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ACI STRUCTURAL JOURNAL

TECHNICAL PAPER

Title no. 109-S26

Behavior of Circular and Square Reinforced Concrete Bridge Columns under Combined Loading Including Torsion by S. Suriya Prakash, Qian Li, and Abdeldjelil Belarbi Reinforced concrete (RC) bridge columns can be subjected to flexural, axial, shearing, and torsional loading during earthquake excitations, resulting in complex failure modes. However, in spite of its explicit occurrence during earthquake excitations and significant effect on final failure modes, the torsional loading effect on the seismic performance of RC columns has not been studied in depth. In particular, understanding interacting behavior of each loading condition should be preceded to satisfy the increased demand for seismic design. In this context, this study aims at improving the knowledge of seismic performance of RC bridge columns under combined loading, including torsion through the experimental study carried out by Missouri University of Science and Technology. The experimental study focused on investigating the effect of different cross-sectional shapes (circle and square), hysteretic torsional and flexural response, damage distribution, and ductility characteristics with respect to various torsion-to-bending moment (T/M) ratios. Finally, interaction diagrams were established based on experimental results. Keywords: circular columns; combined loading; reinforced concrete; seismic performance; square columns; torsion.

INTRODUCTION Reinforced concrete (RC) bridge columns can be subject to multi-directional ground motions that result in the combination of axial force, shearing force, and flexural and torsional moments. The addition of significant torsion is more likely in skewed or horizontally curved bridges, in bridges with unequal spans or column heights, and in bridges with outrigger bents. This combination of seismic loadings can result in complex flexural and shear failure of bridge columns. Moreover, the cross-sectional details also affect the seismic behavior of RC bridge columns, such as damage distribution and ductility characteristics. Several experimental studies have been performed to investigate the behavior of columns under bending and shearing with and without axial compression (Kent 1969; Ang et al. 1989; Mander et al. 1988). Rational and accurate models are available for analyzing the interaction between axial and flexural loads on RC columns (Park and Ang 1985; Priestley and Benzoni 1996; Lehman et al. 1998). However, knowledge of the interaction between flexural and torsional moments in the behavior of RC bridge columns is limited. Few researchers have investigated the effects of combined loading and cross-sectional shape on the seismic performance of bridge columns. The effect of combined flexure and torsion with compression has also not been studied intensively; most tests have focused on static monotonic loads. Otsuka et al. (2004) conducted cyclic loading tests on nine rectangular RC columns under pure torsion, flexure and shear, and various ratios of combined flexural and torsional moments. The authors found that the hysteresis loop of torsion was significantly affected by the spacing of the transverse reinforcement. Later, Tirasit and Kawashima (2007) ACI Structural Journal/May-June 2012

tested RC columns under combined cyclic flexure and torsion with three different rotation-drift ratios and formulated a nonlinear torsional hysteretic model. The authors concluded that the flexural capacity of RC columns decreases as the rotation-drift ratio increases and the damage tends to occur above the flexural plastic hinge region. Recently, Belarbi et al. (2008) presented a state-of-the-art report on the behavior of RC columns under combined loadings and discussed the directions for further research. They found that the effect of degradation of concrete strength in the presence of shear and torsional loads, and confinement of core concrete due to transverse reinforcement, significantly affected the ultimate strength of concrete sections under combined loading. They also suggested developing simplified constitutive models to incorporate softening and confinement effects. Prakash and Belarbi (2009) reported the results of tests on several circular columns under combined loadings with various spiral ratios and torsion-to-moment (T/M) ratios. They reported that the effects of combined loading decrease the flexural and torsional capacity and affect the failure modes and deformation characteristics. They also concluded that the transverse reinforcement, which may be adequate from a flexural design point of view, could be inadequate under the presence of torsional loading. A careful review of related literature (Hsu 1993; Rahal and Collins 1995; Bentz 2000; Otsuka et al. 2004; Belarbi et al. 2010) indicated that there have been few studies reporting on the behavior of RC circular columns under combined loading. The experimental study described herein investigated the effect of cross section on seismic behavior of RC columns under combined loading, including torsion, as well as the interacting behavior of flexural and torsional moment. This paper presents the results of four square and four circular column tests under cyclic flexure and shear, pure cyclic torsion, combined cyclic flexure and shear, and torsion. RESEARCH SIGNIFICANCE The effect of cross-sectional shape on the interacting behavior between flexure and torsional moments in the presence of axial compression has not been adequately investigated. The seismic behavior of circular and square columns is significantly different under combined loading due to the transverse reinforcement configurations, transverse confinement of core concrete, and distribution of shear stress flow. As a result, this study tries to establish a practical interaction diagram for circular and square section columns under ACI Structural Journal, V. 109, No. 3, May-June 2012. MS No. S-2010-062.R2 received July 4, 2011, and reviewed under Institute publication policies. Copyright © 2012, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the March-April 2013 ACI Structural Journal if the discussion is received by November 1, 2012.

