Post-earthquake recoverability of existing RC bridge piers retrofitted with FRP composites

Construction and Building Materials 24 (2010) 980–998

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Post-earthquake recoverability of existing RC bridge piers retrofitted with FRP composites Mohamed F.M. Fahmy a,*, Zhishen Wu a,1, Gang Wu b a b

Dept. of Urban & Civil Eng., Ibaraki University, Japan International Institute for Urban Systems Engineering, Southeast Univ., Nanjing 210096, China

a r t i c l e

i n f o

Article history: Received 16 April 2009 Received in revised form 3 November 2009 Accepted 18 November 2009 Available online 21 December 2009 Keywords: Seismic Bridges RC columns Recoverability Secondary stiffness Residual deformation Fiber-reinforced polymers Design

a b s t r a c t The novel concept of this paper is to investigate the required recoverability of existing important reinforced concrete (RC) bridges retrofitted with fiber-reinforced polymers (FRP) to restore their original functions after a moderate or strong earthquake. Hence, this paper presents an up-to-date literature search on the inelastic performance of 109 FRP-retrofitted columns with lap-splice deficiency, flexural deficiency, or shear deficiency. The study is conducted in the following steps: using post-yield stiffness as a seismic index, the effectiveness of FRP jackets in enhancing the inelastic stage performance of non-ductile reinforced concrete columns is scrutinized for the available database; the performance of columns which successfully achieved post-yield stiffness is categorized in accordance with the required recoverability after an earthquake; and according to the definition of a controllable recoverable structure, the appropriate composite jacket thickness is calculated. In the view of a proposed mechanical model of an FRP–RC damage-controllable structure, 61 columns of the available database exhibited idealized lateral performance with stable post-yield stiffness, or secondary stiffness. Lateral drift at the end of the recoverable state is defined from the hysteretic responses of 39 columns and is visualized as a ratio of column lateral drift by the end of the post-yield stiffness with explicit consideration for the effect of both column cross-section shape and deficiency. Finally, suitable FRP design assumptions and concepts certifying the reality of post-yield stiffness are given. Furthermore, in the light of Seismic Design Specifications of Highway Bridges in Japan, a FRP strengthening design guideline that considers and evaluates structural recoverability is proposed. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction The damages incurred by many concrete bridges under the effect of near-fault ground motions have led to the implementation of several significant improvements to bridge design codes. Recent advances in earthquake engineering favor performance based approaches for the seismic design of new structures and for the assessment and rehabilitation of existing structures located in active seismic zones. In the seismic design of structures, it is important to have a clear vision of the desired seismic performance. Important decision making questions like, ‘‘What is the required performance for the structure during and after an earthquake?” are undoubtedly important. Generally, new seismic design philosophies for bridges recommend that important bridges subject to a near-land-large-scale interplate earthquake or an inland earthquake near the structure should be able to sustain the expected

* Corresponding author. Mobile: +81 80 3274 2057; fax: +81 294 38 5268. E-mail addresses: [email protected] (M.F.M. Fahmy), zswu@mx. ibaraki.ac.jp (Z. Wu), [email protected] (G. Wu). 1 Tel.: +81 294 38 5179; fax: +81 294 38 5268. 0950-0618/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2009.11.020

maximum lateral force in the inelastic stage with limited damages, to ensure quick recoverability. In Japan, a new code called ‘‘Seismic Design Code for Railway Structures” (in Japanese) has been published recently, which reflects recent advances in earthquake engineering. It includes some new ideas for seismic design drawn from lessons learned from the devastating Hyogoken-Nanbu Earthquake of January 17, 1995, [23]. In Fig. 1 the seismic performance of structure is categorized into 3 levels that correspond to the required level of repair after an intense earthquake. These performance levels are defined by the degree of structural recovery necessary after an earthquake. This is an established relationship between the levels of earthquake motion and seismic performance, with two levels of earthquake motion defined in the code. One is the so-called L1 earthquake motion (level I), which has a recurrence probability of a few times during the service life of the structure. The other is the L2 earthquake motion (level II), which is caused by a nearland-large-scale interplate earthquake or an inland earthquake close to the structure. For L1 earthquakes, the structural seismic performance I (SPI) should be satisfied by all the structures designed. For L2 earthquakes, seismic performance II (SPII) should

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

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Fig. 1. Relationship among seismic performance levels and damage levels of member (bridges and viaducts).

be satisfied by the structures with greater importance and seismic performance III (SPIII) by all structures. Furthermore, seismic performance levels are also connected to the state of damage of the members. Since the damage level of a member will strongly influence the structural seismic performance, proper determination of this quality is important. It is appropriate to determinate damage levels by considering the relationship among member properties, damage state, and repair method. To ensure post-earthquake recoverability of the various infrastructure systems, attention has been drawn to the development and implementation of innovative systems and materials in new structures to improve their performance under seismic loads. In the study by Iemura et al. [21], the Unbonded Bar Reinforced Concrete structure is proposed as a high-seismic performance structure. This structure has the stable post-yield stiffness of the load–displacement relationship and it might be a suitable structure for a level II earthquake. Another investigation revealed that the seismic performance of new RC structures might be improved by weakening the bonding between rebar and concrete [32]. To minimize residual displacements in reinforced concrete columns, Sakai et al. [34] reports that incorporating an unbonded prestressing strand at the center of a lightly reinforced concrete cross-section can achieve restoring force characteristics similar to a conventionally designed column upon loading, but with substantially less residual displacement upon unloading. Ikeda et al. [22] proposed a new design concept for concrete piers in which vertical prestressing was introduced only in the critical sections, e.g. the bottom portion of the pier. If the residual deformations are found to be excessive, it was suggested by Christopoulos and Pampanin [8] that the following design decisions are applicable; appropriately changing material properties (e.g. steel with high strain hardening), and changing the reinforcement properties and section design to increase the post-yield stiffness at a section level, since residual deformations are primarily a function of the post-yield stiffness. In Japan, existing RC bridges constructed in earthquake-prone regions before the enforcement of modern seismic design codes are inherently vulnerable to earthquakes. When subject to a strong earthquake, different modes of failure have been noted for bridge columns constructed prior to 1971. In the past decade, an increased interest in the use of advanced nonmetallic materials, i.e. fiber-reinforced polymers (FRP), has been observed. The use of FRP represents an innovative and effective technology for strengthening, retrofitting, and upgrading of existing concrete structures due to their beneficial characteristics [35,44,27]. In view of that, extensive studies have investigated the seismic behavior of col-

umns with square, rectangular, and circular cross-sections wrapped with FRP composites, to test the enhanced ductility of bridge columns under the seismic action. Pseudo dynamic test results revealed that a ductile member may be suddenly destroyed by a significant pulse-like wave before it is able to utilize its ductile behavior to dissipate seismic energy [7]. Moreover, Kawashima [24] evaluated near-field ground motions in the 1948 Fukui earthquake (M7.1) and showed that the predicted response velocity of the 5% damping ratio reached about 7 m/s at period of 1.7 s, i.e., Kobe earthquakes is not necessarily the strongest that hit Japan. Consequently, in addition to the required ductility, a gradual increase of the strength (positive post-yield stiffness) during the inelastic stage is possibly an appropriate fuse to assist in the restoration of the original structure functions after an earthquake. It is apparent that the post-yield stiffness and final permanent deformations should be used as seismic measures for recoverable structures. So, in this study, increasing the post-yield stiffness by additional confinement of the concrete core using FRP is a reasonable option for existing bridges designed before the 1971s, where the required strength in the inelastic stage can be met and the residual deformation would be minimized. Hence, the effectiveness of FRP jackets in enhancing the inelastic stage performance of non-ductile reinforced concrete columns is scrutinized for a large experimental database. Also, residual deformations of columns successfully achieved post-yield stiffness are employed to define the end of the recoverable state based on Seismic Design Specifications of Highway Bridges in Japan. Ultimately, design guideline specifying the appropriate FRP jacketing according to the definition of a controllable recoverable structure is proposed. 2. Seismic behavior of existing RC bridge columns Lap splice failure at the connection between the footing and the column, shear failure, and confinement failure of the flexural plastic hinge region are the failure modes observed in existing reinforced concrete bridge columns under a seismic load/deformation input [35]. These three failure modes are potentially related to poor detail in the longitudinal lap splices, improper transverse confinement, and insufficient shear strength [43,5,19]. For cyclically tested control columns with lap-splice deficiency, significant degradation was observed during cycles between 2dy and 3dy and failure occurred at 3dy (dy is the lateral yield displacement) [43,18,9,14,2]. For circular columns with shear deficiency, Xiao et al. [44] reported that inclined shear cracks became dominant during the loading cycles corresponding to dy to 2dy, also Xiao et al. [44] and Li and Sung [29] showed that significant degradation

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was observed during cycles between 2dy and 3dy and that failure occurred at 3dy for cyclically tested control columns. Haroun and Elsanadedy [17] declared that rectangular as-built columns failed in shear without showing ductile behavior: the column failed at a lateral deformation of 0.8dy. Shear failure is identified as the most dangerous failure mode since it is the most likely to cause the total collapse of existing bridges [44]. For columns with inadequate horizontal confinement, Chai et al. [3] tested large-scale circular column with continuous longitudinal reinforcement. The test results showed no failure till lateral deformation of 5dy, when the compression buckling of longitudinal reinforcement destroyed the integrity of the concrete compression zone. Kawashima et al. [25] tested two large-scale circular columns (A1 and B1) with different tie reinforcement ratio, 0.256% and 0.128%, respectively; and they were designed to fail in flexural. It was noticed in the test that concrete spalled off for 0.15 and 0.22 of the column height in A1 and B1, respectively. Buckling of main bars occurred in specimen A1 at a lateral displacement of 3.5% of the column height (3.5% lateral drift), but buckling of main bars of specimen B1 was at 3.0% drift. Column lateral strength decreased to less than 50% of the maximum at 4% and 3.5% drifts in A1 and B1, respectively. Plastic hinge failures typically occur with some displacement ductility and are limited to shorter regions in the column. Thus, these failures are less destructive and, because of their inelastic flexural deformations, are more desirable than the brittle column shear failures of the entire column [35]. To ensure post-earthquake recoverability of the existing RC bridges, attention should be paid to improve their performance under seismic loads. Thus, there is an urgent need to upgrade existing older RC columns to current seismic design standards in regions with high seismicity. 3. Post-yield stiffness and residual deformation in seismic design Since the strength requirement for the L2 earthquake is much higher than the L1, the existing RC bridge columns that satisfy L1 must be enlarged and/or increased in reinforcement to meet the new requirements. However, if a suitable FRP retrofitting is used effectively to assure the post-yield stiffness, the L2 design criteria may be met without dramatically increasing the column section size or the amount of reinforcement. Moreover, minimum irrecoverable deformation would be in case the structure has positive

Fig. 2. Effect of post-yield stiffness on the residual deformation.

post-yield stiffness. Fig. 2 shows three potential responses of a structure under the action of an earthquake. The key difference between these responses is the inelastic performance, i.e., negative, zero, or positive post-yield stiffness. At the same lateral drift, unloading stiffnesses are parallel in accordance with Takeda model [38], where, the unloading stiffness K is a function of column first stiffness K1 and ductility l, (Eq. (1)). It is evident from Fig. 2 that negative post-yield stiffness results in a large residual displacement response, which in turn is a disadvantage that should be avoided in order to quickly recover the structure. This large residual displacement significantly complicates the repair work after the earthquake [13].

