydrift limit established in Section 12.12 of ASCE/SEI 7-05.Experimental results from columns tested to axial loadfailure at the University of California (Lynn 2001; Sezen2002) show that specimens with significantly less transversereinforcement than that specified by the proposals summarizedin Section 5.3 were able to sustain drift demands before axialload failure exceeding 3.5% of the story height. It must benoted, however, that all columns tested by Lynn (2001) andSezen (2002) were made with normal-strength concrete andthat there were no references found addressing the axial loadfailure of columns with high-strength concrete.

5.5—Use of high-yield-strength reinforcementfor confinement

Because the amount of confinement required in columns isproportional to the compressive strength of the concrete,congestion problems arise in potential plastic hinge regionsof columns with high-strength concrete, particularly in thebeam-column joints. Conversely, the amount of requiredconfinement reinforcement is inversely proportional to theyield strength of the reinforcement, which presents the possi-bility of decreasing the volume of transverse reinforcement,thereby relieving congestion.

Several studies done at the University of Ottawa haveinvestigated the use of high-strength reinforcement for theconfinement of high-strength concrete columns (Saatciogluand Razvi 1998; Razvi and Saatcioglu 1999; Lipien andSaatcioglu 1997; Saatcioglu and Baingo 1999; Saatciogluand Razvi 2002). The researchers tested a total of 66 nearlyfull-size circular and square columns, with concrete strengthsranging between 8700 and 18,000 psi (60 and 124 MPa), undereither monotonically increasing concentric compression or aconstant compression accompanied by incrementallyincreasing lateral deformation reversals. Three differentgrades of transverse reinforcement were used, with yieldstrengths of 60,000, 83,000, and 145,000 psi (414, 572, and1000 MPa). The researchers concluded that, given the rightcombination of parameters, transverse reinforcement withyield strengths up to 145,000 psi (1000 MPa) can be effectivein confining high-strength concrete columns, increasing thecolumn lateral drift ratio up to a minimum of 5% in heavilyloaded columns (0.43Po) and 8% in lightly loaded columns(0.22Po). The researchers focused on finding how much ofthe additional strength available in transverse reinforcementwith higher nominal yield strengths could be mobilized by arelatively brittle material like high-strength concrete beforesignificant strength degradation. They observed that theeffectiveness of transverse reinforcement increased withconfinement efficiency, the volumetric ratio of steel, and thelevel of axial compression. The efficiency of confinement isimproved by selecting a superior reinforcement arrangement,


either in the form of circular hoops or spirals, where hooptension results in uniform confinement pressure, or byselecting well-distributed longitudinal reinforcement laterallysupported by perimeter and overlapping hoops, crossties, orboth. According to the researchers, a square column with12 longitudinal bars in which each bar is supported by thecorner of a hoop or the hook of a crosstie provides anexample of a superior arrangement, while a square columnwith four corner bars tied by perimeter hoops exemplifies apoor reinforcement arrangement for rectilinear reinforcement.Similarly, the spacing of transverse reinforcement along thecolumn height affects the efficiency of confinement quitesignificantly. It was shown that a spacing of 1/4 of thesmaller cross-sectional dimension was adequate to providesufficient confinement efficiency, with reductions in efficiencyoccurring as the spacing approached 1/2 of the smallercross-sectional dimension. The confinement efficiency wasquantified empirically by Razvi and Saatcioglu (1999).Accordingly, the confinement efficiency parameter kveequals 1.0 for closely spaced circular hoops or spirals, and canbe computed by Eq. (5-24) for rectilinear reinforcement.

Tests of columns under concentric compression indicatedthat square columns with 12,000 to 18,000 psi (83 to 124 MPa)concrete and confinement efficiency parameter kve ≥ 0.5experienced yielding of transverse reinforcement with yieldstrength of 145 ksi (1000 MPa) when the volumetric ratio ofreinforcement was approximately 2%. Circular columnswith similar properties required a smaller volumetric ratio of1.3% to trigger the yielding of 145 ksi (1000 MPa) reinforcementwhen spiral reinforcement (kve = 1.0) was used. The yieldingof high-strength transverse reinforcement was recorded at orimmediately after column strength, often just before theonset of significant strength degradation. The followingexpression was suggested by Razvi and Saatcioglu (1999)for the computation of transverse steel stress at or shortly afterthe attainment of strength under concentric compression

(5-28)

where ρtc is the area ratio of transverse reinforcement; fco′ isthe in-place strength of unconfined concrete in the column inpsi (often taken as 0.85fc′ ); and Es is the modulus of elasticityof reinforcing steel.

According to Razvi and Saatcioglu (2002), the upper limiton the yield strength of steel may be taken as 200,000 psi(1379 MPa) because this was the maximum yield strength oftransverse reinforcement used (Nagashima et al. 1992) in thehigh-strength concrete column tests evaluated.

The level of axial load was found to be another parameterthat affects the effectiveness of high-strength transversereinforcement for columns subjected to lateral loading(Saatcioglu and Baingo 1999). Spirals with 145 ksi (1000 MPa)yield strength developed their tensile strength in columnswith 18,000 psi (124 MPa) concrete before significantstrength decay, when the level of axial load was 0.43Po.

When the level of axial compression dropped to 0.22Po, thestress in spirals did not exceed approximately 110,000 psi(758 MPa). Steel with 90 ksi (621 MPa) yield strength waseffective in all columns tested. Saatcioglu and Razvi (2002)recommended a limit of 110 ksi (758 MPa) on the yieldstrength of transverse reinforcement for confinement designwhen column axial compression is at least 20% of its strengthunder concentric loading, and 90 ksi (621 MPa) otherwise.

Otani et al. (1998) and Otani (1995) described the use ofhigh-strength reinforcement in the seismic design guidelinesfor high-rise reinforced concrete buildings in Japan.

According to Otani (1995), high yield strength is normallyattained by heat treatment of hot-rolled, chemicallycontrolled killed steel. The chemical composition of thereinforcing steel must be carefully controlled to developlarge elongations at fracture, especially when welding isused to splice closed hoops and stirrups. Shear reinforcementis provided in the form of rectangular hoops and stirrups with135-degree hooks, circular or rectangular spirals, supplementaryties with 135- or 90-degree hooks, or welded closed hoopsand stirrups. The yield strength is defined by the 0.2%permanent offset. The fracture strain is measured over agauge length of eight times the nominal bar diameter, andmust not be less than 0.05 at any region of the bar, includingsections where bars have been connected through welding.Four types of high-yield-strength bars were developed inJapan as part of the New RC project for use as transversereinforcement, with yield strengths ranging from 99,000 to185,000 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 ofUHY685 reinforcement (Hokuetsu Metal Co. 1990) are:a) minimum yield strength of 99,000 psi (683 MPa); b) minimumtensile strength of 128,000 psi (883 MPa); and c) minimumfracture strain of 0.10. The nominal diameters of these barsare 0.35, 0.39, 0.50, and 0.63 in. (9.00, 9.53, 12.7, and15.9 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 198.6mm2), respectively (Otani 1995). According to Otani et al.(1998), a second type of Grade 685 reinforcement(USD685B) was developed for use as longitudinal reinforce-ment in plastic hinge regions. The yield strength ofUSD685B reinforcement must range between 99,000 and110,000 psi (683 and 758 MPa), and the ratio of yieldstrength to tensile strength must be less than or equal to 0.8.This type of reinforcement must have a strain of at least0.014 at the upper-bound yield stress of 110,000 psi (758 MPa)to ensure an adequate yield plateau.

KSS785 steel bars—Mechanical characteristics ofKSS785 reinforcement (Kobe Steel Ltd. 1989; SumitomoElectrical 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); andc) minimum fracture strain of 0.08. Nominal diameters of thesebars are 0.24, 0.31, 0.38, and 0.50 in. (6.35, 7.94, 9.53, and12.7 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).

fs Es 0.0025 0.21kveρtc

fco′--------------3+

⎝ ⎠⎜ ⎟⎛ ⎞

fyt≤=


SPR785 steel bars—Mechanical characteristics of SPR785reinforcement (Tokyo Steel Co. 1994) are: a) minimumyield strength of 114,000 psi (786 MPa); b) minimum tensilestrength of 135,000 psi (931 MPa); and c) minimum fracturestrain 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 givenominal 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) manu-facture Type D SBPD(N/L) 1275/1420 bars conforming tothe requirements of the Japanese Standards Association(1994) JIS G 3137, “Small Size-Deformed Steel Bars forPrestressed Concrete,” which requires: a) a minimum yieldstrength of 185,000 psi (1276 MPa); b) a minimum tensilestrength of 206,000 psi (1420 MPa); and c) a minimumfracture strain of 0.05. The JIS G 3137 specification wasinstituted following the establishment of ISO 6934 (1991)(Steel for the Prestressing of Concrete; Part 3: Quenched andTempered Wire; and Part 5: Hot-Rolled Steel Bars with orwithout Subsequent Processing), but the JIS requires morerigorous control of the chemical composition of the steel.Furthermore, the amount of impurities in SBPD1275/1420high-strength shear reinforcement is controlled more rigorouslythan required by the JIS G 3137 specification. The minimumstrain at fracture is set to 0.07 because the bars are normallybent 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 corre-spond 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 designof high-rise structures using high-strength materials devel-oped as part of the research initiative sponsored by theMinistry of Construction in Japan (Japan Institute ofConstruction Engineering 1993). According to Otani et al.

(1998), these seismic design guidelines limit the yieldstrength 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 rein-forcement 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 reinforcementyield strengths ranging between 37,000 and 183,000 psi (255and 1262 MPa), and volumetric transverse reinforcementratios ranging from 0.17 to 6.64%. Because specimens withtransverse 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 reinforce-ment. The ratio of measured to calculated limiting drift ratioaccording to the equation proposed by Brachmann et al.(2004b) versus the yield strength of the transverse reinforcementis shown in Fig. 5.4, where the yield strength of transversereinforcement was limited to 120,000 psi (827 MPa) in thecalculation of the limiting drift ratio regardless of the actualyield strength. The broken line in Fig. 5.4 represents a linearregression between the ratio of measured to calculated drift(computed limiting the yield strength of the reinforcement to120,000 psi [827 MPa]) and the actual yield strength of thereinforcement.

The suggestion by Brachmann et al. (2004a,b) to limit theyield strength of the transverse reinforcement to 120,000 psi(827 MPa) is consistent with the observations by Saatciogluet al. (1998) and Kato et al. (1998) that the effectiveconfining pressure decreases and the probability of bucklingof the longitudinal reinforcement increases with increasinghoop spacing. Similarly, the NZS 3101 design provisionestablishes an upper limit of 116,000 psi (800 MPa) for thenominal yield strength of the transverse reinforcement.

5.6—Maximum hoop spacing requirementsfor columns

Section 21.4.4.2 of ACI 318-05 allows a maximumspacing of transverse reinforcement in regions of potentialplastic hinging of 1/4 of the minimum member dimension,six times the diameter of the longitudinal reinforcement, and4 in. (102 mm). The 4 in. (102 mm) spacing requirement maybe increased linearly up to 6 in. (152 mm) as the spacing ofcrossties or legs of overlapping hoops decreases from 14 to8 in. (356 to 203 mm). The ICBO ER-5536 document (2001)suggests that the maximum spacing of hoops within plastichinge regions should be 5 in. (127 mm). The rationale for thisprovision stems from the fact that in the experimentalresearch used as the basis for the aforementioned document(C4 Committee 2000), satisfactory behavior was observed inspecimens with a maximum hoop spacing of 6 in. (152 mm).Englekirk and Pourzanjani indicate in the C4 report (2000),however, that test results by Azizinamini et al. (1994)contradict this observation. In specimens with an axial loadratio of 0.2 and concrete compressive strength of approximately14,500 psi (100 MPa), Azizinamini et al. observed that themode of failure changed from yielding of the transversereinforcement to buckling of the longitudinal reinforcement

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


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

5.7—Confinement requirements for high-strength concrete beams

The only confinement requirements for concrete in plastichinge regions of beams established in ACI 318-05 are interms of the maximum spacing allowed between hoops.

Unlike in the case of ACI 318-05, Eq. (21-2) to (21-4), forcolumns, there are no equations that set the minimumamount of transverse reinforcement that must be used inbeams. Such a lack of requirement is of some concern forhigh-strength concrete beams because test results previouslysummarized show that the limiting drift ratio of beams isproportional to the volumetric confinement index cp (Fig. 5.5).The data in Fig. 5.5 indicate that to maintain a level ofdeformability, the product of ρvr fyt must increase with theconcrete compressive strength.

Ghosh and Saatcioglu (1994) summarized test results fromhigh-strength concrete beams under monotonic and cyclicloading by several researchers. Based on tests by Fajardo andPastor (Pastor et al. 1984) under monotonic loading, theyconcluded that the addition of lateral tie steel increases thedisplacement ductility of beams provided that the volumetricconfinement index is greater than 0.11. The definition of thevolumetric confinement index used by Ghosh and Saatcioglu,however, included the effects of the compression reinforcement

cp = (ρvr + ρ′) (5-29)

A volumetric confinement index of 0.11, calculated asdefined in Eq. (5-29), corresponded to a displacementductility of approximately 3. For beams with volumetricconfinement indexes below 0.11, increasing the volumetricconfinement index in the plastic hinge region resulted insmall increases in displacement ductility. In cases where thevolumetric confinement index exceeded 0.11, increasing thevolumetric confinement index resulted in significant

fyt

fc′-----

increases in displacement ductility. Ghosh and Saatcioglu(1994) attributed the low deformability of the beams withlower amounts of transverse reinforcement to the lack ofconfinement of the concrete in the compression zone.

Brachmann et al. (2004a) proposed an equation for theminimum amount of transverse reinforcement for adequateconfinement of reinforced concrete beams based on experi-mental results. For members without axial load, theminimum amount of confining reinforcement is given by

(5-30)

Equation (5-30) was calibrated so that the probability ofoverestimating the limiting drift in a beam with the amountof transverse reinforcement provided in accordance toEq. (5-30) would be 15% for the data set used (one standarddeviation from the mean). Figure 5.5 shows the measuredlimiting drift ratios and those calculated with Eq. (5-30) for62 specimens with fp ≤ 0.1, and concrete compressivestrengths 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 sampleof 62 specimens considered, the probability of underestimatingthe limiting drift of beam elements with Eq. (5-30) wasapproximately 10%.

