Published online 26 July 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.512
Cyclic tests of post-tensioned precast CFT segmental bridge
columns with unbonded strands
Chung-Che Chou
∗;†;‡and Yu-Chih Chen
§Department of Civil Engineering; National Chiao Tung University; 1001 Ta-hsueh Rd.; Hsinchu 300; Taiwan
SUMMARY
Two ungrouted post-tensioned, precast concrete-lled tube (CFT) segmental bridge columns were tested under lateral cyclic loading to evaluate the seismic performance of the column details. The specimens included a load stub, four equal-height circular CFT segments, and a footing. Strands were placed through the column and post-tensioned to provide a precompression of the column against the footing. One specimen also contained energy-dissipating devices at the base to increase the hysteretic energy. The test results showed that (1) both specimens could develop the maximum exural strength at the design drift and achieve 6% drift with small strength degradation and residual displacement, (2) the proposed energy-dissipating device could increase energy dissipation in the hysteresis loops, and (3) the CFT segmental columns rotated not only about the base but also about the interface above the bottom segment. This study proposed and veried a method to estimate the experimental
exural displacement using two plastic hinges in the segmental column. Copyright ? 2005 John
Wiley & Sons, Ltd.
KEY WORDS: precast CFT segmental bridge column; unbonded strand; two plastic hinges
INTRODUCTION
Many studies [1–4] are available on the cyclic response of a concrete-lled tube (CFT) column, which consists of a steel tube lled with concrete. The tube not only raises the compression strength and ultimate strain of conned concrete but also provides the column’s exural strength. A bulge forms at the compression face of the plastic hinge region near the column base after the steel reaches yield strain, and increases with the load or drift until
∗Correspondence to: Chung-Che Chou, Department of Civil Engineering, National Chiao Tung University, 1001
Ta-hsueh Rd., Hsinchu 300, Taiwan.
†E-mail: [email protected] ‡Assistant Professor.
§Graduate Student Researcher.
Contract=grant sponsor: Continental Engineering Corporation Contract=grant sponsor: Dywidag Systems International
tensile fracture of the tube occurs. Both energy dissipation and ductility are increased because of the connement from the steel tube, but loading the column to high drift produces large residual deformation.
To decrease the residual displacement of the column and avoid cast-in-place concrete con-struction, the application of precast segmental technology to the column may be a possible solution [5]. Hews and Priestley [6] investigated the cyclic behaviour of four unbonded pre-cast concrete segmental columns under dierent aspect ratios, initial post-tensioning forces, and tube thicknesses. The bottom segment was encased in a steel tube and the upper segments were reinforced with standard spiral reinforcement. All specimens behaved in a ductile man-ner with low residual displacement, but severe spalling of concrete directly above the bottom segment except in the base was unexpected. The test results showed that the columns rotated about the base and the top interface of the bottom segment, but did not clarify the exural displacement of the column due to rotations at the two locations.
OBJECTIVE
The goals of this study were: (1) to investigate experimentally the behaviour of two ungrouted post-tensioned, precast CFT segmental bridge columns under lateral cyclic loading, (2) to examine whether the hysteretic energy dissipation of the column increased with the proposed device equipped at the base, and (3) to develop a method for estimating the experimental, exural displacement of the segmental column caused by rotations at the base and the interface above the bottom segment, respectively.
CFT SEGMENTAL COLUMN SPECIMEN DESIGN
Two full-scale post-tensioned CFT segmental bridge columns with a height of 14:7 m, a dia-meter of 3 m, and a supported dead weight of 22 MN (equal to 0:1fcAc) were designed using the displacement-based approach [7]. The 28-day concrete strength,fc, was specied as 35 MPa; the parameter Ac was the total concrete area. The column with an assumed eective damping value of 10% [6], of which half was assumed for hysteretic and elastic, was designed for 3.5% drift. The design ground acceleration based on soil type C [8] was specied as 0:7g. To conduct a cyclic test of the column in the laboratory, the specimen was one-sixth of the prototype, with a corresponding design lateral force and moment, Md, at the base of 194 kN and 475 kN-m [9], respectively.