K1 K ¼ pffiffiffiffi

l

ð1Þ

The 1996 Seismic Design Specifications of Highway Bridges in Japan specifies that the residual displacement should not be greater than 1% of the piers height [23], and it provides the following equation for evaluation:

dres ¼ C R ðlR  1Þð1  rÞdy

ð2Þ

where dres is the residual displacement of a pier after earthquake; lR, the response ductility factor of pier; r, the (K2/K1) bilinear factor defined as a ratio between K2 (post-yield stiffness) and K1; CR, the factor depending on the bilinear factor r, and dy is the yield displacement. The equation explicitly verifies that as the r ratio increases, the residual displacement will decrease accordingly, and it can be concluded that the piers with high r values have a higher seismic performance. 4. Idealized load–deformation model of FRP–RC damagecontrollable structures The need for structural systems to withstand large earthquake forces without compromising life-safety and the recent progress of experimental and analytical studies on retrofitting of deficient bridges have brought the challenge of designing a quickly recoverable structure to the research forefront. Here, the authors propose a mechanical model for a damage-controllable structure using FRP. Fig. 3 shows the mechanical model of the proposed structure, where the lateral response proceeds along O–A–B–C–D–E–F. The behavior of a general RC flexural structure whose lateral response is along O–A0 –B0 –C0 –D0 –F0 is also given for comparison. Prior to the cracking of concrete, lines OA and OA0 corresponding to both types

Fig. 3. Idealized load–deformation behavior of proposed damage controlled structures.

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

of structures share similar stiffnesses. The stiffness of the proposed structure, K1, is slightly greater than K1 of the general RC structure after concrete cracking. The most remarkable difference occurs after the yielding of the steel reinforcement: after point C and C0 . For the general RC structure, the deformation increases dramatically almost without any increase in load carrying capability: along line C0 D0 no post-yield stiffness is demonstrated. However, with the proposed approach, the structure can still carry the load even after the steel reinforcement yields and hardening behavior has been exhibited along line CD. The stiffness K2 between points C and D is termed the ‘‘secondary stiffness” in this paper. Due to the existence of secondary stiffness, the dramatic increase in deformation and residual deformation can be effectively controlled after the reinforcement yields, and the load carrying capacity can be further improved. Based on the codes requirements for ductile structures to withstand strong earthquakes, the proposed structure is characterized by the part DE after the hardening zone, where favorable ductility is demonstrated. The ultimate drift (du) corresponding to point F or F0 for the proposed structure and the general RC structure, respectively, is defined for both structures to be at 20% strength decay. The use of 20% strength decay as the failure criterion is consistent with that employed by previous researchers, since it is reasonable to accept some strength decay during seismic response of a structure before it can be considered to have failed [33]. According to the mechanical behavior shown in Fig. 3, the load– deformation of the proposed structure can be divided into four main zones; Zone 1: from point O to B; Zone 2: from point B to D; Zone 3: from point D to E; and Zone 4: after point E. Zone 1 corresponds to a stage of no damage or concrete cracking. Under a small earthquake, the mechanical behavior should be controlled in this zone, and the original function of the structure can be maintained without any repair and displacement of elements. Zone 2 corresponds to the hardening behavior after the yielding of steel reinforcements, where a distinct secondary stiffness is demonstrated and the dramatic deformation can be effectively controlled. Under a medium or strong earthquake, the mechanical behavior of the proposed structure should be within Zone 2. Thus, damage can be effectively controlled by the secondary stiffness. The original function of the structures can be quickly recovered through repairs after a medium or large earthquake. Zone 3 corresponds to ductile behavior after hardening, where favorable ductility is demonstrated under a large earthquake. The proposed structure can be kept in place for a relatively long time without collapse during a large earthquake, though severe damage may occur. The original function of the structures may be recovered through the replacement of some elements. During a severe earthquake, the mechanical behavior may enter Zone 4 with collapse. The proposed mechanical model can satisfy a seismic design philosophy that holds that the structure suffers no damage under a small earthquake, exhibits prompt recoverability under medium earthquake, and does not collapse under a large earthquake.

5. Realizing post-yield stiffness of existing RC bridge columns retrofitted with FRP Since the major goal of this paper is to check the recoverability of FRP-retrofitted columns, the following discussion mainly applies to the inelastic performance of the available database in terms of finding successful FRP-retrofitting for columns having clear postyield stiffness; column inelastic hysteric response is represented here by its skeleton lines. The starting point of the post-yield stiffness is defined to be the point at which the theoretical ideal mo-

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ment capacity Mi of the as-built column is fulfilled, while the end point is that corresponding to the maximum lateral capacity. The theoretical ideal moment capacity is calculated using ACI rectangular stress block for concrete in compression, which has a mean 0 0 , the measured concrete compression strength fco stress of 0.85 fco and steel yield strength fy, and an ultimate concrete compression strain of 0.003 [1]. The maximum lateral capacity is evaluated from the experimental results of the available database. Details, dimensions, and material properties of composite-jacketed columns are detailed in Table 1. 5.1. Seismic performance of FRP retrofitted lap-spliced columns There are considerable research efforts being directed at developing and applying FRP retrofit strategies to upgrade the seismic performance of deficient lap-spliced columns [43,35,5,9,18, 14,2,16]. Two retrofitted circular column were tested by Xiao and Ma [43]. The tested retrofitted circular column C2-RT4 successfully reached the ideal flexural capacity at a drift ratio of 2.08%, at which degradation of column strength started. The increase in FRP layers by one layer engaged the hoop strain to 0.001, and the entirely retrofitted C3-RT5 circular column gained strength over the ideal flexural capacity, which appears to be an ascending straight line till a drift ratio 2.62%, Fig. 4a. Haroun and Elsanadedy [18] tested columns of circular and square cross-sections. For the FRP retrofitted circular columns, FRP jackets for columns CF-R1 and CF-R2 were designed for a jacket strain of 0.004 to give a minimum confinement pressure of 2.0 MPa within the lap-splice zone. Composite jackets for columns CF-R3 to CF-R6 were designed for a hoop strain of 0.001 to give a minimum confinement pressure of 1.0 within the lap-splice zone. The design considered for the retrofitted circular columns CF-R3 to CF-R6 behaved similarly and demonstrated a significant improvement in their cyclic performance with a gradual increase in the lateral capacity over the theoretical flexural strength until a drift ratio 4%, which evidenced the appearance of the secondary stiffness, also columns CF-R4 and CF-R6 were able to maintain their strength constant before strength degradation, Fig. 4b. The two samples CF-R1 and CF-R2 successfully achieved the theoretical strength, but the realized post-yield stiffnesses were smaller than those by the remainder of the columns. The hysteric response of all square jacketed columns (one of these columns was a quasi-circular section with continuous confinement) had a very limited improvement in clamping on the lap-splice region and failed to realize the existence of post-yield stiffness. It has been shown that directly applying the FRP or steel jacket to large rectangular RC columns is ineffective in providing confinement to concrete except at corners of the cross-section [5]. For large columns, the size effect may become more important. In order to improve confinement efficiency of direct carbon FRP (CFRP) jackets, a new retrofit method ‘‘CS retrofit method” (Carbon fibersteel method) is proposed by Chang and Chang [5]. Three rectangular columns, B5L17-C8S10, B6L21-C12S10, and B7L21-C12S5 are retrofitted with the using the new method. The new retrofitting method enabled the large size of rectangular column to come in the ideal lateral strength, and enhanced the post-yield behavior by the gradual increase of the lateral strength, Fig. 4c. Although, columns B6L21-C12S10 and B7L21-C12S5 were tested under the effect of axial loads higher than that of column B5L17-C8S10, the increase of FRP thickness facilitated the upgrading of their hysteretic responses. Where the post-yield stiffnesses were almost identical and the columns demonstrated the ability to maintain their lateral capacities till a drift ratio 6.5%.

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Table 1 Details, dimensions, and material properties of composite-jacketed columns. Axial load (kN)

Main steel

Transverse steel

0 Yield fco (MPa) stress of main steel (MPa)

Yield stress of lateral steel (MPa)

Composite jacket properties Type

tj within plastic hinge zone (mm)

Tensile Tensile strength Modulus (MPa) (GPa)

Specimen No. 2

S

Shear

1800

Single

600  600

–

529

30#6

32.2

400.2

320.2

CFRP

0.03

2774

246.0

Specimen No. 3e

S

Shear

1800

Single

600  600

–

529

30#6

30.7

400.2

320.2

CFRP

0.17

3646

235.0

Specimen No. 4

S

Shear

1800

Single

600  600

–

529

30#6

29.5

400.2

320.2

AFRP 0.03

2260

115.0

Specimen No.5

S

Shear

1800

Single

600  600

–

529

30#6

d = 6 mm/ 400 mm d = 6 mm/ 400 mm d = 6 mm/ 400 mm d = 6 mm/ 400 mm

30.1

400.2

320.2

AFRP 0.28

2500

107.0

a

be

R R

Shear Flexural

2438 3658

Double Single

406  610 489  730

– –

507 1780

#2/127 mm #2/127 mm

34.5 34.5

303.2 303.2

303.2 303.2

CFRP 3.30 CFRP 10.20

1300 1300

124.0 124.0

Ce d

C C

Lap-splice Lap-splice

3658 3658

Single Single

D = 610 D = 610

381 381

1780 1780

22# 6 14 # 8 + 28 #7 26#6 26#6

#2/127 mm #2/127 mm

34.5 34.5

303.2 303.2

303.2 303.2

CFRP 6.12 CFRP 5.10

1300 1300

124.0 124.0

Xiao and Ma [43]