Equation (5-30) requires a higher amount of transversereinforcement for high-strength concrete beams than thatcalculated using the current ACI 318-05 approach of propor-tioning the transverse reinforcement to resist, in most prac-tical circumstances, 100% of the shear demand (ACI 318-05,Section 21.3.4.2). A comparison based on assumptions of aspan length to beam depth ratio of 10, an effective depthequal to 90% of the beam height, a width-height ratio of thecore equal to 2, and a limiting drift ratio of 2% indicates thatthe amount of reinforcement would increase by a factor ofapproximately 0.2fc′ /ρl fyl , where ρl is the longitudinalreinforcement ratio and fyl is the yield strength of the longitu-

ρvr 12DRlim( )2 fc′fyt

----- 0.12fc′fyt

-----≥=

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


dinal reinforcement. The difference is most significant forlightly reinforced beams. For beams with normal-strengthconcrete, the amount of transverse reinforcement would beapproximately the same as required by the current code,while in the case of beams with high-strength concrete, theamount of transverse reinforcement would increase by asmuch as a factor of 4. Before a code change is implemented,such an increase in the amount of transverse reinforcementshould be justified on the basis of experimental evidenceshowing inadequate performance of high-strength concretebeams under cyclic loading.

Experimental research on column collapse indicates thatvertical load-carrying capacity is lost soon after the lateralload-carrying capacity has degraded to zero (Yoshimura andNakamura 2002; Elwood and Moehle 2005), and that thelateral drift at axial failure decreases with axial load. Elwood(2002) and Elwood and Moehle (2005) developed a modelconsistent with the observation from experimental researchthat the drift ratio at axial failure is inversely proportional tothe axial load demand. From this research, it follows that therisk of catastrophic failure at drifts slightly higher than thelimiting drift ratio (defined as that corresponding to a 20%reduction in strength) decreases as the amount of axial loadon the member decreases. For this reason, it is reasonable toadopt a lower margin of safety for proportioning the amountof transverse reinforcement needed to reach a target limitingdrift ratio in beams than in columns. Brachmann et al.(2004a) provided expressions with various probabilities ofoverestimating the limiting drift ratio. The expressioncorresponding to the mean response (such that the probabilityof overestimating the limiting drift ratio in a beam with theamount of transverse reinforcement provided in accordanceto Eq. (5-31) would be 50%) is given by

(5-31)

Because the volume of transverse reinforcement requiredby Eq. (5-31) is 44% of that required by Eq. (5-30), theamount of transverse reinforcement required in beams iscloser to that calculated using the approach in ACI 318-05.A comparison based on assumptions of a span length tobeam depth ratio of 10, an effective depth equal to 90% ofthe beam height, a width-height ratio of the core equal to 2,and a limiting drift ratio of 2% indicates that the amount ofreinforcement would increase by a factor of approximately0.09fc′ /ρl fyl where ρl is the longitudinal reinforcement ratioand fyl is the yield strength of the longitudinal reinforcement.In this case, the amount of transverse reinforcement requiredby Eq. (5-31) in lightly reinforced beams (ρl = 0.01) wouldrange between approximately 1/2 the amount currentlyrequired by ACI 318-05 for beams with normal-strengthconcrete and two times the amount calculated using ACI 318-05for beams with high-strength concrete.

5.8—Maximum hoop spacing requirements

for high-strength concrete beamsAccording to Section 21.3.3.2 of ACI 318-05, the

maximum hoop spacing in flexural members of specialmoment frames must not exceed d/4, eight times the diameterof the smallest longitudinal bar, 24 times the diameter of thehoop bars, and 12 in. (305 mm). A similar spacing requirementis established in Section 21.12.4.2 of ACI 318-05 for beamsof intermediate moment frames. Although the upper limit forthe hoop spacing is 12 in. (305 mm), it is important to notethat the requirements related to bar size and d/4 are likely toresult in significantly smaller upper limits on spacing.Consequently, the 12 in. (305 mm) spacing limit is not thecontrolling criterion for most practical cases. For instance, across section with an effective depth of 24 in. (610 mm), No. 7longitudinal bars, and No. 3 hoops would have a maximumhoop spacing of 6 in. (152 mm), significantly lower than thenominal 12 in. (305 mm) limit established by ACI 318-05.

The ICBO ER-5536 document (2001) proposed an upperlimit 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 ofexperimental results from beams with hoop spacing largerthan 4 in. (102 mm) is a concern in determining whether thereduction 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 andSaatcioglu (1994) had stirrup spacing ranging from 3 to 12 in.(76 to 305 mm). The width of the test region ranged between6.56 and 7.38 in. (167 to 187 mm), and the depth wasapproximately 12 in. (305 mm). Beams with a hoop spacingof 12 in. (305 mm) exhibited the worst performance, withductility ratios on the order of 2 or 3. All beams with a stirrupspacing of 6 in. (152 mm) or less exhibited displacementductilities higher than 4. This observation raises concernsabout the 12 in. (305 mm) spacing limit adopted by ACI 318-05particularly because these beams were not subjected to thedeterioration of the core that would occur under loadreversals. The conclusions by Ghosh and Saatcioglu (1994)about the effects of confinement also seem to indicate that thereis no compelling reason to have different procedures todetermine the amounts of confinement in beams and columns.

5.9—RecommendationsThere are several recommendations deemed necessary for

proper confinement of sections with high-strength concrete.Research by Brachman et al. (2004a,b), and Saatcioglu andRazvi (2002) has indicated that the current provisions forconfinement in ACI 318-05, even though the effect of axialload is neglected, result in sufficient amounts of confinementto achieve limiting drift ratios of at least 2% in most cases.The main disadvantage of the current provisions is that thesafety afforded is not uniform for all columns, and theamount of transverse reinforcement required in memberswith lower levels of axial load is overly conservative.Although excessive conservatism does not pose a safetyconcern, it creates significant congestion problems thathinder the use of high-strength concrete.

ρvr 8DRlim( )2 fc′fyt

----- 0.12fc′fyt

-----≥=


Experimental research shows that a viable alternative toreduce congestion in plastic hinge regions is the use of high-strength transverse reinforcement. There is consensus amongresearchers that there should be an upper limit to the nominalyield strength of the transverse reinforcement used forconfinement purposes of approximately 120 ksi (827 MPa).

The experimental data that were reviewed did notsubstantiate the need to reduce the maximum hoop spacingin beams or columns. Although there was a greater concernin the case of beams because the upper limit for hoop spacingestablished by ACI 318-05 is 12 in. (305 mm), a closerreview shows that spacing limits in terms of the diameter ofthe longitudinal and transverse reinforcement should beadequate to prevent buckling of the longitudinal reinforcement.Research results and experimental evidence indicate that theamount of confinement afforded by the current spacing limitsshould be sufficient to achieve drift ratios (approximatelysimilar to the rotation of the plastic hinge in units of radians)on the order of 0.02 without catastrophic failure. For thesereasons, it was deemed unnecessary to introduce confinementrequirements 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 concretecolumns in special moment frames (SMF). The basis for theproposed equations is the approach by Saatcioglu and Razvi(2002), with some minor conservative modifications tosimplify 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 tomeet the confinement requirements for high-strengthconcrete columns. The yield strength of the reinforce-ment can be measured by the offset method of ASTM A370 using 0.2% permanent offset.

• Transverse reinforcement required as follows in (a)through (c) shall be provided unless a larger amount isrequired by ACI 318-05, Sections 21.4.3.2 or 21.4.5:

(a)The area ratio of transverse reinforcement shall notbe less than that required by Eq. (5-32)

(5-32)

where

– 1 ≥ 0.3 (5-33)

and

≥ 0.2 (5-34)

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

columns with circular geometry shall be in theform of spirals or hoops, for which kve = 1.0. Rein-forcement for columns with rectangular geometryshall be provided in the form of single or overlap-ping hoops. Crossties of the same bar size andspacing as the hoops shall be permitted. Each endof the crosstie shall engage a peripheral longitu-dinal reinforcing bar. Consecutive crossties shallbe alternated end for end along the longitudinalreinforcement. The parameter kve for rectangularhoop reinforcement shall be determined by Eq. (5-35)

(5-35)

(c)If the thickness of the concrete outside theconfining transverse reinforcement exceeds 4 in.,additional transverse reinforcement shall beprovided at a spacing not exceeding 12 in.Concrete cover on the additional reinforcementshall 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 tomeet the confinement requirements for high-strengthconcrete columns. The yield strength of the reinforce-ment can be measured by the offset method of ASTM A370 using 0.2% permanent offset.

• Transverse reinforcement required as follows in (a)through (c) shall be provided unless a larger amount isrequired by ACI 318M-05, Sections 21.4.3.2 or 21.4.5:

(a)The area ratio of transverse reinforcement shall notbe less than that required by Eq. (5-36)

(5-36)

where

– 1 ≥ 0.3 (5-37)

and

≥ 0.2 (5-38)

(b)Transverse reinforcement shall have either circularor rectangular geometry. Reinforcement forcolumns with circular geometry shall be in theform of spirals or hoops, for which kve =1.0. Rein-forcement for columns with rectangular geometryshall be provided in the form of single or overlap-ping hoops. Crossties of the same bar size andspacing as the hoops shall be permitted. Each end

ρt 0.35fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ 1

kve

-----------Pu

Agfc′-----------=

Ag

Ach

--------

Pu

Agfc′-----------

kve0.15bc

shx

--------------- 1.0≤=

ρt 0.35fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ 1

kve

-----------Pu

Agfc′-----------=

Ag

Ach

--------

Pu

Agfc′-----------


of the crosstie shall engage a peripheral longitudinalreinforcing bar. Consecutive crossties shall be alter-nated end for end along the longitudinal reinforce-ment. The parameter kve for rectangular hoopreinforcement shall be determined by Eq. (5-39).

(5-39)

(c)If the thickness of the concrete outside theconfining transverse reinforcement exceeds 100 mm,additional transverse reinforcement shall beprovided at a spacing not exceeding 300 mm.Concrete cover on the additional reinforcementshall not exceed 100 mm.

The term hx is defined as the maximum horizontal spacingof hoop or crosstie legs perpendicular to bc , in.

Section 21.12.3 of ACI 318-05 requires that the designshear strength φVn of beams and columns of intermediatemoment frames be no less than: a) the sum of the shear asso-ciated with development of nominal moment strengths of themember at each restrained end of the clear span and the shearcalculated for factored gravity loads; and b) the maximumshear obtained from design load combinations that includeE, with E assumed to be twice that prescribed by thegoverning code for earthquake-resistant design.

If the dimensions of a column are maintained constant, theratio of axial load demand to balanced failure load decreasesas concrete compressive strength in the column increases.Under the current design provisions in Section 21.12.3 ofACI 318-05, the amount of transverse reinforcementincreases with the nominal flexural strength of columns,which decreases as the ratio of axial load to balanced loaddecreases (assuming that the column is not compressioncontrolled). For this reason, it is possible that the amount oftransverse reinforcement required by the aforementionedprovision be similar or even less for columns with high-strength concrete than it is for columns with similar dimensionsmade with normal-strength concrete. This is inconsistentwith the conclusions from the literature review presented inSections 5.2 and 5.3 of this report, which indicate that theamount of confinement needed for ductile behavior in columnsincreases with increasing concrete compressive strength.

To prevent the sudden failure of columns with high-strength concrete in intermediate moment frames (IMF), it isrecommended that a minimum amount of confinementreinforcement be added to the provisions in the code. Theconfinement reinforcement requirement for IMF columns inITG-4.3R is based on a design expression developed bySaatcioglu and Razvi (2002), and modified by ACI ITG 4 tofacilitate its use for design. One of the key assumptionsadopted by ACI ITG-4 in deriving this requirement is that a20% reduction in lateral strength at a drift ratio of 1.5%corresponds to a tolerable level of damage for intermediatemoment frames. This criterion is related to the level ofdamage deemed reasonable for this type of a lateral-force-resisting system, and should not be interpreted to mean that

intermediate moment frames must be proportioned so thatdrift ratios are kept below 1.5%. This assumption is consistentwith the fact that the R factor for the IMF traditionally hasbeen set by building codes to approximately 60 to 75% ofthat for a SMF. For example, according to ASCE 7-05, the Rfactor for an IMF is 5, while that for a SMF is 8. If the Rfactor is taken as a measure of the ductility demands(including inherent overstrength) and it is assumed that themaximum nonlinear displacement is approximately equal tothe maximum displacement of a linear system (Shimazaki1988; Lepage 1997; Browning 2001) (implying that Cd ≈ R),the difference in R factors implies that the SMF is expectedto experience nearly 8/5 (or 1.6 times) as much plastic rotationdemands as the IMF. Lower plastic rotation demands implylower strain demands on the concrete and a reduction in theamount of confinement reinforcement required. This reductionis indirectly recognized in these recommendations by using1.5% drift ratio instead of 2.5% when deriving the requirementsfor confinement reinforcement for the IMF. To furthersimplify the calculation, a value of kve = 0.5 is adopted forcolumns with rectilinear transverse reinforcement. Consideringthat a value of kve = 1.0 is used in columns with spiral reinforce-ment, this assumption implies that the rectilinear confiningreinforcement arrangement being used is 71% as effective asthat of spiral reinforcement.