Based on the research of Hewes and Priestley [6], the lateral force–lateral displacement relationship of a post-tensioned concrete segmental column exhibited a negative post-elastic stiness in an early stage when the maximum axial force in the column exceeded 0:4fcAc. With this axial load ratio, limited in the column to avoid such behaviour, and the maximum strand force, conservatively limited to 0:5fpuAst, the area of the strands, Ast, was calculated as follows:
Ast=
0:4fcAc 0:5fpu
wherefpu(= 1860 MPa) is the ultimate tensile strength of the strand. Nineteen 15-mm diameter seven wire, uncoated, low-relaxation ASTM A416 Grade 270 strands were placed at the mid-depth of the cross-section.
The bottom segment was encased in an A36 steel tube with a wall thickness of 5mm, which violates AISC’s [10] required minimum thickness. The thickness in this study was specied to limit the extreme bre concrete compression strain, as calculated using the conned concrete model [11], to less than 0:5cu at the design drift and to the ultimate strain, cu, at 6% drift. The other segments were encased in a 3-mm thick A36 steel tube. The steel tube did not extend to the full height of the segment, but terminated 25 mm above the face of the concrete to prevent contact between the steel tubes or between the bottom tube and a footing when the column was subjected to lateral loading. No segment used any transverse or longitudinal reinforcement. With the required lateral force at the design drift, the strand area from Equation (1), and the strain limits, the initial post-tensioning force calculated based on an iterative sectional analysis [6] was 2494 kN, equivalent to 44% of the ultimate strand strength.
The bottom segment height was specied to minimize the gap opening at the top interface of the bottom segment in combined axial and exural loadings. The moment distribution along the column height for the design drift is shown in Figure 1, where M2; 1 and M2; 2 are the moment capacities when the neutral axis position is located at the extreme bre and cross-section centroidal axis above the bottom segment, respectively. The intersection of M2; 1 to the moment distribution gives the height of the bottom segment as 1549 mm; the top interface of the bottom segment does not open in lateral loading. The intersection of M2; 2 to the moment distribution gives the height of the bottom segment as 415 mm; the top interface of the bottom segment opens after the design drift. The moment capacity, M0:004, indicates that the extreme bre concrete compression strain above the bottom segment has reached 0.004. The intersection of M0:004 to the moment distribution gives the height of the bottom segment as 292 mm. As shown in Figure 2, each test specimen was composed of four CFT segments, each of which had an outside diameter (OD) of 500 mm and a height of 500 mm plus cementitious and epoxy layers on the segment interface for leveling.
Specimen 2, as shown in Figure 2(b), included external energy-dissipating devices at the base to increase not only the energy dissipation but also the moment resistance. Figure 2(c)
0 100 200 300 400 500 Moment (kN-m) 0 500 1000 1500 2000 2500
Height above Footing (mm)
0.0 0.2 0.4 0.6 0.8 1.0
Normalized Column Height
M2,2 M0.004
Moment Distribution (3.5% Drift) M2,1
(a) (b)
(c)
Figure 2. Specimen elevation (dimensions in millimeters): (a) Specimen 1; (b) Specimen 2; and (c) close-up of energy-dissipating device.
presents a close-up of an energy-dissipating device, which consisted of a 5-mm thick A36 Reduced Steel Plate (RSP) and stieners at both ends. The smallest sectional area, ARSP, of the RSP was determined in order to provide 10% design moment, Md, as follows:
ARSP= 0:1Md Le × 1 sin 64◦ × 1 Fy (2)
where Fy(= 248 MPa) is the specied yield strength of A36 steel and Le(= 860 mm) is the distance between the two devices. Stieners were provided at both ends of the RSP to decrease the unbraced length so that according to AISC [10, Chapter E], the buckling strength was calculated to be 0:97 Fy with the eective length factor of 0.5. Shear studs were placed inside the tube to transfer force in the RSP to the concrete. No shear keys between the segment interface were provided, since the substantial axial force produced by unbonded strands created a greater friction force (554 kN) than applied lateral force (194 kN). The friction coecient was assumed to be 0.2 in computing the friction force.