C2-RT4 C3-RT5e C4-RP4

C C C

Lap-splice Lap-splice Lap-splice

2440 2440 2440

Single Single Single

D = 610 D = 610 D = 610

381 381 381

712 712 712

26#6 26#6 26#6

#2/127 mm #2/127 mm #2/127 mm

44.8 44.8 44.8

462.0 462.0 462.0

462.0 462.0 462.0

GFRP 9.60 GFRP 12.80 GFRP 9.60

552 552 552

48.3 48.3 48.3

Xiao et al. [44]

CS-ISJ-RTe

C

Shear

1830

Double

D = 610

–

654

20#6

37.1

303.0

303.0

GFRP 7.62

552

38.0

CS-CSJ-RTe

C

Shear

1830

Double

D = 610

–

654

20#6

d = 6 mm/ 130 mm d = 6 mm/ 130 mm

37.1

303.0

303.0

GFRP 5.08

552

38.0

A2

C

Flexural

1360

Single

D = 400

–

182

12D16

30.0

296.0

296.0

CFRP

0.11

3481

230.0

A3

C

Flexural

1360

Single

D = 400

–

182

12D16

27.5

296.0

296.0

CFRP

0.22

3481

230.0

B2

C

Flexural

1360

Single

D = 400

–

182

12D16

30.0

296.0

296.0

CFRP

0.11

3481

230.0

B3

C

Flexural

1360

Single

D = 400

–

182

12D16

d = 6 mm/ 150 mm d = 6 mm/ 150 mm d = 6 mm/ 300 mm d = 6 mm/ 300 mm

27.5

296.0

296.0

CFRP

0.22

3481

230.0

ST-1NT

C

Flexural

1470

Single

D = 356

–

0 Six 25 M 0.563 Ag fco

#3/300 mm

40.4

493.0

457.0

GFRP 1.25

394a

19.7

C C C C C C C

Flexural Flexural Flexural Flexural Flexural Flexural Flexural

1470 1470 1470 1470 1470 1470 1470

Single Single Single Single Single Single Single

D = 356 D = 356 D = 356 D = 356 D = 356 D = 356 D = 356

– – – – – –

0 0.563 Ag fco 0 0.563 Ag fco 0 0.276 Ag fco 0 0.28 Ag fco 0 0.28 Ag fco 0 0.557 Ag fco 0 0.554 Ag fco

Six Six Six Six Six Six Six

#3/300 mm #3/300 mm #3/300 mm #3/300 mm #3/300 mm #3/160 mm #3/160 mm

40.4 40.4 44.8 40.8 41.6 42.8 43.9

493.0 493.0 493.0 493.0 493.0 493.0 493.0

457.0 457.0 457.0 457.0 457.0 457.0 457.0

GFRP CFRP CFRP GFRP CFRP GFRP CFRP

394a 937a 1874a 394a 937a 394a 937a

19.7 72.5 145 19.7 72.5 19.7 72.5

C

Lap-splice

2440

Single

D = 610

381

712

20#6

461.6

344.8

GFRP 12.70

551

48.2

CF-R8

C

Lap-splice

2440

Single

D = 610

381

712

20#6

44.8

461.6

344.8

GFRP 15.90

551

48.2

CF-R9

f

C

Lap-splice

2440

Single

D = 610

381

645

20#6

31.0

303.2

303.5

GFRP 12.70

689

37.9

C

Lap-splice

2440

Single

D = 610

381

645

20#6

31.0

303.2

303.5

GFRP 12.70

689

37.9

C

Shear

1830

Double

D = 610

–

1779

10#6

d = 6 mm/ 127 mm d = 6 mm/ 127 mm d = 6 mm/ 127 mm d = 6 mm/ 127 mm d = 6 mm/ 127 mm

44.8

f

37.1

292.8

403. 5

CFRP

1392

111.6

Masukawa et al. [30]

Seible et al. [35]

Kawashima et al. [25]

Sheikh and Yau [37]

Sample

ST-2NT ST-3NT ST-4NT ST-5NT ST-6NT R-1NT R-2NT Elsanadedy [9]

f f f f

CF-R7

CF-R10 CS-R5

f

f

25 M 25 M 25 M 25 M 25 M 25 M 25 M

2.50 1.00 0.50 1.25 1.00 2.50 1.00

4.30

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

Cross- Deficiency Column Bending Column Lapsection height dimensions splice (mm) (mm) length (mm)

Author

CS-P2 CS-P3

f

Shear Shear

3660 2440

Single Double

D = 1829 D = 610

– –

0.0 592

24#14 26#6

ASC-2NS

S

Flexural

1473

Single

305  305

–

0 0.38 Ag fco

ASC-3NS ASC-4NS ASC-5NS f ASC-6NS ASCR-7NS ASCR-8NS

S S S S S S

Flexural Flexural Flexural Flexural Flexural Flexural

1473 1473 1473 1473 1473 1473

Single Single Single Single Single Single

305  305 305  305 305  305 305  305 305  305 305  305

– – – – – –

0.65 0.65 0.65 0.38 0.38 0.62

Ag Ag Ag Ag Ag Ag

Chang et al. [6]

FRL-100 SFRL-100e FCL100e FCL100-1e FCL100-2e FR1e FR2 FRSe FCSe FCS-1e FCS-2e

R R C C C R R R C C C

Lap-splice Lap-splice Lap-splice Lap-splice Lap-splice Flexural Flexural Shear Shear Shear Shear

3250 3250 325 3250 3250 3250 3250 1750 1750 1750 1750

Single Single Single Single Single Single Single Single Single Single Single

600  750 600  750 D = 760 D = 760 D = 760 600  750 600  750 600  750 D = 760 D = 760 D = 760

760 760 760 760 760 1800 1800 – – – –

0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

Ag Ag Ag Ag Ag Ag Ag Ag Ag Ag Ag

Chang and Chang [5]

B5L17-C8S10e

R

Lap-splice

3250

Single

600  750

760

B6L21-C12S10e

R

Lap-splice

3250

Single

600  750

890

R

Lap-splice

3250

Single

600  750

890

(.190.25) 0 Ag fco (.280.43) 0 Ag fco (.270.41) 0 Ag fco

S

Flexural

1473

Single

305  305

–

S S S S S S

Flexural Flexural Flexural Flexural Flexural Flexural

1473 1473 1473 1473 1473 1473

Single Single Single Single Single Single

305  305 305  305 305  305 305  305 305  305 305  305

CF-R1

C

Lap-splice

3658

Single

CF-R2 CF-R3e CF-R4 f CF-R5 f CF-R6e RF-R1 RF-R2 RF-R3 RF-R4

C C C C C S S Q-C S

Lap-splice Lap-splice Lap-splice Lap-splice Lap-splice Lap-splice Lap-splice Lap-splice Lap-splice

3658 3658 3658 3658 3658 3658 3658 3658 3658

f

C

Shear

CS-R2 f CS-R3 f CS-R4 f CS-P1e RS-R1 f RS-R2

C C C C R R

Shear Shear Shear Shear Shear Shear

Lacobucci et al. [27]

e

B7L21-C12S5 Memon and Sheikh ASG-2NSS [31] ASG-3NSS ASG-4NSS ASG-5NSS ASG-6NSS f ASGR-7NSS ASGR-8NSS Haroun and Elsanadedy [18]

Haroun and Elsanadedy [17]

CS-R1

29.6 39.3

508.5 485.7

– 345.5

GFRP 9.80 CFRP 4.10

425 128

23.4 115.1

Eight 20 M 2#3/300 mm

36.5

465.0

500.0

CFRP

1.00

962a

76.4

0 fco 0 fco 0 fco 0 fco 0 fco 0 fco

Eight Eight Eight Eight Eight Eight

2#3/300 mm 2#3/300 mm 2#3/300 mm 2#3/300 mm 2#3/300 mm 2#3/300 mm

36.9 36.9 37.0 37.0 37.0 42.3

465.0 465.0 465.0 465.0 465.0 465.0

500.0 500.0 500.0 500.0 500.0 500.0

CFRP CFRP CFRP CFRP CFRP CFRP

2.00 1.00 3.00 2.00 1.00 3.00

962a 962a 962a 962a 962a 962a

76.4 76.4 76.4 76.4 76.4 76.4

0 fco 0 fco 0 fco 0 fco 0 fco 0 fco 0 fco 0 fco 0 fco 0 fco 0 fco

30#6 30#6 30#6 30#6 30#6 32Ø16 32Ø16 30#6 30#6 30#6 30#6

#3/130 mm #3/130 mm #3/130 mm #3/130 mm #3/130 mm #3/130 mm #3/130 mm #3/300 mm #3/300 mm #3/300 mm #3/300 mm

16.7 16.7 20.0 20.0 20.0 26.0 25.5 16.7 16.7 16.7 16.7

421.8 421.8 425.2 425.2 425.2 343.0 343.0 421.8 425.2 425.2 425.2

412.0 412.0 426.2 426.2 426.2 490.0 490.0 412.0 426.2 426.2 426.2

CFRP CFRP CFRP CFRP CFRP CFRP CFRP CFRP CFRP CFRP CFRP

1.10 1.10 + steel plateb 0.83 0.55 0.55hz + 0.275vlc 0.55 1.10 0.55 0.55 0.41 0.28

3540 3540 3540 3540 3540 3540 3540 3540 3540 3540 3540

236.0 236.0 236.0 236.0 236.0 236.0 236.0 236.0 236.0 236.0 236.0

0.02Ag

#3/130 mm

17.0

433.9

————

CFRP

235.0

0.02Ag

#3/130 mm

20.8

518.8

————

CFRP

0.02Ag

#3/130 mm

20.8

518.8

————

CFRP

1.10 + steel plateb 3525 thickness = 10 mm 1.65 + steel plateb 3525 thickness = 10 mm 1.65 + steel plateb 3525 thickness = 5 mm

0 Eight 20 M 2#3/300 mm 0.366 Ag fco

42.5

465.0

457.0

GFRP 2.50

450a

19.8

– – – – – –

0 0.621 Ag fco 0 0.619 Ag fco 0 0.364 Ag fco 0 0.616 Ag fco 0 0.363 Ag fco 0 0.616 Ag fco