The following changes to ACI 318-05 are recommendedfor 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 tomeet the confinement requirements for high-strengthconcrete columns. The yield strength of the reinforce-ment can be measured by the offset method of ASTM A370 using 0.2% permanent offset;

• For columns with concrete compressive strength greaterthan 8000 psi and rectilinear transverse reinforcement, thearea ratio of transverse reinforcement shall not be lessthan that required by Eq. (5-40)

(5-40)

where

– 1 ≥ 0.3 (5-41)

and

≥ 0.2 (5-42)

• For columns with concrete compressive strengthgreater than 8000 psi and transverse reinforcement inthe form of circular hoops or spirals, the area ratio oftransverse reinforcement shall not be less than thatrequired by Eq. (5-43)

kve0.15bc

shx

--------------- 1.0≤=

ρc 0.3fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ Pu

Agfc′-----------=

Ag

Ach

--------

Pu

Agfc′-----------


(5-43)

where

– 1 ≥ 0.3 (5-44)

and

≥ 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 tomeet the confinement requirements for high-strengthconcrete columns. The yield strength of the reinforce-ment can be measured by the offset method of ASTM A370 using 0.2% permanent offset;

• For columns with concrete compressive strength greaterthan 55 MPa and rectilinear transverse reinforcement, thearea ratio of transverse reinforcement shall not be lessthan that required by the following equation

(5-46)

where

– 1 ≥ 0.3 (5-47)

and

≥ 0.2 (5-48)

• For columns with concrete compressive strengthgreater than 55 MPa and transverse reinforcement inthe form of circular hoops or spirals, the area ratio oftransverse reinforcement shall not be less than thatrequired by the following equation

(5-49)

where

– 1 ≥ 0.3 (5-50)

and

ρc 0.2fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ Pu

Agfc′-----------=

Ag

Ach

--------

Pu

Agfc′-----------

ρc 0.3fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ Pu

Agfc′-----------=

Ag

Ach

--------

Pu

Agfc′-----------

ρc 0.2fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ Pu

Agfc′-----------=

Ag

Ach

--------

≥ 0.2 (5-51)

CHAPTER 6—SHEAR STRENGTH OF REINFORCED CONCRETE FLEXURAL MEMBERS

In flexural members made with high-strength concrete,the strength of the paste is similar to or higher than that of theaggregates. As a result, cracks tend to propagate through theaggregates and have a smoother surface than in normal-strength concrete (ACI Committee 363 1992). A smoothercrack surface reduces the effect of aggregate interlock onshear strength, which theoretically implies a reduction in theconcrete component of the total shear strength.

The effect of compressive strength on the shear forcecarried by the transverse reinforcement can be analyzedusing a variable angle truss model (Fig. 6.1). The equilib-rium equations for a variable angle truss model with auniform compression field (Joint ACI-ASCE Committee445 1998) indicate that the average shear stress carried bythe truss mechanism is given by

(6-1)

where j is the ratio of internal lever arm (the distancebetween the tension force in the reinforcement and thecompression force carried by the concrete) to the effectivedepth, and αt is the angle of inclination of the compressivestrut. Equation (6-1) shows that if all other parameters in abeam remain constant, the shear stress carried by the trussmechanism increases as the angle of inclination of the strutαt decreases. The same model indicates that the compressivestress in the struts of the compression field fc is given by

(6-2)

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

Pu

Agfc′-----------

vsVs

bwd---------

Av fs j

bws----------- 1

αttan-------------= =

fcvs

αt αtsincos---------------------------=

Fig. 6.1—Variable angle truss model with uniform compressionfield.


capacity of the struts. Equation (6-1) shows that a reductionin the strut angle leads to an increase in the shear forcecarried by the reinforcement, increasing the effectiveness ofthe transverse reinforcement.

After inclined cracking occurs, the force carried by theconcrete is expected to decrease with increasing compressivestrength due to reduced aggregate interlock. The oppositeoccurs with the force carried by the reinforcement throughthe truss mechanism, which is expected to increase due to thehigher strength of the concrete in the struts of the web. Conse-quently, one of the most significant concerns in calculating theshear strength of members with high-strength concrete ispreventing the sudden failure of members with relatively smallamounts of transverse reinforcement, for which the maximumshear force that can be carried by the truss mechanism issimilar to or smaller than the shear force corresponding toinclined cracking. In members with high amounts of transversereinforcement, theory suggests that the reduction in the shearforce carried by the concrete is offset by an increase in theeffectiveness 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 parameterson the test/calculated ratio obtained with Eq. (11-3) and (11-5)of ACI 318-05 for nonprestressed beams without transversereinforcement

ACI 318 Eq. (11-3)

ACI 318 Eq. (11-5)

Test results presented in Fig. 6.2 and 6.3 are from the data-base of shear tests developed by Reineck et al. (2003).Although the figures indicate that there is no bias withrespect to the compressive strength of concrete, they show asignificant problem for members with light amounts oflongitudinal reinforcement.

Collins and Kuchma (1999), Nilson (1994), Ahmad et al.(1986), and Ahmad and Lue (1987) point out that thisproblem is of most significance for lightly reinforced slenderbeams with high-strength concrete. Figures 6.2 and 6.3 alsoshow that the shear strength of members without transversereinforcement may be affected by the effective depth of themember (Joint ACI-ASCE Committee 445 1998). Althoughthere is considerable debate about the proper model to quantifythe effect of size (Joint ACI-ASCE Committee 445 1998),Collins et al. (1993) stated that tests of high-strengthconcrete beams conducted by Kuchma et al. (1997) showedthat this effect is not significant if longitudinal reinforcementis distributed throughout the depth of the member. The reportby Joint ACI-ASCE Committee 445 (1998) summarizesseveral equations that have been proposed to more accuratelyreflect the effects of compressive strength, longitudinalreinforcement ratio, and effective depth on shear strength ofmembers without transverse reinforcement.

Vc 2 fc′ bwd (fc′ in psi)=

Vc 0.17 fc′ bwd (fc′ in MPa)=

Vc 1.9 fc′ 2500ρwVudMu

---------+⎝ ⎠⎛ ⎞ bwd 3.5 fc′ bwd fc′ in psi( )≥=

Vc 0.16 fc′ 17.2ρwVudMu

---------+⎝ ⎠⎛ ⎞ bwd 0.29 fc′ bwd fc′ in MPa( )≥=

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

fc′


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

6.2—Effect of compressive strength on inclined cracking load of flexural members

ACI 318-89 (ACI Committee 318 1989) placed an upperlimit of 100 psi (8.3 MPa) on the term for calculatingthe shear strength of reinforced concrete beams, joists, andslabs. This upper limit was based on experimental results(Mphonde and Frantz 1984; Elzanaty et al. 1986), whichindicated that the ratio of measured to calculated inclinedcracking load in beams increased with the compressive strengthof concrete at a lower rate than indicated by Eq. (11-3) or(11-5) of ACI 318-89. Similar behavior was observed in astudy on the shear strength of high-strength concrete beamswithout transverse reinforcement by Thorenfeldt andDrangsholt (1990). The inclined cracking load remainedalmost constant in spite of an increase in compressivestrength from 11,300 to 14,200 psi (78 to 98 MPa).

These and other test results raised concerns about the shearstrength of high-strength concrete flexural members withsmall amounts of transverse reinforcement. ACI 318-89allowed the limit of 100 psi (8.3 MPa) on the term to beexceeded if transverse reinforcement sufficient to carry a

nominal shear stress of 50 psi (0.34 MPa), multiplied by thefactor fc′ /5000 ≤ 3, fc′ in psi ( fc′ /35 ≤ 3 [fc′ in MPa]), wasprovided to prevent sudden shear failures at the onset ofinclined cracking. The use of the factor fc′ /5000 ≤ 3 resultedin a step-wise increase in the amount of transverse reinforce-ment with compressive strength, requiring that the productof the transverse reinforcement ratio and the yield strength ofthe transverse reinforcement (ρt fyt) be at least 50 psi (0.34 MPa)for concrete compressive strengths below 10,000 psi (69 MPa),and double that amount (ρt fyt = 100 psi [0.69 MPa]) forconcrete compressive strengths slightly higher than 10,000 psi(69 MPa). The amount of transverse reinforcement increasedlinearly with compressive strength up to a maximum ρt fyt of150 psi (1.03 MPa) for a concrete compressive strength of15,000 psi (103 MPa). Experimental results by Roller andRussell (1990) showed that the amount of transverse reinforce-ment that resulted in a nominal shear stress of 150 psi(1.03 MPa) was barely sufficient to ensure a safe estimate ofstrength 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 etal. 1969; Mattock et al. 1976; Walraven et al. 1987; Rollerand Russell 1990), a new form of ACI 318, Eq. (11-13), wasintroduced in ACI 318-02 to estimate the minimum amountof transverse reinforcement in beams, with the goals ofincreasing the safety of the estimates and eliminating thesteep increase that occurred at a concrete compressivestrength of 10,000 psi (69 MPa). The minimum amount oftransverse reinforcement is given by

fc′

fc′

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

fc′


ACI 318 Eq. (11-13)

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 compressivestrengths of 10,500, 17,400, and 18,200 psi (72, 120, and125 MPa). There were five beams with compressivestrengths of 17,400 psi (120 MPa), for which the design shearstress vs (equal to the product of the transverse reinforcementratio ρt and the yield strength of the hoops fyt) carried by thetruss mechanism ranged from 0.3 to 8.9 (psi)(0.025 to 0.74 [MPa]). The beam with the lightestamount of transverse reinforcement (vs = 0.3 (psi) [vs =0.025 (MPa)]) had a shear strength below the nominalvalue 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 Vncalculated using ACI 318, Eq. (11-6) (Vc term), and ACI318, Eq. (11-17) (Vs term), of the ACI 318-83. Although forthese four beams the ratio of measured to nominal strengthdecreased with the amount of transverse reinforcement, thetests were within the range allowed by ACI 318, which placesan upper limit of vs = 8 (psi) (vs = 0.66 [MPa]), onthe nominal shear strength attributed to the truss mechanism.The two remaining series of tests, with compressivestrengths of 10,500 and 18,200 psi (72 and 125 MPa), wereprimarily aimed at determining the minimum amount oftransverse reinforcement needed to prevent sudden failuresafter inclined cracking.

Av min, 0.75 fc′bws

fyt

-------- (fc′ in psi)=

Av min, 0.062 fc′bws

fyt

-------- (fc′ in MPa)=

fc′ fc′fc′ fc′

fc′fc′

fc′ fc′

As observed in Fig. 6.4, the ratio of measured to nominalshear strength of the beams with 10,500 psi (72 MPa)concrete in the study by Roller and Russell (1990) was notvery sensitive to the nominal strength provided by the trans-verse reinforcement, while the opposite was true for thebeams with 18,200 psi (125 MPa) concrete. While providingvs = 50 psi (0.34 MPa) resulted in an adequate estimate ofstrength for beams with a concrete compressive strength of10,500 psi (72 MPa), the same amount resulted in an uncon-servative estimate of strength for the beams with concretecompressive strengths of 17,400 and 18,200 psi (120 and125 MPa). In both cases, tests showed that a minimum vs ofapproximately 150 psi (1.03 MPa) would have been necessaryto obtain a strength above the nominal value given by Eq. (11-5)of ACI 318-83.

6.4—Shear strength of members with low shear span-depth ratios

A series of tests was conducted in Japan to investigate theshear strength of high-strength concrete members(Sakaguchi et al. 1990). The series included six beams withshear span-depth ratios ranging between 1 and 1.14, anddifferent amounts of transverse reinforcement. The purposeof the tests was to determine the inclined cracking load andultimate shear strength of the beams. Concrete compressivestrength was maintained constant at approximately 13,000 psi(90 MPa). The principal variable was the product ρt fyt, where ρtis the transverse reinforcement ratio defined as ρt = Av/bws andfyt is the yield strength of the transverse reinforcement.

According to the truss model adopted in ACI 318-05, theproduct ρt fyt represents the average shear stress carried bythe reinforcement in slender beams (ρt fyt = vs = Vs/bwd),that, in the tests by Sakaguchi et al. (1990) ranged from 0 to1150 psi (7.9 MPa). In beams with ρt fyt lower than 260 psi(1.8 MPa) (ρt fyt/fc′ = 2%), inclined cracking propagatedrapidly, leading to a sudden shear failure. In specimens withρt fyt of 725 and 1145 psi (5 and 7.9 MPa) (ρt fyt/fc′ higher than5.5%), both the shear and longitudinal reinforcement yieldedbefore failure at a load considerably exceeding the inclinedcracking strength. The conclusions from the study bySakaguchi et al. (1990), based on tests of deep beams, differfrom those by Roller and Russell (1990). Sakaguchi et al.focused on the amount of transverse reinforcement needed topreclude failure at the onset of inclined cracking and achieveyielding of the transverse reinforcement before failure. Theyfound that for beams with a compressive strength of approxi-mately 13,000 psi (90 MPa), the amount of transverse rein-forcement needed to develop a truss mechanism and preventsudden failure after inclined cracking was approximately vs= ρt fyt = 260 psi (1.8 MPa) (5.2 times 50 psi), which corre-sponds to 2.3 (psi) (0.19 [MPa]) significantlyhigher than the ρt fyt = 0.75 (psi) (0.06 [MPa])required by ACI 318-05 for flexural members.

The study by Sakaguchi et al. (1990) raises concerns aboutthe behavior of members with low shear span-depth ratiossubjected to cyclic loading. ACI 318-05 requires that suchmembers be proportioned using nonlinear analysis or in

fc′ fc′fc′ fc′

Fig. 6.4—Ratio of measured to nominal strength versuscalculated shear strength provided by truss mechanism forbeams with high-strength concrete tested by Roller andRussell (1990).


accordance with Appendix A of the Code, which outlinesprovisions for the use of strut-and-tie models.

Strut-and-tie models are a methodology for memberdesign that can be applied to different types of structuralmembers, including deep beams and structural walls.Although Chapter 6 of this document addresses shear designand Chapter 8 addresses the design of structural walls, someof the reference material presented in this chapter about thebehavior and design of members with low shear span-depthratios is based on studies of deep beams and walls. Suchmaterial is included in this chapter only when it is relevant tothe topic of strut-and-tie models.

Little reference material is available on the use of strut-and-tie models for the seismic design of deep beams madewith high-strength concrete. The Architectural Institute ofJapan (AIJ) seismic design guideline (1994) includes adesign procedure for beams that is based on the superposition oftwo different strut-and-tie models. The AIJ model is inconsistentwith the provisions in Appendix A of ACI 318-05. The AIJprocedure includes two reduction factors applied to thecompressive strength of the concrete struts that Appendix Aof ACI 318-05 does not include.

