SeismicstrengtheningofRCcolumnsusingexternalsteelcageweb.iitd.ac.in/~drsahoo/Publications/stcg-eesd-09.pdf · RC slab–column frame model strengthened by ductile steel bracing and

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2009; 38:1563–1586Published online 7 April 2009 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.917

Seismic strengthening of RC columns using external steel cage

Pasala Nagaprasad, Dipti Ranjan Sahoo and Durgesh C. Rai∗,†

Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur-208016, India

SUMMARY

Steel caging technique is commonly used for the seismic strengthening of reinforced concrete (RC)columns of rectangular cross-section. The steel cage consists of angle sections placed at corners and heldtogether by battens at intervals along the height. In the present study, a rational design method is developedto proportion the steel cage considering its confinement effect on the column concrete. An experimentalstudy was carried out to verify the effectiveness of the proposed design method and detailing of steel cagebattens within potential plastic hinge regions. One ordinary RC column and two strengthened columnswere investigated experimentally under constant axial compressive load and gradually increasing reversedcyclic lateral displacements. Both strengthened columns showed excellent behavior in terms of flexuralstrength, lateral stiffness, energy dissipation and ductility due to the external confinement of the columnconcrete. The proposed model for confinement effect due to steel cage reasonably predicted momentcapacities of the strengthened sections, which matched with the observed experimental values. Copyrightq 2009 John Wiley & Sons, Ltd.

Received 10 December 2007; Revised 28 January 2009; Accepted 3 February 2009

KEY WORDS: RC column; seismic strengthening; confinement; batten; steel caging; cyclic lateral load

1. INTRODUCTION

A large number of existing reinforced concrete (RC) buildings are not designed in accordance withadvanced seismic codes and many have suffered severe damage or complete collapse during pastearthquakes on account of inadequate shear strength, flexural strength and ductility of columns[1, 2]. The primary deficiencies of these columns included items, such as insufficient longitudinaland transverse reinforcement, and inadequate lap splices for longitudinal reinforcement. Suchcolumns need to be strengthened in such a way that their failure mechanism changes from brittleto ductile mode. It is also desirable that strengthening technique is not only less interruptive,less time consuming and less expensive, but also should result in minimum loss of floor area.

∗Correspondence to: Durgesh C. Rai, Department of Civil Engineering, Indian Institute of Technology Kanpur,Kanpur-208016, India.

†E-mail: [email protected]

Contract/grant sponsor: Indian Institute of Technology Kanpur

Copyright q 2009 John Wiley & Sons, Ltd.

1564 P. NAGAPRASAD, D. R. SAHOO AND D. C. RAI

One such technique is steel caging, which consists of steel angles at the corners of RC columnsand steel straps at few places along the length. This technique is generally regarded as practical,fast and cost-effective, which helps to improve the global seismic behavior of the structure byincreasing lateral strength, ductility and shear capacity of structural members [3]. This is widelyused in construction, particularly in Japan, Taiwan and the United States [4, 5] and also has foundapplication in retrofitting the damaged RC columns after earthquakes [6, 7].

Several researchers have investigated strengthening of RC columns using steel jackets [8–11].Dritsos and Pilakoutas [3] developed a theoretical model to determine the effective confiningstresses of column concrete due to steel cage assuming that the composite action at the interfaceof steel and concrete element is mobilized due to Poisson’s expansion and interface friction.Experimental investigations on damaged RC columns showed that the axial compressive strengthand ductility was greatly improved by strengthening using steel cage and steel encasement approach[12]. However, considerable improvement in shear strength with stable hysteretic loops at higherductility levels was only achieved when the columns were retrofitted over the entire length usingsteel jackets [13].

Masri and Goel [14] conducted an experimental research on a one-third scale, two-story, two-bayRC slab–column frame model strengthened by ductile steel bracing and external steel jacketing.Significant flexural contribution from jacketing elements (i.e. vertical angles at corners and hori-zontal battens) was noted. A method was developed to compute this flexural contribution ofstrengthened column appropriately accounting for the observed load-sharing mechanism betweenangles and battens. However, the model underestimated the observed values as it did not includethe composite effect due to the confinement provided to concrete by steel jacketing elements.

In the present study, rectangular RC columns, more typical of building columns, were externallystrengthened by steel caging technique using four longitudinal steel angles and battens. Theintermediate gap between steel cage and RC column was not filled with any kind of binder materials.An experimental investigation was carried out on both ordinary and strengthened columns underconstant axial load and gradually increasing cyclic lateral load in order to verify the effectivenessof the proposed design method and the detailing of steel cage battens within the potential plastichinge regions. In order to size various elements of steel cage for an effective and efficient design,a rational method is proposed that accounts for the confinement effect of steel cage on the existingcolumn and prevents premature failure of steel cage.

2. THEORETICAL MODEL FOR CONFINEMENT

In the steel caging technique of strengthening rectangular section RC columns, passive confinementof the column concrete is externally developed by the steel cage due to Poisson’s effect becauseof lateral restraint provided by steel angle members at corners. As shown in Figure 1, a portion ofcolumn concrete near battens of the steel cage is unconfined due to absence of confining pressure,which is similar to the case of rectangular hoops of RC column where the concrete near the side ofhoops remains unconfined. As a result, the theoretical model for confinement of concrete proposedby Mander et al. [15] for rectangular hoops can be applied to the confinement produced by externalsteel caging.

