seismic behavior of rc columns with interlocking spirals under combined loadings including torsion

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Procedia

Engineering Procedia Engineering 00 (2011) 000–000

www.elsevier.com/locate/procedia

The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction

Seismic Behavior of RC Columns with Interlocking Spirals under Combined Loadings Including Torsion

Qian. Li a and A. Belarbi b

1 Department of Civil and Environmental Engineering, University of Houston, USA 2 Department of Civil and Environmental Engineering, University of Houston, USA

Abstract

Reinforced concrete (RC) columns of skewed and curved bridges with unequal spans or column heights can be subjected to combined loading including axial, flexure, shear, and torsion loads during earthquakes. This combination of seismic loading can induce the complex flexural and shear failure of bridge columns. Seismic performance of bridge RC columns is largely controlled by the level of confinement provided by transverse reinforcement. Interlocking spirals are commonly used in non-circular RC bridge columns because they can provide more effective confinement than rectangular hoops and simplify the column fabrication. However, the seismic behavior of columns with interlocking spirals has been studied only to a limited extent with respect to the hysteretic behavior of pure torsion and the interaction between flexure, shear, and torsion. The presence of torsion significantly affects the inelastic flexural response of RC members under seismic loadings and results in brittle failure modes. This paper presents an experimental study on the inelastic behavior of the RC columns with double interlocking spirals under combined action of cyclic flexural and torsional moments. The columns were designed with aspect ratio (H/B=5.5) and tested under various loading conditions: cyclic pure torsion, and combined cyclic flexure and torsion. The hysteretic torsional and flexural response, damage distribution, stiffness degradation and ductility characteristics with respect to various torsion-to-bending moment (T/M) ratios are discussed. The significant confinement of interlocking spirals to core concrete and its effect on the torsional resistance under combined loadings is also highlighted. Finally, interaction diagrams were established based on experimental results. © 2011 Published by Elsevier Ltd. Keywords: RC column; interlocking spirals; combined loading; seismic performance; torsion.

a Corresponding author: Email: [email protected] or [email protected] b Presenter: Email: [email protected]

1877–7058 © 2011 Published by Elsevier Ltd.doi:10.1016/j.proeng.2011.07.161

Procedia Engineering 14 (2011) 1281–1291

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1. INTRODUCTION

Reinforced concrete (RC) bridge columns could be subjected to combined flexural, axial, shear, and torsional loading during earthquake excitations. Significant torsional effects on columns can happen in the cases of skewed or horizontally curved bridges, bridges with unequal spans or column heights, bridges with outrigger bents, arch ribs and L shape bridge piers. Due to the irregular structural configurations, the specific seismic consideration is required to design these bridges to withstand extreme multi-directional ground motions. The combination of seismic loadings can result in complex flexural and shear failure of bridge columns.

The confinement provided by the transversal steel is an essential factor in improving the seismic performance of RC members in terms of strength, ductility and energy dissipation capacity. In non-circular column such as rectangular and oval column, interlocking spirals are frequently adapted as transverse reinforcement because of both better transverse confinement and easier fabrication at construction site. The California Department of Transportation (Caltrans) “Bridge Design Specifications (BDS)” and “Seismic Design Criteria Version (SDC)” are the only codes in the United States that state provisions for the design of columns with interlocking spirals. Tanaka and Park (1993) firstly performed cyclic horizontal loading test on three columns with interlocking spirals, while one column with rectangular hoops and cross ties was tested as well for the comparison. The test results showed that the volume of transverse reinforcement being required for the confinement of core concrete could be reduced significantly by using interlocking spirals other than rectangular hoops and cross ties. In the past decades, just a few experimental studies (Buckingham et al. 1994; Tsitotas and Tegos 1996; Benzoni et al 2000; Mizugami 2000; and Correal and Saiidi 2004) have been performed to investigate the seismic behavior of the RC columns with interlocking spiral under bending- shearing with and without axial compression. In addition, the research efforts for interaction between bending, shear and torsion for RC bridge columns is limited (Hsu, H.L. and Wang 2000; Otsuka et al., 2004; Tirasit and Kawashima, 2005; Belarbi et al., 2008a; 2008b; and Suriya Prakash et al., 2008).

