experimental investigation of conditions of lateral shear reinforcements in rc columns accompanied...

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2007; 36:1685–1699Published online 17 May 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.712

Experimental investigation of conditions of lateral shearreinforcements in RC columns accompanied by

buckling of longitudinal bars

Yuichi Sato1,∗,†,‡ and HuneBum Ko2,§

1Department of Urban and Environmental Engineering, Kyoto University, Kyoto 615-8540, Japan2Department of Architecture, Inha Technical College, 253 Yonghyun-dong, Nam-ku, Incheon 402-752, Korea

SUMMARY

This study presents a cyclic load test of four RC columns to obtain data on stresses and strains onlateral shear-reinforcing bars that contact buckled longitudinal reinforcing bars. The specimens includecolumns laterally jacketed with all-elastic fibre-reinforced polymer (FRP) sheets. The buckling lengthsand modes in the longitudinal bars of the four column specimens stabilized at a buckling deflection (=lateral deformation of buckled longitudinal bar) from 0.3 to 0.6mm. The yield portion ratio rby of shearreinforcement around the buckled longitudinal bars was introduced as an index of the development ofbuckling conditions. Here, the yield portion ratio rby was defined as the ratio of the length of the regionwhere the shear reinforcements yield lby, to the buckling length lb. The rby values of the tested columnsranged from 0.45 to 0.76. The test results show that the buckling stress and the specific compressive stressof the longitudinal bars in the columns were smaller than those of the bare bars. Copyright q 2007 JohnWiley & Sons, Ltd.

Received 25 October 2006; Revised 28 March 2007; Accepted 5 April 2007

KEY WORDS: reinforced concrete; column; reinforcing bar; buckling; 1300MPa-class steel; fibre-reinforced polymer (FRP)

1. INTRODUCTION

Reinforcing bars may be susceptible to buckling failures when the bars are located near thesurface of a concrete member and subjected to high levels of compressive stress. When barsbuckle, the associated concrete cover spalls and ceases to contribute to the member’s flexure andshear resistance. Instability of steel-reinforcing bars has long been a concern because of, on the

∗Correspondence to: Yuichi Sato, Department of Urban and Environmental Engineering, Kyoto University, Kyoto615-8540, Japan.

†E-mail: [email protected]‡Assistant Professor.§Associate Professor.

Copyright q 2007 John Wiley & Sons, Ltd.

1686 Y. SATO AND H. KO

one hand, concern over the seismic safety of the reinforced concrete structure and, on the otherhand, the complexity of the buckling. It is widely recognized that the conditions related to thebuckling of steel material strongly depend on the hysteresis and deformation of the applied load.Consequently, it has been customary to numerically compute buckling hysteresis, based on theclassical formulations of force equilibrium and deformation compatibility.

Another method for modelling and analysing buckling using an energy approach was first devel-oped by Scribner [1]. Scribner formulated the energy status of buckled bars and their surroundingshear reinforcement and concluded that the buckling length extended through three-fourths of thedepth of the members. Mau and El-Mabsout [2] used the finite-element model, which includes alongitudinal bar and a number of ties. Based on monotonic analyses with varied tie spacings, theinfluence of the slenderness ratio of the longitudinal bars on the buckling behaviour was discussed.Monti and Nuti [3] extended the buckling model’s energy approach to cyclic load conditions. Thedeveloped model was then compared to the experimental results of the behaviour of the buckling ofbare steel bars. Falk and Govindjee [4] presented several analyses to help examine the influence ofthe initial force given by lateral ties, which are necessary to cause the longitudinal bars to buckle.Dhakal and Maekawa [5] improved the energy formulation by adopting discretized calculationsthat depended on the number and spacing of the lateral shear-reinforcing bars. Dhakal implementedthis formulation into a finite-element algorithm and presented corroborating analyses.