As the compressive stress of concrete in column approaches its uniaxial compressive strengthvalue, lateral strains become very high due to progressive internal cracking. As a result, transverseplates (battens) of the steel cage are subjected to large tensile stresses, which in turn provide

Copyright q 2009 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2009; 38:1563–1586DOI: 10.1002/eqe

SEISMIC STRENGTHENING OF RC COLUMNS 1565

Figure 1. Confinement of RC column due to steel caging: (a) half-body equilibrium at battened portionof steel cage; (b) effective confinement in plan; and (c) effective confinement in elevation.

passive confinement to the concrete. If a uniform tensile force is assumed to develop in battens, theaverage confining pressure along both x- and y-directions of column section may be determinedfrom the equilibrium of half-body diagram as shown in Figure 1(a) and can be expressed as follows[3]:

�x = 2As fybys

(1)

�y = 2As fybx s

(2)

The effective area of confined concrete in plan and elevation can be determined by assuming anarching action of confining stresses between the steel angles as shown in Figure 1(b) and (c).The arching action can be assumed to act in the form of a second degree parabola with an initialtangent slope of 45◦ [15]. Accordingly, the effective confining stresses in x- and y-directions ofcolumn section can be expressed by [3]

�xe =

(1− b2xe+b2ye

3bxby

)(1− se

2bx

)(1− se

2by

)

(1−�sl)

2td

sbyfy (3)

�ye = bybx

�xe (4)



Figure 2. Confinement strength ratio due to lateral confining stresses [15].and the effective center-to-center spacing of battens can be given by

se=s−(d+2c) (5)

Confined strength ratio (or confinement factor), k, can be defined as the ratio of confined compres-sive strength, fcc, to unconfined compressive strength, fco, of concrete. The confined compressivestrength of concrete can be obtained using the general solution of multi-axial failure criteriondeveloped by Mander et al. [15] in terms of the lateral confining stresses (i.e. �xe and �ye). Asshown in Figure 2, the confined strength ratio can be obtained using confinement curves proposedby Mander et al. [15] for rectangular hoops.

Peak confined strain, �cc, and ultimate confined strain, �cu, can be obtained using followingexpressions [15, 16]:

�cc = �co

[1+5

(fccfco

−1

)](6)

�cu = 0.0035+0.1(�xe+�ye)

fco(7)

The value of peak unconfined compressive strain of concrete, �co, can be taken as 0.002. It isassumed that the value of confined compressive stress at the ultimate strain is 85% of the confinedcompressive strength and the distribution of strain is linear along the column cross-section. Momentcapacity of column section confined with the steel cage can be determined from its material andgeometric properties using assumed stress–strain behavior of the confined concrete.

3. DESIGN OF STEEL CAGE

Moment capacity of a strengthened RC column can be taken as a sum total of moment capacitiesof the confined RC column section and steel angle sections of the steel cage. Since compressive



strength of concrete confined with steel cage depends on the size of steel angles, spacing and sizeof battens, number of battens, etc., the design of an economical steel cage of required amountof confinement action and reliable flexural capacity involves a trial-and-error procedure. Thetheoretical model proposed by Masri and Goel [14] is considered in this study for design of battensof the steel cage. An overstrength factor of 1.25 was used to determine the design shear force andbending moment for each batten so that steel angle sections yield prior to battens.

The design values of shear force, H ′ba, and bending moment, M ′

ba, on battens depend on (a)moment capacity of angle sections, Mnv, (b) number of battens on each side of cage, N , and (c)spacing of angle sections, bcl, and can be related as follows:

H ′ba = 1.25Mnv

2b′N(8)

M ′ba = H ′

babcl2

(9)

Center-to-center spacing and clear spacing of battens can be obtained by comparing the lateralstiffness and the shear strength of two models, namely, the original and the refined models [14].The original model assumes that steel angles and battens of the steel cage form a unit sectionsuch that the moment capacity, Mnv, and the moment of inertia, I , of the steel cage are constantthroughout its length. The refined model considers the difference between the lateral stiffness ofthe battened portion of angles and the unbattened ones along the length of steel cage. Further, theplastic hinges are assumed to form at both ends of the portion of steel angles between adjacentbattens. Thus, the moment capacity and the moment of inertia of the battened portion of steel cageare equal to that of the unit section used in the original model. However, the moment capacityand moment of inertia of unbattened portion of steel cage are simply four times of a single steelangle section.

In the original model, ultimate shear capacity, Vsc, and lateral stiffness, Ksc, of the unit sectioncan be given by

Vsc = 2Mnv

h(10)

Ksc = 12E I

h3(11)

where h is the story height as shown in Figure 3. In the refined model, the ultimate shear capacityof steel cage, V ′

sc, depends on moment capacity of individual angles, Mang, and clear spacing ofbattens, h′. Similarly, the lateral stiffness of steel cage, K ′

sc, depends on (a) moment of inertia ofsingle angle, Iang, (b) number of battens, N , and (c) center-to-center spacing of battens, s.