A careful review of related literature indicated that there have been few studies reporting on the seismic behavior of RC columns with interlocking spirals under combined loadings. Accordingly, the knowledge of the interaction between flexural and torsional moments in the behavior of the RC bridge columns with interlocking spirals is also limited. This paper presents the results of three oval columns with interlocking spirals under pure cyclic torsion, and combined cyclic flexure and shear and torsion with different T/M ratio. The effects of combined loading on hysteretic torsional and flexural response, damage distribution and progression, ductility characteristics and stiffness degradation with respect to various torsion-to-bending moment (T/M) ratios will be discussed. Finally, interaction diagrams were established based on experimental results.

2. EXPERIMENTAL PROGRAM

2.1 Specimen Details

Three half-scale test specimens were designed to represent typical existing bridge columns as shown in Figure 1. Each of the columns had the oval cross section of 610 mm×915 mm and the clear concrete cover of 25.4 mm. The total height of the specimen was 4.2 m with an effective height of 3.35 m measured from the top of footing to the centerline of applied loads. Thus, all the specimens were designed to maintain the same aspect ratio of 5.5. Three oval columns with interlocking spirals were tested under combined loading at T/M ratios of 0.2, 0.4 and ∞. Table 1 summarizes the reinforcement details of the test specimens. Twenty No. 8 bars (25 mm in diameter) provided longitudinal reinforcement with a ratio of 2.13%. Spiral reinforcement was provided by No. 4 bars (12.5 mm in diameter) with a pitch of 70 mm to obtain transverse reinforcement ratios of 1.32%. An axial load equivalent to 7% of the axial capacity of

Qian. Li and A. Belarbi / Procedia Engineering 14 (2011) 1281–1291 1283

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columns was applied during testing to simulate the superstructure dead load on the column in a bridge typically which varied between 5 and 10% of the capacity of the columns.

2.2 Materials Property

The concrete was supplied by a local Ready-Mix plant; a 28-day design cylinder compressive strength of 34.5 MPa was requested. Deformed bars were used in all specimens for spirals and longitudinal bars with expected design yield strength of 415 MPa. Standard tests for compressive strength, splitting tensile strength, modulus of rupture of concrete, and tension tests on steel coupons were conducted. Table 1 provides the actual material properties on the day of testing.

910mm

25mm Diameter Longitudinal

9mm Spirals @ 70mm O.C.

560mm

PVC Pipe to Attach Loading Mechanism

3352mm560mm

1524mm

910

915mm

610mm

25mm Diameter Longitudinal

9mm Spirals @ 70mm O.C.

560mm

PVC Pipe to Attach Loading Mechanism

38mm Cover

25mm Cover

3352mm

Cover 38mm

PVC Pipe Assembly ToApply Axial Load

PVC Pipe Assembly ToApply Axial Load

(b) Side Elevation(a) End Elevation

B B BB

(c) Cross Section B-B

610 mm

13mm Stirrups19 mm Longitudinal

2134 mm

70mm Pitch

51 mm PVC forColumn Lifting

20 Diameter 25 mm Lgitudinal bars ρl = 2.13%9 mm Spirals @ 70 mm ρs = 1.32%

25.4mm610 mm

25mm Longitudinal Bar9 mm Spiral

254mm～38

～30

～30 "～37

～38

～37

915mm

A

B C

D

EF

Figure 1: Sectional Details of Oval Column with Interlocking Spirals.