A concern arises at this point over the theoretical validity of the energy approach to the bucklingphenomenon. The length, mode, and compressive bearing capacity of buckled steel could varyinfinitely depending on the load hysteresis. Thus, energy statuses might also vary infinitely andcannot be determined based on the principle of minimum work. Experimental observations haveshown, however, that buckled longitudinal bars in largely deformed RC columns maintain theirbuckling length and mode after the deformations exceed certain rotation angles. It has also beenobserved that the buckling lengths of the longitudinal bars were always an integer times the spacingof the lateral shear-reinforcing bars and did not exceed D, the depths of the columns [6]. Thisevidence indicates that a stable energy condition developed in the region around the buckled barsin each deformed RC column. From the viewpoint of structural engineering and seismic safety,evaluations of the beginning of the buckling and the bearing capacity of the buckled bars aresomewhat valuable even if the complete paths of load hysteresis could not be traced.

Among the influential factors of the energy approach to the buckling problem (slenderness ratioof longitudinal bars, initial force given by lateral ties, etc.), this paper focuses on the elastic/plasticstatus of lateral reinforcement since no experimental data regarding stresses and strains of lateralshear on reinforcing bars have been presented in the previous research, although the stress–strainhysteresis of buckled longitudinal bars has often been provided [2, 3, 7–10]. It has long beenbelieved that lateral shear reinforcement does not yield (e.g. [11]), while Dhakal developed amodel that considers the yielding of shear reinforcement [5]. In Dhakal’s analyses, 33–50% of theshear-reinforcing bars (ties) that were in contact along the buckling length of the longitudinal barsyielded, while the rest of the bars remained elastic, although no comparison was made betweenthe analyses and the test because of the lack of experimental data.

This study conducted a cyclic load test of four RC columns [12] to obtain data on the stresses ofthe shear reinforcements that are in contact with the buckled longitudinal bars. Two specimens wereconstructed: laterally jacketed with all-elastic fibre-reinforced polymer (FRP) sheets with varieddegrees of stiffness and rupture stress. Here, the ‘yield portion ratio’ of the shear reinforcementaround the buckled longitudinal bars was defined and quantified as an index of the developmentof the buckling conditions. Specific compressive stresses of the buckled longitudinal bars were

Copyright q 2007 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2007; 36:1685–1699DOI: 10.1002/eqe

LATERAL SHEAR REINFORCEMENTS IN RC COLUMNS 1687

also estimated in order to quantify the bearing capacity of the bars. The observed data generallycoincided with the assumptions used in previous research and strengthened the theoretical validityof the energy approach to buckling analysis.

2. EXPERIMENTAL PROGRAMME

Four column specimens, K1, K2, K3, and K4, consisting of different kinds of shear reinforcementwere constructed. Figure 1(a) and Table I present the details of the specimens. Each specimen

Figure 1. Test specimens and measuring devices: (a) specifications of specimens; (b) locationsof transducers; (c) transducers for buckling measurement; (d) measuring buckling deflection;

and (e) correction of buckling deflection.



Table I. Specification of specimens and test results.

Specimen f ′c (MPa) �t (%) �w (%) �F (%) �FEF (MPa) P0/(bD f ′

c) Vexp (kN)

K1 37.0 0.90 0.45 0 0 0.15 +425/−490K2 1.52 0 0 +518/−557K3 0.79 0.17 436 +514/−574K4 0.79 0.18 74 +515/−472

f ′c, compressive concrete strength; �t, cross-sectional area ratio of longitudinal steel bars; �w,

cross-sectional area ratio of lateral steel bars; �F, cross-sectional area ratio of FRP sheet; EF,elastic modulus of FRP sheet; P0, axial force; Vexp, maximum shear force (positive/negative).