Eight Eight Eight Eight Eight Eight

2#3/300 mm 2#3/300 mm 2#3/300 mm 2#3/300 mm 2#3/300 mm 2#3/300 mm

42.7 43.3 43.7 44.2 44.2 44.2

465.0 465.0 465.0 465.0 465.0 465.0

457.0 457.0 457.0 457.0 457.0 457.0

GFRP GFRP GFRP GFRP GFRP GFRP

5.00 2.50 1.25 7.50 2.50 7.50

450a 450a 450a 450a 450a 450a

19.8 19.8 19.8 19.8 19.8 19.8

D = 610

381

645

26#6

#2/127 mm

36.0

299.1

210.4

CFRP

0.70

4168

231.5

Single Single Single Single Single Single Single Single Single

D = 610 D = 610 D = 610 D = 610 D = 610 610  610 610  610 610  610 610  610

381 381 381 381 381 381 381 381 381

645 645 645 645 645 832 832 832 832

26#6 26#6 26#6 26#6 26#6 28Ø19,G60 28Ø19,G60 28Ø19,G60 28Ø19,G60

#2/127 mm #2/127 mm #2/127 mm #2/127 mm #2/127 mm Ø6/127 mm Ø6/127 mm Ø6/127 mm Ø6/127 mm

36.9 32.8 37.7 39.7 33.1 35.4 41.9 42.2 42.2

299.1 299.1 299.1 299.1 299.1 443.4 443.4 443.4 443.4

210.4 210.4 210.4 210.4 210.4 448.3 448.3 448.3 448.3

CFRP GFRP CFRP GFRP CFRP CFRP CFRP CFRP GFRP

0.70 11.40 1.70 12.70 8.30 4.00 4.00 2.50 22.90

4430 744 4382 641 937 4168 4430 4382 744

230.1 36.5 226.0 36.4 63.0 231.5 230.1 226.0 36.5

2440

Double

D = 610

–

645

20#6

Ø6/127 mm

40.8

299.1

210.4

CFRP

0.70

4168

231.5

2440 2440 2440 2440 2440 2440

Double Double Double Double Double Double

D = 610 D = 610 D = 610 D = 610 457  610 457  610

– – – – – –

645 645 645 645 676 676

20#6 20#6 20#6 20#6 20#6 20#6

Ø6/127 mm Ø6/127 mm Ø6/127 mm Ø6/127 mm Ø6/127 mm Ø6/127 mm

39.2 34.2 37.6 35.7 38.1 39.3

299.1 480.7 480.7 480.7 299.1 299.1

210.4 444.4 444.4 444.4 210.4 210.4

CFRP GFRP CFRP CFRP CFRP CFRP

0.70 10.30 1.20 2.30 1.00 1.00

4430 424 1245 1245 4382 4430

230.1 18.5 103.8 103.8 226.0 230.1

20 M 20 M 20 M 20 M 20 M 20 M

20 M 20 M 20 M 20 M 20 M 20 M

– d = 6 mm/ 127 mm

235.0 235.0

985

(continued on next page)

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

C C

f

986

Table 1 (continued) Axial load (kN)

Main steel

Transverse steel

0 Yield fco (MPa) stress of main steel (MPa)

Yield stress of lateral steel (MPa)

Composite jacket properties Type

tj within plastic hinge zone (mm)

Tensile Tensile strength Modulus (MPa) (GPa)

RS-R3e RS-R4e RS-R5 f RS-R6f

R R R R

Shear Shear Shear Shear

2440 2440 2440 2440

Double Double Double Double

457  610 457  610 457  610 457  610

– – – –

676 676 676 676

20#6 20#6 20#6 20#6

Ø6/127 mm Ø6/127 mm Ø6/127 mm Ø6/127 mm

44.0 44.0 44.0 42.6

299.1 299.1 299.1 299.1

210.4 210.4 210.4 210.4

CFRP GFRP CFRP GFRP

1.00 7.60 5.20 7.60

4168 744 937 641

231.5 36.5 63.0 36.4

CCR-Ie

C

Flexural

1500

Single

D = 375

–

0 0.2 Ag fco

30.9

372.0

332.0

CFRP

0.88

2600

220.0

CGR-Ie

C

Flexural

1500

Single

D = 375

–

0 0.2 Ag fco

12D12 mm d = 6 mm/ 60mmd 12D12 mm d = 6 mm/ 60mmd

38.7

372.0

332.0

GFRP 4.00

468

33.0

CL1-1.0Ce

C

Shear

800

Single

D = 360

–

1200

34.9

382.4

319.8

CFRP

0.17

3945

249.6

CL2-2.5Ce

C

Shear

800

Single

D = 360

–

1200

34.9

382.4

319.8

CFRP

0.42

3945

249.6

CL4-4.5Ce

C

Shear

800

Single

D = 360

–

1200

20D25 mm d = 6.5 mm/ 150 mm 20D25 mm d = 6.5 mm/ 150 mm 20D25 mm d = 6.5 mm/ 150 mm

34.9

382.4

319.8

CFRP

0.75

3945

249.6

CH1 1.5De

C

Flexural

1100

Single

D = 360

–

1200

382.4

319.8

DFRP 0.39

1832

59.6

CH2 2.5D

C

Flexural

1100

Single

D = 360

–

1200

34.9

382.4

319.8

DFRP 0.65

1832

59.6

CL3 4De

C

Shear

800

Single

D = 360

–

1200

20D25 mm d = 6.5 mm/ 150 mm 20D25 mm d = 6.5 mm/ 150 mm 20D25 mm d = 6.5 mm/ 150 mm

34.9

e

34.9

382.4

319.8

DFRP 1.03

1832

59.6

Wu et al. [39]

CL3BFRPe

C

Shear

800

Single

D = 360

–

1200

20D25 mm d = 6.5 mm/ 150 mm

34.9

382.4

319.8

BFRP

2.00

2332

106.0

Brena and Schlick [2]

CFRP-05e

C

Lap-splice

1085

Single

D = 240

305

0 0.05 Ag fco

9#4

440.0

440.0

CFRP

0.02

3800

227.0

KFRP-05

C

Lap-splice

1085

Single

D = 240

305

0 0.05 Ag fco

9#4

23.9

440.0

440.0

AFRP 0.03

2000

120.0

CFRP-15e

C

Lap-splice

1085

Single

D = 240

305

0 0.15 Ag fco

9#4

23.9

440.0

440.0

CFRP

0.02

3800

227.0

KFRP-15e

C

Lap-splice

1085

Single

D = 240

305

0 0.15 Ag fco

9#4

d = 6 mm/ 75mmd d = 6 mm/ 75mmd d = 6 mm/ 75mmd d = 6 mm/ 75mmd

23.9

e

23.9

440.0

440.0

AFRP 0.03

2000

120.0

CAF1-2Ne

C

Lap-splice

2010

Single

D = 356

470

0 6#6 0.059 Ag fco

24.9

465.0

492.0

CFRP

1.00

1019

79.0

CAF1-5N

C

Lap-splice

2010

Single

D = 356

470

0 0.32 Ag fco

25.1

465.0

492. 0

CFRP

1.00

1019

79.0

CBF1-6Ne

C

Lap-splice

2010

Single

D = 356

470

0 6#6 0.059 Ag fco

26.5

465.0

492.0

CFRP

1.00

1019

79.0

SAF1-8N SAF1-10N SBF1-11Ne SBRF1-12N

S S S S

Lap-splice Lap-splice Lap-splice Lap-splice

2010 2010 2010 2010

Single Single Single Single

305  305 305  305 305  305 305  305

470 470 470 470

0 0.065 Ag fco 0 0.43 Ag fco 0 0.065 Ag fco 0 0.065 Ag fco

8#6 8#6 8#6 8#6

Hoops, #3/ 300 mm Hoops, #3/ 300 mm Spirals, #3/ 80 mm #3/300 mm #3/300 mm 2#3/300 mm 2#3/300 mm

26.7 26.8 27.0 27.2

465.0 465.0 465.0 465.0

492.0 492.0 492.0 492.0

CFRP CFRP CFRP CFRP

1.00 1.00 1.00 1.00

1019 1019 1019 1019

79.0 79.0 79.0 79.0

C14FP1

R

Lap-splice

1400

Single

200  400

420

0.0

8D14

39.0

550.0

651.1

CFRP

0.13

3500

230.0

C14FP2

R

Lap-splice

1400

Single

200  400

420

0.0

8D14

39.0

550.0

651.1

CFRP

0.26

3500

230.0

C16FP1

R

Lap-splice

1400

Single

200  400

480

0.0

8D16

40.0

528.0

651.1

CFRP

0.13

3500

230.0

C16FP2

R

Lap-splice

1400

Single

200  400

480

0.0

8D16

40.0

528.0

651.1

CFRP

0.26

3500

230.0

Shan et al. [36]

Wu et al. [41]

Wu et al. [42]

Ghosh and Sheikh [14]

Harajli [15]

Sample

6#6

d = 8 mm/ 50 mm d = 8 mm/ 50 mm d = 8 mm/ 50 mm d = 8 mm/ 50 mm

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

Cross- Deficiency Column Bending Column Lapsection height dimensions splice (mm) (mm) length (mm)

Author

6D14 0.0 420 D = 200 1800 CrFP2

C

Lap-splice

Double

6D14 0.0 420 D = 200 Double 1800 Lap-splice C CrFP1

0 Note: C = circular, S = square, R = rectangular, Q-C = quasi-circular, D = circular cross-section diameter, d = diameter of steel reinforcement, Ag = gross section area mm2, and fco = concrete compressive strength MPa. CFRP = Carbon FRP, AFRP = Aramid FRP, GFRP = Glass FRP, DFRP = Dyneema FRP, and BFRP = Basalt FRP. a Values shown based on theoretical thicknesses given by the original authors for tensile tests of composite coupons. b Steel plates were used before FRP wrapping. c Hz. = horizontal FRP wrapping, vl. = vertical FRP layers. d Spiral reinforcement. e Columns successfully achieved post-yield stiffness and evaluated using the residual deformations. f Columns successfully achieved post-yield stiffness.