Table 1: Mechanical Properties of Concrete and Steel used in Columns

PROPERTY Oval Columns with Interlocking Spirals

H/B(5.5)-T/M(∞) H/B(5.5)-T/M(0.6) H/B(5.5)-T/M(0.2)

Compressive Strength fc, MPa 35.3 36.2 37.2

Modulus of Rupture fcr, MPa 3.42 3.55 3.65

Spiral Reinforcement Ratio (%) 1.32 1.32 1.32

Transverse Yield Strength fty, MPa 454

Longitudinal Yield Strength fly, MPa 529

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2.3 Test Setup and Instrumentation

Cyclic torsion and combined cyclic flexure, shear and torsion were driven by controlling the force or displacement of two horizontal servo controlled hydraulic actuators. Cyclic pure torsion was created by imposing equal but opposite directional forces with the two actuators. Combined cyclic torsional and flexural moments were generated by applying different specific forces or displacements with each actuator. The ratio of the imposing flexural moment to torsional moment was controlled by maintaining the ratio of the forces or displacements in the two actuators. A hydraulic jack was setup on top of the columns to apply for axial load; this jack transferred the axial load to the column via seven un-bonded prestressing steel strands. The axial load was measured by a load cell between the hydraulic jack and the top of the load stub. The twist and horizontal displacements of the columns were measured by string transducers at multiple heights above the column footing. Electrical strain gages were attached to the surface of the spirals and transverse reinforcement and mounted at various heights along the whole column in various patterns.

2.4 Loading Protocol

Testing of the specimen under combined flexure, shear, and torsion was conducted in load control mode at intervals of 10% of the predicted yielding load force (Fy) until monitored the first yielding of the longitudinal bars. The horizontal displacement corresponding to yielding of the first longitudinal bar was defined as a displacement ductility one (μΔ=1). While the specimen under pure torsion was loaded in load control mode at 10% intervals of the predicted yielding of the first transverse bar (Ty). The rotation corresponding to yielding of the first spiral was defined as a twist ductility one (μθ=1). After the first yield, the tests were conducted in displacement control mode until the ultimate failure of the specimens at specific levels of ductility. Meanwhile, T/M ratios were controlled at designed value of 0.2, 0.6 and ∞. Three cycles of loading mode were performed at each ductility level intending to provide an indication of stiffness degradation characteristics. For flexural moment, the loading in the BF or CE direction was defined as positive and that in the FB or EC direction as negative cycles as shown in Figure 1 (c). For torsional moment, counter-clockwise torque was defined as positive cycles, and that in the clockwise direction as negative cycles.

3. TEST RESLTS AND DISCUSSIONS

3.1 Columns under Cyclic Pure Torsion

In spite of the fact that understanding the behavior of RC columns under pure torsion is obvious to generalize further analysis under combined loadings, very few experimental studies have been conducted on the behavior of RC oval sections with interlocking spirals under pure torsion. The torsional hysteresis curve of the column tested under pure torsion is shown in Figure 2. The torsional moment-twist curves are approximately linear up to cracking torsional moment at the level of 50% Ty; thereafter they become nonlinear with a decrease in the torsional stiffness. During the positive cycles of twisting, the two interlocking spirals were unlocked resulting in reduction of the confinement effect on the core concrete and causing significant spalling of concrete. While during the negative cycles of loading, the two spirals were locked with each other increasing confinement of spirals to the core concrete which contribute to the seismic behavior of it. Hence the load resistance on the negative cycles was higher than the positive cycles of loading at higher ductility levels due to the extra confinement effect caused by the locking and unlocking actions of the spirals. This locking and unlocking effect is showed in the asymmetric nature of the torsional hysteresis curve observed in Figure 2. Figure 3 indicates the progression of damage in the specimen. Under pure torsional loading, significant diagonal cracks started developing near mid-height on the column. As the test processed, diagonal cracks continued to develop at an inclination of 42 to 45 in

Qian. Li and A. Belarbi / Procedia Engineering 14 (2011) 1281–1291 1285

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the form of spirals. The cracks lengthened and widened with the increase of applied torsion before the yield loading as shown in Figure 3 (a). Spalling of cover concrete was observed at a ductility level of one and spalling region spread along the whole column from bottom to top when the torsion loading reached a ductility level of six as shown in Figure 3 (b). Although the cover concrete spalled along the entire length of the column, significant core concrete crushing led to the formation of a torsional plastic hinge near higher mid-height of the column as shown in Figure 3 (c) which is significantly different from typical flexural plastic hinge zone located at the bottom of columns. The failure sequence in this specimen were in the order of shear cracking, spalling, spiral yielding, longitudinal bar yielding and then overall failure by significant core concrete degradation and longitudinal bar twisted extremely. In addition, the longitudinal bars located within the interlocking region transferred the shear stress from spiral to spiral by dowel action of those longitudinal bars considerably contributing to resisting torsional load at high ductility level.