was 2800mm long and 400mm thick. The central part of each was 1200mm long and 400mmwide. This represents a short column of M/VD= 1.5, which is a typical column proportion inthe lower storey of a high-rise RC condominium in a seismic region. The top and bottom partsof each specimen were widened to 1000mm to facilitate their fastening in the loading apparatus.Ten steel bars with a diameter of 19mm were arranged as flexural reinforcement for specimensK1–K4 (�t = 0.90%). The applied axial force ratio P0/(bD f ′

c) was 0.15.Specimen K1 consisted of high-strength steel spirals 9mm in diameter (db = 9mm). The cross-

sectional reinforcement ratio of the spiral �w was 0.45%. In contrast, specimen K2 was confinedwith a larger number of normal strength steel hoops and internal ties (db = 10mm, �w = 1.68%).Specimens K3 and K4 were confined with externally jacketed FRP sheets, as well as a smallernumber of steel hoops (db = 10mm, �w = 0.79%). Specimen K3 was jacketed with four layers ofcarbon fibre sheets, each 0.167mm thick and 60mm wide. The cross-sectional reinforcement ratioof the sheet �F was 0.167%. Specimen K4 was jacketed with two layers of polyacetal fibre sheets.Polyacetal is a polymer with a low elastic modulus of 40GPa and a tensile strength of 1900MPa.The applied sheet was 0.368mm thick per layer and 60mm wide (�F = 0.184%). The sheets ofspecimens K3 and K4 were wrapped with 60mm spacing to allow observation of cracking. Theproperties of the concrete, steel, and FRP sheets are listed in Table II.

Figure 1(b) shows the location of 52 displacement transducers used to measure the deformationof a test column. Eight of these transducers were attached to the longitudinal bars to measurethe buckling deflection. Figure 1(c) is an illustration of the devices used to measure the bucklingdeflection. The transducers were attached to a steel shaft welded to the bars 100mm above theboundary between the column and the base. Forty-four displacement transducers were installed onthe side of the column to observe the deformation. Strain on the steel bars and FRP sheets wasmeasured by approximately 100 strain gauges (SG). The locations of the gauges are indicated inFigure 1. The specimens were subjected to reversed cyclic loads. Figure 2 shows the relationshipbetween shear force and rotation angle in the specimens.

Specimen K1 achieved a maximum shear force of 490 kN at a rotation angle R = 1%. Theshear capacity then decreased as the rotation angle increased because of a bond-splitting failurealong the longitudinal bars. A severe concrete fracture was observed in the shear-cracked regionat R = 3.3% (Figure 3). This region behaved as a kind of plastic hinge, and the longitudinal barsbuckled along a length four times that of the spiral spacing (280mm).

Specimen K2 maintained its shear capacity up to R = 6.7%, although concrete crushing and barbuckling were observed in the hinge region. The longitudinal bars buckled along a length twicethat of the hoop spacing (140mm).



Table II. Material properties.

Specimen Direction db (mm) As (mm2) fy (MPa) fu (MPa) Es (GPa) �sh (×10−3) Esh (GPa)

SteelK1 Lateral 9 64 1398 1481 194 7.3 0.92K2,K3,K4 Lateral 10 71 360 504 167 28.0 0.65K1,K2,K3, K4 Longitudinal 19 287 400 588 157 12.0 0.79

Specimen f ′c (MPa) �c (×10−3) f ′

t (MPa)

ConcreteK1,K2,K3, K4 37.0 2.59 3.10

Specimen Fibre tF (mm) fu (MPa) EF (GPa)

FRPK3 Carbon 0.33 4340 261K4 Polyacetal 0.368 1900 40

Figure 2. Relationship between shear and rotation angle.



Figure 3. Fracture conditions of specimens.

Specimen K3 maintained a shear capacity of more than 400 kN at R = 5%, but presented arelatively pinched hysteresis response in comparison to specimen K2. The maximum tensile strainof the carbon fibre sheet recorded during the loading was 0.0056. The sheet showed almost nodamage except some ruptures of several filaments in the hinge region. The response of specimenK3 indicated that the carbon fibre sheet prevented spalling of the cover and considerably enhancedthe ductility of the concrete. The observed buckling length of the longitudinal bars was 150mm.

