91

394 ACI Structural Journal/July-August 1994

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI Structural Journal, V. 91, No. 4, July-August 1994.Received July 1, 1992, and reviewed under Institute publication policies. Copyright

© 1994, American Concrete Institute. All rights reserved, including the making ofcopies unless permission is obtained from the copyright proprietors. Pertinent discus-sion will be published in the May-June 1995 ACI Structural Journal if received byJan. 1, 1995.

Steel Jacket Retrofitting of Reinforced Concrete Bridge Columns for Enhanced Shear Strength—Part 1: Theoretical Considerations and Test Design

by M. J. Nigel Priestley, Frieder Seible, Yan Xiao, and Ravindra Verma

A theoretical and experimental investigation conducted to study the shearfailure mode of reinforced concrete bridge columns designed before 1971,and to establish the effectiveness of full-height steel jackets for enhancingthe seismic shear strength, is described.

In this first part of a two-part paper, theoretical considerations relatingto assessing the shear strength of existing columns of circular or rectangu-lar sections are presented. Current design approaches are compared withmore recently developed, and less conservative, predictive methods. Mod-els are presented for predicting the enhancement to shear strength providedby circular or elliptical (for rectangular section) jackets. Design details ofan experimental test program to determine “as-built” and retrofitted col-umn shear strength are presented.

Keywords: bridges (structures); columns (supports); ductility; earth-quake-resistant structures; flexural strength; reinforced concrete; shearstrength.

Shear failure of squat bridge columns has been one of themajor problems associated with the performance of rein-forced concrete bridges under earthquake excitations. Suchshort and, hence, relatively stiff members tend to attract agreater portion of the seismic input to the bridge during anearthquake and require the generation of large seismic shearforces to develop the moment capacity of columns. On theother hand, estimation of flexural strength based on elasticmethods, along with much less conservative shear strengthprovisions during the 1950s and 1960s, frequently resultedin actual shear strength of “as-built” bridge columns beingsignificantly less than the flexural capacity. Since the trans-verse reinforcing steel was generally inadequately anchoredin the cover concrete, which can be expected to spall offunder cyclic loading, the problem is compounded. Hence,shear failure is likely in such columns, accompanied by rapidstrength, stiffness, and physical degradation. This has beenevidenced by the brittle shear failure of bridge columns inCalifornia during the 1971 San Fernando earthquake,1 the1987 Whittier Narrows earthquake,2 and the 1989 LomaPrieta earthquake.3 Typical details of a squat circular bridgecolumn for a multicolumn bent designed and constructed inthe pre-1971 era are shown in Fig. 1(a).

Following the 1971 San Fernando earthquake, there wasan increased emphasis on theoretical and experimental

research related to the seismic response of bridges to estab-lish safer seismic design procedures. The research emphasisin the U.S. was focused on developing analytical tools forperforming sophisticated time-history analyses for bridges,while in Japan and New Zealand extensive experimentaltesting was initiated to develop a rational understanding ofthe seismic behavior of various bridge components.4-8 Thisresearch has been based on the principles of capacity designapproach,9 in which ductile flexural response of concretestructures is assured by setting the shear strength above themaximum feasible shear force corresponding to the flexuralstrength developed in the plastic hinge regions. Thisapproach requires that the prediction of shear forces likely tobe generated in the columns during an earthquake is notdirectly related to code-specified empirical coefficients, butto a rational examination of inelastic deformation mecha-nisms likely to develop at large ductility levels.

Previous studies conducted by Ang, Priestley, and Paulay6

and Wong, Paulay, and Priestley8 have addressed some ofthe issues related to seismic response of well-confined squatcircular reinforced concrete columns under uni- and multidi-rectional earthquake loading, based on small-scale circularcolumns tested as vertical cantilevers. Ang, Priestley, andPaulay6 showed that most design codes are extremelyconservative and inconsistent in their shear design proce-dure. They observed that the actual shear capacity ofcolumns decreased with increasing flexural ductility, assuggested in a model originally proposed by ATC-6,10 andthat the degraded shear strength mainly relied on the shearforce carried by the transverse reinforcement provided in theform of hoops or spirals. Hence, any seismic shear designapproach for reinforced concrete bridge columns should alsoconsider the influence of flexural ductility on the columnshear strength during inelastic levels of seismic response.

Title no. 91-S39

ACI Structural Journal/July-August 1994 395

Comparatively little systematic research has been carriedout to investigate the shear performance of rectangular rein-forced concrete bridge columns with longitudinal reinforce-ment evenly distributed around the four faces. However,there have been major experimental studies in the U.S.,notably by Woodward and Jirsa,11 and in Japan, by a numberof researchers,12 on rectangular columns more typical ofbuilding columns, with comparatively small numbers oflongitudinal reinforcing bars.

The research just described provided a reasonable basis forthe design of new bridge columns for seismic forces.However, there remained a need for further verification and,if necessary, modification of the design approaches, espe-cially for assessment of columns under reversed curvature,with realistic levels of longitudinal reinforcement, lowaspect ratios, and low levels of transverse reinforcementtypical of the bridge columns designed in the pre-1971 era.

Following the 1971 San Fernando earthquake, the Cali-fornia Department of Transportation (Caltrans) embarked onan extensive bridge seismic assessment and retrofitprogram,13 which is based on ongoing experimental andanalytical research being conducted at several institutions. Amajor research program was started in 1987 at the Universityof California at San Diego, to study various problems relatedto the seismic response of bridges. The first phase of theproject investigated the enhancement of inadequate andundependable flexural strength and ductility capacity of tallflexure-dominated bridge columns by encasing the plastichinge regions of the columns with steel jackets. With circularcolumns, circular cylindrical jackets are constructed in twohalf-shells slightly oversized for easy installation, welded insitu up the vertical seams, and with the gap between thecolumn and the jacket filled with grout to provide continuitybetween the jacket and the column. With rectangular

columns, the jacket is rolled to an elliptical shape, with thelarger gaps between casing and column filled with concreterather than grout. The elliptical shape is needed to provide acontinuous confining pressure by passive restraint in poten-tial plastic hinge regions. For flexural retrofit, only thepotential hinge regions need to be retrofitted.