317

S. Suriya Prakash is a Design Engineer at Structural Group Inc., Baltimore, MD. He received his PhD from Missouri University of Science and Technology, Rolla, MO. His research interests include seismic design and repair and rehabilitation of reinforced concrete and masonry structures using advanced construction materials. Qian Li is a PhD Candidate in the Department of Civil Engineering at Missouri University of Science and Technology. His research interests include seismic design and analytical modeling of reinforced concrete structures. Abdeldjelil Belarbi, FACI, is a Distinguished Professor of Civil Engineering and Department Chair of the Civil and Environmental Engineering Department at the University of Houston, Houston, TX. He is Chair of ACI Subcommittee 440-E, FRPProf Education, and Joint ACI-ASCE Subcommittee 445-A, Shear and Torsion-Strut and Tie. He is a member of ACI Committees 341, Earthquake-Resistant Concrete Bridges; and 440, Fiber-Reinforced Polymer Reinforcement, and Joint ACI-ASCE Committees 343, Concrete Bridge Design; and 445, Shear and Torsion. His research interests include constitutive modeling of reinforced and prestressed concrete as well as the use of advanced materials and smart sensors in civil engineering infrastructure.

combined loading, and profile the differences between the two sections with respect to hysteretic torsional and flexural response, damage distribution, and ductility. EXPERIMENTAL PROGRAM Specimen details Half-scale test specimens were designed to represent typical existing bridge columns. Figure 1(a) and (c) show the circular

specimen dimensions and cross-section details, respectively. Similarly, the square specimen dimensions and cross-section details are shown in Fig. 1(b) and (d), respectively. Both circular and square columns had an aspect ratio of 6. The total height of the circular column was 4.5 m (177.2 in.) with an effective height of 3.66 m (144 in.) measured from the top of the footing to the centerline of the applied forces, while the total height of the square columns was 4.2 m (165.4 in.) with an effective height of 3.35 m (132 in.). Circular and square columns with similar longitudinal and transverse reinforcement ratios were tested under combined loading at T/M of 0.2 and 0.4. Table 1 summarizes the reinforcement details of the test specimens. An axial load equivalent to 7% of the axial concrete capacity (0.07Agfc′) of columns for both circular and square columns was applied during testing to simulate the dead load on the column in a bridge. Material properties The concrete was supplied by a local concrete plant; a 28-day design cylinder compressive strength of 34.5 MPa (5 ksi) was requested. Deformed bars were used in all specimens. The design yield strengths of transverse and longitudinal reinforcement were expected to be 415 MPa (60 ksi). Table 1 provides the actual material properties of the circular and square columns on the day of the testing.

Fig. 1—Circular and square column sectional details. (Note: 1 mm = 0.0394 in.) Table 1—Mechanical properties of concrete and steel used in columns Circular columns

Square columns

Property

H/D(6)T/M(0)

H/D(3)T/M(∞)

H/D(6)T/M(0.2)

H/D(6)T/M(0.4)

H/B(6)T/M(0)

H/B(6)T/M(∞)

H/B(6)T/M(0.2)

H/B(6)T/M(0.4)

Compressive strength fc′, MPa (ksi)

33.4 (4.84)

28.0 (4.06)

41.2 (5.97)

41.2 (5.97)

36.3 (5.26)

34.6 (5.02)

40.5 (5.87)

40.4 (5.86)

Modulus of rupture fcr, MPa (ksi)

3.52 (0.51)

3.42 (0.50)

3.86 (0.56)

3.93 (0.57)

3.73 (0.54)

3.57 (0.52)

3.68 (0.53)

3.64 (0.53)

Spiral reinforcement ratio, %

0.73

1.32

1.32

1.32

1.32

1.32

1.32

1.32

Transverse yield strength fty, MPa (ksi)

450 (65.25)

454 (65.83)

Longitudinal yield strength fly, MPa (ksi)

457 (66.27)

512 (74.24)

318

ACI Structural Journal/May-June 2012

Fig. 2—Test setup. Test setup and instrumentation Cyclic uniaxial bending, torsion, and combined bendingshear and torsion were generated by controlling two horizontal servo-controlled hydraulic actuators shown schematically in Fig. 2. The axial load was applied by a hydraulic jack on top of the load stubs; this jack transferred the axial load to the column via seven unbonded high-strength prestressed steel strands. Cyclic torsion; flexure and shear; and combined flexure, shear, and torsion were generated by controlling the force or displacement of two horizontal servo-controlled hydraulic actuators. A number of instruments were used to measure the applied loads, deformations, and internal strains. The axial load was measured by a load cell between the hydraulic jack and the top of the load stub. Electrical strain gauges were attached to the surface of the longitudinal and transverse reinforcement to measure strains, permitting study of the deformation of reinforcement under different loading conditions. Testing of specimens normally lasted 1 to 2 days. Although the data obtained were high quality, further corrections were needed. Correcting procedures included filtering the data to remove the noise of the excess data collected during the pauses in the testing. The data were reduced and analyzed by comparing results for each column based on various parameters. Loading protocol Testing was conducted in load control mode until first yielding of the longitudinal bars for all circular and square columns under flexure and shear as well as combined flexure, shear, and torsion. For columns under pure torsion, the testing was under load control until the first yielding of the transverse reinforcement. The first yielding of the longitudinal bars and transverse reinforcement was monitored during the testing by the data acquisition system and by carefully analyzing the data of strain gauge readings. For the columns under flexure-shear and combined flexure, shear, and torsion, the yielding of longitudinal and transverse reinforcement was analyzed carefully at the lower height of columns where the flexural and torsional moments are at maximum. Under pure torsion, the first yielding of the transverse reinforcement can occur anywhere along the full length of the column. Hence, all transverse reinforceACI Structural Journal/May-June 2012