Hence, the ultimate shear capacity and the lateral stiffness of the steel cage comprising of foursteel angles can be expressed as follows:

V ′sc = 2M ′

h′ = 8Mang

h′ (12)

K ′sc = 48E Iang

s3(N−1)(13)



Figure 3. Theoretical design models of steel cage: (a) original model and (b) refined model [14].

The clear spacing of battens can be determined such that the shear strength of steel cage in therefined model would be equal to that of the unit section in the original model. Using Equations(10) and (12), the required clear spacing of battens can be given by

h′ = 4Mangh

Mnv(14)

Similarly, the center-to-center spacing of battens can be determined so that the lateral stiffness ofsteel cage in the refined model would be equal to that of the unit section in the original model.Using Equations (11) and (13), the required center-to-center spacing of the battens can be expressedas follows:

s=h

[3

√4Iang

I (N−1)

](15)

The design of battens of steel cage should satisfy above requirements to avoid the premature failureof angle sections under lateral loading conditions.

4. EXPERIMENTAL INVESTIGATION

4.1. Test specimen

RC columns of a moment resisting frame subjected to lateral loads under seismic conditionstypically bend in double-curvature. The points of inflection can be assumed at its mid-heightdividing the entire column into two cantilever parts of length equal to one-half of the story height(Figure 4). Thus, the part of column from the base to its point of inflection was considered fortest specimens in the present experimental study.

Three test specimens were investigated under constant axial compressive load and graduallyincreased cyclic lateral displacements, out of which two specimens were strengthened using four



Figure 4. (a) RC column subjected to lateral load under seismic condition; (b) bending moment diagram;(c) deflected shape; and (d) part of RC column considered as test specimens in the present study.

longitudinal steel angles and welded transverse battens. These specimens are designated as RCO,RCS1 and RCS2, where the letters ‘O’ and ‘S’ stand for ‘ordinary’ and ‘strengthened’, respectively,and the numerals ‘1’ and ‘2’ indicate the specimen number. Each test specimen consisted ofRC column of size 200mm×250mm×1275mm with an RC footing of size 900mm×720mm×400mm as shown in Figure 5.

High-yield strength-deformed (HYSD) steel bars (of specified yield strength as 415MPa) wereused for both longitudinal and transverse reinforcement in each specimen. The longitudinal rein-forcement in columns consisted of six numbers of 16mm diameter HYSD bars, whereas thetransverse reinforcement consisted of 8mm diameter HYSD bars at a center-to-center spacingof 100mm. Similarly, the HYSD bars of 10mm diameter were used for longitudinal as well astransverse reinforcement in the footing of specimens. The ultimate moment capacity of columnsection at an axial compressive load of 450 kN (i.e. 32% of ultimate axial load) was computed as55.3 kNm using stress–strain properties of concrete and steel reinforcement as per Indian Standardprovisions [17]. The primary objectives of the experimental study for the specimen RCO were tocharacterize the force-deformation behavior and to determine the actual moment capacity of theRC column.

Both strengthened specimens (RCS1 and RCS2) were designed such that the moment capacitiesof columns would be nearly two times that of the specimen RCO. A step-by-step procedure forthe design of steel cage for the specimen RCS1 is presented in the Appendix. Each strengthenedspecimen consisted of hot-rolled Indian Standard sections ISA35×35×[email protected]/m for steelangle sections and 6mm thick mild steel plates for battens [18]. The width of end battens for thespecimen RCS1 was about one and half times that of intermediate battens; whereas the size ofend battens for the specimen RCS2 was about two times that of the specimen RCS1. However, thesize of intermediate battens and their spacing were exactly same for both strengthened specimens(Figure 5). Such detailing of end battens helps to evaluate the effect of end batten in the confinementeffect of steel cage and the overall behavior of strengthened columns.

Cement concrete mix for each test specimen was designed for a characteristic cube compressivestrength, fck, of 25MPa at a water–cement ratio of 0.5. Table I summarizes the cube compressive



Figure 5. Details of test specimens: (a) reinforcement detailing of specimen RCO; (b) specimen RCS1;and (c) specimen RCS2 (all dimensions are in millimeters).

Table I. Material properties of concrete and steel used in test specimens.

Cube compressive strength (MPa)

Concrete 7 days 28 days Day of testing

RCO 20.6 32.5 38.0Specimen RCS1 25.8 37.7 45.5

RCS2 25.6 34.7 39.9

Size of rebars Yield strength (MPa) Tensile strength (MPa)

8mm 438.5 542.010mm 489.0 668.016mm 468.4 623.2

Angle section 353.0 498.0Batten plate 330.0 518.0

strength of concrete at different days of curing. In addition, coupon tests for rebars, angle sectionsand batten plates were carried out as per Indian Standard provisions [19] to determine their yieldand ultimate strengths in tension (Table I).



Figure 6. Steel caging technique of strengthened RC column.

4.2. Strengthening technique

In this technique, steel angles were first placed at each corner of the existing RC column withoutusing any binder materials in the gap between them. In order to ensure a tight fit between the steelcage and RC column, the steel angles were held close to concrete by means of C-clamps prior towelding of battens as shown in Figure 6. Steel cage was then welded to base plate, which in turnwas attached to the RC footing using high-strength bolts of 20mm diameter as shown in Figure 7.These bolts were inserted into the footing by drilling holes of 200mm depth and filling the gapbetween concrete and bolts with epoxy mortar.