EXPERIMENTAL PROGRAM Construction and test procedure
First, the PVC pipe for the tendon duct was positioned at the centre of each tube, and the strand anchorage was positioned at the centre of the load stub and footing reinforcement cages. Then, the column segments, load stubs, and footings were cast with concrete, cured, and delivered to the laboratory to be assembled by passing strands through the tendon duct and the anchorage (see Figure 3). The specimens were post-tensioned with a hydraulic stressing
Figure 3. Specimen assembly sequence: (a) rst segment; (b) second segment; (c) third segment; and (d) fourth segment.
ram, which included a pressure transducer and a calibration chart to compute the hydraulic ram load. Four strain gauges mounted on strands were connected to a data acquisition system with real-time display to monitor axial strains. The total initial post-tensioning force after losses was 2365 and 2462 kN for Specimens 1 and 2, corresponding to 95 and 99% of the design force, respectively.
A 500-kN actuator was placed at the load stub (see Figure 4), and the specimen was then tested statically with a pre-dened displacement history, consisting of one drift cycle with amplitudes of 0.1, 0.15, 0.2 and 0.3%, followed by three drift cycles with amplitudes of 0.4, 0.6, 0.9, 1.5, 2, 3, 4, 5 and 6%. The concrete compressive strengths at 28 days and on the day of testing are listed in Table I.
4 3 2 1 500 kN Actuator Tie-down 3300 Curvature Instrumentation S Footing 850 2030 420 19-15 mm Grade 270 low-relaxation prestressing strands Segment 3340 Load Stub N
Figure 4. Test setup.
Table I. Concrete compressive strength.
Design strength 28 days D.O.T.∗
Specimen no. (MPa) (MPa) (MPa)
1 35 46 53
2 35 46 54
Results of experiments
Flexural cracks of Specimen 1 at the base and the interface between segments 1 and 2 were noted before 0.6% drift, and continued to open and extend with increasing drift. The cover concrete spalled on the compression face of the base and of the interface between segments 1 and 2 at drifts of 2 and 3%, respectively. Figure 5 presents a photograph of segments 1 and 2 on the tension and compression faces at 4% drift, showing a 13-mm crack opening on the tension face at the base, larger than the 3-mm opening at the interface between segments 1 and 2. Figure 5(d) shows concrete crushing at the base, resulting in strength degradation by 4% at the maximum drift of 6% (see Figure 6(a)). The residual displacement was 10 mm, 7% of the maximum displacement, after the specimen completed a 6% drift cycle.
For Specimen 2, with the energy-dissipating devices at the base, a exural crack at the interface between segments 1 and 2 was observed at the same drift level as for Specimen 1. A exural crack at the base was noticed at a larger drift of 0.6%, corresponding to the buckling of an RSP in one energy-dissipating device during compression. The buckled RSP could be pulled straight into the strain hardening range in tension loading to provide energy dissipation; both RSPs fractured during the rst push and pull loading cycles to 4% drift, reducing the
Figure 5. Specimen 1 at 4% drift: (a) opening between segments 1 and 2; (b) opening at base; (c) spalling between segments 1 and 2; and (d) crushing at base.
-150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 L atera l F o rc e (kN ) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%)
Pull Direction Push Direction
-150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 Lateral Displacement (mm) -250 -200 -150 -100 -50 0 50 100 150 200 250 L at er al F o rce ( k N ) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%)
Pull Direction Push Direction
(a)
(b)
Figure 6. Lateral force versus lateral displacement response: (a) Specimen 1; and (b) Specimen 2.
exural strength (see Figure 6(b)). Figure 7 shows a photograph of segments 1 and 2 on the tension and compression faces at 4% drift, which exhibits less opening and damage at the base than seen in Specimen 1. The test was stopped after completing three cycles of 6% drift with a residual displacement of 15 mm, 10% of the maximum displacement.