For both circular and rectangular columns, the steel jacketacts as passive confinement reinforcement for ductileresponse. Dilation of the flexural compression zone isrestrained by the hoop stiffness of the jacket, placing theconcrete in radial compression, thus enhancing its compres-sion strength and effective ultimate compression strain.Restraint by the jacket of dilation on the flexural tension sideof the column also provides an effective constraint againstbond failure of longitudinal bar lap splices in the hingeregion.14,15

It is apparent that a steel jacket should also be effective inproviding shear strength enhancement to squat bridgecolumns with inadequate shear reinforcement. The jacketmay conservatively be idealized as a series of independentclosely spaced peripheral hoops with thickness and spacingequal to the jacket thickness. If shear strength enhancementis needed, the jacket will normally be required over the fullheight of the column, as shown in Fig. 1(b). Note that a gapis provided between the jacket and the cap beam or footingto minimize flexural strength enhancement, which mightcause excessive forces to develop in adjacent members.Within potential plastic hinge regions, the required jacketthickness will be the greater of requirements for ductility andshear strength enhancement.

In this first part of a two-part paper, theoretical consider-ations relating to the shear strength of existing and retrofittedcolumns are discussed, and the design of the test program ispresented. In the companion paper, experimental results arepresented and compared with predicted response.

RESEARCH SIGNIFICANCEThe research described in this and the companion paper16

has formed the basis for retrofit assessment and design ofsquat shear-dominated bridge columns in California. A largenumber of bridge columns have already been retrofitted withsteel jackets to enhance the seismic shear strength. Data anddesign equations presented in the two papers provide thejustification for this current assessment and retrofit effort.

THEORETICAL CONSIDERATIONSThe ASCE-ACI Joint Task Committee 32617 summarized

results of research conducted during the first half of thecentury, focusing on the ultimate shear strength of reinforcedconcrete members, primarily based on simple beam sheartests. Further rational models were developed to study theshear transfer and failure mechanisms in reinforced concrete(RC) members, and these were included in the recommenda-tions of the ASCE-ACI Joint Task Committee 426 proposedin 1971.18 In a recently held international conference onconcrete shear in earthquakes,19 it was concluded thatmodern theories on shear are capable of satisfying not onlyequilibrium conditions, but also compatibility conditionsand the constitutive laws, enabling the prediction of not only

ACI member M. J. Nigel Priestley is Professor of Structural Engineering in theDepartment of Applied Mechanics and Engineering Sciences at the University of Cali-fornia, San Diego. His teaching and research interests are in reinforced andprestressed concrete structures, masonry structures, and earthquake-resistant design.He is the author or coauthor of many technical papers, a member of ACI Committee531, Concrete Masonry Structures, and has been recipient or corecipient of manyawards, including ACI's 1984 and 1989 Raymond C. Reese Awards.

ACI member Frieder Seible is a professor of structural engineering at the Universityof California, San Diego. He received his PhD from the University of California,Berkeley. His research combines large-scale experimental testing and nonlinear ana-lytical modeling of structural systems. He is a member of ACI Committee 341, Earth-quake-Resistant Concrete Bridges.

ACI member Yan Xiao is a research scientist and a lecturer in the Department ofApplied Mechanics and Engineering Sciences at the University of California, SanDiego. He received his BS in civil engineering from Tianjin University, China, and hisMEng and DrEng in structural engineering from Kyushu University, Japan. Heworked with Aoki Corporation in Tokyo, Japan, prior to joining UC San Diego. Hisresearch and teaching interests are in the earthquake-resistant design of reinforced,prestressed concrete and steel-concrete composite structures. He is the author and co-author of several technical papers in these fields.

ACI member Ravindra Verma is a senior bridge engineer at CRSS Civil Engineers,Inc., Irvine, Calif. He received his BS in civil engineering from the Institute of Tech-nology, Varanasi, India, and his MS and PhD degrees in structural engineering fromthe University of California, San Diego, in June, 1993. He has co-authored severaltechnical papers and reports on seismic design and retrofit of bridge columns, and hasbeen the recipient of a 1992 EERI student award. His research interests are in seismicanalysis and earthquake-resistant design of reinforced concrete bridges.


the member shear strength, but also force-deformationresponse of simple members.

However, it is still a common agreement that much moreextensive research is needed to develop a universally accept-able and generally applicable shear theory, especially foranalyzing the shear response of more complicated structuralmembers. At this stage, a wide variety of theoretically andexperimentally based shear strength equations and models areavailable for analyzing the response of RC members under thecombined influence of axial, bending, and shear forces, oftenwith widely varying assumptions and sometimes arriving atvery different end results for the same problems.

Current shear design approaches for columnsMany design codes still follow the traditional 45-deg

analogous truss approach to evaluate the amount of transversereinforcement required for shear strength. This is usuallyaccompanied by conservative empirical predictions of theoverall concrete shear-carrying capacity. However, in recentyears, several design codes have adopted more rational sheardesign procedures, primarily based on the provisions of thevariable angle truss approach. The new Canadian Code20 hasadopted some of the essential features of the diagonalcompression field theory,21 while the modern CEB-FIP22

provisions involve plasticity theory-based analyses. Thesecodes allow a wide range of values for the permissible angleof inclination of the principal diagonal compressive stresswith the member longitudinal axis, and also include criteriafor various possible limit states. The influence of ductileflexural response on shear strength is not, however, currentlyconsidered by the new approaches.

In the following sections, shear strength equations adoptedby ACI 318-8923 and the shear design proposal by Ang,Priestley, and Paulay6 are evaluated, and a recently devel-oped modification of Priestley; Verma; and Xiao’s approachis advanced.24 A detailed critical review of some of the otherprevious theoretical and experimental studies on shearresponse of RC members is provided elsewhere.25

ACI 318-89 shear design approachThe ACI approach23 considers separate transverse steel

shear-resisting mechanisms Vs and concrete shear-resistingmechanisms Vc in providing the total nominal shear strengthVn as given by Eq. (1) through (3)

Vn + Vs + Vc (1)

Vs = Av fyh(d/s) (2)

Fig. 1—“As-built” and retrofitted squat circular bridge columns (1 in. = 25.4 mm; Grade40: fy = 275 MPa; Grade 60: fy = 414 MPa).