4.3. Test set-up and loading protocol

Test specimens were simultaneously subjected to constant axial compressive load of 450 kN andgradually increasing reversed cyclic lateral displacements at free end. Two servo-hydraulic actuatorsof rated force capacities of 500 and 250 kN and stroke lengths of 125mm were used to apply axialload and lateral displacement, respectively. These actuators were supported by reaction blocksattached to the laboratory strong floor by means of studs as shown in Figure 8(a). As the loadsapplied to the test specimen lie in a horizontal plane, roller bearing was used at free end of testspecimens to restrain its possible downward displacement due to self-weight of actuators.

Several strain gauges were used to monitor the state of strain in column section and steel cage.Four strain gauges were attached to the longitudinal reinforcement at corners and the angle sectionsof steel cage at a distance of 125mm from the face of footing of each test specimen. In addition,



Figure 7. Steel cage-to-foundation connection: (a) top view and (b) front view(all dimensions are in millimeters).

Figure 8. Details of test set-up and loading protocol used in the present study: (a) testset-up and (b) displacement history.

several Linear Variable Displacement Transformers (LVDTs) were also used to monitor the lateraldisplacement of the column as well as footing of test specimens as shown in Figure 8(a).

As per ATC-24 [20], a multiple-step loading history consisting of symmetric cycles of increasingamplitude in predetermined steps may be adequate to assess the seismic performance of a compo-nent. Further, the primary objective of this experimental investigation was to evaluate the ultimatelimit states of test specimens, which can be achieved only by large inelastic excursions. Hence,gradually increased reversed cyclic displacements as shown in Figure 8(b) were chosen as thedisplacement history for each specimen in this study. Drift ratio may be defined as the ratio ofmaximum displacement of free end of RC column to its length measured from the top of footingto the point of lateral load application. The displacement history consisted of drift ratios of ±0.2,



±0.4, ±0.7, ±1.1, ±1.7, ±2.5, ±3.3, ±4.2, ±5.0, ±6.7 and ±8.3%. Each cycle of displacementhistory was repeated for three times at any level of drift ratio. It may be noted that the variationin magnitude of the axial compressive load and the sequence of load application in RC columnmay influence the lateral strength, stiffness, deformation capacity and shape of hysteretic loops oftest specimens [21, 22].

5. EXPERIMENTAL RESULTS

5.1. Hysteretic response

Lateral load–displacement response (hysteretic response) and damaged states of all test specimensare compared in Figure 9. The specimen RCO behaved elastically up to 1.1% drift ratio and,thereafter, flexural and shear cracks developed in column concrete near footing. The flatteningof hysteresis loops during 1.7% drift ratio excursion level indicated the onset of rebar yielding,which was further confirmed from the strain gauge data as described later. Severe cracking andcrushing of the column concrete during the first cycle of 2.5% drift ratio excursion caused suddenloss of resistance and caused complete collapse of the specimen RCO. As shown in Figure 9(a),the specimen RCO experienced somewhat smaller value of displacement as compared with theapplied one in each cyclic excursion level indicating a minor loss of applied displacement in thetest set-up. In contrast, both strengthened test specimens exhibited full and stable hysteresis loopseven at the larger levels of drift ratio. For the specimen RCS1, the yielding of angle sections ofthe steel cage was noted at 3.3% drift ratio and the failure of angle sections in the end panelassociated with severe crushing of column concrete was observed at 8.3% drift ratio leading tothe complete collapse of the specimen. The repetitive cyclic buckling under lateral load causedthe failure of steel angles. Figure 9(b) shows the hysteresis loops for the specimen RCS1 up to6.7% drift ratio as it was not possible to monitor the lateral displacement of column at 8.3% driftratio. A sudden drop followed by significant loss of stiffness was observed in each hysteresis loopduring unloading of the specimen RCS1.

Similar to the specimen RCS1, the specimen RCS2 exhibited sudden drop in strength associatedwith significant change in stiffness during unloading process at each excursion level as shown inFigure 9(c). At 8.3% drift ratio, a single crack in the column concrete and the yielding of steelangles near the footing were observed in the specimen RCS2. Even though the specimen RCS2was damaged to some extent, its complete collapse was not observed unlike other specimens (RCOand RCS1) and it could have sustained a few more cycles of lateral displacement excursions priorto collapse.

5.2. Lateral strength

Lateral strength at any displacement level was determined by averaging peak lateral resistancein both directions of cyclic excursion. The observed maximum lateral strength of the specimenRCO was 64.4 kN at a drift ratio of 1.7% against the design value of 51.2 kN. Design momentcapacity of 55.3 kNm for the column section at an axial compressive load of 450 kN was dividedby lever arm (i.e. the distance of 1.08m measured from the top of footing to the point of loadapplication) to obtain the design lateral strength of the specimen. Both strengthened specimensRCS1 and RCS2 reached the design strength of 102.4 kN (i.e. two times the design strength of the



Figure 9. Damaged state and hysteretic response of test specimens: (a) specimen RCO;(b) specimen RCS1; and (c) specimen RCS2.

specimen RCO) due to the added steel elements. The specimen RCS1 carried maximum lateralload of 120.9 kN at a drift ratio of 3.3%, which gradually reduced at the larger drift ratios due tothe onset of buckling of steel angles near the end battens.

