Stresses, deformations and damages of various joints in precast concrete segmental box girder bridges subjected to direct shear loading

Engineering Structures 206 (2020) 110151

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Stresses, deformations and damages of various joints in precast concrete segmental box girder bridges subjected to direct shear loading

T

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Ghafur H. Ahmeda, , Omar Q. Azizb a b

Erbil Polytechnic University, Highway & Bridge Engineering Department, Kurdistan Region, Iraq Salahaddin University-Erbil, Civil Engineering Department, Kurdistan Region, Iraq

A R T I C LE I N FO

A B S T R A C T

Keywords: Shear strength Joint Prestressing Axial strain Shear key Deformation Shear failure Displacement Segmental bridge

Precast segmental concrete bridges involve multiple concrete segments joined together by posttensioning, and have the advantages of rapid construction, low-cost, and excellent quality control. Joints that represent locations of discontinuity are prominent factors affecting overall structural behavior of segmental bridges. In this study, a comprehensive analysis is performed for thirteen tested specimens with different joint types, subjected to direct shear loading, to assess the shear behavior of joints in precast box girder segmental bridges. The analysis focused on understanding the role of prestressing force, concrete compressive strength, presence of epoxy, and number of shear keys on: the stress and strain level in reinforcing bars, prestressing strands, displacements, type, time and mechanisms of sequential cracking and of damage level in the joints. The results showed that increasing of the confining pressure to 4.5 MPa and/or number of shear keys from 6 to 10, can highly improve both of the elastic stiffness and the plastic ductility of the segmental bridges, and changes the brittle behavior of the epoxied joints to a gradual strength degradation mode; the relative displacement of the dry joints is double of that in their identical epoxied joint; and the strains in the top layer reinforcement of the top slabs for keyed joints are ten times higher than that in the flat joint specimens.

1. Introduction The development, worldwide acceptance, and simple concepts of segmental construction in the field of posttensioned concrete segmental bridges represent one of the most interesting achievements in the bridge engineering [1–3]. Segmental box bridges are the typical solutions to many bridge problems with superior low life cycle costs, durability, fast construction and practical, versatile, aesthetically pleasing, excellent serviceability, minimal disruptions at ground level, and perfect quality control [4–6]. The joints between segments represent locations of discontinuity through which shear and compressive stresses must be transferred [7–9]. Despite their importance, still little information is available on shear strength and the behavior of these joints. The keys are essential for aligning segments during construction and shear transfer while the epoxy cures [10,11]. Early forms of these bridges normally used reinforced single keys on the web section, however, current practice is to use multiple keys that are generally unreinforced, distributed over the height of the web and flanges, may be dry or epoxied [2,3]. Epoxy acts as a lubricant for jointing and compensates for the irregularities between the joined surfaces [11]. The accepted theory for evaluating shear strength of keyed dry joints

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considers that the shear forces are transmitted across the joint through the mechanical interlock from shear keys and the friction between the joint flat faces [1,12,13]. Since 1950s, researchers have done studies on the shear strength and behavior of the joints in segmental bridges [14]. Liu et al. [15] conducted direct shear tests of joints, and the test parameters were: confining stress, concrete type, joint type, joint shape and number of keys, and arrangement of steel reinforcement. The results show that higher shear strength of the joints can be achieved with higher confining pressure, higher tensile strength, and the addition of fibers. Large-keyed joints showed a minor increase in shear capacity (9.7%) compared with three-keyed joints. A calculation method for the shear strength of concrete dry joints based on Mohr’s circle was established, and a simplified formula for calculating the shear strength of dry joints with different compressive strengths was developed. Jiang et al. [16] tested a total of 14 specimens, which included three monolithic specimens, six segmental specimens with dry joints, and five segmental specimens with epoxy joints. The study focused on the effects of joint location, joint types, joint number, and shear span-depth ratios. It was found that location of the joint plays an important role in the shear strength of dry joints when compared with monolithic specimens. The

Corresponding author. E-mail address: [email protected] (G.H. Ahmed).

https://doi.org/10.1016/j.engstruct.2019.110151 Received 7 May 2019; Received in revised form 6 November 2019; Accepted 25 December 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