ment gauges were carefully monitored during the testing and analysis. For circular columns, the lateral loading in the A-C direction and torsional moment in a counter-clockwise direction was defined as positive, and in the opposite direction, it was defined as negative, as shown in Fig. 1(c). Similarly, for the square columns, the lateral loading in the D-A direction and torsional moment in a counter-clockwise direction was defined as positive, and that in opposite direction was defined as negative, as shown in Fig. 1(d). Columns under flexure—For circular columns, the load was applied in load control mode at intervals of 25, 50, 75, and 100% of the predicted yielding lateral load Fy from moment-curvature analysis. The horizontal displacement corresponding to yielding of the first longitudinal bar was defined as a displacement ductility level of 1 (mD = 1). Similarly, for square columns, the load control mode was imposed at intervals of every 10% of the predicted yielding lateral load Fy under flexure and shear as well as combined flexure, shear, and torsion loading conditions. For load control before yielding, cyclic flexure and shear loads were generated by applying equal forces in the same direction with the two actuators. After the first yielding of longitudinal bars, the tests were performed in displacement control mode. Three cycles of loading were performed at each displacement ductility level to provide the strength and stiffness degradation characteristics until the ultimate failure of the specimens. Testing was continued until the strength deteriorated to more than 80% of the peak capacity or the stroke capacity was attained, whichever occurred first. Columns under pure torsion—The circular column under pure torsion was loaded in load control mode at intervals of 25, 50, 75, and 100% of the predicted yielding torque Ty from the softened truss model (STM). Pure torsion was created by driving equal but opposite directional forces with the two actuators. The data acquisition system was closely monitored for the first yielding of the transverse reinforcement while testing at real time. The twist corresponding to yielding of the first transverse reinforcement was defined as a twist ductility level of 1 (mq = 1). The square column under pure torsion was loaded at every 10% intervals of the predicted yielding of the first transverse bar (Ty). The test was carried out under displacement/stroke control to main319

Fig. 3—Hysteresis curves under flexure and lateral load. (Note: 1 mm = 0.0394 in.)

Fig. 4—Failure modes of columns under flexure and shear at: (1) longitudinal bar yield; (2) ultimate; and (3) final failure. tain the T/M of ∞ after the first yielding of the transverse reinforcement. The stroke of the actuator was controlled to achieve the required twist of column using a computer program based on the geometry of the actuator system. Columns under combined loading—Testing was conducted in load control mode until the first yielding of the longitudinal bars for columns under combined flexure, shear, and torsional loads. Combined cyclic torsional and flexural moments were generated by applying different specific forces with each actuator to maintain the desired T/M. Thereafter, the testing was carried out under displacement/stroke control to maintain the desired T/M by adjusting the stroke of the actuator system. A program was written to calculate the twist and displacement at the center of the column based on the stroke of the actuators. Also, the stroke of the actuators needed to calculate the required displacement and twist at the center of the column could be back-calculated. The aforementioned feedback system was used to control the desired T/M during the testing. TEST RESULTS AND DISCUSSIONS Columns under flexure Circular column—Figure 3(a) shows the flexural hysteresis of the circular column up to a ductility of 8. The column began exhibiting flexural cracks near the bottom on sides A and C after cyclic loading the column to 50% of Fy. Figure 4(a) shows the progression of damage up to final failure. These cracks continued to grow and new cracks 320

appeared on both sides of the column as higher levels of loading were applied, as shown in Fig. 4(a)-(1). The cover concrete started spalling at a drift of approximately 3.2%, which is defined as the ratio of lateral displacement and column height, as shown in Fig. 4(a)-(2). The failure mode of the specimen began with the formation of a flexural plastic hinge at the base of the column, followed by core degradation, and finally by the buckling of longitudinal bars on the compression side at a drift of approximately 12.7%. During the last cycle of loading, a longitudinal bar started buckling during unloading, as shown in Fig. 4(a)-(3). The yielding zone of the longitudinal bars was approximately 610 mm (24 in.) from the base of the column. The spirals remained elastic until a ductility level of 6, after which they yielded. Square column—Figure 3(b) shows the flexural hysteresis of the square column. The column started to show flexural cracking near the bottom 400 mm (15.8 in.) above the footing on sides AB and CD after cyclically loading the column to 40% of Fy. Figure 4-(2) shows the progression of damage in the square column. With development of these cracks and the appearance of new cracks in a higher position with increasing levels of ductility, the cover concrete started to spall at a drift of approximately 2% when the column was loaded to a ductility level of 3, as shown in Fig. 4(b)-(2). During the last cycle at a ductility level of 12, almost all the longitudinal bars buckled during unloading, as shown in Fig. 4(b)-(3). The yielding zone of the longitudinal bars was approximately 600 mm (23.6 in.) from the base of the ACI Structural Journal/May-June 2012