Specimen K4 exhibited a less-ductile hysteretic response than did specimen K3. The maxi-mum tensile strain of the polyacetal fibre sheet was 0.0162, and no ruptures were observed inthe sheets. Similar to specimen K1, the shear capacity decreased at rotation angles larger than1% because of a bond-splitting failure along the longitudinal bars, and the buckling occurred ina region with large diagonal cracks although the jacketed polyacetal fibre sheets kept the coverfrom spalling. The buckling length was 150mm, which was equal to that of specimen K3. Thesheet delaminated when the rotation angle exceeded 6% during the final loading cycle. The de-lamination was intended to reduce the shear capacity of the specimen at the final stage but notsignificantly affect the behaviour after the shear deterioration at R = 1%. The observations ofspecimens K3 and K4 indicate that a fibre sheet with a low degree of stiffness is less effective thanone with high degree of stiffness with respect to ductility enhancement. Then again, the sheet’sjacketing did not reduce the buckling length even when sheets with a high degree of stiffness wereused.

3. DISCUSSION

Figure 4(a) shows the relationship between buckling deflections �b (Figure 1(d)) and the rotationangle for the corner longitudinal bars while Figure 4(b) shows the relationship for the inner bars.The corresponding measuring locations of the bars were under compression in the positive rotationangle and under tension in the negative. Since the measuring locations (100mm from the columnbase) did not correspond to the points of maximum deflection, the deflections were corrected by



Figure 4. Relationship between buckling deflection of longitudinal bar and rotationangle: (a) corner bar and (b) inner bar.

Equation (1), assuming cosine-curved deformation of the buckled bar (Figure 1(e))

�b = �bmeasured × 2

1 − cos(2�× 100/ lb)(mm) (1)

Equation (1) amplifies the bucking deflections of specimen K1 by 23%, K2 by 64%, and K3 andK4 by 33%. Berry and Eberhard [13] suggested that buckling was often observed at low driftsafter large tension cycles. In the present test, significant increases in the buckling deflections werealso observed in the inner bars of specimens K1 from the second tension cycle of 3.3% to the firstcompression cycle of 5.0%; K2 from the second tension cycle of 5.0% to the final compressioncycle; K3 from the first tension cycle of 5.0% to the second compression cycle of 5.0%; and K4from the first tension cycle of 5.0% to the second compression cycle of 5.0%. In comparison tospecimens K1 and K2, however, the increasing rates of buckling deflections of specimens K3 andK4 were relatively small, especially for the corner bars. For this reason, the FRP sheets jacketingspecimens K3 and K4 were judged to have effectively restrained the buckled bars even after thesteel hoops yielded.

Figure 5(a) shows the relationship between the confining stress and rotation angle. Here, theconfining stress is defined as the stress of shear reinforcement (including the FRP sheet) multipliedby the cross-sectional area ratio of the shear reinforcement. The shear reinforcement stresses were



Figure 5. Relationships between stresses in specimens and rotation angle: (a) confinement stress; (b) cor-ner longitudinal bar stress; (c) inner longitudinal bar stress; (d) bond stress along corner longitudinal

bar; and (e) bond stress along inner longitudinal bar.

derived from the measured strains given by the displacement transducers applied to the plastichinge zone (transducer numbers 38, 42, 44, 45, 47, and 51, indicated in Figure 1(b)). The strainswere converted into stresses using a modified Ramberg–Osgood model [14]. Figure 5(b) shows



Figure 6. Relationship between confining stress and buckling deflection.

the relationship between the stress of the longitudinal bars and the rotation angle for the cornerbars while Figure 5(c) shows the relationship for the inner bars. These bar stresses were derivedfrom SG on the boundary between the column and the stub. Several sets of stress data ceasedhalfway during the loading because of breakage of the SG. However, the observed data indicatedthat the longitudinal bars of the four specimens attained the yield stress at rotation angles largerthan R = 0.5%.