Engineering Structures 206 (2020) 110151

G.H. Ahmed and O.Q. Aziz

failure processes and failure modes were independent of joint types. Jiang et al. [17] established a numerical model to investigate the direct shear behavior of single-keyed dry joints. It was found that the ultimate shear capacity increased about 121% when the confining pressure increased from 0.1 to 3.0 MPa, it was very low under confining pressure of 0.1 MPa; it increased about 203% when the key depth increased from 15 to 40 mm. Kaneko and Mihashi [18] conducted an analytical study to describe the transition behavior between large single curvilinear cracks and diagonal multiple joint cracks. The change in geometry of the key causes strain localization that resulting in the formation of multiple cracks. Turmo et al. [19] presented a FE model for joints under combined shear and flexure. It was revealed that, in segments with closed joints, shear is transferred along the entire height of the web; while in an open joint, the shear flow is limited to the compressed zone. When the neutral axis reaches the upper flange, a great compression arch is formed starting at the prestressing anchorages, which is responsible for shear flow. The joints located at mid-span, are always subjected to low shear forces; and the joints near to the support segments are always remained closed to design loads. Raison and Christy [20] studied shear slip of dry joints. It was concluded that the first crack formed at the bottom corner of the male key at 72–80% of the ultimate shear. Although much research has been performed on the behavior of the joints and important facts were discovered, however, the segmental bridges still have many problems, like, cracking of the concrete edges adjacent to joints and corrosion of the tendons for dry joints, sudden failure of epoxied joints, the design provisions and formulations proposed by various authors, lead to values that can vary by 100%, and most importantly, the major structural failures in the past had been attributed to inadequate joint design and detailing [11,12]. In this investigation, test results of thirteen box specimens were presented and analyzed. Experiments were conducted on a model, with a geometry closely resembling the keyed joint of actual box girder bridges that, rarely studied in literature. The study is focusing on the; stresses and strains in: longitudinal bars at top and bottom slabs, shear stirrups and the strands; concrete stresses and strains in the flanges and the webs; vertical displacement of different joint types; initiation time and location of the first crack, and load-crack relations considering time-lapse. The joints are of different mechanical characteristics, by the variation in the prestressing load level and eccentricity, concrete compressive strength, number of shear keys, and presence of epoxy against dry joints. The most common problem of the epoxied joints is sudden and brittle failure; however, a solution is proposed to this problem. This study is also intending to provide optimized values of most effective parameters to be implemented in the design of stronger and safer segmental bridges aside, and less stresses, strains and displacements on the other side.

Table 1 Mix proportions, workability and hardened concrete properties at age of 90 days. Concrete test/mix type

NSC

HSF

HSS

VHS

Cement (kg/m3) Fine aggregate (kg/m3) Coarse aggregate (kg/m3) Fly ash (kg/m3) Micro-silica (kg/m3) Super-plasticizer (L/m3) Water (L/m3) Water/binder

310 870 1120 – – – 186 0.60

390 820 940 160 – 3.9 193 0.35

440 920 1060 – 35 4.4 166 0.35

450 945 1080 – 54 4.5 116 0.23

Slump (mm) Slump flow (mm)

200 420

> 230 760

> 230 830

160 330

Compressive strength (MPa) Split tensile strength (MPa) Elastic modulus (GPa)

42.8 4.07 26.0

72.7 4.69 31.4

91.2 6.30 41.1

118.9 7.28 44.2

of the model was exactly proportional to the standard section to a scale of one-eighth, and the web angles are the same; however, the thickness of the webs was increased from 50 mm to 120 mm and the thickness of slabs was increased from 28 mm to 100 mm. Increasing of the thicknesses was necessary for obtaining logically and practically acceptable dimensions. Using a larger scale factor (like ¼) was a better representative of the real section, whereas it leads to the much stronger specimens that exceeding the capacity of the testing machine of 2500 kN. Interlocking was provided by ten or six shear keys (Fig. 1) distributed to the height of the webs and the slabs, for transferring of the shear stresses during loading, and for fitting of the segments at the time of posttensioning. In this type of the specimens, the upper web shear keys can represent the shear keys located near to the top slab-web connection in real segmental box sections where the stress flow is not normal to the web section, and could cause both horizontal and vertical shear stresses; the same case is true for the bottom web shear keys; while the middle web shear keys can represent the stress case at the majority of the shear keys located at the middle of the real segmental box structure webs. 2.3. Prestressing and reinforcement details Longitudinal, transverse and shear reinforcement was ASTM A615 [23] G420-Ø10 mm deformed steel bars, having mechanical properties shown in Table 2. Reinforcement details are shown in Figs. 2 and 3. It was intended to fail specimens in the joints; therefore extra reinforcement was provided to prevent non-desired failure modes. The strands were ASTM A416 [24] G1860-∅12.5 mm (Table 3), low relaxations; inserted inside Ø25 mm PVC ducts, without grouting (Fig. 2). The jacking force was varied from 40 to 120 kN depending on the specimen design. In Fig. 3 and rest of the upcoming figures, the left segments are males and the right ones are females.