Fig. 5—Torsional hysteresis under pure torsion. (Note: 1 kN-m = 0.73576 kip-ft.)

Fig. 6—Damage of column under pure torsion at: (1) transverse bar yield; (2) peak torsional moment; and (3) overall failure. column. The transverse reinforcement remained elastic until a ductility level of 8. As observed in the circular column, the failure mode of the specimen began with the formation of a flexural plastic hinge 580 mm (22.8 in.) above the base of the column, followed by core concrete degradation due to crushing of the concrete. The column finally failed by the buckling and rupturing of longitudinal bars and the rupturing of transverse bars on the compression side at a drift of approximately 8%. Columns under cyclic pure torsion In practice, torsional loads usually occur in combination with other actions, such as flexure and shear forces. However, understanding the behavior of members subjected to pure torsion is necessary for a generalized analysis of a structural member under combined loading including torsion. Circular column—The torsional hysteresis curve of the column tested under pure torsion is shown in Fig. 5(a). Under pure torsional loading, significant diagonal cracks started developing near midheight on the column at lower levels of ductility. Figure 6(a) shows the progression of damage in the specimen. Soon after the yielding of spirals, spalling was observed. The angle of diagonal cracks was approximately 40 degrees relative to the cross section (horizontal) of the column. During the positive cycles of twisting, the spirals were unlocked, causing significant spalling, and reducing the confinement effect on the core concrete, which ACI Structural Journal/May-June 2012

is termed the “unlocking effect.” On the other hand, during the negative cycles of loading, the spirals were locked, thus contributing to the transverse confinement of the core concrete and increasing the strength of it, which is termed the “locking effect.” This locking and unlocking effect is reflected in the asymmetric nature of the hysteresis loop observed at higher levels of loading, as shown in Fig. 5(a). At higher ductility levels, the load resistance on the negative cycles was higher than the positive cycles of loading due to the added confinement effect generated by the locking actions of the spirals. Dowel action contributed significantly to the load resistance at higher cycles of loading. At higher rotations, the torsional resistance was significantly less until the longitudinal bars were engaged to resist the applied torsional moment. Although the cover concrete spalled along the entire length of the column, significant spalling and core degradation led to the formation of a torsional plastic hinge near midheight of the column, as shown in Fig. 6(a)-(3). The damage pattern of the column under pure torsion was significantly different from that of the column under flexure and shear. Square column—Figure 5(b) shows the torsional momenttwist hysteresis response of the square column. The torsional moment-twist curves are approximately linear up to cracking torsional moment; thereafter, they become nonlinear with a decrease in the torsional stiffness. Under pure torsional loading, significant shear cracks started developing near midheight on the column at lower levels of 60% Ty. The 321

Fig. 7—Comparison of flexural hysteresis behavior under combined loading. (Note: 1 mm = 0.0394 in.)

Fig. 8—Comparison of torsional hysteresis behavior under combined loading. (Note: 1 kN-m = 0.73576 kip-ft; 1 deg/m = 0.0254 deg/in.) typical pattern and progression of damage in the square column under pure torsion is shown in Fig. 6(b). As the test progressed, diagonal cracks continued to propagate at an inclination of 40 to 42 degrees relative to the cross section (horizontal) of the column. Spalling of cover concrete was observed at a ductility level of 1 and the spalling region spread along the entire column from bottom to top when the torsion loading reached a ductility level of 8. At higher levels of loading, a plastic hinge formed near midheight of the column due to significant concrete spalling and core degradation similar to circular column specimen. Finally, the transverse reinforcement was ruptured in the plastic hinge zone. Columns under cyclic combined flexure, shear, and torsion A total number of four columns—two for square and two for circular—were tested for combined loading test as T/M of 0.2 and 0.4, respectively. The results of tests on columns 322

under flexure and shear and pure torsion were used as the benchmarks for analyzing the behavior of specimens under combined flexure, shear, and torsion. Circular columns—Figures 7(a) and 8(a) show the flexural and torsional hysteresis behaviors of the two columns tested under combined flexure and torsion. The asymmetric nature of the flexural envelopes under combined flexure and torsion is both due to the locking and unlocking actions of spirals and the fact that one face is subjected to higher shearing stresses. The latter factor is a result of the additive nature of the components of shear stresses from shear and torsion. Figure 9(a) shows the typical damage state of a circular column under combined flexural and torsional moment. Flexural cracks first appeared near the bottom of the column. With increasing cycles of loading and the effects of T/M, the angle of the cracks became more inclined at increasing heights above the top of the footing. In both columns, failure was initiated due to severe combinations of shear and flexural cracks leading to progressive spalling ACI Structural Journal/May-June 2012

Fig. 9—Comparison of damages under combined loading at: (1) longitudinal reinforcement yield; (2) peak torsional moment; and (3) overall failure.