Hysteretic energy dissipation of Specimen 1 was associated with the plastic straining of concrete in compression, but that of Specimen 2 was associated with the plastic straining of an RSP in tension and of concrete in compression. Figure 8(a) shows that the hysteretic energy dissipation of Specimen 2 is about 50% higher than that of Specimen 1 before 4% drift. The percentage increase starts to decrease after fracture of the RSP, which corresponds to the variation of the equivalent viscous damping [7] as shown in Figure 8(b). Before fracture of RSPs, the computed equivalent viscous damping of Specimen 2 is 9%, higher than 6.5% of Specimen 1. The increase in equivalent viscous damping is not signicant
Figure 7. Specimen 2 at 4% drift: (a) opening between segments 1 and 2; (b) opening at base; (c) spalling between segments 1 and 2; and (d) crushing at base.
because it reduces the maximum displacement of a single column bent bridge by 8% based on Eurocode 8 [12] 14% 11:5% = 5%[7=(2 + 14)]1=2 5%[7=(2 + 6:5)]1=2 = 0:92 (3)
where 14%, 11:5%, and 5% are the displacements for damping levels of 14, 11.5 and 5%, respectively. Note that 5% elastic viscous damping is included in Equation (3).
Strand force was computed from the strain gauge readings and the strand area. Figure 9 shows that once the gap opens, the strand force starts to increase with increasing drift, reaching 55% of the ultimate strand strength at 6% drift. A loss of the initial post-tensioning force, which was caused by concrete crushing at the base, was computed to be about 10% after the specimen completed 6% drift cycles.
Figure 10 shows the distribution of curvature along the column height for both the push and pull directions. Because the gap opening at the base exceeded measuring range of the displacement transducers after 5% drift, the curvatures at 6% drift were not obtained.
0 1 2 3 4 5 6 Drift(%) 0 1 2 3 4 5 6 Drift(%) 0 20 40 60 80 100 120 H y stereti c E n ergy (kN -m ) Specimen 1 Specimen 2 0 1 2 3 4 5 6 7 8 9 10 E q uival en t Visco u s Dam p in g ( % ) Specimen 1 Specimen 2 (a) (b)
Figure 8. Hysteretic energy and equivalent viscous damping versus drift relationships: (a) hysteretic energy; and (b) equivalent viscous damping.
The experimental curvatures were calculated as = t−c
DL (4)
where t is the elongation of a displacement transducer on the tension side of the segment, c is the shortening of a displacement transducer on the compression side of the segment at the same height level, D is the distance between these two displacement transducers, and L is the gauge length. The gap opening at the base is bigger than that at the interface between segments 1 and 2, leading to the curvature of Specimen 1 at the base larger than that at the interface for all drift levels (see Figure 10(a)). Additional lateral restraining to segment 1 of Specimen 2, provided by the energy-dissipating device, reduces rotation of segment 1. Thus, the curvature of Specimen 2 (see Figure 10(b)) at the base is smaller than that at the interface for a drift less than 4%. After the fracturing of RSPs, the gap opening at the interface reduces in size with increasing drift (see Figure 11), producing a smaller curvature than seen at 4% drift.
2200 2400 2600 2800 3000 Strand Force (kN) Specimen 1 Specimen 2 0 1 2 3 4 5 6 Drift(%)
Figure 9. Strand force versus drift relationship.
-0.0002 -0.0001 0 0.0001 0.0002 0 100 200 300 400 500 600 700 800 H e ig h t a b o v e F o o ting ( mm) H e ig ht a b ove F o oti n g ( m m ) 0.6 % 0.9 % 2 % 3 % 4 % 5 % Push Direction Pull Direction -0.0002 -0.0001 0 0.0001 0.0002 Curvature (mm-1) Curvature (mm-1) 0 100 200 300 400 500 600 700 800 0.6 % 0.9 % 2 % 3 % 4 % 5 % Push Direction Pull Direction Footing L 3 L 1 L 7 L 5 L 4 L 2 L 6 L 8 Footing L 3 L 1 L 7 L 5 L 4 L 2 L 6 L 8 (a) (b)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) 0 5 10 15 20 Gap Ope n in g ( m m ) Base Interface between Segments 1 and 2 Specimen 1 Specimen 2
Figure 11. Gap opening versus drift relationship.