Figure 5(d) shows the relationship between the bond stress of the longitudinal bars and therotation angle for the corner bars while Figure 5(e) shows the relationship of the inner bars atthe same measuring points. All specimens attained bond stresses larger than 6MPa. SpecimenK1 presented the poorest bond capacity, which corresponded to significant bond-splitting failure(Figure 3). This bond-splitting failure was expected to aggravate the instability of the longitudinalbars in specimen K1. In contrast, specimen K2 possessed the largest bond capacity because of theheaviest lateral steel reinforcement. Specimen K3 also attained large bond stress in the inner bar,although relatively small bond stress was observed in the corner bar. The corner bar of specimenK4 presented a large bond capacity due to the confinement by the FRP sheet although significantbond-splitting cracks were observed.

Figure 6 shows the relationship between the confining stresses and buckling deflections. Thehoops of specimens K1 and K2 yielded a confining stress at around 5–6MPa, and their bucklingdeflections increased drastically. A significant increase in the buckling deflection was similarlyobserved in specimen K4 at a confining stress of 3MPa, which corresponded to the yielding ofthe hoops. The increase in the confining stress ceased at a buckling deflection of 0.6 mm and thestresses remained almost constant at larger displacements for specimens K1 and K2 while thoseof specimens K3 and K4 continued to increase. Hence, considerations are required for not onlythe elastic condition of the confining reinforcements but also for their plastic condition in orderto investigate the buckling mechanism.

The buckling deflections of specimens K1, K3, and K4 exceeded 0.5mm (dbt/40) before thehoops yielded. Even specimen K2 presented a buckling deflection of 0.1mm (dbt/200). For thesereasons, the buckling of the longitudinal bars was supposed to begin before the hoops yielded.



Table III. Buckling conditions.

Specimen K1 K2 K3 K4

Rotation angle at shear failure Rs (%)∗ 1.0 (+1)¶ — — 1.0 (−1)¶

Buckling conditionsBuckling length (mm) 280 140 150 150Buckling length by Dhakal’s model [5] (mm) 280 140 200 250Rotation angle at buckling Rb1 (%)† 3.3 (+1) 5.0 (+1) 3.3 (−1) 3.3 (−1)Compressive stress at Rb1 (MPa) −42.6 +18.7 −28.5 −17.5Maximum compressive stress attained (MPa) −151.1 −320.8 −241.8 −244.8Rotation angle at initial splitting crack Rcv1 (%)‡ 0.5 (+1) 1.0 (+1) 1.0 (+2) 1.0 (+1)Rotation angle at cover spalling Rcv2 (%)§ 2.0 (+2) 1.0 (−2) — —

∗Rs, rotation angle at which shear force decreased by 80% of the maximum shear force.†Rb1, rotation angle at which buckling deflection exceeded 1.0mm.‡Rcv1, rotation angle at which initial splitting crack occurred at plastic hinge region.§ Rcv2, rotation angle at which cover spalled at plastic hinge region.¶ (+1), first positive cycle; (−1), first negative cycle; (+2), second positive cycle; and (−2), second negativecycle.

Table III presents the experimental results of the buckling of the longitudinal bars. The bucklinglengths of the four specimens were compared with analytical lengths based on Dhakal’s model [5].Rb1 is defined as the rotation angle at which the measured buckling deflection �bmeasured exceeded1mm. Rb1 of specimens K1, K3, and K4 were 3.3%, while that of specimen K2 was 5%. Notethat these rotation angles Rb1 do not always correspond to the relationships in Figure 4 becauseFigure 4 only presents two examples among a total of eight measuring points. The compressivestresses of the longitudinal bars were lower than 50MPa for all specimens, although the bars hadattained compressive stresses of 150MPa or larger. Regarding the decrease of compressive stressof the longitudinal bars from 150 to 50MPa or lower, the compressive bearing capacities of thebars had considerably deteriorated at Rb1. Therefore, it was assumed that the lengths and modesof the buckling of the longitudinal bars had stabilized at Rb1.