2. Experimental program 2.1. Concrete and materials Four concrete mixes were used in this study. The HSS mix was a micro-silica based high strength concrete that was used for ten specimens, and three additional mixes were prepared, including a fly ash based high strength concrete (HSF); a normal strength concrete (NSC); and a very high strength concrete (VHS). The concrete materials were: ordinary Portland cement 42.5R; fine aggregate according to ASTM C33 [21]; fluvial coarse aggregate with nominal max size of 12.5 mm, micro-silica with 93% of SiO2; fly ash class F; and sika viscocrete-5930 as super-plasticizer. Mix proportions, workability and mechanical properties of the mixes are shown in Table 1.

2.4. Fabrication of the test specimens The reinforcement cages were prepared precisely (Fig. 4a), and the specimens were cast in separate matching (Fig. 4b). Steel molds were used for faces of the joints with fine tolerance geometry, using AutoCAD controlled cutting machine. Posttensioning works have performed 24 h before starting of the tests. For epoxy joint specimens, both faces of the joints were covered with an epoxy layer of 1–2 mm, minutes before application of posttensioning forces. The initial setting of the epoxy was 6 min, with the tested compressive strength of 76.8 MPa for hardened 50 mm cubes. Initially each of the strands were tensioned individually to 25% of the jacking force, and then to the full tension of 100%, immediately (Fig. 4c). The joints exhibited a uniform closure and a good epoxy squeeze out, since the applied stress was much higher than the

2.2. Size and shape of the test specimens Modeling of the specimens is based on the standard box section (3000-1) provided by AASTO-PCI-ASBI [22]. The exterior dimensions 2

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Fig. 2. Transverse reinforcement details and locations of the prestressing ducts.

2.5. Test setup and loading mechanism The testing machine consisted of a strong steel frame shown in Fig. 5a. The load was applied through a hydraulic jack to the load cell, and then transferred to two 200 × 200 mm, 50 mm thick steel plates using a 100 × 150 mm steel beam, which was dividing the load into two regions, through Ø50 mm smooth bars (Fig. 5b). The supports consisted of steel plates and steel box sections. The support were braced internally, and restricted against horizontal movement. The support contact plates were able to rotate smoothly with the rotation of the segments during loading. The aim of longitudinal setup in Fig. 6a is to locate the load resultant 100 mm away from edge of the joint, which results the shear span/depth ratio of 0.3 (< 0.5), thus the direct shear failure of the joints can be ensured [26]. The load setup in transverse direction shown in Fig. 6b was intended to minimize the activity of transverse bending moments, and transfer the load to the webs directly. 2.6. Instruments and measurements Load measurements were taken from a load cell with 1500 kN capacity and a resolution of 0.1 kN, connected to a digital load indicator (Fig. 7). The vertical displacement was measured at the joints by using calibrated analogue dial gauges with the capacity of 50 mm and an accuracy of 0.01 mm (Fig. 7). For clarification of dial gauges observations, magnification lenses were used. Strains were measured for the steel bars marked in Fig. 8 and the observations were recorded by a 16 channel data logger. The data logger was connected with a computer, the observations were recorded automatically every 5 s (Fig. 7), and the data was auto-saved in an Excel file. Type of the strain gauges was BF120–6AA, used for measuring the axial strains in the bars. The strain gauges were attached to a smoothened length of the bars, and then covered with a layer of varnish, a liquid silicon layer, and a plastic tape, to prevent the gauges from wetting and the concrete casting impacts (Fig. 8). It is known that the strand wires are wound in helical shape; the wires have no deformations or ribs. Therefore, strain gauges were

Fig. 1. Dimensions and shear keys details (a) 6 shear key specimens (b) 10 shear key specimen (c) web keys-side view (d) web keys-top view (e) flange key-side view.

minimum value of 0.3 MPa specified by AASHTO LRFD-2017 [25]. The prestressing force was transferred to the concrete through four 8 × 100 × 200 mm steel plates.