Fig. 2—Degradation of concrete shear capacity with displace-ment ductility.


(3)

In the preceding equations, Av , fyh , and s are the total cross-sectional area, yield strength, and spacing of the transversereinforcement, respectively; fc′ (in psi) is the specifiedconcrete compressive cylinder strength; Ag is the cross-sectional area of the member specified in square in. and P (inlb) is the axial load. The shear strength is based on anaverage shear stress assumption on the effective crosssection bw d, where bw is the web width, or diameter, of thecircular cross section, and d is the effective depth, assumedequal to the distance from the extreme compression fiber tothe centroid of the longitudinal tension reinforcement in theopposite half of the circular member. For members such ascolumns with distributed longitudinal reinforcement, d = 0.8hor 0.8D is assumed for rectangular or circular sections, respec-tively. For circular columns, the effective shear area is thusequal to 0.8D2, which exceeds the gross sectional area(0.785D2). The shear strength equations in the 1990 CaltransBridge Design Specification Manual26 are identical to thepreceding ACI provisions.

In the ACI 318-8923 provisions for shear design, thedesigner also has an option to adopt a more detailed and,hence, presumably a more exact and less conservative,approach to estimate the concrete shear capacity.

The relevant equations are

(4)

where

(5)

The value of Vc calculated by Eq. (4) and (5) has an upperlimit of

(6)

In Eq. (4) and (5), Mu and Vu are the factored moment andshear force on the section under consideration, D is theoverall section depth or column diameter, and ρω is thetensile steel ratio taken as 0.5ρt for columns. Eq. (4) and (5)allow for the influence of axial load, a spect ratio, and longi-tudinal reinforcement content on the concrete shear-carrying

capacity. However, it has been pointed out by previousresearchers6 and reconfirmed on the basis of the currentresearch that the exact method is more conservative overmost of the axial load ratio range than the approximateequation, giving little incentive for a designer to go throughthe mathematically more rigorous approach. It was also previ-ously shown that the exact approach implies a hyperbolicincrease in vc with increasing axial load ratio, with instabilityof the design equations at moderate-to-high axial load levels.

Shear design model by Ang, Priestley, and PaulayBased on the results of testing 25 small-scale squat

circular columns under axial and cyclic loading, thefollowing equations were proposed by Ang, Priestley, andPaulay6 for evaluating the maximum shear strength ofcircular columns. This approach involved the use of thetraditional additive principle. For brittle shear failure, thesteel truss and concrete mechanisms are defined by

(7)

(8)

where α = 2/(M/VD) ≥ 1.0, M is the moment, Ash is the cross-sectional area of spiral or circular hoop, V is the shear force,D′ is the diameter of the circular hoops or spiral reinforce-ment, and other terms are as previously defined. In Eq. (8),the effective shear area Ae was assumed equal to 0.8Ag. Eq. (7)is based on analysis of effective shear resistance provided bytransverse reinforcement, assuming a 45-deg analogous trussmechanism.

Ang, Priestley, and Paulay6 also suggested a relationshipfor reduction in the strength of the concrete shear-resistingmechanisms with increasing flexural ductility. This wasaccompanied by enhanced truss mechanism strengthinvolving steeper shear plane inclinations mobilizing greatertransverse reinforcement, using equations based on plasticitytheory, as follows

(9)

and

(10)

where cotθ = . The mechanical degree of shearreinforcement ψ is defined equal to ρs fyh /vfc′ , and v < 1 is afactor for reduced effective compression strength of concretediagonal compression struts. A value of v = 0.2 was found to

Vc 2 1 P2000Ag---------------------+⎝ ⎠

⎛ ⎞ fc′ bwd (psi)=

Vc 0.17 1 P2000Ag---------------------+⎝ ⎠

⎛ ⎞ fc′ bwd (MPa)=

Vc 1.9 fc′ 2500ρωVud

Mm---------+⎝ ⎠

⎛ ⎞ bwd (psi)=

Vc 1.6 fc′ 17.2ρωVud

Mm---------+⎝ ⎠

⎛ ⎞ bwd (MPa)=

Mm Mu Pu4D d–

8----------------⎝ ⎠⎛ ⎞–=

Vc 3.5 fc′ bwd 1Pu

500Ag---------------+ (psi)=

Vc 0.29 fc′ bwd 1Pu

3.45Ag-----------------+ (MPa)=

Vsπ4--- 2Ash

ii-fyh⎝ ⎠

⎛ ⎞D′s

------=

Vc 4.455α 1 3Pfc′ Ag---------------+⎝ ⎠

⎛ ⎞ fc′ Ae (psi)=

Vc 4.455α 1 3Pfc′ Ag---------------+⎝ ⎠

⎛ ⎞ fc′ Ae (MPa)=

Vc 2.27 fc′ 0.8Ag( ) (psi)=

Vc 0.185 fc′ 0.8Ag( ) (MPa)=

Vsπ2---

Ash fyhD′ θcot

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

1 ψ–( ) ψ⁄


be appropriate at μΔ = 6, based on columns tested by Ang. Itshould be noted that for circular columns, the volumetrictransverse reinforcement ratio ρs is defined equal to 4Ash/Ds′ .In Eq. (10), an upper limit to the value of cotθ = 2.15 for θ =25 deg was included. It was also proposed that Eq. (8) for Vcbe proportionally reduced for ρs ≤ 1 percent.

The shear strength was considered to decrease from theinitial value, given by Eq. (7) and (8) to the ductile valuegiven by Eq. (9) and (10) as the ductility increased, in accor-dance with the relationship shown in Fig. 2(a). Morerecently, Wong, Paulay, and Priestley8 have shown thatcircular columns tested with multidirection ductile responseexhibit similar behavior, though the shear strength decreasesat lower ductility levels. Their suggested relationship is alsoincluded in Fig. 2(a).