-30 -20 -10 0 10 20 30Twist ( degree )

-800

-400

0

400

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-1000

-600

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Torq

ue (

kn -

m)

-8 -4 0 4 8-6 -2 2 6

Twist / Length ( deg / m )

Interlocking Oval ColumnPure Torsion

First Yield of Spiral

Ultimate TorqueLocking

Unlocking

(a)Yield

(b) Peak Torque (c) Overall Failure Figure 2 - Torsional Hysteresis under Pure Torsion

Figure 3– Damage of Column under Pure Torsion

3.2 Columns under Cyclic Combined Flexure, Shear and Torsion

Two oval columns with interlocking spirals were tested under combined loading at T/M ratio of 0.2 and 0.6, respectively. Figure 4 shows the comparison on flexural and torsional hysteresis behaviors of the two specimens under combined flexure and torsion. The flexural cracks first appeared in the interlocking region near the bottom of the column at 40% of the yield strength, which is a lower load level than thatapplied column under pure torsion. Due to the increased cycles of loading and the effects of T/M ratio, the angle of the flexural cracks became more inclined and more shear crack occurred at increasing heights. For the specimen loaded at T/M ratio of 0.6, longitudinal bars and spirals yielded at the same time of predicted yield loading. Error! Reference source not found. (1) shows the damage progression of the specimen under combined loading at T/M ratio of 0.6. Soon after the yield of longitudinal bar and spirals, spalling of concrete cover and large shear crack at an inclination of 45 was observed at the middle height of column around 5.7 ft as shown in Error! Reference source not found. (1)-(a). The spalling region developed down to bottom of column at the higher ductility level and spread all along the 2/3 height of column at final failure stage as shown in Error! Reference source not found. (1)-(c). While for the specimen loaded at T/M ratio of 0.2, longitudinal bar yielded firstly at the predicted yield loading and spirals yielded later at the higher ductility of six due to the lower T/M ratio. The concrete cover spalling did not happen until higher ductility level of three at the bottom of column and spread upward along the column to the lower height of column around 2 ft till the final failure. Error! Reference source not found.(2) shows the typical damage state of the specimen under combined loading at T/M ratio of 0.2.

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In both columns, failure was initiated by severe combination of shear and flexural cracks leading to progressive spalling of the cover concrete and finalized with severe core degradation followed by buckling and breaking of longitudinal bars. Core degradation locations for these two specimens were observed lower than that under pure torsion which indicates change of torsional plastic hinge location due to the effect of bending. However, the specific location of the plastic hinge depends on applied torsion to moment (T/M) ratio.

-400 -200 0 200 400-300 -100 100 300

Displacement ( mm )

-400

-200

0

200

400

-500

-300

-100

100

300

500

Load

( kn

)

-12 -8 -4 0 4 8 12-10 -6 -2 2 6 10

Drift / L ( % )

-1500

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0

500

1000

1500

-1250

-750

-250

250

750

1250

Ben

ding

Mom

ent (

kn

- m )

Interlocking oval columnT / M = 0.2T / M = 0.6

First Yield of Long. Bars

Ultimate Load

-10 0 10

-15 -5 5 15

Twist (degree)

-800

-400

0

400

800

-600

-200

200

600

Torq

ue (k

n-m

)

Interlocking oval columnT/M=0.6T/M=0.2

-3 0 3-4.5 -1.5 1.5 4.5

Twist / Length ︵ deg

/ m

︶

Ultimate Torque

First Yield of Spiral

Rotation was not Increased due to Displacement Limit of Actuator

Unlocking

Locking

(1) Flexural Hysteresis (2) Torsional Hysteresis

Figure 4 - Comparison of Hysteretic Behavior under Combined Loading

(1) T/M = 0.6

(2) T/M = 0.2

Qian. Li and A. Belarbi / Procedia Engineering 14 (2011) 1281–1291 1287 Author name / Procedia Engineering 00 (2011) 000–000 7