Table 2 Mechanical properties of reinforcing bars.

Avg. (3 tests) ASTM A615

Nominal diameter (mm)

Nominal area (mm2)

Yield strength (MPa)

Ultimate strength (MPa)

Elongation (%)

9.887 9.5 min.

76.8 71 min.

543.7 420 min.

654.1 620 min.

17.3 9 min.

3

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Fig. 3. Longitudinal reinforcement details in a section through a web (all bars are ∅10 mm).

attached directly to surface of one of the wires, after cleaning of the surface. The strain gauge wires were extended out from the ducts through a (3 mm deep) groove that cut under the prestressing anchorage bearing plates (Fig. 9a). Two strain gauges were attached, one strain gauge (P1) for the top strands, and another one (P2) for the bottom strands, as shown in Fig. 9a. Type of the strain gauges used for measuring surface strains of concrete was BF120–80AA. The strain gauges were attached to concrete after posttensioning process. The concrete surface was cleaned and the strain gauges were fixed to the specified location with a thin layer of fast dry glue (Fig. 9b). Locations of the strain gauges were similar to that attached to reinforcing bars. Strain gauge C1 and C2 were fixed to the top surfaces of the top slab and bottom surface of the bottom slab, respectively. Strain gauges C3 and C4 were attached to the mid height of the male and female segments, respectively. When the loading process was started, the specimens were monitored from the first step until failure, in addition to direct human observation, four HD cams were used. The cams can capture the events with in 1/12 s, and they were used for monitoring of the: load cell, dial gauges, data logger, strain indicators, and inspection of the front face and the joint zone.

3. Parameters and details of the test specimens A list of specimens was prepared, as illustrated in Table 4. The effective posttensioning forces and concrete stresses were calculated based on step by step calculations of the losses. The studied parameters are: confining stress level and the prestressing force eccentricity, concrete compressive strength, number of shear keys with and without epoxy. The main goal of this study is to discover relations between the parameters a side, and, material stresses and specimen deformations in the other side. Specimen IDs in Table 4 were chosen so that they can be easily recognized. In the second group, 35P means, the four top strands were less tensioned to work like 3–80 kN common strands, and the bottom strands were more tensioned to be equivalent to 5–80 kN strands. In G3, NSC, HSF, HSS and VHS were based on their reference mixes. The only variable for G4 was the number of shear key, that the notations 00KE, 06KE, and 10KE were used for a flat, a six shear key, and a ten shear key specimen, respectively. The only difference between G4 and G5 is that the letter (E) is used for epoxied joints and the letter (d) is used for dry joints.

Fig. 4. Preparation of the test specimens (a) a reinforcing cage, (b) two cast segments, (c) a posttensioned specimen.

4. Test results and discussions The ultimate load resistance and the failure modes are shown in Table 4. In the main failure mode (M1) the diagonal shear cracks were appeared at the webs, the specimens were exhibited a sudden and a very brittle failure within 1/12 s. However, five specimens were showed failure mode (M2) in which, the diagonal web cracks and flange shear cracks were observed clearly, and the strength degradation was gradually happened.

Table 3 Mechanical properties of prestressing strands.

Avg.(4 tests) ASTM A416

Steel area (mm2)

Breaking load (kN)

Ultimate strength (MPa)

Yield strength (MPa)

Weight (g/m)

Elongation (%)

99.3 98.7 min

187.6 183.7 min

1889.0 1861.2 min

1700.1 1675.1 min

781 775 min

5.6 3.5 min

4

Engineering Structures 206 (2020) 110151

G.H. Ahmed and O.Q. Aziz

Fig. 5. (a) Testing machine, and (b) load setup on the top slab.