Proposed shear design modelAs part of the present study, Ang, Priestley, and Paulay's6

equations for circular columns were simplified and extendedin applicability to rectangular columns. In this proposedapproach, the shear strength is given by an additive equationof the form

Vu = Vc + Vs + Vp (11)

where Vc is the concrete shear contribution, consistingprimarily of aggregate interlock and dowel action, resultingfrom flexure alone, Vs is the shear carried by transverse rein-forcement in truss action, and Vp is the shear capacityprovided by axial load through arching action.

The form of Eq. (11) will be recognized as being differentfrom other approaches in that the axial load term is separatedfrom the “concrete contribution” term. Conventionalapproaches [e.g., Eq. (3) and (8)] combine the effects in acomposite form, on the basis that the influence of axial loadon the onset of diagonal cracking cannot be separated fromthe concrete tension strength. However, this implies that thecombined strength of concrete mechanisms and axial loadeffects remains equal to the shear strength developed atinitial diagonal cracking. Experimental evidence6,25,27 doesnot support this assumption.

In the proposed approach, a rather simple mechanism forthe influence of axial load P on shear strength is advanced. Itis assumed that the influence of axial load P in a columnsubjected to reversed bending is primarily represented by aninclined compression strut between the compression zones atthe column ends, with an angle γ subtended between thecolumn axis and inclined compression strut, as shown in Fig.3. Assuming the axial load strut to pass through the center ofthe compression zones at the column ends, the additionalshear resistance is thus equal to the horizontal component ofthis strut given by

Vp = Ptanγ = P(D – a)/H (12)

where D is the section depth or column diameter, H is theheight of the column subjected to reversed bending, and a isthe compression zone depth at the critical sections. Note thatEq. (12) implies that as the aspect ratio of the columndecreases, the contribution to shear capacity of the axial loadwill increase, and that for very slender columns, the axialload contribution to shear strength may be rather minimal.Also, as the axial load increases, the effectiveness of theaxial load contribution to column shear strength willdecrease as the depth of the compression zone a increases.This approach has similarities to a method developed forpredicting the upper bound of shear force that could becarried by a member.

A further difference from Ang, Priestley, and Paulay's6

approach is that the truss mechanism described by the termVs in Eq. (11) is permitted a steeper inclination than 45 deg.Based on experimental results, a value of θ = 30 deg betweencolumn axis and principal tension cracking is assumed, forboth initial and ductile strength, giving the following expressionfor Vs

for circular columns

D′/s (13a)

Vu Vc Vs Vp+ +=

Vsπ2---l

AshlfyhD′

s------------------------ 30degl 0.865πAshlfyh=cot=

Fig. 3—Evaluation of axial load contribution to columnshear capacity.

Fig. 4—Definition of D′ for truss mechanism strength.


for rectangular columns

D′/s (13b)

In Eq. (13), D′ is the distance between centers of theperipheral hoop or spiral, as defined in Fig. 4.

The concrete component for both circular and rectangularcolumns reduces with increasing ductility in accordancewith the form of Fig. 2(b), given by

psi (14)

where k reduces from 3.5 for μΔ ≤ 2 to 1.2 for μΔ ≥ 4. InEq. (14), the effective shear area is taken as 0.8 Agross forboth circular and rectangular columns. The ductility adjust-ment is thus applied only to the concrete component in theproposed model.

As discussed elsewhere,24 these adjustments to the modelof Ang, Priestley, or Paulay provide an improved agreementfor a wide range of experimental data, and extend theapplicability to rectangular columns.

The significance of the difference between the proposedequations and the ACI approach can be gaged by comparativeanalyses of columns. Fig. 5 shows results of analyses forcircular and rectangular columns with low transverse steelratios, such as are commonly experienced in bridge columnretrofit considerations. The columns have a maximumsection depth (or diameter) of 60 in. (1.524 m) and aresubjected to double bending. Two column heights wereconsidered, H = 15 ft (4.57 m) and 30 ft (9.14 m), givingeffective aspect ratios of M/VD = 1.5 and 3, respectively.The proposed equations predict much higher initial shearstrength than the regular ACI equations. Ductile shearstrength may be greater or less than ACI values, dependenton the column aspect ratio. It is also shown that the ACIrefined approach predicts lower strength than the standard

Vs

AvlfyhD′

s--------------------- 30deg 1.73Avlfyh=cot=

Vc k fc′Ae=

approach over the practical range of axial load ratios, withexcessively rapid increase in predicted shear strength in therange 0.3fc′Ag ≤ P ≤ 0.4fc′Ag. The influence of aspect ratio israther insignificant in the ACI refined approach comparedwith the proposed approach.

Shear strength enhancement by steel jacketingThe use of steel jackets to enhance shear strength of

columns is not new. Sakino and Ishibashi28 investigated theseismic performance of concrete-filled tubular columns butfound that plastic buckling of the steel tube in the hingeregions tended to occur when the columns were subjected tolarge cyclic lateral displacements. Tomii, Sakino, and Xiao29

investigated steel-jacketed short columns in building struc-tures as a measure to prevent shear failure. To avoid thebuckling of the jacket observed by Sakino and Ishibashi,28

the jacket was deliberately debonded from the existingcolumn, thus insuring that the jacket acted only as hoop rein-forcement rather than also participating in flexural strength.Although satisfactory results were obtained by Tomii,Sakino, and Xiao29 for circular columns, it was found thatdegradation of response was inevitable for rectangularcolumns confined by rectangular jackets, even when verythick jackets were used. This was primarily due to inadequateconfinement of concrete and compression reinforcement in

Fig. 5—Comparison of shear strength for bridge columns with low transverse reinforce-ment using ACI and proposed equations (fy = 45 ksi; fc′ = 5 ksi) (1 ksi = 6.90 MPa; 1 kip =4.45 kN; 1 in. = 25.4 mm).

Fig. 6—Rectangular section confined by a rectangular tube.


the flexural plastic hinge region, as shown in Fig. 6, ratherthan due to inadequate shear performance.