Fig. 10—Comparison of envelopes for load-displacement curves. (Note: 1 mm = 0.0394 in.) of the cover concrete. Additionally, both columns failed due to severe core degradation followed by buckling of longitudinal bars on side C, as shown in Fig. 9(a)-(3). Square columns—Most of the behaviors are similar to those of circular columns with respect to structural performance such as crack patterns or failure modes, but there is no locking and unlocking effect, which is mainly caused by torsion. Figures 7(b) and 8(b) show the flexural and torsional hysteresis behaviors of the column. Due to the effect of combined loading, torsional and flexural strengths are considerably reduced according to the applied T/M, as observed in the circular columns. Figure 9(b) shows the damage characteristics and failure sequence of the columns under combined flexure and torsion. Side BC of the column exhibited more damage than side AD in the columns due to higher shear stresses in side BC. Core degradation was observed up to 1100 mm (43.3 in.) from the base of the column, compared to 560 mm (22 in.) under flexure. This higher level of core degradation shows that the plastic hinge location is affected by the existence of torsion. Indeed, it shifted to a higher location with increasing T/M. EFFECT OF CROSS-SECTIONAL SHAPE ON PERFORMANCE Strength, stiffness degradation, and failure modes The lateral load-displacement envelopes and torsional moment-twist envelopes under different loading conditions are compared in Fig. 10 and 11. Due to the effect of combined ACI Structural Journal/May-June 2012

loading, torsional and flexural strengths dropped considerably according to the applied T/M. For columns tested with increasing T/M, the flexural strength and stiffness significantly degraded with an increase in ductility level due to the effect of torsion. The yielding and ultimate displacement increased while the yielding and ultimate lateral load decreased with an increase in the T/M, as shown in Fig. 10(a) and (b). For columns tested with decreasing T/M, the torsional strength and stiffness considerably degraded due to the effect of flexure. Torsional stiffness degraded faster under combined loading, including torsion, than it did under pure torsion for both circular and square columns based on the comparison in Fig. 11(a) and (b). 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 in circular columns, as shown in Fig. 11(a), is due to the locking and unlocking actions of spirals; there is no locking and unlocking effect in the square column because of the symmetric transverse reinforcement configuration. Spalling of the cover concrete is a significant physical phenomenon indicating the degradation level of RC structures. Under flexural loads, the spalling is influenced by the cover-to-lateral-dimension ratio, the amount of transverse reinforcement, the axial load ratio, and the aspect ratio. Under torsional loadings, the cover concrete is assumed to spall off before the ultimate torsional capacity is reached; 323

Fig. 11—Comparison of envelopes for torque/twist curves (envelope value is maximum loaddisplacement value at first cycle of each ductility). (Note: 1 kN-m = 0.73576 kip-ft.)

Fig. 12—Torsion and bending interaction at peak torque: (a) circular; and (b) square. (Note: 1 kN-m = 0.73576 kip-ft.) the shear flow path is related to the dimension of the stirrups. Thus, the timing of spalling is important from a design point of view; whether it occurs before or after reaching the peak load determines the effective cross-sectional dimensions to be used in the design calculations. If spalling occurs before the peak load is reached, the clear concrete must be subtracted from the actual dimensions during design calculation. The damage/spalling zone location significantly changed according to the T/M. For the lower T/M of 0.2, the damage distribution in the circular column was localized to 26% of the total height of the circular column, compared to 23% in the square column. For a higher T/M of 0.4, the spalling zone spread to 66% of the total height of the circular column, whereas it was 36% of the square column. These differences indicate that the damage distribution is more localized in the square column compared to the circular column due to flexure-dominant behavior. Flexure-shear-torsion interaction Figure 12 shows the interaction diagram between flexural and torsional moment for both circular and square columns. The locking and unlocking action of spirals is significant 324

in circular columns but not observed in square columns. It can be observed that circular columns reach their torsional capacity and, subsequently, flexural capacity, while the square columns reach their torsional and flexural strength simultaneously. The failure sequence in all specimens is flexural cracking, however, followed by diagonal shear cracking, longitudinal bar yielding, spalling of concrete cover, and spiral yielding. Final failure occurred by buckling and rupturing of the longitudinal bars after severe core degradation. It should be noted that the T/M is close to the desired loading ratio in all the specimens until peak torsional moment. Soon after reaching the peak torsional strength, the desired loading ratio could no longer be maintained because torsional strength degraded much faster. ANALYTICAL STUDIES Flexural analysis A conventional layer-by-layer approach was applied to analyze the moment-curvature relationship of all columns. This flexural analysis was performed by iterating the extreme compressive fiber strain ec of concrete within a cross section from the initial increment value to the ACI Structural Journal/May-June 2012