Figure 5 - Comparison of Damages under Combined Loading at (a) Longitudinal Reinforcement Yield (b) Peak Torsional moment and (c) Overall Failure

The asymmetric nature of the flexural and torsional behavior under combined flexure and torsion shown in Figure 4 (1) and (2) are both due to the locking and unlocking actions of spirals and the fact that one side of the specimen cross section is always subjected to higher additive shear stress of the two components of shear stresses from flexure and torsion leading to more damage and less load resistance . At the same reason, the positive cycle always reached the peak loading force first and the negative cycle could still obtain higher peak loading at the next ductility level. It is clearly shown that torsional and flexural strength and post-crack stiffness considerably decrease due to the increasing torsion to flexure ratio. Also, the deterioration of column strength and stiffness is significant in the first loading cycle and tends to become less significant after columns undergo some more loading repetitions. Due to the effect of combined loading, the secondary torsional stiffness was found to degrade faster than that observed under pure torsion due to bending moment effect.

3.3 Strength, Stiffness Degradation and Failure Modes

The lateral load-displacement and torsional moment-twist envelopes under different loading condition are compared in Figure 6 and Figure 7. In addition, the maximum lateral load and torsional capacities, and the maximum displacement and rotation of specimens in the first cycle of each ductility are summarized in Table 2. Due to the effect of combined loading, torsional and bending strengths dropped considerably according to the applied T/M ratio compared to pure flexure and torsion tests. For columns tested with increasing T/M ratios, the flexural strength and stiffness significantly degraded with an increase in ductility level due to the effect of torsion. The ultimate displacement and the ultimate lateral load decreased with an increase of T/M ratio, but the yield load and displacement remain the similar level as show in Figure 6 and Table 2. For columns tested with lower T/M ratios, the yielding and ultimate twist significantly dropped as the yielding and ultimate torsional strength degraded due to the effect of flexure as shown in Figure 7 and Table 2. Torsional stiffness degraded faster under combined loading including torsion than it did under pure torsion. Meanwhile, the strength and stiffness degraded with more loading cycles at each ductility level for all the columns. The asymmetric nature of the torsional envelopes is also mainly caused by the locking and unlocking actions of spiral.

-400 -200 0 200 400-300 -100 100 300

Displacement ( mm )

0

100

200

300

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500

50

150

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( kn

)

-10 -5 0 5 10-7.5 -2.5 2.5 7.5

Drift / L ( % )

0

400

800

1200

1600

200

600

1000

1400

Bend

ing

Mom

ent (

kn

- m )

T / M =0.6T / M = 0.2

Locking Unlocking

YieldUltimate

Figure 6 - Comparison Of Lateral Load-Displacement Envelopes


-30 -20 -10 0 10 20 30Twist ( degree )

0

200

400

600

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Torq

ue (

kn -

m )

-8 -4 0 4 8-6 -2 2 6

Twist / Length ( degree / m )

Pure TorsionT / M = 0.6T / M = 0.2

Locking Unlocking

YieldUltimate

Figure 7 - Comparison Of Torsional Moment-Twist Envelopes

Spalling of the cover concrete is a significant physical phenomenon indicating the degradation level of RC structures. Under torsional loadings, the cover concrete spalled off before the ultimate torsional capacity is reached; the shear flow path is related to the dimension of the spirals. Thus, the timing of spalling is important from a design point of view; concrete cover is not taken into account determining the effective cross-sectional dimensions to be used in the design calculations since it occurs before reaching the peak load. The damage/spalling zone location significantly changed according to torsion to moment (T/M) ratio as shown in Table 3. The failure sequence in the specimens under combined loading is flexural cracking, followed by shear cracking, longitudinal bar yielding, spalling of concrete cover, and spiral yielding; while that under pure torsion is shear crack, followed by spiral yielding, spalling of concrete, and ultimate torque. Final failure for all columns was occurred by buckling of the longitudinal bars after severe core degradation.