Rcv1 in Table III is defined as the rotation angle at which bond-splitting cracks appeared along thelongitudinal bars. The splitting cracks appeared at Rcv1 = 0.5% in specimen K1 and at 1.0% in theother specimens. Rcv2 is the rotation angle at which the cover concrete spalled at the plastic hingeregions. The cover concrete of specimens K1 and K2 spalled at Rcv2 = 1.0 and 2.0%, respectively.In specimens K3 and K4, as mentioned above, the cover concrete did not spall because of the FRPsheet jacketing.

As observed in the test, the buckling behaviours of specimens K2 and K3 were formed ina flexural plastic hinge while those of specimens K1 and K4 were associated with shear andbond-splitting failure. In specimens K1 and K4, it is assumed that diagonal cracking results ingreater shear demand on the lateral reinforcement and, therefore, less resistance to bar buckling.In addition, in specimen K1, diagonal cracks acted to spread the plastic hinge and spalling of thecover concrete, hence lengthening the buckling. Therefore, the following discussions are exclusivelyabout specimens K2 and K3.

The relationship between the specific compressive stresses of the longitudinal bars and thebuckling deflections was investigated to identify the beginning of the buckling. Here, specific



Figure 7. Relationship between specific compressive stress and buckling deflection:(a) corner bar and (b) inner bar.

Figure 8. Relationship between tangent stiffness of confinement and buckling deflection (average).

compressive stress is defined as the maximum compressive stress that a longitudinal bar on thecompression side attains during half a loading cycle. Figure 7 shows the specific compressivestresses of the corner bars (a) and the inner bars (b) at instances when the measured bucklingdeflections (�bmeasured) exceeded 0.1, 0.3, 0.6, 1.0, and 2.0mm. Figure 7 indicates that the specificcompressive stress of specimen K2 decreased as the buckling deflection increased while the specificstress of specimen K3 increased. This increase in stress indicated that the carbon fibre sheet ofspecimen K3 resisted the lateral displacement of buckling and maintained the compressive bearingcapacity of the bars.

Figure 8 shows the relationship between the tangent moduli of the shear reinforcement stiffnessand the buckling deflections. The tangent modulus of steel becomes zero at the yielding point.



Figure 9. Relationship between specific compressive stress and tangent modulus of confinement.

In the test, however, elastic and plastic stiffness existed simultaneously because all the hoops didnot yield at the same buckling deflection in a specimen. Figure 8 indicates the weighed averageof the tangent moduli. The tangent moduli decreased as the buckling deflections became smalleralthough specimen K3 maintained a relatively large moduli because of the elastic FRP sheets. Figure9 shows the relationship between the specific compressive stresses of the longitudinal bars and thetangent moduli of the stiffness of the shear reinforcement. Figure 9 presents a positive correlationbetween the specific compressive stresses and the tangent moduli. This observation coincides withDhakal’s view that yielding of shear reinforcement reduces effectiveness in restraining buckledlongitudinal bars.

For these reasons, buckling deflection is effectively restrained by increasing the stiffness of theshear reinforcement as well as by increasing the confining stresses, although post-yield strain-hardened lateral steel may still restrain buckling deflection. Many researchers have already pointedout this, and the authors’ test results confirm that it is valid even for columns with externallyjacketed all-elastic FRP shear reinforcements.