230.0 3500 0.26 CFRP 651.1 539.0 39.0

230.0 3500 0.13 CFRP 651.1 539.0 39.0

230.0 3500 0.26 CFRP 651.1 617.0 32.0 6D20 0.0 600 200  400 Single 1400 Lap-splice C20FP2

R

1400 C20FP1

R

Lap-splice

Single

200  400

600

0.0

6D20

d = 8 mm/ 50 mm d = 8 mm/ 50 mm d = 8 mm/ 50 mm d = 8 mm/ 50 mm

32.0

617.0

651.1

CFRP

0.13

3500

230.0

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

987

5.2. Seismic performance of FRP-retrofitted columns with shear deficiency In recent years, due to some of the excellent properties of fiberreinforced polymers, retrofitting structures with FRP has drawn increased attention, especially for improving the shear strength and ductility of reinforced concrete columns [35,30,6,29,17,44, 41,42,39]. Existing studies on FRP-confined concrete columns are concentrated on changing the brittle shear failure of columns subject to seismic activity to ductile one, but a few researchers have pointed to the enhancement of both column strength and ductility. Haroun and Elsanadedy [17] tested eleven FRP retrofitted squat columns, five circular columns and six rectangular columns. The composite jackets for circular columns (CS-R1 and CS-R2) and the rectangular columns (RS-R1 and RS-R5) were designed to induce a lateral pressure of 2.1 MPa within the plastic hinge regions. Jackets for circular columns (CS-R3 and CS-P1) and for rectangular columns (RS-R2, RS-R3, RS-R4, and RS-R6) were to provide a confinement pressure of 2.1 MPa for the entire height, while the jacket for CS-R4 was to provide a lateral pressure of 1.0 MPa for the entire height. It is evident from Fig. 5a and b that the different applied design assumptions, for the FRP confinement pressure, affected the inelastic performance of both rectangular and circular columns. Wrapping the entirety of rectangular columns with FRP to give a minimum confinement pressure of 2.1 MPa enabled RS-R3, RSR4, and RS-R6 to maintain their lateral capacities, after a clear existence of post-yield stiffness, to lateral deformations higher than those of RS-R1 and RS-R5, as shown in Fig. 5a. In case of circular columns CS-R3 and CS-P1, the considered FRP design assumption facilitated the continuous increase of the lateral strength over the ideal theoretical capacity till a lateral drift ratio 4%. Although the design assumptions considered for (CS-R1 and CS-R2) and (CSR4) were adequate to assure the existence of post-yield stiffness, early termination of the strength increase was noticed at a lateral drift 1.9%, and then columns strength kept constant up to a lateral drift of 3.2%. The seismic response of three retrofitted short circular columns with different numbers of CFRP layers was studied by Wu et al. [41]. With respect to the strength performance of the retrofitted columns during the inelastic stage, the three columns CL1-1C, CL2-2.5C, and CL4-4.5C had a gradual gain in the strength over the theoretical one up to drift ratio of >2, 4.4, and 6, respectively. It was noted from the failure mode of these columns that one CFRP layer is enough to increase the column’s theoretical strength capacity but not enough to change the shear failure mode to flexural one, Fig. 5c. Columns CL2-2.5C and CL4-4.5C had 2.5 and 4.5 layers, respectively, which was enough to modify the mode of failure to a flexural and ductile one and post-yield stiffness was evident, as shown in Fig. 5c.

5.3. Seismic performance of FRP-retrofitted columns with flexural deficiency The wide spread use of FRP applications triggered researchers to develop and apply retrofit strategies to upgrade the seismic performance of deficient plastic hinge regions of columns [35,6,25, 37,27,31,36]. Continuous fibers were used in a circumferential direction to confine the columns, since this can improve the inelastic deformation capacity of flexural plastic hinge regions. Fig. 6 shows a comparison between the inelastic performances of as-built rectangular column and FRP jacketed rectangular column b [35]. Seible et al. [35] calculated the appropriate composite jacket thickness for upgrading the limited inelastic deformation at the plastic hinge region of column under the effect of seismic action; this action is also appropriate for inducing a secondary stiff-

988

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

Fig. 4. Post-yield stiffness of FRP-retrofitted columns with lap-splice deficiency.

Fig. 5. Post-yield stiffness of FRP-retrofitted columns with shear deficiency.

Fig. 6. Post-yield stiffness of FRP-retrofitted columns with flexural deficiency.

ness after the elastic and maintains the maximum capacity up to a drift ratio 5.8%.

6. Recoverability limit of FRP-retrofitted bridge columns After scrutinizing the inelastic performance of 109 FRP-retrofitted columns with lap-splice deficiency, flexural deficiency, or shear deficiency, 61 columns exhibited idealized lateral performance with stable secondary stiffness. The hysteretic responses of these 61 samples were represented by the moment–curvature relationship for six samples, skeleton curve of load–deformation relationship for 16 samples, and complete hysteretic load–deformation response for 39 samples. To categorize columns, which successfully achieved secondary stiffness, in accordance with the required

recoverability after an earthquake; it is necessary to consider the residual deformation as an important performance index. The residual deformation, which is defined as the displacement of zero-crossing at unloading on the hysteresis loop, should not exceed 1% of the column height (recoverability limit) for rapid restoration of structural functions after an earthquake. The deformation corresponding to residual deformation equal to 1% of the column height is experimentally defined from the hysteretic curves of 39 scale-model tests, which are listed in Table 2. It is noteworthy that, conservatively, the values listed in Table 2 correspond to the smaller achieved secondary stiffness during the reversed cyclic loading of each column. Fig. 7 shows the lateral drifts of these columns at recoverability limit in comparison with the maximum achieved drifts (point D or E of Fig. 3 according to column response). Fig. 7a displays columns with flexural and lap-splice deficiencies, and columns with shear deficiencies are depicted in Fig. 7b. Below the line representing the lateral drifts of the columns at the recoverability limit, columns are within the recoverable state; and beyond this line, columns residual drifts are over 1%, which means columns enter into the irrecoverable state. Although, lateral deformation at the recoverability limit of any of these samples does not correspond to a specific point on the idealized lateral load–deformation relationship of FRP–RC damage-controllable structure; it is noticeable that most columns could not stay recoverable until point D of Fig. 3 (end point of the achieved post-yield stiffness). A ratio (u) between column lateral deformation corresponding to the recoverability limit (ddres = 0.01L) and deformation by the end of post-yield stiffness (dD) is defined for the 39 columns, since this ratio has a considerable importance in the FRP-jacketing design as it will be shown in a later section. With respect to both column deficiency and cross-section shape, averages of these values are listed in Table 3.

Table 2 Idealized response parameters of experimentally tested 55 FRP–RC columns. Sample

dyia (mm)

Hyib (kN)

dic (mm)

Hi d (kN)

dDe (mm)

HDf (kN)

dEg (mm)

HEh (kN)

dui (mm)

HF j (kN)

d yk (mm)

ddR = 0.01hl (mm)

K1m (kN/ mm)

K2n (kN/ mm)

0 o fl/fco

Masukawa et al. [30]

Specimen No. 3

8.0

326.4

15.2

420.9

40.0

459.8

–

–

45.9

367.8

10.3

40.0

40.8

1.57

0.066

Seible et al. [35]

b c

30.4 19.0

537.3 178.0

30.4 31.1

537.3 205.7

160.9 146.9

673.5 286.7

213.0 197.5

673.5 286.7

– 256.8

– 277.9

30.4 22.0

79.4 91.8

17.7 9.4

1.04 0.70

1.314 0.757

Xiao and Ma [43]

C3-RT5

16.7

224.4

33.3

294.3

69.2

323.6

–

–

100.5

294.3

21.9

88.5

13.5

0.82

0.388

Xiao et al. [44]

CS-ISJ-RT CS-CSJ-RT

6.6 6.6

423.0 423.0

19.6 26.7

598.8 598.8

56.0 60.4

653.0 635.0

117.0 137.0

653.0 635.0

– –

– –

9.4 9.4

– 37.6

63.8 63.8

1.49 1.08

0.372 0.248

Elsanadedy [9]

CS-R5 CS-P2 CS-P3 CF-R8 CF-R9 CF-R10

8.0 23.1 14.5 12.7 11.1 14.7

585.4 3160.0 574.4 216.8 181.3 179.6

8.0 30.2 35.3 27.0 16.8 23.8

585.4 3406.5 733.9 280.0 211.5 211.5

55.8 119.8 137.6 65.9 72.6 50.1

740.4 4046.5 960.1 315.0 250.0 227.5

78.4 – – – – 95.5

740.4 – – – – 227.5

– – – 125 145.2 165.5

– – – 252 200.8 182

8.0 24.9 18.5 16.4 12.9 17.4

– – – – – –

73.5 136.8 39.7 17.1 16.4 12.2

3.24 7.14 2.21 0.90 0.69 0.61

0.529 0.154 0.436 0.641 0.925 0.925

Chang et al. [6]

SFRL-100 FCL100 FCL100-1 FCL100-2 FR1 FRS FCS FCS-1 FCS-2

21.5 15.8 22.4 15.8 15.3 12.9 7.6 12.7 8.7

400.0 260.1 270.6 267.1 245.0 745.0 452.6 532.6 536.5

21.0 39.5 61.1 36.1 31.3 14.5 22.0 20.7 21.9

390.0 364.6 364.6 384.3 314.5 769.7 635.7 635.7 635.7

97.4 163.7 129.7 130.5 84.2 52.6 88.2 122.3 85.8

512.8 470.0 411.0 474.1 357.9 941.0 865.2 930.2 833.4

– – 161.8 163.2 100.0 – – – –

– – 411.0 474.1 357.8 – – – –

129.8 201.1 195.5 195.3 130.0 74.0 105.9 – 93.7

410.2 376.0 369.7 404.6 286.2 752.8 779.0 – 666.7

21.0 22.1 30.1 22.7 19.6 13.3 10.7 15.2 10.3

79.8 89.5 86.8 88.2 73.9 43.3 51.6 51.0 49.7

18.6 16.5 12.1 16.9 16.1 58.0 59.2 41.8 61.6

1.61 0.85 0.68 0.95 0.82 4.50 3.47 2.90 3.09

0.701 0.384 0.256 0.256 0.225 0.350 0.307 0.231 0.154

Chang and Chang [5]

B5L17-C8S10 B6L21-C12S10 B7L21-C12S5

14.3 28.6 27.3

352.5 357.7 396.6

28.6 50.7 46.3

426.0 484.5 484.5

130.0 167.5 193.4

555.9 617.9 654.2

– 238.0 227.2

– 617.9 654.2

185.7 – –

444.7 – –

17.3 38.8 33.4

86.0 106.6 110.7

24.6 12.5 14.5

1.28 1.14 1.15

0.684 0.839 0.839

Haroun and Elsanadedy [18]