Table 2 Comparison of Test Results

Table 3 Comparison of Column Damage

UNIT ID Concrete Damage

Damage Zone Location Spalling Length Core Crushing Depth

T/M=0.2 37” 6”- 10” 3”-13”

T/M=0.6 90” >12” 12”- 28”

T/M=∞ Entire Totally 75”- 101”

Specimen T/M Max. Lateral Load

(kN) Max. Displacement

(mm) Max. Torque

(kN-m) Max. Rotation

(Degree) Positive Negative Positive Negative Positive Negative Positive Negative

1 ∞ -- -- -- -- 756.6 -826.2 23.1 -22.9 2 0.6 64.2 -69.9 147.4 -158.39 561.4 -727.2 13.2 -8.5 3 0.2 87.7 -90.9 312.0 -289.9 280.3 -431.4 4.3 -3.9


-2000 -1000 0 1000 200-1500 -500 500 1500

Bending Moment ( kn - m)

0

200

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600

800

1000

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300

500

700

900

Torq

u ( k

n - m

)

T/M=0.2T/M=0

.6T/M=0.2T/M=0.6

T/M=0 T/M=0

Locking Unlocking

ExperimentAnalytical Prediction

T/M ratio was not constantdue to locking effect

Figure 8 - Torsion-Bending Moments Interaction Diagrams

-2000 -1000 0 1000 200-1500 -500 500 1500

Bending Moment ( kn - m )

0

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400

600

800

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500

700

Torq

ue (

kn -

m )

T/M=0.6T/M=0.2

Peak Torque

Peak Bending Moment

Figure 9 - Torsion-Bending Moments Loading Curves

3.4 Flexure-Torsion Interaction

Experimental results of the columns under pure torsion and analytical results of the columns under flexure were used as the benchmarks for analyzing the behavior of specimens under combined flexure, shear, and torsion. The test results of three columns and predicted result of one column were used to create the interaction diagrams between flexural and torsional moment as shown in Figure 8. A conventional layer-by-layer approach was applied to predict the bending strength of the specimen under pure flexure. The interaction between flexure and torsion depends on significant factors such as the amount of transverse and longitudinal reinforcement, configuration of transverse confinement, aspect


ratio of the section, and concrete strength. The interaction curves are slightly different in the positive and negative cycles owing to the locking and unlocking effect of spiral. The torsional capacity as well as bending capacity has been found to reduce due to the effect of combined bending and torsion. Additionally the torsional-bending moment loading curves for the tested columns indicated the loading T/M ratio during the entire process of test as shown in Figure 9. The column tested under T/M ratio of 0.2 failed mainly in flexure mode, and the ultimate torsional and flexural strength were attained simultaneously at the same cycle in the unlocking side. However, the ultimate flexural strength reached earlier than the torsional strength in the locking side. The torsion-to-bending moment (T/M) ratio was maintained constant of 0.2 until the peak bending moment as shown in Figure 9 and then bending strength significantly degraded resulting in un-constant T/M ratio. The column tested under T/M ratio of 0.6 failed mainly in torsion mode. The ultimate strength under bending and torsion reached simultaneously at the same cycle in the unlocking side, while the ultimate strength under torsion was reached earlier than the bending strength in the locking side. The torsion-to-bending moment ratio was maintained constant of 0.6 until the peak torsional moment as shown in Figure 9 and then it was hard to keep a constant T/M ratio due to faster torsional strength degradation.

4. SUMMARY AND CONCLUSIONS

Experimental study was conducted on the effect of combined cyclic flexure and torsion on the behavior of oval RC columns with double interlocking spirals. The test results of three columns under pure torsion and combined flexure and torsion were presented and discussed. Based on the preliminary test results and discussions from this study, the following major concluding remarks are drawn:

• The failure of oval interlocking-spirals column under pure torsion was induced by significant crossed diagonal shear cracks leading to concrete cover spalling along the entire-height of column and formation of a torsional plastic hinge with severe core concrete degradation near the mid-height of column, which was significantly different the typical flexural plastic hinge zone located at the bottom of column.

• The ultimate lateral load and displacement capacity of the columns decreased with increasing torsion to moment (T/M) ratio due to the effect of torsion. Similarly, the decrease of T/M ratio resulted in the degradation of the torsional moment and ultimate twist capacity owning to the flexure. In addition, the locking and unlocking effect caused the asymmetric response of all specimens from the ductility level of one, owning to the winding and unwinding interaction mechanism of two interlocking spirals to the core concrete.