In the present study, circular cylindrical jackets were usedfor circular columns, but elliptical jackets were used toprovide the necessary confinement and shear strengthenhancement to rectangular columns. Tests15 have estab-lished that elliptical jackets provide excellent enhancementof flexural performance of inadequately confined columns,since continuous confinement is provided by hoopmembrane action in the jacket.

The shear strength enhancement provided by circular orelliptical cylindrical jackets can be conservatively estimatedby considering the jacket to act as a series of independenthoops of thickness and spacing tj , where tj is the jacket thick-ness. Thus, by analogy to Eq. (13a) for the truss mechanismstrength of circular hoops, the shear strength enhancementVsj provided by a circular jacket is

(15)

where Dj is the outside diameter of the steel jacket, and fyj isthe yield strength of the steel jacket. Results from this test

Vsjπ2---

tj2fyj Dj tj–( ) 30 degcot

tj--------------------------------------------------------- 0.865πtjfyj Dj tj–( )= =

series and allied tests using composite material jackets30

indicate that θ = 30 deg is a suitably conservative assumptionof the diagonal strut inclinations for retrofitted columns.

For an elliptical jacket, the shear strength enhancementmay be determined by consideration of equilibrium of forcesparallel to the applied shear, as shown in Fig. 7. The ellipticalsteel jacket is assumed to yield in hoop tension as a conse-quence of resisting shear. Considering the equilibrium ofapplied shear and jacket hoop tension forces parallel to theapplied shear along a diagonal crack inclined at angle θ = 30deg to the axis, the total shear capable of being carried by thejacket is

(16)

where .The numerical result for the elliptical integration of Eq.

(16) is shown in Fig. 8, which may be approximated by thefollowing linearizations

Strong direction:

(17a)

Weak direction:

(17b)

Note that Eq. (17) degenerates to Eq. (15) when Bj = Dj(circular tube), and is also correct when Bj /Dj = 0, approxi-mating a rectangular case with two parallel surfaces.However, Eq. (16) will tend to be rather conservative whenBj /Dj > 1.5, for evaluating the weak direction strength.

Steel jacket design for retrofitThe shear strength Vru of the retrofitted columns must

exceed the shear force Vf° in the column corresponding tomaximum feasible flexural strength developing in thecolumn plastic hinges. Thus, for a column of height H indouble bending

φsVru ≥ Vf° = 2M°/H (18)

where φs is the shear strength reduction factor, and M° is theoverstrength flexural capacity, which should be based onhigh estimates of material strengths, and should incorporatethe effects of strain hardening and concrete confinement.Reinforcement yield strength should be taken as 55 and 75ksi (379 and 517 MPa) for Grades 40 and 60 reinforcing bars,respectively. A value of fce′ = 1.5fc′ nom should be assumedfor the concrete compressive strength, even though higherstrengths are probable in many older bridges, since fc′ islikely to influence Vu (primarily the concrete contribution,Vc) more than M°.

Vsj 2 fyjtj θ δcoscot xdDj tj–

2---------------–

Dj tj–

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

∫ 4fyjtj 30 deg δcos xd°

Dj tj–

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

∫cot= =

δ 1 1 tan2δ+⁄ 1 1 dy dx⁄( )

2+⁄= =cos

Vsj 3.46fyjtjDj tj– 1 1 π4---–⎝ ⎠

⎛ ⎞Bj Dj⁄–=

Vsj 3.46fyjtj Bj tjii-–⎝ ⎠

⎛ ⎞ 1 1 π4---–⎝ ⎠

⎛ ⎞Dj Bj⁄–=

Fig. 7—Shear strength contribution from elliptical steel jacket.

Fig. 8—Numerical results of integration for shear strengthof elliptical jacket.


Confinement of the compression zone of circular columnsby a radial pressure of

(19)

corresponding to yield of the jacket in hoop tension shouldbe assumed. For rectangular sections confined by ellipticaljackets, the lateral confining stress varies across the section.Fig. 9 shows that, considering a unit length of a rectangularcolumn transversely confined by an elliptical jacket, theequivalent confining stress of yield of the jacket can beexpressed by

Strong direction:

(20a)

Weak direction:

(20b)

where β is the tangential angle of the elliptical jacket at thecorner of the column section, which can be calculated by thefollowing equations

Strong direction:

(21a)

Weak direction:

(21b)

and where B and D are the section dimensions of the originalrectangular columns.

COLUMN SHEAR TESTSDetails of test setup

To study the brittle shear failure mode of “as-built” squatcircular and rectangular bridge columns and to establish theeffectiveness of full-height steel jackets as a retrofitmeasure, eight circular and six rectangular columns weretested using the test setup shown in Fig. 10(a). Dimensionsof the columns are given in Fig. 11. Columns were designedat a model:prototype scale of 0.4:1.0 and were constructedwith a footing and top load stub to provide realistic boundaryconditions at the two critical interfaces. The test setup was

fl′l2fyjtj

Dj 2tjii-–⎝ ⎠

⎛ ⎞--------------------------=

fl′2fyjtj βcos

B-------------------------=

fl′2fyjtj βcos

D-------------------------=

β tan1– BjiD

Dj Dj2 D2–

------------------------------ iii--

⎝ ⎠⎜ ⎟⎜ ⎟⎛ ⎞

=

β tan1– DjiB

Bj Bj2 B2–

---------------------------- iii--

⎝ ⎠⎜ ⎟⎜ ⎟⎛ ⎞

=

designed to subject the columns to axial loading and cyclicshear forces under reversed curvature, with the point ofcontraflexure occurring at the column midheight, as shownin Fig. 10(b). A stiff loading arm connected the column topto a horizontal double-acting actuator, with the forces trans-ferred from the loading arm to the top load stub primarily bymeans of torsion at the four pins located in the stub. Load-stub rotation was minimized by using a load-balancingsystem that included an actuator maintained at constant forcebalancing the weight of the loading arm. Axial load wasapplied to the test columns using two 2-in.- (51-mm)-diameterhigh-strength flexible rods, each bar being stressed with acenter-hole jack that reacted against the test floor, transmit-ting the bar force to the column by means of a cross-beammounted on top of the load stub.

Fig. 10(a)—Details of shear test setup.