CF-R2

22.9

111.7

42.2

148.7

161.6

175.72

–

–

196.9

148.7

30.5

–

4.9

0.226

0.276

CF-R3 CF-R4 CF-R5 CF-R6

20.6 18.8 22.0 24.9

110.3 110.6 111.0 109.8

33.2 40.7 33.7 45.4

146.3 149.1 150.2 146.5

162.7 143.3 155.2 206.3

187.9 181.4 192.6 194.0

– 159.3 – –

– 181.4 – –

203.2 209.3 193.8 246.3

176.0 162.7 157.4 169.1

27.3 25.3 29.8 33.2

86.2 – – 96.3

5.4 5.9 5.1 4.4

0.32 0.31 0.35 0.30

0.848 0.648 0.672 0.770

CS-R1

5.1

322.3

8.3

447.4

44.6

507.6

78.6

507.6

82.55

483

7.1

–

63.2

1.66

0.234

CS-R2 CS-R3 CS-R4 CS-P1 RS-R1 RS-R3 RS-R4

5.3 16.5 12.7 15.7 7.4 7.6 8.4

320.3 447.5 450.6 446.1 394.4 402.8 403.2

15.6 29.3 26.4 36.5 11.1 15.6 13.0

445.1 588.2 597.2 592.3 510.1 517.8 517.8

45.3 100.0 66.6 100.4 41.9 53.1 52.6

482 714.6 661.2 686.5 609.2 585.6 621.4

81.2 – – – – 72.3 71.5

482 – – – – 585.6 621.4

465 – 74.2 – 83.38 104.3 106.5

89.4 – 641.7 – 487.4 510.8 510.4

7.4 21.7 16.8 20.8 9.6 9.8 10.8

– – – – – 50.3 46.9

60.4 27.1 35.5 28.4 53.3 53.0 48.0

1.24 1.79 1.59 1.48 3.22 1.81 2.61

0.259 0.419 0.130 0.263 0.440 0.363 0.492

Haroun and Elsanadedy [17]

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

Author

(continued on next page)

989

990

Table 2 (continued) dyia (mm)

Hyib (kN)

dic (mm)

Hi d (kN)

dDe (mm)

HD f (kN)

dEg (mm)

HE h (kN)

dui (mm)

HFj (kN)

dyk (mm)

ddR = 0.01hl (mm)

K1m (kN/ mm)

K2n (kN/ mm)

0 o fl/fco

RS-R5 RS-R6

8.1 8.6

403.0 401.9

10.8 31.0

517.8 516.2

57.9 74.1

618.4 572.9

– –

– –

100.7 114.9

557.9 543.0

10.4 11.0

– –

49.8 46.7

2.13 1.31

0.424 0.438

Shan et al. [36]

CCR-I CGR-I

4.5 7.0

70.2 81.9

9.4 12.0

91.3 105.3

88.5 137.5

146.8 192.0

– –

– –

117.0 –

135.3 –

5.8 9.0

53.2 55.8

15.8 11.7

0.70 0.69

0.395 0.258

Wu et al. [41]

CL1-1.0C CL2-2.5C CL4-4.5C

5.8 5.7 6.0

438.4 424.6 482.4

7.5 7.3 6.0

482.3 482.3 482.3

18.2 35.3 48.3

559.9 640.0 722.8

– – –

– – –

24.2 47.2 61.3

548.6 618.7 578.2

6.4 6.4 6.0

– 21.0 20.9

75.2 74.8 80.6

7.26 5.64 5.68

0.105 0.262 0.472

Wu et al. [42]

CH1 1.5D CH2 2.5D CL3 4D

9.1 9.9 6.0

288.0 350.8 419.7

13.5 9.9 7.9

350.8 350.8 482.3

37.8 62.7 29.7

400.0 428.6 551.1

48.5 84.5 42.3

400.0 428.6 551.1

70.0 139.5 60.0

393.1 409.3 506.4

11.0 9.9 6.9

31.0 27.1 18.7

31.8 35.3 70.4

2.03 1.47 3.16

0.113 0.188 0.301

a b c d e f g h i j k l m n o

Wu et al. [39]

CL3-BFRP

6.1

482.3

6.1

482.3

42.3

691.8

49.0

691.8

56.7

553.4

6.1

20.7

78.7

5.79

0.742

Brena, and Schlick [2]

CFRP-05 KFRP-05 CFRP-15 KFRP-15

15.2 12.2 17.0 14.5

29.5 29.5 24.3 31.5

15.2 12.2 22.0 14.5

29.5 29.5 31.5 31.5

65.6 69.1 64.2 69.0

46.0 50.5 51.8 52.9

– 87.3 – 93.4

– 50.5 – 52.9

96.7 99.0 107.8 114.5

40.7 40.4 44.6 48.9

15.2 12.2 22.0 14.5

37.9 34.8 51.2 50.3

2.0 2.4 1.4 2.2

0.33 0.37 0.48 0.39

0.022 0.019 0.022 0.019

Ghosh and Sheikh [14]

CAF1-2N CBF1-6N SBF1-11N

10.2 14.8 12.6

52.1 52.9 50.0

10.2 14.8 26.1

52.1 52.9 67.9

64.3 81.9 53.7

76.5 77.9 76.7

82.0 – 74.5

76.5 – 76.7

151.5 107.5 89.0

61.2 62.3 61.4

10.2 14.8 17.1

43.1 32.3 35.0

5.1 3.6 4.0

0.45 0.37 0.32

0.230 0.216 0.247

Lateral displacement at first yield of longitudinal reinforcement. Lateral load at first yield state. Lateral displacement at the theoretical ideal strength. Theoretical ideal strength. Lateral displacement at endpoint of the secondary stiffness (point D, Fig. 3). Maximum strength (defined from the hysteretic response of the tested samples). Lateral displacement at point E, Fig. 3. Maximum strength. Ultimate lateral displacement corresponding to lateral strength P80% of maximum strength. Strength corresponding to ultimate lateral displacement. Idealized lateral yield displacement. Lateral displacement corresponding to 0.01 h residual deformation. First stiffness. Secondary stiffness. Confinement ratio.

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

Sample

Author

991

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

Fig. 7. Recoverability limit of FRP-retrofitted RC bridge columns with: (a) flexural and lap-splice deficiencies and (b) shear deficiencies.

Table 3 Ratio between lateral drift corresponding to recoverability limit and column drift by the end of post-yield stiffness. Column deficiency

Shear

Cross-section

Circular

Rectangular

Lap-splice Circular

Rectangular

Circular

Rectangular

u = (ddres = 0.01L/dD)

0.53

0.89

0.591

0.672

0.565

0.686

7. Design conditions assure the existence of post-yield stiffness using FRP As an initial attempt to determine conditions that guarantee the existence of post-yield stiffness, the authors used the main design assumptions and considered the tested samples that have successfully achieved post-yield stiffness. 7.1. FRP design conditions for plastic hinge confinement It is widely accepted that confining concrete columns with FRP composites acts to provide support to longitudinal reinforcement and restrains the lateral expansions on the core concrete, which in turn enables higher strains sustained by the compression concrete prior to failure. This means that there is a high probability of steel hardening, and consequently an increase in the envelope lateral load capacity of the columns. Coupled with this, confining the core concrete enables increasing the concrete compression strength, which is a further consistent reason for the existence of the post-yield stiffness. The region of the column over which enhanced confinement should extend is designated as the plastic end region. Here, the available experimental results were scrutinized to find out practical design conditions that are necessary for improving the flexural deficiency of this region; where, the ef-

Flexural

0 ) and lateral stiffness fects of FRP lateral confinement ratio (fl/fco (qjEj) on both achieved column lateral drift and strength are studied.

fl ¼ 0:5qj fj

ð3Þ

qj ¼ 4tj =D for circular column qj ¼ 2tj ðb þ hÞ=ðbhÞ for rectangular column

ð4Þ ð5Þ

where fl, is the confinement strength of FRP; fj, the ultimate tensile strength of FRP; tj, the total thickness of FRP jacket, qj, the volumetric ratio of FRP to concrete; and Ej is the elastic modulus of FRP. Table 4 demonstrates the effect of the confinement ratio on both achieved lateral drift (corresponding to point D of Fig. 3) and ultimate strength (Pa) of some of the available scale-model tests. Except the following two case studies, it is clear from Table 4 that the increase of lateral confinement ratio is followed by a proper enhancement of the achieved lateral drift and strength. The increase of the confinement ratio of column CF-R6 by 18.8% exceeding that of column CF-R4 enabled it to achieve a higher lateral drift and strength; however the increase of the confinement ratio of column CF-R3 by 26% over that of column CF-R5 was only responsible for 5% increase of the lateral drift and could not cause further enhancement of the column strength. In an attempt to find a sound reason for this result, mechanical properties of the fibers

992

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

Table 4 Effect of confinement ratio increase on both column lateral strength and drift ratio. Author Haroun and Elsanadedy [18]

Chang et al. [6] Wu et al. [41]

Wu et al. [42]

Haroun and Elsanadedy [17]

Sample

0 ) (Asfy)/(Agfco

(Axial load)/ 0 (Agfco )

qjEj

0 fl/fco

0 % of fl/fco increase

Drift ratio% at point D

% of drift increase

Pa (kN)

Pi (kN)

P a/ Pi

(GPa)