Table 2—Comparison of results with moment-curvature analysis for flexure Circular Spiral ratio of 0.73%

Square Spiral ratio of 1.32%

Transverse ratio of 1.32%

Parameter

Model

Experiment

Model

Experiment

Model

Experiment

Flexural moment at first yielding My, kN-m (k-ft)

520 (383)

502 (369)

524 (386)

542 (399)

512 (377)

530 (390)

Ultimate flexural moment M0, kN-m (k-ft)

805 (592)

850 (625)

860 (633)

854 (628)

940 (692)

965 (710)

Table 3—Comparison of results with STM for pure torsion Circular Spiral ratio of 0.73%

Square Spiral ratio of 1.32%

Transverse ratio of 1.32%

Parameter

Model

Experiment

Model

Experiment

Model

Experiment

Pure torsional capacity T0, kN-m (k-ft)

520 (383)

502 (369)

524 (386)

542 (399)

480 (353)

525 (386)

ultimate compressive strain capability of the concrete. For each of the iterations, the neutral axis was determined by iterating through the section depth until the axial force was balanced—that is, to satisfy both the compatibility and equilibrium conditions. The concrete sections were broken up into layers and integrated through their depth during the analysis. The force at each layer was determined by multiplying the stress, which is calculated from the strain at each specific location by the area of the layer. Table 2 summarized the accuracy of the analytical flexural analysis for the columns tested under flexure in this study. The strength of tested columns under flexure varied from 95 to 98% of the calculated flexural capacities. Modified compression field theory (MCFT) model for shear capacity Vecchio and Collins (1986) and Collins and Mitchell (1991) offered a detailed description of MCFT accounting for the contribution of the tensile stresses in the concrete between the cracks. Collins et al. (2000) found that MCFT offers good predictions for circular sections among wellestablished analytical models for shear behavior. In MCFT relationships, q is the angle between the x-axis and the direction of the principal compressive average strain. These average strains, accounting for the compatibility relationships of cracked concrete, are measured over base lengths that are greater than the crack spacing to include more cracks. For specific applied loads, the angle, the average stresses, and the average strains can be calculated from three equilibrium equations in terms of average stresses; from two compatibility equations in terms of average strains; and from the constitutive relationships for materials linking average stresses and strains. Response 2000 is an implementation of the MCFT-based model within the framework of sectional analysis originally developed for RC elements. This study used computer program Response 2000, which assumes that sections remain plain and there is no transverse clamping stress across the depth of a cross section to predict the shear strength of circular and square columns containing various transverse reinforcements. The pure shear capacity of the circular columns, with spiral ratio of 0.73% and 1.32%, is generated by Response 2000 as 1205 and 1659 kN (270 and 372 kips), respectively. For square columns with transverse reinforcement ratio of 1.32%, the pure shear capacity reached 1122 kN (252 kips). ACI Structural Journal/May-June 2012

STM for pure torsion This section describes the development of model for predicting the torsional strength of circular and square RC members based on the original STM, including the effect of concrete tension stiffening and Poisson’s ratio. Adoption of tensions stiffening on the STM is important because it allows a continuous prediction of RC members before and after the first cracking state and reduces overestimation of the ultimate torsional moment. In this study, Greene and Belarbi’s (2009) model was adopted in the proposed STM model, which was validated by the test data available in literature. The proposed STM model follows most of the concepts and procedures used in the original STM model. Given the cross section dimensions, the transverse and longitudinal reinforcement, and the material properties, a displacementcontrolled solution to the equations was developed by firstly selecting ed and er, then assuming trial values of td for thickness of shear flow zone. Next, an iterative procedure was used to determine the values for the assumed variables by the equilibrium equations, compatibility equations, and stressstrain relationships. This process identified a single point on a torsional moment-twist curve. Additional points are found by varying the selected values of ed from a near-zero value (0.0001) to a maximum value that caused peak torsional moment. Accordingly, the entire torsional response from zero to its peak can be calculated by varying ed. Detailed formulation of the analytical model and validation with test data can be found elsewhere (Prakash 2009). Table 3 gives the calculated values of the pure torsional capacity for the circular and square columns according to STM. Torsion-bending-shear interaction curves The interaction of shear, torsion, and bending capacities can be calculated using the semi-empirical dimensionless equations suggested by Elfgren et al. (1974) based on the skew bending theory, as shown in Eq. (1). The Elfgren Model idealized a rectangular member as a box with reinforcement lumped into the four corners as “stringers.” The force in the stringers is induced by an applied torsional moment, bending moment, and shearing force combined using superposition. The axial loading effect to the interaction curves is not included because the applied axial load (7% of the axial strength for the specimens) is significantly less to completely inhibit flexural/diagonal cracking and restrain elongation due to torsion and flexure. The pure flexural capacity, pure shear 325

Fig. 13—Torsion-bending-shear interaction diagrams for circular and square columns. (Note: 1 kN = 4.45 kips; 1 kN-m = 0.73576 kip-ft.) capacity, and pure torsion capacity were calculated herein using the aforementioned models.