Fig. 9—Equivalent confining stress provided by ellipticalsteel jacket

Fig. 10(b)—Loading conditions.


Design considerationsThe design of the test specimens was primarily governed

by the need to simulate typical column axial load ratios(P/fc′Ag) column aspect ratios (M/VD), and reinforcementdetails. Two values of axial load ratio equal to 0.06 and 0.18were considered for circular columns, corresponding to axialloads of 133 kips and 400 kips (591.6 kN and 1779.2 kN),respectively, and representing a practical range for bridgecolumn bents. For rectangular columns, an axial load ratio of0.06 corresponding to an axial load of 114 kips (507 kN) wasconsidered. Columns were constructed with aspect ratios of2 or 1.5 to simulate the critical moment-to-shear-span ratioof typical squat bridge columns, and to investigate the influ-ence of aspect ratio on the column shear strength. The “as-built” column reinforcement, material properties, and detailsresulted in the ratio of the predicted column shear strength tothe column ideal flexural capacity being much less thanunity based on Caltrans (and, hence, ACI) design specifica-tions, but close to unity based on design equations developedby Ang, Priestley, and Paulay.6 Flexural strength predictionswere based on measured material strengths and followingrecommendations based on previous research conducted byMander, Priestley, and Park.5

Longitudinal reinforcement consisted of 26 No. 6 (19.05-mm-diameter) Grade 40 or 60 bars evenly distributed in the24-in.-(610-mm)-diameter circular column, with a constant

cover of 0.8 in. (20 mm) from the column edge, as shown inFig. 11(a). The 16-in.-(406-mm)-wide and 24-in.- (610-mm)-deep rectangular column contained 22 No. 6 Grades 40and 60 bars, which were evenly distributed along the sides ofthe column, with a constant cover of 0.8 in. (20 mm), asshown in Fig. 11(b). Transverse reinforcement in the testspecimens consisted of No. 2 (6.35-mm-diameter) Grade 40circular or rectangular hoops at a spacing of 5 in. (127 mm).

The main parameters considered in the test programincluded the column axial load ratio, column aspect ratio,and the strength of the longitudinal flexural reinforcement.For each situation, two “as-built” columns were constructed,with one of each pair being subsequently retrofitted with afull-height cylindrical steel jacket. Table 1 illustrates thedesign variations in the various test specimens. Circularcolumn units 1, 3, 5, and 7, and rectangular column units 1,3, and 5 were tested in the “as-built” conditions, while theremaining specimens were tested with full-height steeljackets. Two types of steel jackets were fabricated, using3/16-in.- (4.76 mm)-thick hot-rolled ASTM A36 and 1/8-in.-(3.18 mm)-thick hot-rolled ASTM A569 11-gage steel,respectively. The former was based more on requirementsfor flexural ductility than shear, and, as a consequence, thetwo columns with 3/16-in. (4.76 mm) jackets were expectedto be “over-retrofitted” for shear. A gap of 0.8 in. (20 mm)was left between the jacket and the footing or upper load

Fig. 11—Reinforcement details of test columns (1 in. = 25.4 mm; #2 = 6.35-mm diameter;#6 = 19.05-mm diameter).


slab, representing the recommended 2-in. (51-mm) gap forfull-scale columns.

Columns were built using materials and design detailsappropriate for typical columns designed in the mid 1960s.A target compressive strength of fc′ = 5000 psi (34.5 MPa) at28 days was used to represent the probable overstrengthassociated with a typical 3000 psi (20.7 MPa) designstrength of the 1960s. A summary of the material strengthsfor the test columns is provided in Table 1, together with aninitial prediction of the column flexural capacity Vif , andinitial and fully ductile shear strengths. Note that, in Table 1,predictions for the initial and ductile shear strength valuesfor the “as-built” columns are based on the model describedin this paper and correspond to a displacement ductilityvalue of μ ≤ 2 and μ ≥ 4, respectively. Predictions for theinitial and final shear strength values for retrofitted columnsare based on summing up the companion “as-built” columnshear strengths with the shear strength enhancementprovided by the steel jackets. This was assessed using Eq.(15) through (17) and assuming a value of θ = 30 deg. Fulldetails of the test programs for circular and rectangularcolumns are available in References 25 and 27, respectively.

Instrumentation and testing procedureAll the shear column units were well instrumented with

strain gages mounted on longitudinal and transverse rein-forcement and on steel jackets, where appropriate. Displace-

ment transducers were installed diagonally, horizontally, andvertically along the column height, as shown in Fig. 10. Thisenabled computation of the column shear and flexure deforma-tion components to be carried out for various stages of testing.

The test units were subjected to a standard cyclic loadingpattern, which consisted of an initial force-controlled stage,followed by displacement control after first yield of thelongitudinal reinforcement was attained. As shown in Fig. 12(a),three complete cycles of displacement to displacementductility factors of μΔ = 1, 1.5, 2, 3, 4, 5, 6, 8, and 10 wereimposed, unless column failure caused premature curtailmentof the test. The displacement ductility factor μΔ is defined asthe ratio of the displacement Δ to the yield displacement Δyof the column. The experimental yield displacement wasdetermined by recording the lateral dis-placement at thecolumn top when the lateral force corresponded to thetheoretical first yield of the extreme longitudinal reinforcementin opposite directions Δy1 and Δy2, and then extrapolating theaverage value to the theoretical ideal flexural capacity Vif , asindicated in Fig. 12(b). Thus, the yield displacement of thecolumn unit is given by

(22)

The predictions for theoretical first yield load Vy and thetheoretical ideal flexural strength Vif were calculated using a