CF-R5

0.19

0.06

3.03

0.672

–

4.24

–

192.6

149.12

1.29

CF-R3 CF-R4 CF-R6 FCL100-1 FCL100 CL11.0C CL22.5C CL44.5C CH1 1.5D CH2 2.5D CS-R4

0.23 0.20 0.23 0.40 0.40 0.63

0.07 0.06 0.07 0.15 0.15 0.34

2.73 2.52 3.43 0.68 1.02 0.46

0.848 0.648 0.770 0.256 0.384 0.105

+26.2 – +18.8 – +50.0 –

4.45 3.92 5.64 3.99 5.04 2.27

+5 – +44 – +26 –

187.9 181.4 194.0 411.0 470.0 559.9

146.27 150.16 146.46 364.59 364.59 482.34

1.28 1.21 1.32 1.13 1.29 1.16

0.63

0.34

1.16

0.262

+149.5

4.41

+94

640.0

482.34

1.33

0.63

0.34

2.08

0.472

+349.5

6.04

+166

722.8

482.34

1.50

0.63

0.34

0.26

0.113

–

3.43

–

400.0

350.79

1.14

0.63

0.34

0.43

0.188

+66.4

5.70

+66

428.6

350.79

1.22

0.25

0.06

0.82

0.130

–

2.73

–

661.2

588.24

1.12

CS-P1 RS-R5 RS-R1

0.26 0.14 0.14

0.06 0.06 0.06

1.57 2.51 1.73

0.263 0.424 0.440

+102.3 – +3.80

4.12 2.37 1.72

+51 – 27

686.6 618.4 609.2

597.18 517.83 510.14

1.15 1.19 1.19

used are examined. Columns CF-R5 and CF-R3 were confined with glass fibers, which have similar elastic modulus; even though, rupture stress of glass fibers confining CF-R5 was lower than that used for column CF-R3 by almost 16%. Thus, it could be concluded that this increase of confinement ratio not only was depending on the increase of fibers thickness, but FRP rupture stress also had an effect. In the second case, the FRP confinement ratio of column RS-R1 was slightly higher than that of column RS-R5; however RS-R1 achieved a lateral drift less than that of column RS-R5 by 27%, almost at the same lateral strength. Since both columns (RS-R1 and RS-R5) were externally confined with carbon fibers of different elastic moduli (231.5 GPa and 63.0 GPa, respectively), it is expected that FRP lateral stiffness affected the performance of both columns. With an emphasis on the effect of FRP lateral stiffness, it is found that the lateral stiffness of the RS-R5 jacket was higher than that of RS-R1 by 45%; consequently, column RS-R5 was able to maintain gradual increase of strength till a drift ratio 2.37% which is almost higher than that achieved by column RS-R1 by 37%. In conclusion, if different FRPs are offered for retrofitting, confinement ratio is not the only factor that controls the choice among those fibers; where lateral stiffness should be considered. In other words, to select from different fibers for retrofitting of a deficient column, these fibers should be designed to equivalent lateral stiffnesses, then the one with highest confinement ratio would be selected for a ductile-recoverable structure. To guarantee the enhancement of both strength and ductility, it is practically crucial to identify a minimum design level of the confinement ratio. By scanning the range of the FRP confinement ratios of the columns achieved post-yield stiffnesses (Table 2), it is noticed that the minimum confinement ratio is 0.02 of samples tested by Berna and Schlick [2]. The authors here could not,

however, attribute this enhancement in the performance of the inelastic stage of those lap-spliced deficient columns to the FRP confinement only, since the thickness of concrete cover of those columns might have a contribution: concrete cover was 51 mm and column diameter was 240 mm. Excluding these samples from all scale-model tests that successfully achieved post-yield stiffness, FRP lateral confinement ratio is in the range of 0.066– 1.314. To specify the appropriate design level of FRP lateral confinement ratio, both column cross-section shape and its original deficiency are considered. Consequently, Table 5 summarizes the minimum FRP confinement ratios guaranteeing the existence of post-yield stiffness of circular and rectangular columns with different deficiencies. The listed values highlight the effect of longitudinal steel reinforcement configuration, namely, continuous or lap-spliced reinforcement. Where the minimum confinement ratio of columns with lap-splice deficiency is over 0.2, and it is in the range of 0.07–0.12 (according to column cross-section shape) incase columns with continuous reinforcement. It was reported by Wu et al. [40] and Lam and Teng [28] that the minimum values of confinement ratio, which guarantee strain hardening performance of FRP-confined concrete, are 0.13 and 0.07 for circular and rectangular columns, respectively. But, it is noteworthy that the proposed value of the confinement ratio by Lam and Teng [28] for confinement of rectangular columns depends on the efficiency of the fiber used, namely, actual hoop rupture strain, e.g. efficiency factor of carbon FRP (CFRP) is 0.586. Hence, and in view of the results of Table 5, the authors recommend that the minimum design level of the FRP confinement ratio should be P0.12 for columns with continuous reinforcement and P0.25 for columns with lap-spliced reinforcement. The recommended values of the confinement ratios are the same for both circular and rectangular columns, since

Table 5 Minimum design level of confinement ratio based on both column cross-section and deficiency. Column deficiency

Shear

Cross-section

Circular

Rectangular

Lap-splice Circular

Rectangular

Flexural Circular

Rectangular

0 fl/fco

0.105

0.066

0.216

0.247

0.112

0.066

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

Table 5 shows that the minimum confinement ratios of rectangular columns are less than those of circular columns with flexural or shear deficiencies.

ðBÞ Width of the steel plates ðSw1 & Sw2 Þ : Sw1 = ðb-10Þ; Sw2 = ðh-10ÞðmmÞ

ðCÞ Height of the steel plate ðSh Þ : Sh = ðLs þ 10ÞðcmÞ One of the key shear force transfer mechanisms is the aggregate interlock in the inclined cracks which can be controlled by horizontal FRP wrapping to limit the column dilation in the loading direction up to the experimentally determined dilation strain of ed < 0.004 or 0.4% [35,44]. For circular and rectangular columns, composite jackets should be designed to provide a minimum confinement pressure of 2.1 MPa for the entire height without exceeding a jacket strain of 0.004. However, the required jacket thickness of the rectangular columns should be increased by a factor of 1.5, as in the design considered by Haroun and Elsanadedy [17]. These two assumptions for the dilation strain and the confinement pressure value are proposed to be suitable for retrofitted columns to fulfill the goal of this work. 7.3. FRP design conditions for columns with lap-spliced reinforcement The primary objective of the external FRP jacket retrofit is to improve the behavior of the splice, by improving the distribution of bond stress along the splice, and effectively increasing the average bond stress. Additionally, and mainly for a recoverable structure, it is necessary to postpone the onset of splitting and to reduce the severity of the subsequent deterioration. Hence, by using the database of columns with lap-spliced reinforcement and successfully achieved the aim of the study, appropriate design conditions are extracted. For circular columns, a hoop strain of 1000 le is appropriate for the design of the composite jacket to ensure lap-splice clamping [35,18]. A lateral clamping pressure fl(lapsplice) over the lap-splice Ls was taken to be 2.0 MPa for the samples tested by Haroun and Elsanadedy [18], and by Seible et al. [35] based on the following equation:

As fy  þ 2ðdb þ ccÞ Ls 2n

ð6Þ

where p is the perimeter line in the column cross-section along the lap-spliced bar location; n, the number of spliced bars along p; As the area of main column reinforcing bar; fy the yield strength of the longitudinal steel, and cc is the concrete cover to the main column reinforcement with diameter db. But, the authors recommend the supposed criterion by Harajili [15] for seismic FRP bond strengthening, where a minimum development stress fs = 1.25fy is used instead of the fy in Eq. (6) to have the final following form:

flðlapspliceÞ ¼  p 2n

1:25As fy  P 2:0 MPa þ 2ðdb þ ccÞ Ls

ð7Þ

In order to prevent sliding in the lap splices length for rectangular columns, the ultimate strain of FRP should be limited to 0.0015 [5,18]. The lateral clamping pressure over the lap-splice could also be determined from Eq. (7). Steel plates should also be used in the wrapper region of the columns to improve the lateral strength and displacement ductility. Dimensions of the steel plates are given by Chang et al. [4] as follows:

ðAÞ Thickness of the steel plates ðt 1 & t 2 Þ : t 1 = 0:01b; t 2 = 0:01h

ð9Þ

where Sw1, Sw2 are width of the steel plates in the short and long directions of rectangular column, respectively.

7.2. FRP design conditions for column with shear deficiency

flðlapspliceÞ ¼  p

993

ð8Þ

where b and h are width and depth of column, respectively, and t1 and t2 are thicknesses of steel plates in the short and long directions of rectangular column, respectively.

ð10Þ

8. FRP retrofitting design guideline for FRP–RC damagecontrollable structures While the aforementioned assumptions in FRP design would be suitable for enhancing the inelastic stage performance, it is still not a design guideline specifying the appropriate FRP jacketing according to the definition of a controllable recoverable structure. In addition, residual deformations in the event of earthquakes are inevitable, and the increase of residual inclination over a specific limit will change the final performance state of a structure from a recoverable to an irrecoverable, so the accounting for the effect of residual inclination is essential. In other words, an appropriate design should give a clear definition of FRP jacketing to achieve the required performance, specifically, recoverable performance after the effects of a moderate or strong earthquake. So, in the following section a design guideline is proposed based on the Seismic Design Specifications of Highway Bridges in Japan. FRP jacket thickness for plastic hinge confinement initially is defined and recoverability is verified, then FRP jacket thickness is checked for shear deficiency. In case column reinforcement is lap-spliced at plastic hinge zone, FRP jacket thickness is determined and compared with the specified thickness to enhance the flexural deficiency. 8.1. Flexural hinge confinement In JSCE code, a bridge is designed assuming a principal plastic hinge at bottom of pier so that the following requirement is satisfied.

Pa P Ses W

ð11Þ

where

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ses ¼ Ss = 2la  1

ð12Þ

in which Pa is design lateral capacity of a pier, Ses is equivalent response acceleration, W is equivalent weight, Ss is elastic response acceleration that is specified in details by JSCE [23], and la is design ductility factor of a pier. la is determined according to the levels of ground motion (Level-I and Level-II); so, the allowable displacement ductility factor la is provided as

la ¼ 1 þ

du  dy ady

ð13Þ

where du is the ultimate displacement of a pier and a the safety factor depending on importance of bridges and the level of ground motion (a = 3.0 and 2.4 for important and ordinary bridges, respectively, under the Level-I ground motions, and a = 1.5 and 1.2 for important and ordinary bridges, respectively, under the Level-II ground motions). The Seismic Design Specifications of Highway Bridges in Japan adopts Eq. (2) for evaluation and specifies that the residual displacement should not be greater than 1% of the pier height [23]. The value of lR for which the residual deformation of the pier should be checked can be evaluated from Eq. (14):

lR ¼

1 2

( ) 2 Ss W þ1 PR

ð14Þ

where PR is defined in this study as column strength corresponding to recoverable limit, Fig. 8.

994

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

The next design step is to check the ultimate displacement capacity (du,capacity) of the pier. Elsanadedy and Haroun [10,11] used moment curvature analysis of the column section with the inclusion of concrete confinement model and lateral deformations due to bond-slip and/or shear deformations to estimate the ultimate displacement. They conducted a comprehensive study on six different confinement models to define the ultimate drift of FRP jacketed columns. Finally based on their investigations, Hosotani and Kwashima model [20] was developed. The models considered by Elsanadedy and Haroun [10,11] overestimated the ultimate deformation capacity. For columns with lap-splice deficiency, experimental-to-predicted ultimate displacement was found to be 0.75. Also, in case of rectangular columns with shear deficiency this ratio was 0.65. But, the lowest overestimation was for circular columns with shear deficiency, where experimental-to-predicted ultimate displacement was 1.0. Hence, the effect of this overestimation of column deformations should be considered.

du;capacity ¼ cdu;th Fig. 8. Idealized hysteretic response parameters of the damage-controllable structure.