Similarly, the maximum lateral load carried by the specimen RCS2 was 141.5 kN at 6.7%drift ratio, which is about 2.2 times strength of the specimen RCO. Further, the steel cage in thespecimen RCS2 was more effective in increasing the lateral strength at the larger drift ratios as



Figure 10. Comparison of backbone curves.

compared with the specimen RCS1 (Figure 10). For 45◦ shear diagonal crack, shear strength ofthe RC column was computed as 84.1 kN for specified size, spacing and yield stress of stirrups.Maximum lateral loads carried by both strengthened specimens were significantly higher thanthe computed shear strength of the RC column. Hence, both flexural and shear strengths of RCcolumns were enhanced by strengthening using external steel cage.

5.3. Lateral stiffness

Expectedly due to additional stiffness provided by the steel cage, both strengthened specimensRCS1 and RCS2 showed higher initial lateral stiffness as compared with the initial stiffness of11.9kN/mm for the specimen RCO. The initial stiffness of specimen RCS1 was observed as20.5kN/mm, which is about 44% higher than that of the specimen RCO. Similarly, the specimenRCS2 showed an initial stiffness of 16.6kN/mm, which is about 24% smaller than that of thespecimen RCS1. This discrepancy may be attributed to differences in compressive strength ofconcrete of these specimens; the cube compressive strength of concrete of the specimen RCS2 at theday of testing was about 14% smaller than specimen RCS1 (Table I). However, the specimen RCS2showed marginally higher stiffness than that of the specimen RCS1 at subsequent displacementexcursion levels.

5.4. Displacement ductility

Displacement ductility may be defined as the ratio of maximum displacement to the yield displace-ment. The maximum displacement was considered as the displacement at which (a) the failureof specimen was observed or (b) significant damage led to decrease in the load carrying capacityof the specimen. Yield and ultimate displacements of the specimen RCO were observed as 8.5and 17.1mm, respectively, which resulted in a displacement ductility value of 2.0. The specimenRCS1 exhibited yield and ultimate displacements of 14.5 and 70.9mm, respectively. The displace-ment ductility of specimen RCS1 as 4.9 was 2.5 times that of the specimen RCO. Similarly, thespecimen RCS2 showed displacement ductility of 6.4, which corresponds to the yield and ultimate



Figure 11. Strain vs drift ratio response of all specimens.

displacements of 13.5 and 87.0mm, respectively. Thus, the ductility of specimen RCS2 was 3.2times that of the specimen RCO indicating the effectiveness of wider end battens in the plastichinge regions of steel caging in improving inelastic response.

5.5. Strain–drift ratio response

Figure 11 compares the state of strain in rebars and angle steel sections of test specimens atdifferent levels of drift ratio. The envelope values of strain in column rebars and angle sectionswere determined from the average of peak values of strain in both directions of cyclic loading.All column rebars located at corners of the specimen RCO reached their yield limit of 2000micro-strain at 1.7% drift ratio. Similarly, the angle sections of specimen RCS1 reached their peakstrain at 2.5% drift ratio after reaching their yield value of 1800 micro-strain and thereafter, thereduction in strain levels was noted due to initiation of local yielding or buckling. However, steelangle sections of specimen RCS2 reached higher strain levels than that of the specimen RCS1. Thestrain envelopes for rebars of both strengthened specimens follow nearly linear trend and the strainvalues corresponding to the specimen RCS1 were marginally higher than that of the specimenRCS2 at each drift ratio. As expected, the maximum values of rebar strain for the specimen RCOwere much smaller than that of the both strengthened specimens.

5.6. Moment–curvature response

Bending moment experienced by the test specimens is an algebraic sum of the moment due toapplied lateral load and the additional P-delta moment due to constant axial load of 450 kN.Maximum values of curvature at any cyclic excursion level were determined from rebar strain data.As expected, maximum moments experienced by the test specimens at each drift ratio were higherwhen the P-delta effect was considered (Figure 12). The specimen RCO showed a maximumcurvature of 21.6×10−6/mm at 1.7% drift ratio at a bending moment of 74.0 kNm with the



Figure 12. Comparison of moment–curvature response.

P-delta effect and 66.3 kNm without the P-delta effect. Thus, the observed maximum moment forthe specimen RCO was about 34% higher than the design value.

Both strengthened specimens reached the target design moment capacity of 110.6 kNm, whichwas two times the design capacity for the specimen RCO. The moment capacity of specimen RCS1was 146.3 kNm including the P-delta effect, which was nearly twice of the observed momentcapacity for the specimen RCO. The maximum value of curvature exhibited by the specimenRCS1 was about 28.5×10−6/mm, which was 32% higher than that of the specimen RCO. Themaximum moment for the specimen RCS1 was computed as 112.6 kNm without considering theP-delta effect. The specimen RCS2 showed a maximum curvature of 30.9×10−6/mm at maximummoment of 177.5 kNm including the P-delta effect and the corresponding value of moment wascomputed as 138.3 kNm without the P-delta effect at a drift ratio of 6.7%. As compared with thespecimen RCO, maximum values of moment and curvature for the specimen RCS2 increased by140 and 43%, respectively. Hence, the steel cage with wider end battens (equal to three times thewidth of intermediate battens) showed greater resistance to lateral load with significant increasein curvature.