Δy

Δy1 Δy2+

2------------------------⎝ ⎠⎛ ⎞ Vif

Vy′-------=

Table 1—Test column details

Test unitAspect ratio

M/VDAxial load P,

kips fc′ , ksi Pfc′ /Ag

Longitudinal reinforcing bar (26 # 6) fyt , ksi

Transverse reinforcing bar

(#2 hoops) fyh , ksiSteel jacket

details Vif , kips, kips , kips

(a) Circular columns

C1A 2.0 133 4.5 0.065 47 52 — 119 139.6 83.7

C2R 2.0 133 4.93 0.059 47 52fjy = 50.4 ksitj = 3/16 in. 127 774.3 718.4

C3A 2.0 400 5.0 0.177 47 47 — 151 197.6 138.7

C4R 2.0 400 5.1 0.173 47 47fjy = 50.4 ksitj = 3/16 in. 165 832.3 773.4

C5A 2.0 133 5.2 0.056 68 47 — 171 142 85.9

C6R 2.0 133 5.8 0.051 68 47fjy = 41.5 ksi

tj = 1/8 in. 175 489 432.9

C7A 1.5 133 4.45 0.066 68 47 — 222 148 92.7

C8R 1.5 133 4.52 0.065 68 47fjy = 41.5 ksitj = 1/8 in. 226 495 439.7

(b) Rectangular columns

R1A 2.0 114 5.5 0.054 47 52 — 118 143.0 90.6

R2R 2.0 114 5.6 0.053 47 52fjy= 50.4 ksitj = 3/16 in. 123 1021. 0 968.6

R3A 2.0 114 5.0 0.059 68 47 — 160 130.0 80.1

R4R 2.0 114 5.2 0.057 68 47fjy = 50.4 ksitj = 3/16 in. 169 1008.. 958.1

R5A 1.5 114 4.7 0.063 68 47 — 213 134.1 85.4

R6R 1.5 114 4.8 0.062 68 47fjy = 41.5 ksitj = 1/8 in. 226 614.5 565.4

Note: A = as-built; R = retrofitted.1 kip = 4.5 kN; 1 ksi = 6.9 MPa; 1 in. = 25.4 mm.

Vshear

μ 2≤----------------

Vshear

μ 4≥----------------


computer program developed by King, Priestley, and Park7

based on a model for confined concrete proposed by Mander,Priestley, and Park.5

CONCLUSIONSAspects relating to the shear strength of circular and rect-

angular columns were discussed, and the conservatism incurrent ACI design equations was pointed out. The so-calledrefined approach was shown to produce more conservativeresults than the approximate approach for most levels of axialload, and to be excessively sensitive to axial load levels at highratios. It is recommended that this equation be withdrawn.

A set of shear strength equations for circular and rectan-gular columns was proposed, and shown to be considerablyless conservative than current ACI design for low levels ofductility. The proposed approach relates shear strength toflexural ductility, and differs from other design methods inthat the concrete and axial load contributions to shearstrength are considered separately.

Design equations and a design methodology for calcu-lating the required thickness of circular or oval steel jacketsneeded to increase the shear strength of circular or rectan-gular columns, respectively, were presented. The designbasis was that ductile flexural response to high ductilitylevels should be assured.

Physical details of 14 large-scale columns tested to deter-mine the appropriateness of the design equations presentedin this paper were described. Results of the tests of thesecolumns, half of which were tested “as-built,” and theremainder tested after retrofitting with steel jackets, arepresented in a companion paper.

ACKNOWLEDGMENTSThe experimental research described in this paper was carried out at the

Charles Lee Powell Structural Systems Research Laboratory at the Univer-sity of California at San Diego. The research project was funded by the Cal-ifornia Department of Transportation (Caltrans) under Grant No. RTA59G267, and their support is gratefully acknowledged. The comments, sug-gestions, and conclusions made in this paper do not necessarily reflect theviews of Caltrans.

NOTATION

REFERENCES1. Fung, G. C.; LeBeau, R. J.; Klein, E. D.; Belvedere, J.; and Gold-

schmidt, A. P., “Field Investigations of Bridge Damage in the San Fer-nando Earthquake,” Technical Report, Bridge Department, Division ofHighways, California Department of Transportation, Sacramento, Califor-nia, 1971.

2. Priestley, M. J. N., “Whittier Narrows, California Earthquake of Octo-ber 1, 1987—Damage to the I-5/I-605 Separator,” Earthquake SpectraJournal, V. 4, No. 2, 1988, pp. 389-405.

3. Lew, H. S., ed., “Performance of Structures During the Loma PrietaEarthquake of October 17, 1989,” NIST Special Publication 778, NIST,Gaithersburg, MD.

4. Priestley, M. J. N., and Park, R., “Strength and Ductility of ConcreteBridge Columns under Seismic Loading,” ACI Structural Journal, V. 84,No. 1, Jan.-Feb. 1987, pp. 61-76.

Ae = effective shear-resisting areaAg = gross-sectional area

Ash = cross-sectional area of one leg of transverse steelAv = total cross-sectional area of transverse steel at section a = compression zone depthB = rectangular section widthBj = short principal diameter of elliptical jacketbw = web widthD = overall section depth or circular section diameterD′ = distance between centers of peripheral hoop or spiralDj = long principal diameter of elliptical jacket or diameter of circu-

lar jacketd = effective depth of member

fc′ = concrete compressive cylinder strengthfl′ = confining stress

fyh = yield strength of transverse reinforcementfyj = yield strength of steel jacketH = column height

M° = overstrength flexural capacityMu = factored moment

P = axial loads = spacing of transverse reinforcementtj = steel jacket thicknessV = applied shear force

Vc = concrete shear contributionVf° = shear corresponding to M°Vif = ideal flexural strengthVn = nominal shear strengthVp = shear capacity provided by axial load-resisting mechanism

Vru = shear strength of retrofitted columnVs = shear carried by transverse reinforcementVsj = shear strength enhancement by steel jacketVu = ultimate shear strengthVy = shear corresponding to first yield of flexural reinforcementα = aspect ratio factorβ = tangential angle of elliptical jacketΔ = displacementΔy = yield displacementγ = inclination of axial load strut with column axis

μΔ = displacement ductility factorρs = volumetric transverse reinforcement ratioρt = total longitudinal reinforcement ratioρω = tensile reinforcement ratioθ = inclination of diagonal strut with column axis

Fig. 12—Details of loading history.


5. Mander, J. B.; Priestley, M. J. N.; and Park, R., “Theoretical StressStrain Model for Confined Concrete,” Journal of Structural Engineering,ASCE, V. 114, No. 8, Aug. 1988, pp. 1804-1825.