The first factor was originally proposed by Nielsen (1999)and was developed based on test results from beams withuniform stress fields subjected to monotonic loading. It is afunction of the compressive strength of the concrete, and itdecreases linearly as the compressive strength increases

(6-3)

The second factor is a function of the amount of rotationθp expected in a plastic hinge region of a flexural member. Itis given by

βsc = (1 – 15θp)βs ≥ 0.25βs (6-4)

Aoyama (1993) carried out a comparison of measured andcalculated shear strengths for beams and columns subjectedto cyclic loading following the procedure in the 1988 Japa-nese design guideline. He concluded that the method in theJapanese guideline resulted in accurate estimates of thereduced shear strength of both beams and columns subjectedto cyclic loading with various shear span-depth ratios. Heindicated, however, that the method did not perform well formembers with high-strength concrete. Further research atKyoto University showed that the performance of themethod was improved by adopting the strut factor proposedin the draft of the CEB-FIP model code (Comité Euro-Interna-tional du Béton 1988), which is proportional to the reciprocalof the cubic root of the compressive strength of concrete(Watanabe and Kabeyasawa 1998)

(6-5)

Von Ramin and Matamoros (2004, 2006) defined the strutstrength as the product of factors related to the compressivestrength of the concrete (βfc), the angle of inclination of thestrut (βαt), and, in the case of members in which the strutinteracts with a truss mechanism, an additional factor (βta).The strut factor is defined as

βs = βfcβαtβta (6-6)

The work by Von Ramin and Matamoros (2004, 2006) onmembers with low shear span-depth ratios was calibratedusing experimental data from deep beams and structuralwalls with concrete compressive strengths ranging from2200 to 20,300 psi (15 to 140 MPa). Von Ramin developeda base expression for the strut factor using experimentalresults from elements subjected to monotonic loading. Theeffect of load reversals was later introduced by comparingthe base factors for the monotonic loading case to reducedvalues of strength of columns and walls subjected torepeated load reversals into the nonlinear range of response.Following this methodology, Von Ramin and Matamoros(2004, 2006) proposed the following expressions for thecompressive strength factor

(6-7)

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

(6-8)

and in members with transverse reinforcement

(6-9)

where αst is the angle of inclination of the strut with the mainlongitudinal 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 mainstrut in members with low shear span-depth ratios may beapproximated as

cotαst = av /d (6-10)

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

βs 0.7fc′

29,000---------------- (fc′ in psi)–=

βs 0.7fc′

200--------- (fc′ in MPa)–=

βs9

fc′3---------- (fc′ in psi)=

βs1.7

fc′3---------- (fc′ in MPa)=

βfc 0.85 fc′ 36,200⁄ 0.5≥ (fc′ in psi)–=

βfc 0.85 0.004fc′ 0.5 (fc′ in MPa)≥–=

βαt1

1 0.1cot3αst+----------------------------------=

βαt4.6

6.5 0.13cot5αst+------------------------------------------=


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

(6-11)

where ft,l and ft,t are the stresses imposed on the concrete bythe compression fields associated with reinforcementoriented in directions parallel to and perpendicular to themain longitudinal tie. These stresses are calculated based onthe assumption of a uniform compression field (Von Raminand Matamoros 2006) as

(6-12)

and

(6-13)

where ρt,t is the transverse reinforcement ratio for the transversereinforcement oriented perpendicular to the main longitudinaltie, fyt,t is the specified yield strength of the transversereinforcement oriented perpendicular to the main longitudinaltie, ρt,l is the transverse reinforcement ratio for the transversereinforcement oriented in the direction parallel to the mainlongitudinal tie, fyt,l is the specified yield strength of thereinforcement oriented parallel to the main longitudinal tie,αt is the angle between the main longitudinal tie (which isoriented in the vertical direction in the case of structuralwalls) and the struts of the compression field induced by thetransverse reinforcement oriented perpendicular to the mainlongitudinal tie (Fig. 6.5), and αl is the angle between themain longitudinal tie and the struts of the compression fieldinduced by the transverse reinforcement oriented parallel tothe main longitudinal tie.

Equation (6-11) originates from a lower bound plasticitysolution of a strut-and-tie model proposed by Nielsen (1999).

βtaβs fc′ ft t,–( ) βs fc′ ft l,–( )

βs fc′( )2 ft t, ft l,–--------------------------------------------------------=

ft t,ρt t, fyt t,

sin2αt

----------------=

ft l,ρt l, fyt l,

cos2αl

----------------=

A similar approach was proposed by Watanabe and Ichinose(1991), and implemented in the seismic design guidelines ofthe Architectural Institute of Japan (1994).

Von Ramin and Matamoros (2004, 2006) suggested thefollowing limits for the angle of inclination of the struts ofthe compression fields

cotαl ≤ 2cosαst (Fig. 6.5(a)) (6-14)

and

cotαt ≤ (Fig. 6.5(b)) (6-15)

They also suggested a lower limit of 30 degrees for bothangles. The strength provided by the two orthogonal trussmechanisms is given by

Vt,l = ρt,l fyt,lb · a · tan2αl (Fig. 6.5(a)) (6-16)

and

Vt,t = ρt,t fyt,tb · jd · tanαt (Fig. 6.5(a)) (6-17)

The nominal shear strength of members with low shearspan-depth ratios is calculated as

Vn + Va + Vt,t + Vt,l (6-18)

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

Va = βs fc′ wstbsinαst (6-19)

where wst is the strut width, and b is the width of the structuralmember. 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 reinforce-ment and lb is the dimension of the loading plate or supportin the axial direction of the member.

In the case of squat walls in which designers include thestrength provided by the transverse reinforcement, contraryto expectations, Eq. (6-11) will result in a significant reductionin the calculated strength of the strut. In structural walls withthose characteristics, the amount of transverse reinforcementneeded to avoid a reduction in shear strength after inclinedcracking is very large. A larger nominal shear strength maybe obtained by neglecting the effect of the transverse reinforce-ment in the calculation of the strength of the wall, which isconsistent with the behavior observed in tests. In those cases,although the amount of transverse reinforcement does not

αstcot

2---------------

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


affect the nominal shear strength, a minimum amount ofreinforcement 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 abetter estimate of the shear strength is obtained by adding theshear strength of the boundary element, calculated as if itwere a compression member.

Based on test results from columns and beams subjected toload reversals, Von Ramin and Matamoros (2004) suggestedthe following expression for the reduction in the strength ofthe strut as a result of repeated load reversals into thenonlinear range of response

(6-21)

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

βsc = βnl,strutβs (6-22)

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

(6-23)

where

λp = 1 + 2 · (P/Ag fc′ )0.35 (6-24)

Warwick and Foster (1993) also noted the effect ofcompressive strength and shear span-depth ratio on the strutfactor. They proposed the following strut factor expressionfor concrete compressive strengths ranging between 2900and 14,500 psi (20 and 100 MPa)

(6-25)

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

(6-26)

where ε1 is the principal tensile strain in the strut. Based onstrain compatibility, the principal tensile strain is expressedas 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 ofthe reinforcement εy.

A modification of Eq. (6-26) was later proposed byVecchio et al. (1994) for high-strength concrete withcompressive strength ranging up to 10,400 psi (72 MPa)

(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 forproportioning the amount of transverse reinforcement inbeams (flexural members) of special moment frames requirethat the design shear force be calculated on the basis ofopposing probable flexural strengths at the joint faces andthe factored tributary gravity load along the span. The shearstrength must be calculated according to the proceduresoutlined in Chapter 11 of ACI 318-05, which were calibratedbased on tests of members subjected to monotonic loading.The effect of repeated shear reversals is accounted for in thatthe term related to the contribution of the concrete, Vc, must beneglected if the earthquake-induced shear is 1/2 or more of thedesign shear force and the axial force is less than Agfc′ /20.Additional requirements for the amount of transversereinforcement 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, 24times the diameter of the hoop bar, and 12 in. (305 mm).

A similar two-tier approach is used to determine theamount of transverse reinforcement in columns (memberssubjected to bending and axial load) of special moment frames.The shear demand must be calculated on the basis of theprobable moment strengths at the joints and the amount ofreinforcement required for shear strength must be calculated inaccordance with Chapter 11 of ACI 318-05. As in the case ofbeams, the term related to the contribution of the concrete, Vc,must be neglected if the earthquake-induced shear is 1/2 ormore of the design shear force and the axial force is less thanAgfc′ /20. For the majority of practical design cases, the term Vcdoes not have to be neglected in columns because the axial forceis not less than Agfc′ /20. Moreover, the shear strength of acolumn increases as the compressive axial load on it increases.In addition, designers must verify that the amount of transversereinforcement provided is greater than that required by Eq. (21-3)or (21-4) of ACI 318-05. These two equations specify theamount of transverse reinforcement for adequate confinementof the column core under cyclic loading. The latter criterioncontrols for most practical situations.

βnl strut, 18DRlim

ρt fyt fc′⁄( ) 0.01+-----------------------------------------–=

βnl truss,

1

1 1.5 DRlim 6λp⋅⋅+

-----------------------------------------------=

βs 1.25fc′

72,500----------------– 0.72

av

d-----⎝ ⎠

⎛ ⎞– 0.18av

d-----⎝ ⎠

⎛ ⎞2

( fc′ in psi)+=

βs 1.25fc′

500---------– 0.72

av

d-----⎝ ⎠

⎛ ⎞– 0.18av

d-----⎝ ⎠

⎛ ⎞2

( fc′in MPa)+=

βs1

0.8 170ε1+----------------------------=

βs1

0.9 0.27ε1

ε0

----+

-----------------------------=


6.6—Use of high-strength transverse reinforcement

The use of high-strength transverse reinforcement isadvantageous for column confinement. This topic isaddressed in detail in Chapter 5 of this report. Section 11.5.2of ACI 318-05 limits the yield strength of shear reinforce-ment to a maximum of 60,000 psi (414 MPa), which isincreased to 80,000 psi (552 MPa) in the case of weldeddeformed wire reinforcement. It is stated in the commentaryto the code that this provision is intended to limit the widthof inclined cracks at service-load levels.

Otani (1995) described the approach followed by theJapanese code for shear design using high-yield-strengthtransverse reinforcement. The objective of the JapaneseStandard is to limit the width of shear cracks under long-termloads to an acceptable value, particularly in the case ofcolumns, and to provide a safe estimate of strength (5% failureratio on the basis of 1200 test data) for short-term loads.

In the case of beams subjected to long-term loading, themaximum allowable shear force is given by

Vall = bj[αshvc,all + 0.5fyt(ρt – 0.002)] (6-29)

For columns subjected to long-term loading, the allowableshear force is given by

Vall = bjαsh fyt (6-30)

In the case of beams under short-term service loads, theallowable shear force is given by

Vall = bj[αshvc,all + 0.5fyt(ρt – 0.001)] (6-31)

For columns subjected to short-term service loads, theallowable shear force is given by

Vall = bj[vc,all + 0.5fyt(ρt – 0.001)] (6-32)

where

αsh = 1 ≤ ≤ 2 (6-33)

wherevc, all = allowable shear stress in concrete;M = maximum moment in the member due to

service loads;V = maximum shear force in the member due to

service loads (at the same location as M);b = width of compression face of member;j = ratio of internal lever arm to effective depth of

beam (under bending, j = 7/8d);d = distance from extreme compression fiber to

centroid of longitudinal tension reinforcement;and

ρt = ratio of area of distributed transverse reinforce-ment to gross concrete area perpendicular to

that reinforcement (the nominal value of ρt hasan upper limit of 0.006 for long-term loads and0.008 for short-term loads).

The allowable shear stress in the concrete is given by theminimum of fc′ /30 and 70 + fc′ /100 (psi) ( fc′ /30 and 0.5+ fc′ /100 [MPa]) for normalweight concrete under long-termloading. For short-term loading, the allowable stress isincreased by a factor of 1.5. For lightweight-aggregateconcrete, a reduction factor of 0.9 must be applied. Themaximum allowable tensile stress in the shear reinforcementis 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 upperlimit on the allowable tensile stress include: 1) serviceabilityconcerns; and 2) experimental evidence from beams withhigh-strength transverse reinforcement tested in Japanshowing that yielding of the transverse reinforcement wasnot reached at shear failure.

6.7—RecommendationsBased on the body of research that was reviewed, there are

no specific recommendations deemed necessary for thedesign of slender high-strength concrete members for shear.The modification to Eq. (11-13) of ACI 318-05 to make theminimum amount of reinforcement a function of thecompressive strength of concrete provides an adequate solutionto prevent sudden shear failures after inclined cracking inmembers with light amounts of transverse reinforcement.

A study by Sakaguchi et al. (1990) raises concerns aboutthe behavior of members with low shear span-depth ratiossubjected to cyclic loading. There is evidence (Sakaguchi etal. 1990; Kabeyasawa and Hiraishi 1998; Von Ramin andMatamoros 2004, 2006) that the application of the strutfactors specified in Appendix A of ACI 318-05 to the designof high-strength concrete members may be unconservativebecause these factors were calibrated based on test results ofelements loaded monotonically to failure.

In elements subjected to load reversals, concrete mayalternate between states of tension and compression due tochanges in the direction of loading. If the element remains inthe elastic range of response, the width of the cracks thatform while concrete is subjected to tensile strains is not largeenough to cause severe damage, and the use of strut factorsderived for the monotonic loading case is acceptable. Thistype of behavior was observed in tests of deep beamssubjected to load reversals conducted by Uribe and Alcocer(2001) in which failure took place prior to significantinelastic deformations in the flexural reinforcement (peakrecorded strains in the flexural reinforcement at failure wereon the order of 1%).

When elements undergo excursions into the inelasticrange of response, crack widths are significantly larger thanthose observed in the linear range of response due to largerdeformations associated with yielding of the reinforcement.If concrete is not properly confined, this type of behaviorleads to rapid degradation of strength. Furthermore, in someinstances, the compression force may not be sufficient tofully close cracks formed while concrete and reinforcement

4M Vd 1+⁄-------------------------


were subjected to tension. These effects may result inreduced strength for concrete in the struts, or may renderstruts ineffective due to changes in the load path in theelement. To address the aforementioned problems caused byload reversals into the inelastic range of response, severalproposals in the literature suggest that it is necessary toadjust strut factors for monotonic loading when using themfor seismic design. Uribe and Alcocer (2001) indicated thatprocedures for seismic design using strut-and-tie modelsshould account for the reduction in strength of the concretein the struts as well as potential reductions in bond strengthdue to load reversals. They also suggested that properdetailing should include the use of closely spaced hoops tolimit the width of the cracks under tension, and to provideconfinement to concrete in the struts. Expressions for thereduction in strength with inelastic deformations arepresented in the Japanese Design Code (AIJ 1994) and byVon Ramin and Matamoros (2006). In the Japanese DesignCode (AIJ 1994), the capacity of struts is reduced as a functionof the plastic rotation, while in the proposal developed byVon Ramin and Matamoros (2006), the reduction in strengthis a function of deformation demand, amount of confiningreinforcement, and the axial stress on the element.