It should be noted that the position of plastic hinges in strengthened columns shifted away fromthe joint interface region due to external steel cage. In both strengthened specimens, the plastichinges were developed in the first panel just above the end batten. This may give rise to an increasein plastic rotation demand for a given level of interstory drift. However, considering significantimprovement in the moment–curvature response due to strengthening using external steel cage,the required plastic rotational capacity of column sections can be achieved.

5.7. Energy dissipation response

Energy dissipated by test specimens at any drift level of cyclic displacement excursions is the areaenclosed by hysteresis loops. Figure 13 shows the cumulative energy dissipated by each test spec-imen at different levels of drift ratio. As expected, the specimen RCO dissipated the least amountof energy as compared with both strengthened specimens (RCS1 and RCS2) at any displacement



Figure 13. Comparison of energy dissipation capacities of test specimens.

excursion. At drift ratio of 1.7%, the cumulative energy dissipated by the specimen RCO wasnearly 50% of that dissipated by strengthened specimens RCS1 and RCS2. Both strengthenedspecimens dissipated nearly equal amount of energy at all displacement levels, which suggests thatthe larger width of end battens played a minor role in energy dissipation potential.

6. ANALYTICAL INVESTIGATION

The moment capacity of strengthened columns can be computed analytically from the observedvalues of strain in rebars and angle sections using actual material properties of steel and concrete.The stress–strain relationship for confined concrete can be developed using envelope curve proposedby Popovics [23]. Accordingly, longitudinal compressive strength of concrete, fc, at a givenlongitudinal strain, �c, can be expressed as follows [15]:

fc=(

fccxr

r−1+xr

)(16)

where the parameters of Equation (16) are given as follows:

x = �c�cc

(17)

r = Ec

Ec−Esec(18)

Ec = 5000√

fco (MPa) (19)

Esec = fcc�cc

(20)



The values of fcc for both the strengthened specimens were determined using confinement curves(Figure 2) and considering effective lateral confining stresses in both directions of the columnsection as given by Equations (3) and (4). The unconfined cylinder compressive strength ofconcrete was taken as 0.8 times the cube compressive strength at the day of testing as reportedin Table I. The values of confinement strength ratio were 1.40 and 1.45 for the specimens RCS1and RCS2, respectively, which resulted in peak confined cube compressive strength of concreteas 64.4 and 58.0MPa. The moment capacity of RC column was calculated by estimating thestress in concrete and rebars and using stress–strain relationships for steel and concrete as perIndian Standard provisions [17]. Similarly, moment capacity of angle sections was computed bymultiplying the stress corresponding to measured strain in steel angles with the sectional areaand the lever arm. As stated earlier, total moment capacity of the strengthened specimen wasobtained as the sum total of moment capacities of RC column and steel cage. It should be notedthat the contribution of existing stirrups to flexural capacity of strengthened columns was notconsidered in the present study. The columns were detailed only for gravity load requirementsleading to a larger spacing of stirrups and, therefore, the confinement effect of these stirrups wouldbe too small and can be neglected. As a result, the proposed method of computing confiningstresses in RC column provides a lower-bound estimate for the confined compressive strength ofconcrete.

Table II summarizes the computed flexural strengths of steel cage and RC column of bothstrengthened specimens. Peak strain values in steel cage and column rebars for a particulardrift excursion were obtained by averaging maximum recorded values on the same face oftest specimens for three cycles. In addition, strain values at the top fiber of column concretewere derived from observed rebar strains assuming a linear distribution for flexural strainsalong the column depth. It may be noted that although the peak confined compressive strengthof concrete for the specimen RCS2 was about 14% smaller than that of the specimen RCS1due to variation in their unconfined compressive strengths, the maximum value of computedbending moment for the specimen RCS2 was about 6% greater than that of the specimenRCS1. This is largely due to the presence of wider end battens in the expected plastichinge region, which also helped to reduce the likelihood of potential buckling of steel anglesbetween the battens. Bending moment values for the specimen RCS1 were computed only upto 3.3% drift ratio because observed strain values were erratic after buckling of steel anglesections.

Figure 14 compares the observed as well as computed values of bending moment for bothstrengthened specimens at various lateral displacement levels. Maximum values of bending momentfor the specimens RCS1 and RCS2 were computed as 133.2 and 141.1 kNm, respectively (Table II).Both the observed and computed values of bending moment for the specimen RCS1 matched verywell up to 2.5% drift ratio and a maximum difference of 9.0% was observed in their respective peakvalues. Similarly, both the computed and observed values of bending moment for the specimenRCS2 compared very well for initial excursion levels and a maximum difference of about 20%was observed at greater magnitudes of cyclic excursion levels because the strength hardeningeffect as observed in experiments could not be adequately simulated in the analysis. Furthermore,analytical computations are based on the assumption that all battens of the steel cage are of samesize as intermediate battens and, hence, the effect of wider end battens was not considered inthe analysis. Moreover, observed values are derived from strain gage readings, which may be alittle erroneous at large drift levels due to cracking of concrete and local buckling of steel anglesections.



TableII.Com

putatio

nof

bendingmom

ents

atdifferentdriftlevels

ofstrengthened

specim

ens.