2



2

2

 M T V  M  +  T  R +  V  R = 1 0 0 0

(1)

where M0 is the pure ultimate flexural capacity; M is the flexural moment capacity with full interaction determined from combined loading conditions; T0 is the pure torsional moment capacity; T is the torsional capacity with full interaction determined from combined loading conditions; V0 is the pure shear capacity as per the MCFT model; V is the shear capacity with full interaction determined from combined loading conditions; and R is the ratio of transverse reinforcement to longitudinal reinforcement defined as rt/rl. The R term has the effect of shifting the interaction surface along the axis M/M0. Figure 13 shows the behavior of circular and square columns reinforced with transverse ratios of 0.73 and 1.32%. This figure also shows the corresponding test specimens with T/M of 0, 0.2, 0.4, and ∞. The strengths of all specimens are close to the outer interaction surface, indicating that the predictions are in reasonable agreement with the test results. Hence, the equation suggested by Elfgren et al. (1974) for the under-reinforced failure (that is, both longitudinal bars and transverse reinforcement reaching yielding before concrete reaches its compressive strength) accurately predicts the interaction diagrams of columns used in this study. The failure modes of the columns, depending on the cross-sectional parameters such as reinforcement ratios, concrete strength, and the applied axial load ratio, must be carefully considered while deriving the interaction diagrams for columns with different sectional details using the semi-empirical approach considered in this study. FURTHER RESEARCH The shape of a cross section influences the shear flow zone thickness of an RC member under combined loading. In addition, more accurate analytical models must be developed to predict hysteretic behavior under combined loading 326

including torsion. Also, further experimental research at various T/M for a wide range of cross-sectional parameters would provide valuable information on the effect of warping and its significance for the torsion and flexural moment interaction diagrams. Research on the behavior of columns under combined loading with different axial loads is very limited and hence is not clearly understood yet. Typically, building columns have higher axial loads compared to bridge columns. Hence, the results from this study are limited only to the columns with low axial compression loads and should not be generalized to building columns with higher axial loads. Greater axial compression loads would inhibit the diagonal cracking under combined loading including torsion and may change the failure mode. Also, the axial tension loads would enhance the cracking behavior and limit the diagonal compression of the columns. More test results from future research work should clarify the effect of varying axial loads on the behavior of columns under combined loading including torsion. CONCLUSIONS This work conducted an experimental study of the effect of combined cyclic flexure and torsion on the behavior of circular and square RC columns with low axial compression. Hence, the conclusions from this study are limited only to the columns with low axial compression loads. Based on the test results presented herein, the following conclusions can be drawn: 1. The failure of the circular and square columns under pure torsion was caused by significant diagonal shear cracking, leading to the formation of a torsional plastic hinge at the middle-height of the column. The concrete cover spalled along the full height of the column. For circular columns, dowel action of longitudinal bars contributed significantly to the load resistance at higher cycles of loading under pure torsion. 2. The existence of torsion altered the patterns of damage to RC columns under combined loading. Due to high shear stresses from shear force and torsional moment under combined loading, the inclined crack grew significantly, resulting in early spalling of concrete cover even before the point of ultimate shear capacity. ACI Structural Journal/May-June 2012

3. The square and octagonal transverse reinforcement for square columns provided adequate confinement to the core concrete, as did the spiral reinforcement for circular columns. This reinforcement ensured that the square column under flexure and shear obtained nearly the same strength as circular columns. However, its influence on the confinement of concrete core under combined loading requires further investigation. 4. The ultimate lateral load and displacement capacity of the columns degraded with increasing levels of torsion. Similarly, the decrease of T/M resulted in the degradation of the torsional moment and ultimate twist capacity. 5. The locking and unlocking effect of spiral reinforcement significantly affected the failure modes of circular columns under combined torsional and bending moments. However, there was no locking and unlocking effect on square columns due to the symmetric configuration of transverse reinforcement. 6. The analytical predictions of the columns under combined loading considered in this study for flexure and pure torsion were in good agreement with the experimental results. The interaction curves predicted by semi-empirical equations were in good agreement for the columns considered in this study. However, the failure modes of the columns depending on the cross-sectional parameters, such as reinforcement ratios, concrete strength, and the applied axial load ratio, must be carefully considered while deriving the interaction diagrams for columns with different sectional details. ACKNOWLEDGMENTS

This study was funded by the NEES-NSF under Grant No. NEESR-SG: 530737, as well as by the National University Transportation Center and the Intelligent Systems Center of the Missouri University of Science and Technology. Their financial support is gratefully acknowledged.