Fig. 8. Location of the strain gauges attached to the reinforcing bars.

the webs, and the stage is ended by failure of specimen, which is also known as plastic stage. Linearity of the load-displacement was continued up to 65–85% for keyed joints, while it was 40–45% for flat joints. The second result is close to that reported by Jiang et al. [10] that, the load increases linearly with slip up to 40% of the maximum load for 0.5 MPa of the confining stress, then nonlinearity initiates; however, at a higher confining stress of 2.0 MPa, the nonlinearity caused by cracking was gradually overcome. Displacement corresponding to the ultimate load and to 400 kN load (minimum failure load among specimens), are shown in Table 5, the ratio of the increased displacements and the elastic stiffness of the specimens are also presented. When considering the 400 kN correspondent displacements, most of the specimens exhibited displacement of around 2 mm, while the flat joints showed double displacements of their identical specimens with shear keys; the strongest specimens are SP3-1.5P and SP10-10KE with 1.82 mm and 1.33 mm, respectively. The displacement corresponding to ultimate loads are mostly located within 5–7 mm, some specimens showed larger values due to two reasons, either due to the higher load resisted by the specimen that causes the displacement to be increased too, or due to the lack of the epoxy bond and the higher slip in the concrete-concrete contact surfaces in the dry jointed specimens. While the actual benefits of the less displaced

Fig. 6. (a) Test setup in longitudinal direction (specimen length is 2 × 750 mm, width of plates is 200 mm) (b) Test setup in transverse direction (all dimension are in mm).

4.1. Load-vertical displacement relationship In the data analysis of load-vertical displacement relationships, two stages in the load carrying capacity can be discussed. The first stage is a linear stage, in which, when the intensity of shear stress is increased, the vertical displacement is also increased linearly. The second stage began when the diagonal cracks were appeared on the outer surface of

Fig. 7. Load, strains and displacement measurements. 5

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Table 5 Displacements and elastic stiffness of specimens. SP

SP1-CTRL SP2-0.5P SP3-1.5P SP4-35P SP5-53P SP6-NSC SP7-HSF SP8-VHS SP9-00KE SP10-10KE SP11-00Kd SP12-06Kd SP13-10Kd Average

Displacement (mm) corresponding to

Elastic stiffness

400 kN (Δ400)

Ultimate load (Δu)

Δu/Δ400

kN/mm

Ratio to SP1

2.44 4.05 1.82 2.40 2.45 2.98 2.55 2.23 4.82 1.33 7.28 4.64 4.61 3.35

5.27 6.88 12.92 13.60 5.11 7.05 5.37 4.88 11.58 5.93 7.28 10.25 11.33 8.27

2.2 1.7 7.1 5.7 2.1 2.4 2.1 2.2 2.4 4.5 1.0 2.2 2.5 2.9

161 133 217 166 163 132 144 170 – 279 081 086 087 152

1.00 0.83 1.35 1.03 1.01 0.82 0.89 1.06 – 1.73 0.50 0.53 0.54

interesting parameter for increasing the stiffness of the specimens, since the additional four flange shear keys were increased the stiffness by 73%. By comparing specimens having dry and epoxied joints, an obvious improvement in the stiffness can be found for epoxied joints. The epoxy has increased the joint stiffness by 87.2% and 220.7% for 6KE and 10KE, respectively. When considering safety of the bridges and precautions before failures, the plastic ductility is of great interest. In this study, most of the specimens had behaved sudden and brittle failure, but some specimens were showed an important plastic ductility like: 1/23.2, 1/22.2 and 1/20.2 mm/kN, for NSC, 1.5P and 35P, respectively (Fig. 10). It seems to be better to use lower concrete compressive strength, more slab shear keys, and higher prestressing force in the bottom part of the box girders, to have a predictable failure with warning signs.

Fig. 9. (a) Strain gauges used for the strands (b) strain gauges used for concrete.

specimens can be seen by comparing the ratio of (Δu/Δ400), that the dry joint displacements are increased almost twice, just like other specimens, but the specimens 1.5P, 35P and 10KE have increased displacements by 7.1, 5.7 and 4.5 times, respectively. The load–displacement relations are shown in Fig. 10. Displacements corresponding to the ultimate load for six and ten key specimens in dry multi-key joints were higher than that of epoxied joints by 94.5% and 91.1% respectively. Based on these results and those presented by Buyuk et al. [8] and Saibabu et al. [2], it can be concluded that the failure displacement of dry multi-keyed joints is approximately double of that for epoxied joints. The elastic stiffness of the specimens can obviously show the most interested parameters to be considered in design of segmental bridges. Decreasing the confining stress to one half, decreases the elastic stiffness by 17%, while increasing the stress by 50% the stiffness increases 35%. The relative stiffness values of 1.01 and 1.03 in G2 are meant that, changing eccentricity of the prestressing force has a negligible effect on the elastic stage of the specimens, and it depends only on the centroid stresses. For the G3, the elastic stiffness was increased as the concrete compressive strength increased up to a limit of about 80 ± 10 MPa; later the compressive strength has a very little impact. Increasing number of shear keys is the most important