Steelcage

RC

column

Total

Drift

Mom

ent,

Mom

ent,

mom

ent,

ratio

Strain,

Mang

Con

c.Rebar

strain,

Mc

(Mang+Mc)

(%)

� a(kNm)

strain,� c

� s(kNm)

(kNm)

Specim

enRCS1

0.2

0.00

035

10.9

0.00

056

0.00

018

28.4

39.3

0.4

0.00

060

18.8

0.00

076

0.00

037

38.3

57.1

0.7

0.00

093

29.1

0.00

105

0.00

079

50.8

79.8

1.1

0.00

118

37.0

0.00

132

0.00

124

60.3

97.2

1.7

0.00

161

50.5

0.00

160

0.00

183

69.6

120.1

2.5

0.00

469

55.6

0.00

192

0.00

262

77.6

133.2

3.3

0.00

515

55.4

0.00

216

0.00

369

77.1

132.5

Specim

enRCS2

0.2

0.00

036

11.3

0.00

023

0.00

010

20.0

31.3

0.4

0.00

067

21.0

0.00

034

0.00

042

35.1

56.1

0.7

0.00

128

40.0

0.00

056

0.00

043

46.7

86.7

1.1

0.00

151

47.3

0.00

069

0.00

080

56.0

103.3

1.7

0.00

226

55.3

0.00

093

0.00

143

69.4

124.7

2.5

0.00

654

55.8

0.00

111

0.00

211

79.7

135.5

3.3

0.00

316

55.8

0.00

118

0.00

234

83.3

138.7

4.2

0.00

122

55.2

0.00

131

0.00

385

85.9

141.1

5.0

0.00

084

55.1

0.00

128

0.00

509

83.3

138.4

6.7

0.00

083

55.1

0.00

126

0.00

467

83.2

138.3



Figure 14. Comparison of bending moment in test specimens.

7. CONCLUSIONS

The following conclusions can be drawn from the present study:

(i) The performance of deficient RC columns under combined axial and cyclic lateral loadingcan be greatly improved by steel caging technique without using any binder material in thegap between concrete column and steel angles and thus making it simpler to implement atthe site.

(ii) A method was developed to predict the flexural strength of an RC column strengthenedusing external steel cage by modifying the method proposed by Dritsos and Pilakoutas [3]for the effective confinement provided by the steel cage. Further, the method can be used toproportion various elements of a steel cage for the target moment capacity of strengthenedcolumn.

(iii) The proposed design method was found effective and reasonably accurate as demonstratedby testing of two column specimens under constant axial load and increasing cyclic lateraldisplacements. Both specimens reached the target design capacity of two times the momentcapacity of the original RC column. Further, the method was able to predict the load-deformation behavior of strengthened RC columns satisfactorily, using strain measurementsat column rebars and steel angles.

(iv) Detailing of end battens of the steel cage located in the potential plastic hinge region ofRC column plays an important role in improving its overall behavior under lateral loads.Wider end battens in the expected plastic hinge region of steel cage appeared to be effectivein increasing compressive strength of concrete due to enhanced confinement effect and inreducing the likelihood of local buckling of steel angles.

(v) The increase in width of end battens of steel cage also significantly enhanced the plasticrotational capacity and its resistance to lateral loads; however, it had minor effect on overallenergy dissipation potential. Hence, the correct choice for width of end battens dependslargely on the target moment and plastic rotation capacity of strengthened column. However,the width of end battens equal to 1.5 times the width of intermediate battens was found tobe sufficient to achieve the desired moment capacity of strengthened columns.



APPENDIX: DESIGN EXAMPLE

Step Explanation Calculation References

1. Design data: Width of column, bx =200mm; Depthof column, by =250mm; Story height,h=2160mm; Clear cover, dc=40mm;Main rebars=six nos. of 16mm diam-eter; Stirrups=8mm diameter@100mmcenter-to-center; Yield strength ofrebar, fys=415MPa; Design uncon-fined cylinder compressive strengthof concrete, fco=20MPa; Young’smodulus of steel, E=200GPa.

Moment capacity ofstrengthened columnis two times that ofordinary RC column

Moment capacity of ordinary RC columnMu=55.3kNm at an axial compres-sive load of 450 kN [17]. Thus, therequired moment capacity of strength-ened column Mst=110.6kNm

2. Trial angle section:Let us choose foursteel angle sectionsISA 35×35×[email protected]/m

Yield strength of angle section, fy=250MPa; Thickness of angles, t ′ =5mm;Width of single leg of angles, c=35mm;Sectional area, a=327mm2; Distanceof center of gravity from the edgeof section, Cxx =10.4mm; Moment ofinertia, Iang=3.5cm4; Section modulus,Zang=1.4cm3

IndianStandard steelsections [18]

3. Section properties:Section properties ofsteel cage arecomputed only fromfour angles placed atfour corners of RCcolumn.