4. YIELD PORTION RATIO OF SHEAR REINFORCEMENT

Information about the deformation conditions around the subject longitudinal bars is indispensablebecause the bars do not buckle as long as their surrounding hoops do not deform. To evaluate thedegree of deformation of the hoops, we introduce the concept of yield portion ratio rby. The valueof rby is defined as the ratio of the length of region lby, where the shear reinforcements yield tothe buckling length lb (i.e. rby = lby/ lb; see Figure 10(a)). Dhakal assumed that rby at the bucklingof the longitudinal bars ranged from 0.33 to 0.5 [5]. Figure 10(b) shows the relationship betweenthe specific compressive stresses of the longitudinal bars and the yield portion ratio rby. Theyield portion ratios approached 0.76 for specimen K2 and 0.45 for specimen K3. This observationbasically supported Dhakal’s assumption described above.



Figure 10. Yield portion ratio of shear reinforcement along buckling length: (a) definition (rby = lby/ lb)and (b) relationship between yield portion ratio and buckling deflection.

Figure 11. Relationship between compressive bar stress and buckling length:(a) corner bar and (b) inner bar.

5. SPECIFIC COMPRESSIVE STRESS OF LONGITUDINAL BAR

Several researchers have developed reliable stress–strain hysteresis models [2, 3, 7–10]. The barmay buckle at a stress lower than the Euler buckling stress because lateral forces could be in-duced by crushed concrete or deformed hoops. In fact, the buckling stresses of specimens inthis research were lower than the Euler stress. Figure 11 shows the relationship between thestresses that the buckled longitudinal bars attained at the peaks of loading cycles and the buck-ling length. The bucking lengths were normalized by dividing by the bar’s diameter (lb/db).Figure 11(a) shows the case of corner bars, while Figure 11(b) shows the case of inner bars.



If lb/db was the same, the buckling stresses of the corner bars were greater than those of the innerbars because the hoops provided the corner bars with effective lateral confinement. Equation (2)gives the specific compressive stresses of the buckled longitudinal bars based on the test results

fbr = min

[fy, cr

(dblb

)2(√

fyf0

+ �FEF

kF

)](MPa) (2)

where f0 = 100MPa; cr = 2000MPa for the corner bar and 200MPa for the inner bar; andkF = 30MPa.

The above formulation was originally proposed in Tanoue et al.’s [9] research. Tanoue proposeda model for a bare bar whose coefficient cr was assumed to be 5000MPa. The test result ofthis research, however, indicated that cr was considerably less (200–2000MPa, see Figure 8). Incontrast, the specific stresses of the corner bars increased in the specimens with the FRP sheets(specimen K3). Equation (2) reflects these observations.

6. CONCLUSIONS

1. In RC columns without FRP sheet jacketing, the compression bearing capacities of the longi-tudinal bars began to decrease at buckling deflections below 0.3mm. The specific compressivestress, which is defined as the maximum compressive stress that a longitudinal bar on thecompression side attained during half a loading cycle, became constant at buckling deflectionsgreater than 0.6mm. Therefore, it was assumed that the lengths and modes of the bucklingof the longitudinal bars stabilized at buckling deflections between 0.3 and 0.6mm.

2. Conversely, the compressive stresses of longitudinal bars in a column jacketed with a high-elastic modulus FRP sheet (i.e. carbon fibre sheet) continued to increase even at a largebuckling deflection.

3. The buckling deflections were effectively restrained by increasing the stiffness of the shearreinforcement as well as by increasing the confining stresses, even in columns with externallyjacketed all-elastic FRP shear reinforcements.

4. The buckling stresses and the specific compressive stresses of longitudinal bars in RC columnswere less than those of the bare bars.

5. The yield portion ratio rby, which is defined as the ratio of the length of region lby, wherethe shear reinforcements yielded, to the buckling length lb, ranged from 0.45 to 0.76 for thespecimens used in this test.

ACKNOWLEDGEMENTS

The writers gratefully appreciate the assistance of Prof. Bunzo Tsuji, Associate Prof. Minehiro Nishiyama,and the late Shigeru Fujii, Associate Prof. of Kyoto University, Japan. The carbon fibre sheet was providedby Nittetsu Composite Corporation and the polyacetal fibre sheet by Asahi Kasei Corporation.

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