To achieve the aim of a recoverable structure after the action of strong earthquake, allowable ductility of a recoverable structure (la) should not be in excess of lR, i.e., la equals lR. Consequently, the ultimate required lateral displacement (du,req) is computed from

  du;req ¼ dy aðlR  1Þ þ 1

ð15Þ

Pa of columns retrofitted with FRP is calibrated in the light of the current database and is given as follows:

  fl Pa ¼ Pi 1 þ 0:55 0 ¼ Pi k fco

ð16Þ

fl fco0

ð17Þ

k ¼ 1 þ 0:55

wherein Pi is the theoretical ideal lateral capacity = Mi/L, fl is the confinement strength of FRP. Accuracy of Eq. (16) is shown in Fig. 9. Since PR is not distinctively defined, Eq. (16) is slightly modified to include the factor u, which reflects the effect of both column cross-section and deficiency. Hence, the following form is proposed to compute the value of PR

  fl PR ¼ Pi 1 þ 0:55u 0 fco

ð18Þ

Regarding the importance of the existing bridge, level of ground motion, and selected degree of confinement ratio, the ultimate required displacement could be determined through Eqs. (14)–(18).

ð19Þ

where du,capacity = the ultimate capacity of column lateral deformation, du,th = theoretical ultimate deformation calculated based on the employed models by Elsanadedy and Haroun [10,11], and c = knockdown factor (0.75, 0.65, or 1) according to both column deficiency and cross-section shape. Then, the thickness of FRP jacket (tj) is appropriate for the enhancement of flexural deficiency in case

du;capacity P du;req and P a P Ses W It is crucial after this step of design to check the required recoverability. Hence, maximum response deformation (dRmax ) corresponding to recoverability limit could be evaluated through Eq. (2) as follows:

dRmax ¼

0:01L

þ dy C R 1  KK 21

ð20Þ

dy ¼ dyi

Pi Pyi

ð21Þ

K1 ¼

Pi dy

ð22Þ

K2 ¼

Pa  Pi dD  dy

ð23Þ

dD ¼

lR dy u

ð24Þ

Pi ðk  1Þ

K2 ¼ dy luR  dy

ð25Þ

ðk  1Þ

K 2 =K 1 ¼ lR u 1

ð26Þ

where dyi is the lateral displacement at first yield of longitudinal reinforcement. The value of CR was defined in the study by Fahmy et al. [12] for FRP–RC structure to be 0.554 during its recoverable state. Substituting Eq. (26) and the value of CR in Eq. (20), then

dRmax ¼

Fig. 9. Relationship between predicted maximum later strength and experimental results.

0:018L 1

ðk1Þ

þ dy

ð27Þ

ðluR 1Þ

For a recoverable structure after seismic activity, the required recoverable deformation dR should be less than or equal to the maximum response deformation corresponding to recoverability limit.

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

ðdR ¼ lR dy Þ 6 dRmax

ð28Þ

8.2. Shear strength enhancement The jacket thickness for shear deficient retrofit (tj(sh)) can be determined using the difference between the column shear demand Vdemand, which is based on the full flexural over strength in the potential plastic hinges; and the three shear capacity contributions from the concrete Vc, horizontal steel reinforcement Vs, and axial load Vp.

V demand ¼

Pa 1:5Pi  /s /s

ð29Þ

where /s = 0.85 is the strength reduction factor recommended by (ACI 318-2005) [1] for shear. The shear strength of the as-built column based on the three shear capacity contributions is calculated using the UCSD model [26], which provided much better correlation with the experimental results of 65 columns studied by Elsanadedy and Haroun [11] than other examined models.

V na ¼ ush ðV c þ V s þ V p Þ

ð30Þ

where Vna is the nominal shear capacity and ush is the proposed design reduction factor for the UCSD shear model, taken equal to 0.85.

995

Experimental tests on shear deficient columns demonstrated that inclined shear cracking is anticipated at angles h close to 30° to the column axis, so shear cracks can be expected to extend almost twice the member depth from the critical section [44,11]. Xiao et al. [44] derived the shear strength contribution Vj of the composite jacket by comparing it to closely distributed hoops as used in steel jacket design as follows:

Vj ¼

p 2

t jðshÞ fj ðD  cu Þ cotðhÞ for circular columns

V j ¼ 2tjðshÞ fj ðh  cu Þ cotðhÞ for rectangular columns

ð31Þ ð32Þ

where cu is the compression zone depth at the column critical section. The value of fj, which would guarantee the reality of post-yield stiffness, is 0.004Ej. It is worth mentioning that since the required jacket thickness of rectangular columns should be increased by a factor of 1.5, as in the design considered by Haroun and Elsanadedy [17], two thirds of tj (jacket thickness defined for flexural hinge confinement) should be considered in the evaluation of the shear strength contribution of composite jacket. Conservatively, a 45° force transfer mechanism is assumed, or cot h = 1.0, for the jacket design. Therefore, the shear strength contribution of the tj is given by

Fig. 10. Required extent of fiber-reinforced polymer jacket for single and double bending columns with rectangular and circular cross-sections and different deficiencies.

996

M.F.M. Fahmy et al. / Construction and Building Materials 24 (2010) 980–998

V j ¼ 0:0063t j Ej ðD  cu Þ for circular columns

ð33Þ

V j ¼ 0:0053t j Ej ðh  cu Þ for rectangular columns

ð34Þ

Consequently, the shear capacity Vcapacity of the retrofitted column could be computed from

V capacity ¼ V na þ V j

sures lap-splice clamping. Finally, the plastic hinge zone will be retrofitted with the maximum FRP thickness defined from the above three cases. Proposed extents of FRP jacket are shown in Fig. 10 for four different cases, where the required FRP extent of each case is defined in view of applied retrofitting systems to scale-model tests, which successfully achieved the aim of this paper.

ð35Þ

tj is acceptable to prevent shear failure when Vcapacity is higher than Vdemand, and also FRP lateral pressure (fl) is over 2.1 MPa. 8.3. Lap-splice clamping In case column steel reinforcement is lap-spliced at plastic hinge zone, FRP jacket thickness (tj(lapsplice)) should be designed for lap-splice clamping based on the addressed concepts in this study to assure the existence of post-yield stiffness. Hence, this thickness could be defined as follows:

ðflðlapspliceÞ  fh ÞD=2 ¼ Ej ej tjðlapspliceÞ for circular columns

ð36Þ

ðflðlapspliceÞ  fh Þh=2 ¼ Ej ej tjðlapspliceÞ for rectangular columns

ð37Þ

where Eq. (7) estimates the required clamping pressure (fl(lapsplice)), fh represents the horizontal stress level provided by the existing horizontal reinforcement, and ej is 0.001, which appropriately en-

8.4. Outline of the proposed retrofit design methodology A flowchart simply presenting the required design steps is given in Fig. 11, where the retrofit methodology is divided into five major steps to get the proper FRP jacketing that would assure the required recoverability according to the expected design level of ground motion. In the first step seismic response parameters of the existing column (yield strength, ideal theoretical strength, and the corresponding displacements) are determined. The second step designs the FRP jacket for plastic hinge confinement, which satisfies the requirements of the design level of ground motion. In the third step, residual deformation index is applied to investigate the end of the recoverable state. The fourth step includes check for the enhancement of column shear strength. In case the column is lap-spliced at the plastic hinge zone, the final step checks the FRP jacket thickness that provides the necessary clamping pressure.

Fig. 11. Flowchart of the proposed strengthening design guideline.

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9. Conclusions For the enhancement of urban safety, key bridges are required to have not only high strength and ductility, but also high recoverability. This paper is an attempt to discuss the seismic performance of the FRP wrapped bridge columns constructed before 1971s, from the perspective of post-earthquake quick recoverability. The postyield stiffness and residual deformations are identified as two measures for the recoverability of a structure. An idealized load– deformation model of damage-controllable FRP–RC structures is proposed. Then, an up-to-date literature search of 109 bridge columns, pertaining to the inelastic performance of the FRP-retrofitted columns with lap-splice deficiency, flexural deficiency, or shear deficiency is scrutinized to evaluate the recoverability of FRP-retrofitted columns. 1. Sixty-one FRP-retrofitted columns showed that the idealized hysteretic lateral response has clear post-yield stiffness, and consequently, the FRP–RC columns of important bridges could realize a seismic design philosophy that the structure suffers no damage under small earthquakes, exhibits prompt recoverability under medium earthquakes, and does not collapse under large earthquakes. 2. From the hysteretic responses of 39 scale-model tests, retrofitted columns could not stay recoverable to the end point of the achieved post-yield stiffness. A ratio between column deformation at recoverability limit and that by the end of post-yield stiffness is defined with explicit consideration of the effect of both column cross-section shape and deficiency. 3. Suitable FRP design assumptions and concepts certifying the reality of post-yield stiffness are defined and summarized as follows:  The minimum design level of FRP confinement ratio should be P0.12 for columns with continuous reinforcement, and it should be P0.25 in case column reinforcement is lapspiced at plastic hinge zone.  To avoid shear failure, horizontal FRP wrapping should limit the column dilation in the loading direction up to a dilation strain of ed < 0.004.  To postpone the onset of splitting of deficiently lap-spliced reinforcements and to reduce the severity of the subsequent deterioration, a hoop strain of 1000 le is appropriate for the design of the composite jacket for circular and rectangular columns. Along with, steel plates should be used in the wrapper region of rectangular columns.  Incase different fibers are offered for retrofitting of a deficient column, these fibers should be designed to equivalent lateral stiffnesses, then the one with the highest confinement ratio would be selected for a ductile-recoverable structure. 4. Regarding the level of ground motion, importance of the existing bridge, and deficiencies of bridge columns, an advanced strengthening design guideline considering and evaluating structural recoverability is proposed. References [1] ACI Committee 318. Building code requirements for structural concrete (ACI 318-05) and commentary (318R-05). Farmington Hills (MI): American Concrete Institute (ACI); 2005. 430 pp. [2] Brena SF, Schlick BM. Hysteretic behavior of bridge columns with FRP-jacketed lap splices designed for moderate ductility enhancement. J Compos Constr 2007;11(6):565–74. [3] Chai YH, Priestley MJN, Seible F. Seismic retrofit of circular bridge columns for enhanced flexural performance. ACI Struct J 1991;88(5):572–84. [4] Chang KC, Chang SB, Liu KY, Wang PH. Analysis and design of rectangular RC columns with lap-spliced longitudinal reinforcement. NCREE Research Programs and Accomplishments; 2005. p. 29–32.

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