Because the strut factors in Appendix A of ACI 318-05 donot account for the effects of load reversals, the committeerecommends that they only be used to proportion elementsintended to remain elastic for the design earthquake.

Specific recommendations for the design of members withlow shear span-depth ratios using strut-and-tie models arepresented in the following. In the case of bottle-shapedstruts, a recommendation is made based on the strut factorssuggested 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 = βfcβαt ≤ 0.6 (6-34)

where

βfc = 1 – fc′ /30,000 ≥ 0.6 ( fc′ in psi) (6-35)

βfc = 1 – 0.005 fc′ ≥ 0.6 ( fc′ in MPa)

(6-36)

where αst is the angle of inclination of the strut with respectto the main tie.

In the case of members subjected to point loads with singlestruts running between the load and reaction points, the angleof inclination of the strut may be approximated as

(6-37)

βαt1

1 0.1cot3αst+----------------------------------=

αstcosav

d-----=

A comparison between the proposed strut factor and thatcorresponding to bottle-shaped struts in Appendix A of ACI318-05 is presented in Fig. 6.6. As shown in Fig. 6.6, when theangle of inclination of the strut is 35 degrees, the proposed strutfactor becomes equal to that in ACI 318-05 at a concretecompressive strength of approximately 7000 psi (48 MPa).

For struts with uniform cross-sectional area over theirlength, the stress conditions are very similar to those in thecompression zone of members subjected to flexure and axialload. For this reason, it is recommended that the strut factorbe similar to the α1 factor defined of Section 4.8 of thisreport, adjusted for the 0.85 factor in ACI 318, Eq. (A-3). Ininch-pound units, it is recommended that: “for struts withuniform cross-sectional area over their length, the factor βsshall be taken as 1.0 for concrete strengths fc′ up to andincluding 8000 psi. For strengths above 8000 psi, βs shall bereduced continuously at a rate of 0.02 for each 1000 psi ofstrength in excess of 8000 psi, but βs shall not be taken lessthan 0.80.” In SI units, the recommendation is that: “forstruts with uniform cross-sectional area over their length, thefactor βs shall be taken as 1.0 for concrete strengths fc′ up toand including 55 MPa. For strengths above 55 MPa, βs shallbe reduced continuously at a rate of 0.003 for each MPa ofstrength in excess of 55 MPa, but βs shall not be taken lessthan 0.80.”

Because research on the effect of repeated load reversalsinto the nonlinear range of response on strut factors is at anearly stage, it is recommended that the use of strut-and-tiemodels be limited to design of members where significantdegradation of strength under load reversals into thenonlinear range is not expected to take place.

Recommendations about the amount of transverse reinforce-ment needed for proper confinement of the concrete undernonlinear deformations are addressed in Chapter 5 of thisreport.

Fig. 6.6—Comparison between strut factors proposed andthat in Appendix A for ACI 318-05 for bottle-shaped strutswithout transverse reinforcement.


CHAPTER 7—DEVELOPMENT LENGTH/SPLICESAccording to ACI 318-05, the development length of

deformed bars or deformed wires in tension may be calculatedaccording to the following requirements. For cases in which:1) the clear spacing of the bars being developed or spliced isnot less than db, the cover is not less than db, and the stirrupsor ties throughout ld or the splice length are not less than thecode minimum; or 2) the clear spacing of the bars beingdeveloped or spliced is not less than 2db and the cover is notless than db

(7-1)

(7-2)

For cases not meeting the aforementioned spacing, cover,and confinement criteria

(7-3)

(7-4)

Alternatively, the development length of deformed bars ordeformed wires in tension may be calculated with a morecomplex equation: ACI 318 Eq. (12-1)

ACI 318 Eq. (12-1)

in which the term (cb + Ktr)/db ≤ 2.5. The developmentlength calculated with any of the previous formulas must benot less than 12 in. (305 mm).

Due to a lack of test data on bars embedded in high-strength concrete, ACI 318-05 places an upper limit of 100 psi(8.3 MPa) on the term in the previous equations. Thislimit does not allow designers to take advantage of anyincrease in bond strength associated with increases inconcrete compressive strength beyond 10,000 psi (69 MPa).

Research on bond of reinforcement in high-strengthconcrete has shown that there is a significant differencebetween the behavior of members with and without transverse

reinforcement in the splice region (McCabe 1998; Zuo andDarwin 2000; Azizinamini et al. 1993). In high-strengthconcrete members without transverse reinforcement, there isa greater tendency for the cracks to propagate through theaggregate, resulting in smoother failure surfaces than thosefound in normal-strength concrete (McCabe 1998). Whenthe critical failure stress is reached, there is only limitedredistribution of stresses and, as a result, failure tends to bemore sudden and brittle in nature than in normal-strengthconcrete. Zuo and Darwin (2000) observed brittle failures inhigh-strength concrete without significant damage to theconcrete at the interface between the bar and the concrete.Azizinamini et al. (1999b) also indicated that the strengthof specimens without transverse reinforcement cannot beestimated with much accuracy because there are significantvariations in measured strength for similar specimens.McCabe (1998) stated that in members without transversereinforcement, the maximum stress before splittingfailure is related to the fracture properties of the concrete,and not solely to the compressive strength. Because thefracture energy does not increase proportionally to the squareroot of the compressive strength, design expressions based onthe square root function may be unconservative forcompressive strengths greater than 10,000 psi (69 MPa)(McCabe 1998). Zuo and Darwin (2000) proposed a relation-ship between bond force and compressive strength to the1/4 power based on a statistical study of monotonic testsof beams without transverse reinforcement and withconcrete compressive strengths up to 16,000 psi (110 MPa). Ithas also been suggested that the lower water-cementitiousmaterial ratios of high-strength concrete result in less bleedingand sedimentation, which makes the top bar effect lesssignificant 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 concretehave been proposed in ACI 408R-03, based on the statisticalanalysis by Zuo and Darwin (2000). It is proposed in the ACICommittee 408 report that Eq. (12-1) of ACI 318-05 bereplaced by the following

(7-5)

where

c′ = cmin + 0.5db (7-6)

ld

db

-----fyψtψeλ

25 fc′------------------- for No. 6 and smaller bars (fc′ and fy in psi)=

ld

db

-----12fyψtψeλ

25 fc′-------------------------- for No. 6 and smaller bars (fc′ and fy in MPa)=

ld

db

-----fyψtψeλ

20 fc′------------------- for No. 7 and larger bars (fc′ and fy in psi)=

ld

db

-----3fyψtψeλ

5 fc′----------------------- for No. 7 and larger bars (fc′ and fy in MPa)=

ld

db

-----3fyψtψeλ

50 fc′----------------------- for No. 6 and smaller bars ( fc′ and fy in psi)=

ld

db

-----18fyψtψeλ

25 fc′-------------------------- for No. 6 and smaller bars (fc′ and fy in MPa)=

ld

db

-----3fyψtψeλ

40 fc′----------------------- for No. 7 and larger bars (fc′ and fy in psi)=

ld

db

-----9fyψtψeλ

10 fc′----------------------- for No. 7 and larger bars (fc′ and fy in MPa)=

ld

db

----- 340------

fy

fc′---------

ψtψeψsλcb Ktr+

db

------------------⎝ ⎠⎛ ⎞----------------------- (fc′ and fy in psi)=

ld

db

----- 910------

fy

fc′---------

ψtψeψsλcb Ktr+

db

------------------⎝ ⎠⎛ ⎞----------------------- (fc′ and fy in MPa)=

fc′

ld

db

-----

fy

fc′1 4⁄

----------- 2210ω–⎝ ⎠⎛ ⎞ ψtψeλ

70c ′ω Ktr′+

db

------------------------⎝ ⎠⎛ ⎞

-------------------------------------------------------- (fc′ and fy in psi)=

ld

db

-----

42fy

fc′1 4⁄

----------- 2210ω–⎝ ⎠⎛ ⎞ ψtψeλ

70c ′ω Ktr′+

db

------------------------⎝ ⎠⎛ ⎞

-------------------------------------------------------- (fc′ and fy in MPa)=


ω = 0.1 + 0.9 ≤ 1.25 (7-7)

Ktr′ = (0.5tdAtr/sn) (td in inches, Atr in in.2, and fc′ in psi) (7-8)

Ktr′ = (6.25tdAtr /sn) (td in mm, Atr in mm2, and fc′ in MPa)

td = 0.78db + 0.22 (db in inches) (7-9)

td = 0.03db + 0.22 (db in mm)

and

(c′ω + Ktr′ )/db ≤ 4.0 (7-10)

The simplified expressions provided in Section 12.2.2 ofACI 318-05 are proposed to be replaced by the following: forcases in which 1) the clear spacing of the bars being developedor spliced is not less than db, the cover is not less than db, andthe stirrups or ties throughout ld provide a value of Ktr′ /db ≥ 0.5;or 2) the clear spacing of the bars being developed or spliced isnot less 2db, and the cover is not less than db

(7-11)

For cases not meeting the aforementioned spacing, cover,and confinement criteria

(7-12)

The use of transverse reinforcement significantly changesbehavior (Azizinamini et al. 1999b), because the confinementprovided by the transverse reinforcement restrains thedevelopment of splitting cracks. Furthermore, the behaviorbecomes significantly more ductile. Zuo and Darwin (2000)showed the significant effect of transverse reinforcement onbond strength. Their study showed that the best fit betweenbond force and compressive strength for members withtransverse reinforcement was obtained for a power coefficientof 3/4 compared with a coefficient of 1/4 for memberswithout transverse reinforcement.

An alternative design procedure was proposed by Azizinaminiet al. (1999a). Rather than introducing new design equations,the procedure relies on a minimum amount of transversereinforcement over the splice region to take advantage of theconcrete compressive strength and improve the ductility ofthe splices (Azizinamini et al. 1999a). The approachproposed by Azizinamini et al. is based on an analysis of testresults by Darwin et al. (1996), which concluded that the

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

Tb = (Tb in lb, td in in., Asp in in.2, and fc′ in psi) (7-13)

Tb = (Tb in kN, td in mm, Asp in mm2, and fc′ in MPa)

where Tb is the bond force, Asp is the cross-sectional area oftransverse reinforcement crossing the potential plane ofsplitting along the length of splice, n is the number of barsbeing spliced, and fc′ is the specified compressive strength.This equation was used to estimate the amount of transversereinforcement required to achieve an increase in bondstrength proportional to the square root of the compressivestrength. For test data with a concrete compressive strengthof 15,000 psi (103 MPa), the amount of transverse reinforce-ment needed to obtain a safe estimate of the developmentlength of a No. 8 (No. 25) bar with the ACI 318 equationswas approximately

Asp = 0.5nAb,max (7-14)

where n is the number of bars being spliced. A linear adjustmentwas proposed to estimate the amount of transverse reinforce-ment required for members with concrete compressivestrengths other than 15,000 psi (103 MPa) and higher than10,000 psi (69 MPa)

(7-15)

Equation (7-15) was calibrated on the basis of experimentswith concrete compressive strengths of up to 16,000 psi(110 MPa).

Additional requirements are that the maximum spacing ofstirrups in the longitudinal direction not exceed 12 in.(305 mm), a minimum of three stirrups be used through thelength of the splice, and that the bar size for the stirrups be atleast No. 3 (No. 10). The proposal by Azizinamini et al.(1999a) requires that the development length be calculatedusing the equations in Sections 12.2.2 or 12.2.3 of ACI 318-05assuming a value of Ktr = 0. Because the current restriction inthe code applies to concrete compressive strengths greaterthan 10,000 psi (69 MPa), the amount of transverse reinforce-ment proposed previously would be required when thecompressive strength exceeds that threshold. The mainadvantage of the procedure proposed by Azizinamini et al.(1999a) is that it does not require adopting new equations fordevelopment length. There may, however, be additional costif 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 hookedbars in high-strength concrete. Fujii et al. (1998) summarizedresearch on hooked bars in exterior joints carried out in Japan

cmax

cmin

----------

fc′

fc′

ld

db

-----fy

105fc′1 4⁄

--------------------- 20–⎝ ⎠⎛ ⎞ ψtψeλ (fc′ and fy in psi)=

ld

db

-----0.4fy

fc′1 4⁄

----------- 20–⎝ ⎠⎛ ⎞ ψtψeλ (fc′ and fy in MPa)=

ld

db

-----fy

70fc′1 4⁄

------------------ 30–⎝ ⎠⎛ ⎞ ψtψeλ (fc′ and fy in psi)=

ld

db

-----0.6fy

fc′1 4⁄

----------- 30–⎝ ⎠⎛ ⎞ ψtψeλ (fc′ and fy in MPa)=

2177tdAsp

n------- 66+⎝ ⎠

⎛ ⎞ fc′1 4⁄

td

500---------

Asp

n------- 1+⎝ ⎠

⎛ ⎞ fc′1 4⁄

Asp 0.5nAb max, fc′ 15,000⁄( ) fc′ 10,000 (fc′ in psi)≥,=

Asp 0.5nAb max, fc′ 100⁄( ) fc′ 69 (fc′ in MPa)≥,=


as part of the research program on high-strength materials.Compressive strength of concrete in the specimens tested aspart of the study ranged from 5800 to 17,400 psi (40 to120 MPa). All specimens in the testing program failed dueto splitting of the side cover (cover to the side of the bar).

Fujii et al. (1998) indicated that bond force was proportionalto the cubic root of the compressive strength rather than thesquare root of fc′ . Increasing side cover led to increases instrength up to a cover of six bar diameters. The maximumstress developed in specimens with closely spaced bars (barspacings ranging between two and 15 bar diameters) wasapproximately 75% of that observed in bars spaced fartherapart than 30 bar diameters. The maximum stress increasedin proportion to the development length up to a developmentlength of 16 bar diameters, after which the observed increasein maximum stress was negligible. The maximum bar stressalso increased proportionally to the ratio of developmentlength to the lever arm between the tension and the compressionresultants in the beam. Finally, the maximum stress in the barwas found to increase with the amount of transverse reinforce-ment. The increase was proportional to the ratio Asp fyt /s, whereAsp is the cross-sectional area of transverse reinforcementcrossing the potential splitting plane, fyt is the yield strengthof the transverse reinforcement, and s is the spacing. Theincrease was approximately linear, with a maximum of 40%for an Asp fyt /s ratio of 3350 lb/in. (0.59 kN/mm).