6. Ang, B. G.; Priestley, M. J. N.; and Paulay, T., “Seismic ShearStrength of Circular Reinforced Concrete Columns,” ACI Structural Jour-nal, V. 86, No. 1, Jan.-Feb. 1989, pp. 45-59.

7. King, D. J.; Priestley, M. J. N.; and Park, R., “Computer Program forConcrete Column Design,” Research Report No. 86/12, Department ofCivil Engineering, University of Canterbury, Christchurch, May 1986.

8. Wong, Y. L.; Paulay, T.; and Priestley, M. J. N., “Response of CircularReinforced Concrete Columns to Multi-Directional Seismic Attack,” ACIStructural Journal, V. 90, No. 2, Mar.-Apr. 1993, pp. 180-191.

9. Park, R., and Paulay, T., Reinforced Concrete Structures, John Wiley& Sons, New York, 1975, 769 pp.

10. ATC-6, “Seismic Design Guidelines for Highway Bridges,” AppliedTechnology Council, Berkeley, 1981, 199 pp.

11. Woodward, K. A., and Jirsa, J. O., “Behavior Classification of ShortReinforced Concrete Columns Subjected to Cyclic Deformations,” PMF-SEL Report, No. 80-2, July 1980, Department of Civil Engineering, Uni-versity of Texas at Austin.

12. AIJ Structural Committee, “Design for Earthquake Resistant Rein-forced Concrete Buildings Based on Ultimate Strength Concept,” Architec-tural Institute of Japan, 1988, 337 pp.

13. Zelinsky, R., “California Highway Bridge Retrofit Strategy andDetails,” Final Proceedings of the Second Workshop on Bridge EngineeringResearch in Progress, National Science Foundation and Civil EngineeringDepartment, University of Nevada, Reno, Oct. 29-30, 1990.

14. Chai, Y. H.; Priestley, M. J. N.; and Seible, F., “Seismic Retrofit ofCircular Bridge Columns for Enhanced Flexural Performance,” ACI Struc-tural Journal, V. 88, No. 5, Sept.-Oct. 1991, pp. 572-584.

15. Seible, F., and Priestley, M. J. N., “Strengthening of RectangularBridge Columns for Increased Ductility,” Proceedings of the Symposium onPractical Solutions for Bridge Strengthening and Rehabilitation, DesMoines, Apr. 5-6, 1993.

16. Priestley, M. J. N.; Seible, F.; Xiao, Y.; and Verma, R., “Steel JacketRetrofitting of Reinforced Concrete Bridge Columns for Enhanced ShearStrength—Part 2: Test Results and Comparison with Theory,” ACI Struc-tural Journal, V. 91, No. 5, Sept.-Oct. 1994, pp. 537-551.

17. Joint ASCE-ACI Committee 326, “Shear and Diagonal Tension,”ACI JOURNAL, Proceedings V. 59, Jan. 1962, pp. 1-30, Feb. 1962, pp. 277-333, Mar. 1962, pp. 353-395.

18. Joint ASCE-ACI Task Committee 426, “Shear Strength of ReinforcedConcrete Members,” Journal of Structural Engineering, ASCE, V. 99, No.ST6, June 1973, pp. 1091-1187.

19. Hsu. T.; and Mau, S. T., eds., “Concrete Shear in Earthquake,” Pro-ceedings of the International Workshop, University of Houston, Texas, Jan.1991, 518 pp.

20. CSA Committee A 23.3-M84, “Design of Concrete Structures forBuildings (CAN-A23.3-M84),” Canadian Standards Association, Rexdale,1984.

21. Collins, M. P., “Towards a Rational Theory for Reinforced ConcreteMembers in Shear,” Journal of Structural Engineering, ASCE, V. 104, No.ST4, Apr. 1978, pp. 649-665.

22. “CEB-FIP Model Code for Concrete Structures,” 3rd Edition, Apr.1978.

23. ACI Committee 318, “Building Code Requirements for ReinforcedConcrete and Commentary (ACI 318-89/ACI 318R-89),” American Con-crete Institute, Detroit, 1989, 353 pp.

24. Priestley, M. J. N.; Verma, R.; and Xiao, Y., “Seismic Shear Strengthof Reinforced Concrete Bridge Columns,” Journal of Structural Engineer-ing, ASCE, V. 120, No. 8, Aug. 1994, pp. 2310-2329.

25. Verma, R.; Priestley, M. J. N.; and Seible, F., “Assessment of SeismicResponse and Steel Jacket Retrofit of Squat Circular Reinforced ConcreteBridge Columns,” Structural Systems Research Project, Report No. SSRP92/05, University of California, San Diego, June 1993, 400 pp.

26. “Standard Specifications for Highway Bridges Relating to SeismicDesign,” California Department of Transportation, Division of Structures,Sacramento, CA, June 1990.

27. Xiao, Y.; Priestley, M. J. N.; and Seible, F., “Steel Jacket Retrofit forEnhancing Shear Strength of Short Rectangular Reinforced Concrete Col-umns,” Structural Systems Research Project, Report No. SSRP 92/07, Uni-versity of California, San Diego, June 1993, 200 pp.

28. Sakino, K., and Ishibashi, H., “Experimental Studies on ConcreteFilled Square Steel Tubular Short Columns Subjected to Cyclic ShearingForce and Constant Axial Force,” Transactions of the Architectural Insti-tute of Japan, No. 353, July 1985, pp. 81-89.

29. Tomii, M.; Sakino, K.; and Xiao, Y., “Ultimate Moment of Rein-forced Concrete Short Columns Confined in Steel Tube,” Proceedings ofthe Pacific Conference on Earthquake Engineering, V. 2, New Zealand,Aug. 1987, pp. 11-22.

30. Priestley, M. J. N.; Seible, F.; and Fyfe, E., “Column Seismic RetrofitUsing Fiberglass/Epoxy Jackets,” Proceedings of the Third NSF Workshopon Bridge Engineering Research in Progress, La Jolla, Nov. 16-17, 1992,pp. 247-251.

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