Moment of inertia, I =1890cm4;Section modulus, Z =145cm3; Momentcapacity of angle sections, Mang=fy×Zang=0.35kNm; Moment capacityof steel cage, Mnv= fy×Z =36.25kNmCenter-to-center spacing of angles,b′ =by+2(t ′−Cxx )=239mmClear spacing of angles,bcl=by+2(t ′−c)=190mm

4. Design of battens:Assume six numbersof 6mm thick battensused on each face ofthe steel cage, i.e. N =6, t=6mm

Design shear force on battens,H ′ba=1.25×Mnv/(2×b′×N )=15.8kN

Design bending moment on battens,M ′

ba=H ′ba×bcl/2=1.5kNm

Equation (8)

Equation (9)Required depth of battens =√6×M ′

ba/(t× fy)=77.5mm



Required clear spacing,h′ =4×Mang×h/Mnv=83.4mm Equation (14)Required c/c spacing,s=h[ 3

√4Iang/{I (N−1)}]=246.2mm Equation (15)

Design yield strengthof battens, fy=250MPa

Provide 6mm thick and 80mm widthplates as battens at a c/c spacing of235mm, which gives a clear spacing of155mm. For economy purposes, onlyrequirements of batten depth and center-to-center spacing (arising out of stiff-ness requirement) were preferred overclear spacing requirements (arising outof strength considerations). Width of endbattens can be taken as 125mm, whichis about 1.5 times that of intermediatebatten.

5. Confined compressivestress–strain propertiesof concrete

Effective confinement widthbxe=bx +2(t ′−c)=140mm,

bye=by+2(t ′−c)=190mmGross area of column Ac=500cm2

Area of reinforcement Ast=12.06cm2

Area of concrete Acc=487.94cm2

Reinforcement ratio�sl= Ast/Acc=0.025Lateral confining pressures alongx- and y-directions can be given by�x =2As fy/bys=4.1MPa Equation (1)�y =2As fy/bxs=5.1MPa Equation (2)Effective spacing of battens,se=85mm Equation (5)Effective confining stressesin both directions,�xe/ fco=0.09, �ye/ fco=0.11 Equations

(3)–(4)Confining strength ratio, k=1.55 Figure 2Confined compressive strength ofconcrete fcc=k× fco=31MPaPeak and ultimatestrain of concrete�cc=�co[1+5(k−1)]=0.007 Equation (6)�cu=0.0035+0.1((�xe+�ye)/ fco)=0.023 Equation (7)

6. Moment capacity ofstrengthened column:

Using confined stress–strain propertiesof concrete and geometric properties of



Stress–strain behaviorof confined concrete isassumed as parabolicwith linear tail upto 85% of confinedcompressive strengthand the permissibletensile strength inrebar is 0.87 fy.

column section, the moment capacity ofcolumn concrete, Mc is computed as74.2 kNm at an axial compressive loadof 450 kN as per Indian Standard codeprovisions [17].

Thus, the design moment capacity ofstrengthened column, Ms=Mc+Mnv=110.5kNm, which is nearly equal to thedesired value of 110.6 kNm. Hence, thedesign is satisfactory.

NOMENCLATURE

Ac gross area of column sectionAcc area of concreteAs area of the transverse steel stripsAst area of the transverse steel stripsbx ,b width of the column sectionb′ center-to-center spacing of steel anglesbcl clear spacing of steel anglesbxe clear spacing between the angles along the x-directionby , D depth of the column sectionbye clear spacing between the angles along the y-directionc width of the angle sectionc/c center-to-center spacingCxx distance of center of gravity of steel angles from the edged depth of intermediate battendc thickness of clear coverE modulus of elasticity of structural steelEc initial modulus of elasticity of concreteEsec secant modulus of elasticity of confined concrete to the peak stressfc longitudinal compressive strength of concretefcc confined compressive cylinder strength of concretefck characteristic compressive strength of concretefco unconfined compressive cylinder strength of concretefy yield strength of battens and steel anglesfys yield strength of rebarsh story heighth′ clear spacing of battensH ′ba design shear force on battens

I moment of inertia of unit section



Iang moment of inertia of single angle sectionKsc stiffness of steel cage as per the original modelK ′sc stiffness of steel cage as per the refined model

k confinement strength ratioM ′ total moment capacity of angles between battens in the refined modelMang moment capacity of each angle sectionM ′

ba design bending moment on battensMc moment capacity of RC of strengthened columnMnv nominal moment capacity of unit section (steel cage)Ms moment capacity of strengthened columnMst required moment capacity of strengthened columnMu moment capacity of ordinary columnN number of battens on each side of cageQ lateral load in column under seismic conditionr elastic modulus parameters center-to-center spacing battensse effective center-to-center spacing of battenst thickness of battent ′ thickness of steel anglesVsc ultimate shear capacity of steel cage as per the original modelV ′sc ultimate shear capacity of steel cage as per the refined model

x peak strain ratio of confined concrete to unconfined concreteZ section modulus of unit section (steel cage)Zang section modulus of single angle section� lateral displacement�c longitudinal concrete strain�co strain at peak stress of unconfined concrete�cc strain at peak strain of confined concrete�cu ultimate strain of confined concrete�x average lateral confining pressure along x-direction�xe effective lateral confining pressure along x-direction�y average lateral confining pressure along y-direction�ye effective lateral confining pressure along y-direction�sl ratio of the longitudinal reinforcement to area of concrete section

ACKNOWLEDGEMENTS

The authors are grateful to Indian Institute of Technology Kanpur for providing financial support inconducting this study. The assistance of Structural Engineering Laboratory staff in experimental investi-gation is gratefully acknowledged.

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