Fujii et al. (1998) proposed the following expression forthe maximum tensile stress that can be developed in a barwith 90-degree hook

fu = 4000kcckjkdks(fc′ )0.4 ( fu and fc′ in psi) (7-16)

fu = 200kcckjkdks(fc′ )0.4 ( fu and fc′ in MPa)

where kcc is the cover factor, kj and kd are developmentlength factors, and ks is the transverse reinforcement factor.The factors are as follows

(7-17)

(1 ≤ kj ≤ 4) (7-18)

(7-19)

(7-20)

wherecc = clear cover of reinforcement (side cover in this

case) to the outermost anchored bar;db = nominal diameter of the anchored bar;

ldh = development length in tension of deformed baror deformed wire with standard hook, measuredfrom critical section to outside end of hook;

j = ratio of internal lever arm to effective depth ofthe beam section at the column face; and

ds = nominal diameter of bar used as transversereinforcement (positioned at the hook).

The configuration of the hook must satisfy the requirementsof ACI 318-05.

7.3—RecommendationsResearch in bond and development of reinforcement

(McCabe 1998) indicates that design expressions based onthe square root of the compressive strength of the concretemay be unconservative for compressive strengths greaterthan 10,000 psi (69 MPa). Research by Azizinamini et al.(1993, 1999b) and Zuo and Darwin (2000) showed that thetwo main alternatives to correcting this problem were toincrease the development length or to add transverse reinforce-ment. The main advantage of the latter approach is that itimproves the behavior of the spliced or developed barsbecause failure is significantly more ductile. This is particularlyadvantageous in seismic design.

Zuo and Darwin (2000) proposed a relationship betweenbond force and compressive strength to the 1/4 power basedon a statistical study of monotonic tests of beams withouttransverse reinforcement and with concrete compressivestrengths up to 16,000 psi (110 MPa). Their study concludedthat the best fit between bond force and compressive strengthfor members with transverse reinforcement was obtained forcompressive strength raised to the power of 3/4, comparedwith the compressive strength raised to the power of 1/4 formembers without transverse reinforcement.

Because ductile behavior is preferable in earthquake-resistantdesign, it was decided that the use of transverse reinforcementwould be the preferable of the two alternatives. Therefore,the recommendation by Azizinamini et al. (1999a) wasadopted as the basis for the proposed addition to Chapter 21of ACI 318-05. Consistent with the approach adopted in ACI318-05, the design recommendation adopted by thecommittee did not include any limitations to its applicabilityrelated 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 uncoatedbar splices in elements with concrete compressive strength ofup to 16,000 psi (110 MPa). At the time the recommendationwas adopted by the committee, there was a paucity ofexperimental results from splices of epoxy-coated bars withtransverse reinforcement in elements with high-strengthconcrete, and from uncoated and epoxy-coated bars terminatedusing standard hooks in high-strength concrete.

The proposed recommendation is stated in the following:

In inch-pound units:Lap splices of flexural reinforcement shall be permitted

only if hoop or spiral reinforcement is provided over the laplength. When the value of exceeds 100 psi, ld shall becalculated from either 12.2.2 or 12.2.3 with Ktr = 0, and

kcc 0.43 0.1cdb

----------+=

kj 0.80.5ldh

jd--------------+=

kd 0.038ldh

db

------ 0.54 1.0≤+=

ks 0.70.46ds

2

db2

---------------- 1.0≤+=

fc′


transverse reinforcement crossing the potential plane ofsplitting shall be provided over the tension splice length witha minimum total cross-sectional area Asp given by ACI 318,Eq. (21-AA).

Asp = 0.5nAb,max(fc′ /15,000) ACI 318 Eq. (21-AA)

where n is the number of bars or wires being spliced alongthe plane of splitting.

Maximum spacing of the transverse reinforcementenclosing the lapped bars shall not exceed d/4 or 4 in., andthe minimum hoop or spiral bar size shall be No. 3. Lapsplices 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 laplength. When the value of exceeds 25/3 MPa, ld shallbe calculated from either 12.2.2 or 12.2.3 with Ktr = 0, andtransverse reinforcement crossing the potential plane ofsplitting shall be provided over the tension splice length witha minimum total cross-sectional area Asp as given by ACI318M, Eq. (21-AA).

Asp = 0.5nAb,max(fc′ /100) ACI 318M Eq. (21-AA)


Maximum spacing of the transverse reinforcementenclosing the lapped bars shall not exceed d/4 or 100 mm,and the minimum hoop or spiral bar size shall be No. 10. Lapsplices shall not be used

(a) within the joints;(b) within a distance of twice the member depth from the


inelastic lateral displacements of the frame.

Conclusions from Zuo and Darwin (2000) for splices areconsistent with those by Fujii et al. (1998) for hooked bars.Fujii et al. (1998) summarized research on hooked bars inexterior joints carried out in Japan as part of the researchprogram on high-strength materials. Concrete compressivestrengths of the specimens tested as part of the study rangedfrom 5800 to 17,400 psi (40 to 120 MPa). All specimens inthe testing program failed due to splitting of the side cover(cover to the side of the bar). Fujii et al. concluded that bondforce was proportional to the cubic root of the compressivestrength rather than the square root of fc′ .

It is a concern that the current equation for the developmentlength of hooked bars in tension of ACI 318-05 (Eq. (21-6))may result in unconservative estimates for compressive

fc′

strengths above 10,000 psi (69 MPa). While the term has an upper limit of 100 psi (8.3 MPa) in Chapter 12 of ACI318-05, there is no such limit on Chapter 21. Given that noliterature was found evaluating the use of the current ACIprovisions for the development length of hooked bars inmembers with high-strength concrete, a modification toEq. (21-6) of ACI 318-05 is proposed in this report to reducethe likelihood of unconservative estimates. The proposedmodification 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 aggregateconcrete shall not be less than the largest of 8db, 6 in., or thelengths required by ACI 318 Eq. (21-6) and (21-BB)

ldh = ACI 318 Eq. (21-6)

ldh = 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 aggregateconcrete shall not be less than the largest of 8db, 150 mm, orthe lengths required by ACI 318M Eq. (21-6) and (21-BB)

ldh = (ACI Eq. (21-6))

ldh = ACI 318M Eq. (21-BB)

for bar sizes No. 10 through 36.

fc′

fydb

65 fc′----------------

fydb

650 fc′( )1 4⁄---------------------------

12fydb

65 fc′----------------

42fydb

650 fc′( )1 4⁄---------------------------

Fig. 7.1—Proposed modification for development length ofhooks.


The proposed modification results in the same develop-ment lengths as given by ACI 318-05 (Fig. 7.1) for concretecompressive strengths up to 10,000 psi (69 MPa). Forstrengths greater than 10,000 psi (69 MPa), the developmentlength of a hooked bar ldh increases in proportion to thefourth root of the compressive strength, resulting in anincrease in development length (Fig. 7.2) that varies from 0at 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 becompared with the nominal shear strength (Fig. 8.1), whichis calculated as

Vn = γvj Aj ( fc′ in psi) (8-1)

Vn = γvj Aj ( fc′ in MPa) (add factor 1/12 in equation)

where Aj is the effective cross-sectional area within a joint ina plane parallel to the plane of reinforcement generatingshear in the joint, and γvj is a constant equal to 20, 15, or 12for joints confined on all four faces (typically interior joints),joints confined on three faces or two opposite faces (typi-cally exterior joints), and all other (typically corner) joints,respectively. A column face is considered confined if a beamframes into it and the beam is wide enough to cover 3/4 ofthe column face.

The horizontal shear force in the joint must be calculatedbased on the assumption that the stress in the flexural tensilereinforcement of the beams framing into the joint is 1.25fy(Fig. 8.1).

8.1—Confinement requirements forbeam-column joints

For special moment-resisting frames, ACI 318-05 requiresthe same amount of transverse hoop reinforcement as that

fc′

fc′

required in potential plastic hinge regions of columns, unlessthe joint is confined by structural members on all four sides.For rectangular columns, the amount of transverse reinforce-ment through the joint must be at least

(8-2)

Vertical spacing of transverse reinforcement within thelength lo, near the top and bottom of columns, may notexceed 1/4 of the minimum column dimension, six times thediameter of column longitudinal bars, and the longitudinalspacing so. These criteria result in hoop spacing generally inthe range of 4 to 6 in. (102 and 152 mm). This requirementis similar to that included in the design provisions developedby Joint ACI-ASCE Committee 352 (2002).

In the case of joints that are confined by structuralmembers framing into all four sides of the joint, with eachmember 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 1/2the amount of reinforcement in Eq. (8-2), and a maximumhoop spacing of 6 in. (152 mm).

The aforementioned requirements apply to joints ofspecial moment frames only. There are no specific coderequirements for joints of frames that are not part of the

Ash 0.3Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ sbc

fc′fyt

----- 0.09sbcfc′fyt

-----≥=

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

Fig. 8.1—Joint shear stress.


lateral force-resisting system of a building assigned toSeismic Category D or higher. Such joints and joints of inter-mediate moment frames must comply with Section 7.10.4 ofACI 318-05 in the case of spirally reinforced columns, andSection 7.10.5 in the case of tied columns.

Section 7.10.5.2 requires that vertical spacing of ties shallnot exceed 16 longitudinal bar diameters, 48 tie bar or wirediameters, or the least dimension of the compressionmember. Section 7.10.5.4 requires that ties complying withthe aforementioned limitation must be provided at no morethan 1/2 of a tie spacing below the lowest horizontal reinforce-ment in slab or drop panel above. It also requires that tiesmust be located vertically not more than 1/2 of a tie spacingabove the top of footing or slab in any story. Where beamsor brackets frame from four directions into a column,termination of ties not more than 3 in. (76 mm) below thelowest reinforcement in the shallowest of such beams orbrackets is permitted.

Section 7.10.4.6 requires that spirals in a spirally reinforcedcolumn must extend from the top of the footing or slab to thelevel of the lowest horizontal reinforcement in memberssupported above.

Section 7.10.4.7 requires that where beams or brackets donot frame into all sides of a column, ties must extend abovetermination of the spiral to the bottom of the slab or droppanel. No maximum spacing for such ties is specified.

Within the regions of potential plastic hinging at the endsof columns of intermediate moment frames, nonspiral trans-verse reinforcement must be in the form of hoops and mustbe provided at a spacing not to exceed: a) eight times thediameter of the smallest longitudinal bar; b) 24 times thediameter of the hoop bar; c) 1/2 of the smallest cross-sectional dimension of column; and d) 12 in. (305 mm). Theonly requirement concerning transverse joint reinforcement,however, is in Section 21.12.5.5, which requires such rein-forcement to conform to Section 11.11.2. That sectionrequires transverse reinforcement having a minimum cross-sectional area equal to 0.75 c2s/fyt ≥ 50c2s/fyt (0.063 forfc′ in MPa) to be provided over a depth not less than that ofthe deepest framing member. Ghosh et al. (1995) recom-mended that the column end transverse reinforcement, asrequired by Section 21.12.5.2, be continued through joints ofintermediate moment frames, irrespective of whether theyare confined or unconfined.

8.2—Shear strength of exterior jointsSaqan and Kreger (1998) evaluated test results from 26

beam-column connections tested in Japan and the U.S. withconcrete compressive strengths ranging from 6000 to15,500 psi (41 to 107 MPa). The maximum joint shear wascalculated based on the story shears in the specimens at driftratios of 2%.

In the case of exterior joints, only two of the 22 specimensconsidered by Saqan and Kreger (1998) had shear strengthsless than those calculated per ACI 318-05. Saqan and Kreger(1998) attributed the lower strengths observed in the twospecimens to high bond stresses that degraded the shearstrength of the joints prematurely. The ratios of column

depth to beam bar diameter in these two tests were 13.6 and15.7, below the limit of 20 specified by the design provisionsof ACI 318-05 and Joint ACI-ASCE Committee 352 (2002).The average ratio of measured to calculated strength was1.31 for the entire group of exterior joint tests, and theaverage joint shear coefficient γvj was 20.8 compared withthe value of 15 given in ACI 318-05 and the design provisionsof Committee 352.

Of the 22 specimens evaluated, the majority did notcomply with the code requirements for exterior connections,namely that there should be a minimum of two beams onopposite sides of the column with widths of at least 75% ofthe column width. The strict interpretation of this requirementwould have led to classifying the specimens as cornerconnections and adopting a shear coefficient γvj of 12.

Noguchi et al. (1998) presented an overview of experimentalresearch on connections in Japan. The total number ofspecimens with concrete compressive strength over 8700 psi(60 MPa) was 110, with 76 simulating interior connections,and 28 specimens simulating exterior joints without trans-verse beams.

Noguchi et al. (1998) concluded that the provisions forcalculating joint shear strength in ACI 318-89 (same as thosein ACI 318-05) provided conservative results for the testscarried out in Japan. The mean value of the joint shearstrength measured experimentally was approximatelyproportional to the compressive strength raised to the power0.72. The ACI provisions, which assume that joint shearstrength increases with the square root of the compressivestrength, resulted in a safe lower-bound estimate of strength.

8.3—Shear strength of interior jointsSaqan and Kreger (1998) had only four test results from

specimens simulating interior joints. All specimenssustained joint shear strengths higher than the nominalvalues calculated according to ACI 318-05, despite havinglower amounts of transverse reinforcement than dictated byACI 318-05 and the design provisions of Committee 352,and despite not meeting the requirement that beams extendover at least 75% of the width of all column faces. Theyconcluded that on the limited basis of these four tests, thedesign provisions for joint shear strength in ACI 318-05 andthose proposed by Committee 352 provided safe estimates ofstrength 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 provisionsyielded conservative estimates of strength for concretecompressive strengths up to 17,400 psi (120 MPa).