4.2. Relationship between load and rebar strains 4.2.1. Load-top bar strains (S1) for male segments The relationship of load and top bar strains are shown in Fig. 11. Figures were drawn so that overlapping has been avoided by shifting of the starting points horizontally. The recorded strains at ultimate load resistance for specimens 1.5P, 35P, 10KE and 10Kd were exceeded 2000 μs. SP1 behaves differently as the strain in the top bar reinforcement was almost under 100 μs, for load levels below 600 kN,

Table 4 Identification and details of the test specimens. Gr.

G1

G2

G3

G4

G5

SP#

SP2 SP1 SP3 SP4 SP1 SP5 SP6 SP7 SP1 SP8 SP9 SP1 SP10 SP11 SP12 SP13

SP ID

0.5P 1.0P 1.5P 35P 44P 53P NSC HSF HSS VHS 00KE 06KE 10KE 00Kd 06Kd 10Kd

Concrete compressive strength (MPa)

89.9 89.9 92.9 89.5 89.9 93.9 42.8 72.7 89.9 118.9 89.3 89.9 89.6 92.8 94.0 88.7

Jacking force per strand (kN) Top

Bot

40 80 120 60 80 102.2 80 80 80 80 80 80 80 80 80 80

40 80 120 100 80 57.8 80 80 80 80 80 80 80 80 80 80

Effective prestressing force (kN)

304.3 611.8 919.4 610.3 611.8 612.5 609.5 611.2 611.8 612.5 611.8 611.8 611.8 611.9 611.9 611.8

Eccentricity of prestressing force (mm)

37.8 37.8 37.8 71.6 37.8 00.3 37.8 37.8 37.8 37.8 37.8 37.8 37.8 37.8 37.8 37.8

6

Effective concrete compressive stresses (MPa) Top

Centroid

Bottom

0.75 1.51 2.27 0.15 1.51 3.03 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51

1.51 3.04 4.56 3.03 3.04 3.04 3.02 3.03 3.04 3.04 3.04 3.04 3.04 3.04 3.04 3.04

2.68 5.39 8.10 7.48 5.39 3.06 5.37 5.39 5.39 5.40 5.39 5.39 5.39 5.39 5.39 5.39

Ultimate load, Pu (kN)

Failure mode

473.3 742.1 1062.7 698.5 742.1 527.0 554.1 718.1 742.1 751.9 490.6 742.1 843.0 391.0 581.7 661.2

M1 M1 M2 M2 M1 M1 M2 M1 M1 M1 M2 M1 M1 M2 M1 M1

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Fig. 10. Vertical load vs. relative vertical displacement.

while suddenly it was increased with an accelerated rate. That behavior was also visible during loading of the girder, when no visible cracks were observed before a catastrophic failure. The strains for specimens without shear keys i.e. 00KE and 00Kd were in linear relationship with the load by having 192 μs and 368 μs respectively, at ultimate load. Since the confinement pressure was less for specimen 0.5P, the compressive strain for the top bars were less than 100 μs at ultimate shear strength of the girder. In specimen 10KE, an average strain rate of 2.8 μs/kN was recorded up to 440 kN of the applied load; thereafter the strain rate was decreased to only 0.6 μs/kN, which is visually seen to be parallel in slope to 00KE specimen. Remembering that, the strain gauges were calibrated to zero before starting of the tests, while there was an already prestressing force on the bars producing small strains like 52 μs for CTRL and 84 μs for SP3-1.5P.

Fig. 11. Load – Strain (S1) relationship for the top slab, top layer longitudinal reinforcement.