• The existence of torsion altered the patterns of damage RC columns under combined loading. Due to high shear stresses from shear force and torsional moment under combined loading, failure was initiated by the severe combinations of shear and flexural cracks leading to progressive spalling of the cover concrete and finalized with severe core degradation followed by buckling and breaking of longitudinal bars. The location and length of the damage zone changed with applied torsion to moment (T/M) ratio.

• The longitudinal bars located within the interlocking region transferred the shear stress from spiral to spiral by dowel actions which considerably contribute to torsional resistivity at high ductility level.

• Interaction curves between the bending and torsional moment of RC columns with interlocking spirals established in this study can give a glance of further development of analytical methods or a design provision in current code.

5. ACKNOWLEDGEMENTS

This study was funded by NEES-NSF, National University Transportation Center (NUTC) and Intelligent Systems Center (ISC) of Missouri S &T. Their financial support is gratefully acknowledged.


REFERENCES

[1] Buckingham, G.C., Seismic Performance of Bridge Columns with Interlocking Spirals Reinforcement, M.S. Thesis, Washington State University, Pullman, Washington, 1992, 146 pp

[2] Benzoni, G., Priestley, M.J.N., and Seible, F., Seismic Shear Strength of Columns with Interlocking Spiral Reinforcement, 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000, 8 pp

[3] Belarbi, A., Suriya Prakash, S. and Silva, P.; Flexure-shear-torsion interaction of RC bridge columns; Concrete Bridge Conference, St Louis, Missouri, May 5-7, 2008a, Paper No. 6.

[4] Belarbi, A., Suriya Prakash, S. and You, Y.M.; Effect of spiral ratio on behavior of reinforced concrete bridge columns under combined loadings including torsion; Proceedings of the 4th International Conference on Advances in Structural Engineering and Mechanics, Jeju, Korea. May 26-28, 2008b, pp. 1190-1205.

[5] Caltrans, Caltrans Bridge Design Specifications, California Department of Transportation, Sacramento, CA, 2004 [6] Hsu, H.L. and Wang, C-L, , Flexural-torsional behavior of steel reinforced concrete members subjected to repeated loading,

Earthquake Engineering and Structural Dynamics, Vol. 29, 2000, pp. 667-682. [7] Lehman, D.E., Calderone, A.J. and Moehle, J.P., Behavior and design of slender columns subjected to lateral loading;

Proceedings of Sixth U.S. National Conference on Earthquake Engineering, EERI, Oakland, California. May 31-June 4, 1998, Paper No.87

[8] Mizugami, Y., Efficiency of Lateral Reinforcement in Interlocking Spirals Rebar, presented at the 16th US-Japan Bridge Engineering Workshop, October 2-4, 2000, pp. 265-276.

[9] Otsuka, H., Takeshita, E., Yabuki, W., Wang, Y., Yoshimura, T. and Tsunomoto, M.; Study on seismic performance of reinforced concrete columns subjected to torsional moment, bending moment and axial force.; 13th World Conference on Earthquake Engineering, Vancouver, Canada. August 1-6, 2004, Paper No. 393.

[10] Tanaka, H., and Park, R., Seismic Design and Behavior of Reinforced Concrete Columns with Interlocking Spirals, ACI Structural Journal, Vol. 90, No 2, March-April 1993, pp. 192-203.

[11] Tsitotas M.A., and Tegos I.A., Seismic Behaviour of R/C Columns and Beams with Interlocking Spirals, Advance in Earthquake Engineering, Vol. 2, Oct 30-Nov 1, 1996, pp. 449-461.

[12] Tirasit, P., Kawashima, K. and Watanabe, G.; An experimental study on the performance of RC columns subjected to cyclic flexural torsional loading; Second International Conference on Urban Earthquake Engineering, Tokyo, Japan, 2005, pp. 357-364

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seismic behavior of rc columns with interlocking spirals under combined loadings including torsion

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