8.4—Effect of transverse reinforcement onjoint shear strength

The amount of transverse reinforcement in the exteriorjoint specimens reviewed by Saqan and Kreger (1998)ranged from 0.07 to 2.02 times the amount required byACI 318-05. They found no discernible correlation betweenjoint shear strength or mode of failure and the amount oftransverse reinforcement. Of the 22 specimens evaluated bySaqan and Kreger, only five had an amount of transverse

fc′


reinforcement higher than required by ACI 318-05. Theremaining specimens had an average amount of reinforcementthat was 47% of the minimum required, and had joint shearstrengths that were 42% higher than the calculated nominalstrength. Based on this, Saqan and Kreger indicated that theamount of transverse reinforcement in the joint could bereduced for joints with high-strength concrete, although theeffect of axial load should be assessed before such a reductionis put in place.

Noguchi et al. (1998) concluded that transverse reinforcementwas marginally effective in increasing joint shear strength,and that the effect of transverse reinforcement on joint shearstrength was not sensitive to concrete compressive strength.They also found that the effect of transverse reinforcementwas slightly more significant for exterior joints than forinterior joints.

Although experimental results showed that beam-columnjoints with low amounts of transverse reinforcement wereable to attain shear strengths comparable with those of well-reinforced joints, one important additional consideration isthat the same cannot be concluded about the toughness of thejoints. The term “toughness” in this case refers to howsustainable the peak shear strength was upon further loadreversals up to similar or greater joint distortions (Joint ACI-ASCE Committee 352 2002). Noguchi et al. (1998)concluded that the plastic deformation capacity and theductility of joints were enhanced by transverse reinforce-ment in a manner consistent with the behavior of joints withnormal-strength concrete.

8.5—Development length requirements forbeam-column joints

ACI 318-05 criteria for the design of interior beam-column joints in special moment frames subjected to seismicloading include the requirement that the column dimensionparallel to the beam reinforcement must be no less than 20 timesthe diameter of the largest longitudinal bar for normalweightconcrete nor 26 times the bar diameter for lightweightconcrete. These criteria are based on an evaluation of testresults (Zhu and Jirsa 1983) for beam-column joints madewith normal-strength concrete subjected to load reversals. Zhuand Jirsa (1983) concluded that the ratios of column width tobar diameter of 20 to 22 were appropriate to avoid bonddamage at an interstory drift of 3%.

The slip of bars in beam-column joints under load reversalsplays an important role in the ability of reinforced concreteframes to resist seismic loading (Durrani and Wight 1982;Zhu and Jirsa 1983; Ciampi et al. 1982). Based on push-pulltests of bars embedded in beam-column joints with normal-strength concrete, Ciampi et al. (1982) found that to limitbond damage under cyclic loading, anchorage lengthsbetween 25 and 30 bar diameters and between 35 and 40 bardiameters were necessary for Grade 40 and 60 (280 and420 MPa) deformed bars, respectively. The criteria used todefine satisfactory performance were: 1) that the bonddamage be limited to the end region of the embedmentlength; 2) that the hysteretic loops of the anchored barremain stable; and 3) that the strength of the anchorage

continues to increase for slip values larger than the peakvalues during the previous cycles. The evaluation of testresults by Zhu and Jirsa (1983) resulted in the smaller valuesnow used in ACI 318-05. More recent tests, however,support the earlier observations and indicate that the currentdesign criteria will not prevent bond slip, even in the earlieststages of cyclic loading, and that significant bond slip willoccur even under more stringent requirements than those inACI 318-05 (Quintero-Febres and Wight 2001; Joint ACI-ASCE Committee 352 2002).

Development length requirements for beam-column jointsdiffer significantly among the ACI 318-05 (ACI Committee318 2005), the AIJ Design Guideline (AIJ 1994), and theNZS 3101 (Standards Association of New Zealand 1995).While the minimum column dimension requirement inACI 318-05 is insensitive to material properties, designprovisions in the AIJ Design Guideline (AIJ 1994) and inNZS 3101 establish the ratio of bar diameter to column depthas a function of the square root of the concrete compressivestrength and the yield strength of the reinforcement. Thephilosophy behind this requirement is that bond deteriorationcan cause significant loss in the capacity of the connection todissipate energy (pinching behavior). Noguchi et al. (1998),based on the tests of beam-column joints with concretecompressive strengths greater than 8700 psi (60 MPa)carried out in Japan as part of the New RC project, concludedthat specimens with high-strength concrete and high-strength reinforcement demonstrated significantly reducedability to dissipate energy compared with beam-columnjoints made with normal-strength concrete. They indicatedthat while specimens that met the Japanese design guidelinehad adequate behavior, it is not clear if a less stringentrequirement such as that of ACI 318-05 would be sufficientfor adequate toughness under cyclic loading. Theyconcluded that further evaluation of the Japanese designguideline was needed for high-strength materials.

8.6—RecommendationsBecause research indicates that the equations for calculating

the shear strength of joints are conservative for high-strengthconcrete, no change to the code provisions is recommended.There are significant differences in the provisions for theratio of column dimension parallel to the beam reinforcement tothe diameter of the largest longitudinal beam bar (whicheffectively defines the minimum interior column dimension)between ACI 318-05 and both the AIJ Design Guideline(1994) and NZS 3101 (Standards Association of NewZealand 1995). ACI 318-05 requires significantly smallercolumn dimensions for joints with high-strength concrete.Although there is consensus in the literature that theminimum column dimension specified in ACI 318-05 is notsufficient to prevent slip of the reinforcement, this situationis not specific to high-strength concrete. The main difficultyfaced by the ITG was that there were no references foundevaluating the minimum column dimension specified inACI 318-05 when high-strength concrete was used. Althoughthere is experimental evidence from research carried out inJapan that the toughness of joints subjected to repeated load


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

CHAPTER 9—DESIGN OF STRUCTURAL WALLSSeismic design of structural walls is covered in Section 21.7

of ACI 318-05. For walls with low aspect ratios, the primarydesign consideration is shear strength. According to ACI318-05, the nominal shear strength of walls is given by

Vn = Acv(αc + ρt fy) ACI 318 Eq. (21-7)

where the coefficient αc = 3.0 for hw / lw ≤ 1.5, 2.0 for hw /lw≥ 2.0, (fc′ and fy in psi) where the coefficient αc = 0.25 forhw / lw ≤ 1.5, 0.17 for hw/lw ≥ 2.0, ( fc′ and fy in MPa) andvaries linearly in between.

The minimum amount of web reinforcement required bythe code is ρl = ρt = 0.0025, with a maximum spacingbetween bars of 18 in. (457 mm).

In slender walls, the flexural behavior of the walls is mostimportant. The minimum amount of longitudinal reinforcementis specified to prevent premature failure due to rupture of thereinforcement. The significance of this problem is greater forwalls made with high-strength concrete because the depth ofthe neutral axis decreases and the strain demand in thereinforcement increases with compressive strength.

Another mode of failure that the code intends to prevent,or at least postpone, through the use of special boundaryelements at the edges of structural walls is crushing of theconcrete in the compression zone due to flexural demands.According to ACI 318-05, compression zones shall bereinforced with special boundary elements in areas where

(9-1)

where c corresponds to the largest neutral axis depth calculatedfor the factored axial force and nominal moment strength,consistent with the design displacement δu , in. Theseelements allow proper confinement and ductile behavior ofthe compression zone. Due to the amount of transversereinforcement required, however, the use of boundaryelements significantly increases the cost of the walls.

9.1—Boundary element requirementsThe equation to determine whether boundary elements are

required stems from establishing a limiting strain demandεlim that the wall can sustain without special confinement,such that

c = (9-2)

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

φlim = (9-3)

Because the first term within the square brackets is smallcompared with the second, it can be conservativelyneglected to calculate the depth of the neutral axis

c = (9-4)

The previous expression was derived by assuming alimiting strain of 0.003 and rounding the term 2/0.003 = 667down to 600. The design expression implemented in ACI318-05 is thus intended to require special boundary elementsif the strain in the extreme compression fiber of a wallexceeds 0.003 for the design drift demand. In the currentdesign procedure, the limiting strain is independent of theconcrete compressive strength. A limiting strain of 0.003 hasbeen shown to be a safe limit for normal-strength concrete(Wallace 1998). The main concern in applying this provisionto high-strength concrete walls is whether a limiting strain of0.003 remains a safe value as the concrete compressivestrength increases.

Wallace (1998) suggests that a similar limiting strain fornormal-and high-strength concrete can be adopted, althoughgreater conservatism may be prudent for high-strengthconcrete given the relatively brittle behavior of unconfinedhigh-strength concrete.

As previously stated in Section 4.5, Fasching and French(1998) indicate that opinions about the limiting strain forhigh-strength concrete are varied. The test data set theycompiled had limiting strains ranging from 0.002 and 0.005,with an average value of 0.0033. Average values for data setswith the same type of aggregate were all above 0.003.

Bae and Bayrak (2003) suggested adopting a lowerlimiting strain due to observed spalling at lower strains inhighly confined high-strength concrete columns. Theyattribute the premature spalling observed in these columns tothe existence of a failure plane created by closely spaced hoops.

Ozbakkaloglu and Saatcioglu (2004) proposed, on thebasis of moment-curvature analyses, that the limitingconcrete 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 maximummoment resistance and the corresponding extreme compressionfiber strain from a series of moment-curvature diagrams.They concluded that although the optimal values of flexuralstrength were obtained by varying the limiting strain asproposed, the calculated flexural strength was not verysensitive to the limiting strain, and recommended adopting aconstant value of 0.003.

fc′

clw

600 δu hw⁄( )----------------------------- δu hw 0.007≥⁄,≥

εlim

φlim

---------

1lw

---- 0.0025 lw 0.5hw–( ) 2δu

hw

------+

εlim

φlim

---------lw

2δu

εlimhw

---------------

---------------lw

600δu

hw

------

---------------= =


Saatcioglu and Razvi (1998) observed premature spallingof cover concrete in most of the concentrically loadedcolumns that they tested, prior to the development of strainsassociated with concrete crushing. Similar to Bae andBayrak (2003), they attributed the premature spalling inthese columns to a stability failure caused by a failure planeinduced by the presence of closely spaced longitudinal andtransverse steel. Furthermore, they indicated that thisproblem was not observed in columns with widely spacedtransverse reinforcement tested by Rangan et al. (1991) andYong et al. (1988).

9.2—Shear strength of walls with low aspect ratiosTests of low-rise walls with high-strength concrete carried

out in North America are scarce. Wallace (1998) performedan analysis comparing the strength estimated using the sheardesign equation in ACI 318-05 with test results of low-risewalls made of high-strength concrete carried out in Japan.The analysis by Wallace showed that the ratio of measuredto estimated strength decreased with the ratio ρn fy/fc′ . Thestrength of several specimens with ρn fy/fc′ ≥ 0.08 was over-estimated using the ACI 318 equation. He carried out asecond comparison using a design procedure proposed byWood (1990). According to Wood, the shear strength of thewalls is given by

Vn = Asv fy/4 (9-5)

10 Acv ≥ Vn ≥ 6 Acv ( fc′ in psi) (9-6)

0.83 Acv ≥ Vn ≥ 0.5 Acv ( fc′ in MPa)

where Asv is the total area of vertical reinforcement, and Acvis the area of the wall bounded by the web thickness and thewall length. Wallace found that for the high-strength wallswith different amounts of vertical reinforcement tested inJapan, the equation proposed by Wood provided a uniformratio of measured to calculated shear strength. The averageratio of measured to calculated strength was 1.76, with acoefficient of variation of 20%. Wallace also showed that forhigh-strength concrete walls, shear strength was not sensitive tothe amount of web reinforcement, and suggested using ashear strength of 9 Acv (in psi) (0.75 Acv [in MPa])as a safe lower bound.

Kabeyasawa and Hiraishi (1998) presented a summary of21 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 experimentalprogram were the concrete compressive strength, the trans-verse 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 flexuralyielding before shear failure.

Specimens designed to fail in shear had different amountsof web reinforcement. All shear-critical specimens faileddue to crushing of the concrete in the web of the wall.

Specimens with lower amounts of web reinforcement failedafter yielding of that reinforcement, and their strength wassafely estimated by the Japanese seismic design guideline. Inspecimens with high amounts of transverse reinforcement,failure occurred due to crushing of the web concrete beforeyielding of the web reinforcement, and their strength wasoverestimated by the Japanese design guideline. The Japaneseguideline is based on a strut-and-tie approach in which thetotal strength is the sum of the strength contributions fromtruss and arch action. The procedure is based on estimatingthe demand on the concrete placed by the truss mechanism,and whatever capacity is left, if any, is assigned to the directstrut mechanism. Kabeyasawa and Hiraishi (1998) alsoindicated that although the walls designed to fail in flexurewere able to sustain deformations past the yield point of theflexural reinforcement, the energy dissipated, as indicated bythe hysteresis loops, was relatively low. They indicated thatequivalent damping coefficients for the high-strengthconcrete walls were on the order of 5 to 8%, while thesevalues for normal-strength walls are considerably higher, onthe order of 20%. In addition, the hysteresis loops exhibitedpinching behavior.

9.3—Minimum tensile reinforcement requirements in walls

Failure of lightly reinforced structural walls may occur, insome instances at relatively low levels of drift, due to fractureof the tensile reinforcement (Wood 1989). A documentedcase of this type of failure occurred in an eight-story structuralwall building that suffered severe damage and fracture of thetensile reinforcement near the base of the structural wallsduring the 1985 Chilean earthquake (Wood 1989).According to Wood, the damaged walls had calculated tensilestrains in the boundary reinforcement that were twice themeasured fracture strain of the reinforcement.

This problem can be exacerbated by the use of high-strength concrete because the depth of the compression zoneneeded to equilibrate the force in the tensile reinforcement isconsiderably less than in walls with normal-strength concrete.

Based on results from 37 structural wall tests, Woodproposed two different criteria that may be used to determinethe vulnerability of walls to failure due to fracture of thetensile reinforcement. The first criterion uses the calculatedsteel strain in the extreme layer of reinforcement at thenominal flexural strength of the cross section as an indexvalue. Because there were several walls within the set withcalculated steel strains greater than 5% that failed in shear,however, Wood concluded that the calculated steel straincannot be used as the sole criterion for determining thesusceptibility of a wall to fracture of the reinforcement.