REFERENCES

Ang, B. G.; Priestley, M. J. N.; and Paulay, T., 1989, “Seismic Shear Strength of Circular Reinforced Concrete Columns,” ACI Structural Journal, V. 86, No. 1, Jan.-Feb., pp. 45-59. Belarbi, A.; Prakash, S. S.; and Silva, P., 2008, “Flexure-Shear-Torsion Interaction of RC Bridge Columns,” Paper No. 6, Proceedings of the Concrete Bridge Conference, St. Louis, MO, 17 pp. Belarbi, A.; Suriya Prakash, S.; and Silva, P. F., 2010, “Incorporation of Decoupled Damage Index Models in the Performance-Based Evaluation of RC Circular and Square Bridge Columns under Combined Loadings,” Structural Concrete in Performance-Based Seismic Design of Bridges, SP-271, P. F. Silva and R. Valluvan, eds., American Concrete Institute, Farmington Hills, MI, pp. 79-102. (CD-ROM)

ACI Structural Journal/May-June 2012

Bentz, E. C., 2000, “Sectional Analysis of Reinforced Concrete Members,” PhD thesis, Department of Civil Engineering, University of Toronto, Toronto, ON, Canada, 198 pp. Collins, M. P.; Bentz, E. C.; and Kim, Y. J., 2000, “Shear Strength of Circular Reinforced Concrete Columns,” S. M. Uzumeri Symposium: Behavior and Design of Concrete Structures for Seismic Performance, SP-197, S. A. Sheikh and O. Bayrak, eds., American Concrete Institute, Farmington Hills, MI, pp. 45-86. Elfgren, L.; Karlsson, I.; and Losberg, A., 1974, “Torsion-Bending-Shear Interaction for Concrete Beams,” Journal of Structural Engineering, ASCE, V. 100, pp. 1657-1676. Greene, G. G., and Belarbi, A., 2009, “Model for RC Members under Torsion, Bending, and Shear,” Journal of Engineering Mechanics, ASCE, V. 135, No. 9, Parts I and II. Hsu, T. T. C., 1993, Unified Theory of Reinforced Concrete, CRC Press, Boca Raton, FL, 313 pp. Kent, D. C., 1969, “Inelastic Behavior of Reinforced Concrete Members with Cyclic Loading,” PhD dissertation, University of Canterbury, Christchurch, New Zealand, 492 pp. Lehman, D. E.; Calderone, A. J.; and Moehle, J. P., 1998, “Behavior and Design of Slender Columns Subjected to Lateral Loading,” Proceedings of Sixth U.S. National Conference on Earthquake Engineering, EERI, Oakland, CA, 316 pp. Mander, J. B.; Priestley, M. J. N.; and Park, R., 1988, “Observed StressStrain Behavior for Confined Concrete,” Journal of Structural Engineering, ASCE, V. 114, No. 8, pp. 1827-1849. Otsuka, H.; Takeshita, E.; Yabuki, W.; Wang, Y.; Yoshimura, T.; and Tsunomoto, M., 2004, “Study on the Seismic Performance of Reinforced Concrete Columns Subjected to Torsional Moment, Bending Moment and Axial Force,” 13th World Conference on Earthquake Engineering, Paper No. 393, Vancouver, BC, Canada, 10 pp. Park, Y. J., and Ang, A. H. S., 1985, “Mechanistic Seismic Damage Model for Reinforced Concrete,” Journal of Structural Engineering, ASCE, V. 111, pp. 722-739. Prakash, S. S., 2009, “Seismic Behavior of Circular RC Bridge Columns under Combined Loading Including Torsion,” PhD thesis, Department of Civil Engineering, Missouri University of Science and Technology, Rolla, MO, 334 pp. Prakash, S. S., and Belarbi, A., 2009, “Bending-Shear-Torsion Interaction Features of RC Circular Bridge Columns—An Experimental Study,” Thomas T.C. Hsu Symposium on Shear and Torsion in Concrete Structures, SP-265, A. Belarbi, Y.-L. Mo, and A. S. Ayoub, eds., American Concrete Institute, Farmington Hills, MI, pp. 427-454. Priestley, M. J. N., and Benzoni, G., 1996, “Seismic Performance of Circular Columns with Low Longitudinal Reinforcement Ratios,” ACI Structural Journal, V. 93, No. 4, July-Aug., pp. 474-485. Rahal, K. N., and Collins, M. P., 1995, “Analysis of Sections Subjected to Combined Shear and Torsion—A Theoretical Model,” ACI Structural Journal, V. 92, No. 4, July-Aug., pp. 459-469. Tirasit, P., and Kawashima, K., 2007, “Seismic Performance of Square Reinforced Concrete Columns under Combined Cyclic Flexural and Torsional Loadings,” Journal of Earthquake Engineering, ASCE, V. 11, pp. 425-452. Vecchio, F. J., and Collins, M. P., 1986, “The Modified CompressionField Theory for Reinforced Concrete Elements Subjected to Shear,” ACI JOURNAL, Proceedings V. 83, No. 2, Mar.-Apr., pp. 219-231.

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