EVALUATION OF SEGMENTAL COLUMN FLEXURAL DISPLACEMENT Hewes and Priestley [6] attributed large non-linear displacement of the segmental column to a rigid rotation of the entire column about the column base with a plastic hinge, which has a length equal to half the section diameter. This study adopted their concept to calculate the exural displacements of each specimen with curvatures at the base, which were deter-mined by linearly extrapolating the experimental curvatures along the segment 1 height. The computed displacements were divided by the corresponding imposed displacement to obtain the contribution as shown in Figure 12(a). Each drift has two bars; the rst represents the displacement ratios of Specimen 1, and the second represents those of Specimen 2. The exper-imental displacement of Specimen 1 is overestimated due to a xed plastic hinge length used for all drifts. The predicted displacement is smaller than the imposed displacement for Spec-imen 2, since the displacement contributed from rotation at the interface between segments 1 and 2 is not considered in this approach.
Figure 13 shows a schematic column deformation at moderate to high drifts. The column rotates not only about the base but also about the interface between segments 1 and 2; in other words, a plastic hinge is formed on each of these two locations. A method to quantify the exural displacement caused by the two hinges is needed.
Because a clear deviation from the linear lateral force–lateral displacement response is not noted until the crack has propagated to the centroidal axis of the column (called ‘rst yield’), the exural displacement, f, is estimated by
f = 13bH12 (5)
where b is the curvature at the base assuming a linear distribution in the plastic hinge region in segment 1 (see Figure 14), and H1 is the column height measured to the base. The experimental exural displacement, f, is then expressed as
0.0 0.2 0.4 0.6 0.8 1.0 1.2 D is p lacemen t R atio Drift (%) 0.6 0.9 1.5 2 3 5 Drift (%) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Disp lacemen t R atio 0.6 0.9 1.5 2 3 4 5
Hinge above Bottom Segment Hinge at Base;
Elastic Component; (a)
(b)
Figure 12. Distribution of lateral displacement component: (a) one plastic hinge; and (b) two plastic hinges.
where e is the elastic displacement calculated as
e= 1 3 y1× M1 M y1 ×H2 1 (7)
where y1 is the theoretical ‘rst yield’ curvature at the base section, corresponding to the neutral axis position at the centroidal axis of the section; My1 is the theoretical ‘rst yield’ moment at the base; and M1 is the computed moment at the base.
The plastic displacement p1, resulting from rigidly rotating the entire column about the base, is expressed as p1= b−y1× M1 M y1 ×Lp1×H1 (8)
H1 F F P+Fs+∆Fs P+Fs g1 g2 H2 (a) (b)
Figure 13. Schematic column deformation: (a) elastic stage; and (b) inelastic stage.
-0.0002 -0.0001 0 0.0001 0.0002 Curvature (mm-1) 0 100 200 300 400 500 600 700 800 H e igh t abo v e F o o ting ( mm) y1 y2 b Lpr2b Lpr1t Lpr1b 2 Footing L 3 L 1 L 7 L 5 L 4 L 2 L 6 L 8
Figure 14. Plastic hinge region in segments 1 and 2.
where Lp1 is the plastic hinge length in segment 1. The column above segment 1 further rotates about the interface between segments 1 and 2, resulting in an additional plastic dis-placement p2 p2= 2−y2× M2 M y2 ×Lp2×H2 (9)
where 2 is the experimental curvature at the interface between segments 1 and 2, calculated from measurements made by a pair of the displacement transducersL5 andL6 (see Figure 14);
position at the centroidal axis of the section; My2 is the theoretical ‘rst yield’ moment at the interface; M2 is the computed moment at the interface; H2 is the column height measured to the interface, and Lp2 is the plastic hinge length in segment 2.