It was observed that of the subset of 24 walls with a shearstress index greater than 0.75, 20 failed in shear, and of the13 walls that developed a shear stress index less than 0.75,12 failed in flexure. The shear stress index was defined byWood as vmax /vn , where vmax is the maximum shear stressdemand on the wall and

fc′ fc′

fc′ fc′

fc′ fc′


vn = 2 + ρn fy ≤ 8 (psi) (9-7)

vn = /6 + ρn fy ≤ 2 /3 (MPa)

Within the subset of walls with shear stress indexes below0.75, Wood observed that 10 of the 12 walls with totalvertical reinforcement ratios ρwt less than 1% were susceptibleto fracture of the tensile reinforcement. Fracture of thereinforcement was observed in walls with calculated steelstrains in the extreme layer of reinforcement as low as 2.5%.A limit of 4% was proposed as a reasonable boundary foridentifying walls that are likely to fail due to fracture of thereinforcement.

The second criterion is based on the flexural stress indexcfsw, which is representative of the ratio of neutral axis depthto wall length, and is given by

(9-8)

where

(9-9)

whereρwt = total vertical reinforcement ratio of the wall;Aw = gross area of the wall;Aswb = area of vertical reinforcement in the boundary

element of the wall (the participation of thesteel in the compression boundary element isignored in the formulation because it wasassumed that the neutral axis depth is small);

Asww = total area of vertical reinforcement in the webof the wall, excluding boundary elements; and

P = axial load on the wall, with a positive valuerepresenting a compressive force.

Wood noted that of the 27 specimens in which the mainreinforcement did not fracture, 26 had flexural stress indexesgreater than 15%, and suggested that structural walls suscep-tible to fracture of the tensile reinforcement are those with aflexural stress index below 15%.

Both of the two requirements proposed by Wood may beinterpreted as prescribing a minimum amount of tensilereinforcement in structural walls.

9.4—RecommendationsThe literature survey indicates that design provisions for

the detailing of boundary elements in slender walls in ACI318-05 are adequate for high-strength concrete, and nosignificant change is necessary. The technical references inwhich a lower limiting compressive strain was suggested forhigh-strength concrete columns attributed the need for alower limiting strain to the existence of a failure planecaused by closely spaced ties, or to an overestimation of the

flexural strength. The former is not a concern in the case ofend regions of walls without boundary elements, while thelatter is not a concern because the limiting strain of theconcrete is not likely to have a significant effect on thecalculated flexural strength of slender walls.

One area of concern is the behavior of walls with very lightamounts of longitudinal reinforcement. A simple procedurewas proposed by Wood to prevent wall failure due to fractureof the tension reinforcement.

In the case of walls with low aspect ratios, the study byWallace (1998) showed that shear strength equations in ACI318-05 become less conservative as the amount of transversereinforcement increases in walls with high-strengthconcrete. For high amounts of transverse reinforcement, theequation for shear strength in ACI 318-05 was found to beunconservative. One viable option to obtain a uniform levelof safety is to adopt the equations proposed by Wood. Themain disadvantage of this option is that the level of conser-vatism was found to be quite large for high-strengthconcrete. Another alternative is to recommend the use ofstrut-and-tie models following the recommendations presentedin Chapter 6.

The study by Wallace indicated that the current ACIprocedure was unconservative for several high-strengthconcrete walls with ρn fy /fc′ ≥ 0.08. These cases, however,are rare in earthquake-resistant construction. This concernmay be addressed with an addition to the commentary toACI 318-05, Section 21.7.4, indicating that the currentdesign equations may yield unconservative estimates ofshear strength for high-strength concrete walls with highamounts 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 seriesof recommendations for the use of high-strength concrete inseismic design. The main purpose of the literature reviewpresented in the previous chapters on structural design wasto identify specific sections of ACI 318-05 that should berevised to allow for the use of high-strength concrete inseismic design. Although some of the changes that wereproposed were intended to facilitate a smooth transitionbetween normal- and high-strength concrete, the majority ofthem specifically address structural design using high-strength concrete.

The following are specific modifications to ACI 318-05intended for the safe use of high-strength concrete in seismicdesign. Section numbers are noted where applicable. SI unitsare not repeated in this Chapter for clarity. See previouschapters for SI equivalents.

10.1—Proposed modifications to equivalent rectangular stress block

The following changes are proposed to the equivalentrectangular stress in ACI 318-05.

Changes and additions to Section 2.1—α1 = factor relating magnitude of uniform stress in

the equivalent rectangular compressive stress

fc′ fc′

fc′ fc′

cfswρwt fyl P Aw⁄+

fc′----------------------------------=

ρwtAswb Asww+

Aw

-----------------------------=


block to specified compressive strength ofconcrete as defined in 10.2.7.2, Chapter 10.

β1 = factor relating depth of equivalent rectangularcompressive stress block to neutral axis depth,see 10.2.7.3 10.2.7.4, Chapters 10, 18,Appendix B

χ1 = factor relating mean concrete compressivestress at axial load failure of concentricallyloaded columns to specified compressivestrength 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 α1fc′ shall be assumed

uniformly distributed over an equivalent compression zonebounded by edges of the cross section and a straight linelocated parallel to the neutral axis at a distance a = β1c fromthe fiber of maximum compressive strain.

10.2.7.2 For fc′ between 2500 and 8000 psi, α1 shall betaken as 0.85. For fc′ above 8000 psi, α1 shall be reducedlinearly at a rate of 0.015 for each 1000 psi of strength inexcess 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 maximumstrain to the neutral axis, c, shall be measured in a directionperpendicular to that axis.

10.2.7.3 10.2.7.4 For fc′ between 2500 and 4000 psi, β1shall be taken as 0.85. For fc′ above 4000 psi, β1 shall bereduced linearly at a rate of 0.05 for each 1000 psi of strengthin 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 membersconforming to 10.16, or confined columns conforming to21.4.4.1 through 21.4.4.3 for the full height of the column

φPn,max = 0.85φ[0.85fc′ (Ag – Ast) + fyAst] (10-1)


10.3.6.2 For nonprestressed members with tie reinforcementconforming to 7.10.5

φPn,max = 0.80φ[0.85fc′ (Ag – Ast) + fyAst] (10-2)


10.3.6.3 For prestressed members, design axial strengthφPn shall not be taken greater than 0.85 (for members withspiral reinforcement) or 0.80 (for members with tie rein-forcement) of the design axial strength at zero eccentricityφPo calculated assuming concrete stress of χ1fc′ uniformlydistributed across the entire depth of the section.

10.3.6.4 For fc′ between 2500 and 8000 psi, χ1 shallbe taken as 0.85. For fc′ above 8000 psi, χ1 shall bereduced linearly at a rate of 0.015 for each 1000 psi ofstrength in excess of 8000 psi, but χ1 shall not be takenless than 0.70.

10.2—Proposed modifications related to confinement of potential plastic hinge regions

Addition to Section 2.1—kve = confinement efficiency factor. See Eq. (21-YY)

Changes to Section 21.2.5—21.2.5 Reinforcement in members resisting earthquake-

induced forces—Reinforcement resisting earthquake-induced flexural and axial forces in frame members and instructural wall boundary elements shall comply with ASTMA 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 notexceed fy by more than 18,000 psi (retests shall not exceedthis value by more than an additional 3000 psi); and

(b) The ratio of the actual tensile strength to the actualyield strength is not less than 1.25

The value of fyt for transverse reinforcement includingspiral reinforcement shall not exceed 60,000 psi. The use oftransverse reinforcement with a specified yield strength notexceeding 120,000 psi shall be permitted when required tomeet the confinement requirements given by Eq. (21-XX).The yield strength of the reinforcement shall be measured bythe offset method of ASTM A 370 using 0.2% permanentoffset. The requirement of Section 3.5.3.2 shall be inappli-cable 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 isrequired by 21.4.3.2 or 21.4.5.

(a) The area ratio of transverse reinforcement shall not beless than that required by Eq. (21-XX)

(21-XX)

where Ag /Ach – 1 ≥ 0.3, and Pu/Ag fc′ ≥ 0.2.(b) Transverse reinforcement shall have either circular or

rectangular geometry. Reinforcement for columns withcircular geometry shall be in the form of spirals or hoops, forwhich kve = 1.0. Reinforcement for columns with rectangulargeometry shall be provided in the form of single or overlappinghoops. Crossties of the same bar size and spacing as thehoops shall be permitted. Each end of the crosstie shallengage a peripheral longitudinal reinforcing bar. Consecutivecrossties shall be alternated end for end along the longitudinalreinforcement. The parameter kve for rectangular hoopreinforcement shall be determined by Eq. (21-YY)

(21-YY)

(c) If the thickness of the concrete outside the confiningtransverse reinforcement exceeds 4 in., additional transversereinforcement shall be provided at a spacing not exceeding12 in. Concrete cover on the additional reinforcement shallnot exceed 4 in.

ρt 0.35fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ 1

kve

-----------Pu

Ag fc′-----------=

kve0.15bc

shx

--------------- 1.0≤=


Changes to Section 21.12.5—21.12.5.1 Columns shall be spirally reinforced in accor-

dance with 7.10.4 or shall conform to 21.12.5.2 through21.12.5.421.12.5.5. Section 21.12.5.521.12.5.6 shall applyto all columns.

21.12.5.2 At both ends of the member, hoops shall beprovided at spacing so over a length lo measured from thejoint face. Spacing so shall not exceed the smallest of (a), (b),(c), and (d): (a) eight times the diameter of the smallestlongitudinal bar enclosed; (b) 24 times the diameter of the hoopbar; (c) 1/2 of the smallest cross-sectional dimension of theframe member; (d) 12 in. length lo shall not be less than thelargest of (e), (f), and (g); (e) 1/6 of the clear span of themember; (f) maximum cross-sectional dimension of themember; and (g) 18 in.

21.12.5.3 For members in which the specified concretecompressive strength is greater than 8000 psi, transversereinforcement as required in (a) and (b) shall be provided atboth ends of the member over a length lo measured from thejoint face.

(a) Members with transverse reinforcement with rectilineargeometry shall not be less than that required by Eq. (21-ZZ)

(21-ZZ)

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

(21-WW)

where Ag /Ach – 1 ≥ 0.3, and Pu/Ag fc′ ≥ 0.2.21.12.5.321.12.5.4 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 devel-opment length and that crosses the potentialplane of splitting through the reinforcementbeing spliced or developed, in.2

Ab,max = cross-sectional area of largest bar being splicedor 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 providedover the lap length. When the value of exceeds 100 psi,ld shall be calculated using either 12.2.2 or 12.2.3 with Ktr =0, and transverse reinforcement crossing the potential planeof splitting shall be provided over the tension splice length

with a minimum total cross-sectional area Asp given byEq. (21-AA)

Asp = 0.5nAb,max(fc′ /15,000) (21-AA)


Maximum spacing of the transverse reinforcementenclosing the lapped bars shall not exceed d/4 or 4 in., andthe minimum hoop or spiral bar size shall be No. 3. Lapsplices shall not be used:

(a) within the joints;(b) within a distance of twice the member depth from the


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 bepermitted only within the center half of the member length.Lap splices shall be designed as tension lap splices in accor-dance with 21.3.2.3, and shall be enclosed with transversereinforcement conforming to 21.4.4.2 and 21.4.4.3 and themaximum spacing of transverse reinforcement in lap splicesshall be as given by 21.4.4.2. The transverse reinforcementalso shall conform to 21.4.4.3.

21.5.4.1 The development length ldh for a bar with astandard 90-degree hook in normalweight aggregateconcrete shall not be less than the largest of 8db, 6 in., andthe lengths required by Eq. (21-6) and (21-BB)

(21-6)

(21-BB)

for bar sizes No. 3 through 11.21.7.2.3 Reinforcement in structural walls shall be

developed or spliced for fy in tension in accordance withChapter 12, except:

(a) The effective depth of the member referenced in12.10.3 shall be permitted to be 0.8lw for walls;

(b) The requirements of 12.11, 12.12, and 12.13 need notbe satisfied;

(c) At locations where yielding of longitudinal reinforce-ment is likely to occur as a result of lateral displacements,development lengths of longitudinal reinforcement shall be1.25 times the values calculated for fy in tension. When thevalue of exceeds 100 psi, transverse reinforcement witha 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 to21.2.6, and welded splices of reinforcement shall conform to21.2.7; and

(e) When the value of exceeds 100 psi, ld shall becalculated with Ktr = 0.

ρt 0.3fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ Pu

Ag fc′-----------=

ρt 0.2fc′fyt

-----Ag

Ach

-------- 1–⎝ ⎠⎛ ⎞ Pu

Ag fc′-----------=

fc′

ldhfydb

65 fc′----------------=

ldhfydb

650fc′1 4⁄

----------------------=

fc′

fc′


21.7.6.6 Mechanical and welded splices of longitudinalreinforcement of boundary elements shall conform to 21.2.6and 21.2.7. Lap splices shall be designed as tension lapsplices in accordance with 21.3.2.3, except that themaximum spacing of transverse reinforcement shall be asgiven by 21.4.4.2 and the transverse reinforcement shall alsoconform 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 itsnodes

βfc = factor to account for the effect of concretecompressive strength on the effectivecompressive strength of concrete in a strut

βαt = factor to account for the effect of the angle ofinclination of the strut αst on the effectivecompressive strength of concrete in a strut

10.4—Proposed modifications related tostrut-and-tie models

Changes to Appendix A—A.3.2 The effective compressive strength of the concrete

fce in a strut shall be taken as

fce = 0.85βs fc′ (A-3)

A.3.2.1 For a strut of uniform cross-sectional area over itslength βs= 1.0: for fc′ between 2500 and 8000 psi, βs shall betaken as 1.0; for fc′ above 8000 psi, βs shall be reducedlinearly at a rate of 0.02 for each 1000 psi of strength inexcess 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 themidsection 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) 0.6λ; and (b) the product ofβfcβαt , where

βfc = 1 – fc′ /30,000, but βfc shall not be taken less than0.60.

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 ofinclination of the strut may be approximated as

A.3.2.3 For struts in tension members, or the tensionflanges of members, βs = 0.40

A.3.2.4 For all other cases, βs = 0.60

AcknowledgmentsThanks are due to the Carpenters Contractors Cooperation

Committee, Inc., of Los Angeles, Calif., for sponsoringInnovation Task Group 4 and to Joseph C. Sanders for actingas liaison with that group. The members of ITG 4 areindebted to the following individuals for their review ofportions of this document and for their constructivecomments: 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 stressblock parameters. M. Saatcioglu made numerous contributionsrelated to stress block parameters and column confinement,which are gratefully acknowledged.

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αscotav

d-----=


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