Two unknowns, the plastic hinge lengthsLp1 andLp2 in Equations (8) and (9), remain to be determined to calculate the plastic exural displacements p1 and p2. Hines et al. [13] have shown that a plastic hinge’s length is approximately half the plastic hinge region, which is dened as the region where the experimental curvature is larger than the ideal yield curvature. As shown in Figure 14, Lpr1b and Lpr1t are the plastic hinge region in the bottom and top parts of segment 1, and Lpr2b is the plastic hinge region in the bottom part of segment 2. The ideal yield curvatures for segments 1 and 2 are identied as y1 and y2, respectively. Relationships of the plastic hinge region versus drift are shown in Figure 15, in which the plastic hinge region stabilizes after a drift of 2% for two segments. The plastic hinge lengths Lp1 and Lp2 for segments 1 and 2, respectively, are calculated as
Lp1=12(Lpr1b+Lpr1t) (10) Lp2=12(Lpr2b) (11) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) 0 100 200 300 400 500 600 P la st ic H inge Region (m m ) Lpr1b Lpr1t Lpr2b -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) 0 100 200 300 400 500 600 P la st ic H inge Region (m m ) Lpr1b Lpr1t Lpr2b Footing Lpr1b pr1t L pr2b L Footing Lpr1b pr1t L pr2b L (a) (b)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Drift (%) 0 100 200 300 400 500 P la st ic H inge L ength (m m ) 0.0 0.2 0.4 0.6 0.8 1.0 N o rm alized D iam eter LP1 LP2 Specimen 1 Specimen 2
Figure 16. Plastic hinge length versus drift relationships.
The plastic hinge length increases with drift and approximates to half the section diameter in segment 1 and one-fth the section diameter in segment 2 (see Figure 16).
Figure 12(b) shows the ratio of the computed exural displacement e, p1, and p2 to the imposed displacement at selected drifts. The exural displacement caused by the plastic hinge above the bottom segment increases with drift and is more signicant in Specimen 2 than in Specimen 1, since the energy-dissipating devices in Specimen 2 reduces rotation of the bottom segment.
CONCLUSIONS
To avoid cast-in-place concrete construction and reduce the residual displacement of the col-umn, two ungrouted post-tensioned, precast CFT segmental bridge columns were tested under cyclic loading to evaluate the seismic behaviour of the column details. Energy-dissipating devices were placed at a specimen’s base (Figure 2) to increase the energy dissipation of the hysteretic response in the unbonded post-tensioned system. The authors have only investigated the behaviour of the two specimens with a xed axial force ratio, post-tensioned strand force, and number of segments so that the following conclusions are drawn for the study:
(1) All the precast concrete segments were encased in the steel tube, minimizing concrete spalling above the bottom segment and concrete crushing at the base at the design drift of 3.5%. Both specimens could develop the maximum exural strength about the design drift and reach 6% drift with small strength degradation and residual displacement (Figure 6). No fracturing of strands or tube was noted.
(2) The hysteretic energy dissipation per cycle was converted to its equivalent viscous damping, which was 6.5% for Specimen 1 but was 9% for Specimen 2 due to the proposed energy-dissipating device.
(3) The column rotated not only about the base but also about the interface between segments 1 and 2, resulting in large curvatures concentrated at these two locations (Figure 10). A plastic hinge region, dened in a region where curvatures were larger
than the ideal yield curvature (Figure 14), allowed for the calculation of the plas-tic hinge length in the segments (Figure 16). The gure shows that Specimen 2 had a shorter plastic hinge length in segment 1 but a longer plastic hinge length in seg-ment 2 than seen in Specimen 1 because the energy-dissipating devices provided lateral restraining to segment 1 of Specimen 2, resulting in less rotation of segment 1. After the energy-dissipating devices fractured, the plastic hinge lengths for these two speci-mens were close: approximately 0.5 times the section diameter in segment 1 and 0.2 times that in segment 2.
(4) A method to evaluate the experimental exural displacement of the segmental column was developed using two instead of one plastic hinge in the column. Although the majority of plastic exural displacement was contributed by the plastic hinge at the base, for Specimen 2 stiened at the base the eect of second plastic hinge above the bottom segment needed to be included to predict the exural displacement of the column (Figure 12).
ACKNOWLEDGEMENTS
The support of this research project from the Continental Engineering Corporation and Dywidag Systems International in Taiwan is greatly appreciated. The writers express their gratitude to Prof. K. C. Tsai and Dr J. T. Hewes for providing technical advices throughout this program.
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