4.2.2. Load – Bottom bar strains (S2) for male segments The relation between load and the bottom bar strains are of significant complexity. When the segments were subjected to a vertical force, the bending moment was causing tension on the bottom of the girder, by which the bottom rebar was also under tensile forces, however the vertical load was causing that stresses which was attempting to open the joint. The force which resisted against opening of the joints was prestressing forces, and when vertical load was increased, the 7

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a different behavior by having strains of less than 50 μs until the load level of 400 kN, thereafter a 300 μs horizontal shift, and then, it was continued in a low strain rate. Most of the strains were in the limit of about 500 μs, except of specimens 1.5P which had had the strain of 1212 μs, and suddenly returned to 361 μs at failure. When these strains converted to stresses, and knowing that fy = 543.7 MPa; the stress level at the bars was just (0.45fy) and then returned to (0.13fy), while, there was an already 34.4 MPa prestressing stress on the bars, which must be subtracted from the final stress of 0.45fy to become 0.38fy, for SP31.5P. SP10-10KE had a strain of 1932 μs at failure, suddenly was returned to 1260 μs, and in terms of stresses it can be said that the stress level reached (0.71fy) which is the maximum bottom bar stress recorded over the entire specimens. Other specimens had a very low pure stress levels for example the bottom rebar stresses at failure for specimens 00KE and 0.5P were only of +0.025fy and −0.002fy, respectively. Several specimens had a behavior of which the strain value was developed gradually; thereafter it was reversed in direction to decrease the cumulative strain. The phenomenon can be justified by a process of balancing the vertical force and the vertical displacement that attempting to open the joint, but the resistance provided by prestressing was restricting that opening. Loss of shear keys was helping the vertical forces to overcome the prestressing, and finally the crushing of the concrete had happened at the joint by the action of inclined diagonal shear cracks. Specimen SP5-P53 has the strain value of 929 μs for the load level of 260 kN, which was the highest strain rate of 3.6 μs/kN over the entire strains in all specimens. On the other side, the largest rapid change in the strain was recorded for specimen 10KE, in which the strain was changed from 614 μs to 1639 μs, when the load was stepped from 760 kN to 780 kN. The increased strain for this step of loading was 1025 μs; the strain rate of 51.3 μs/kN, and the change in the stress on the bottom bars was increasing from 122.8 MPa to 327.8 MPa. When considering the influence of epoxied joints, the dry joint specimens have similar behavior, disregarding the number of the shear keys. While, when comparing specimens with and without epoxied joints, they have entirely different behaviors. The strain rate for the dry joint specimens compared with epoxied joints was double for no key joints, and triple or more for six key joints. 4.2.3. Load – Shear reinforcement strains (S3), male SG Flow of the stresses in the webs was relatively more regular than that of the bending bars at top and bottom of the girders. The strain rates for the first group were 0.51, 0.66 and 0.80 μs/kN, respectively for 1.5P, 1.0P and 0.5P. The lowest strain rate was recorded for specimen 00KE which was 0.37 μs/kN. In case of group two, the lines were parallel until the load level of 400 kN, thereafter the specimen 53P behaved differently, and the strain rate was increased rapidly by 18.9 μs/kN, so that the strain at the failure reached 2799 μs, which is equivalent to 559.8 MPa or 1.03fy. The second maximum recorded stress was for CTRL specimen which was 370.6 MPa. Other specimens had a relatively lower stress levels, like 35.2, 50.0, 53.4 and 62.6 MPa, respectively for 00KE, NSC, 10Kd and 0.5P. When comparing specimens with and without epoxied joints, the epoxied joints can transfer more stresses to the reinforcing bars, however in case of the dry joints the stress was concentrated on the non-reinforced joint regions, can poorly transfer the shear stresses to the reinforcing bars closest to the joint, and thereby the stress level in shear reinforcement at failure for 10Kd was only 24.4 MPa, whereas at the same load level the stress on the shear reinforcement of 10KE was 99.8 MPa.

Fig. 12. Load – Strain (S2) relationships for bottom slab, bottom layer longitudinal reinforcement.

prestressing force was proportionally increased too. Increased portion of tensile forces on the strands had transferred to the sections and producing an additional compressive stresses over the concrete and the embedded rebar. The strain measurements of the bottom bars were not exceeded 2000 μs in any specimen, as shown in Fig. 12. CTRL specimen again had

4.2.4. Load–shear reinforcement strains (S4), female SG The shear stresses of the joints were smoothly transferred to the shear reinforcement at the webs of the female segments. SP1 had the maximum strain value of 2376 μs, which is equivalent to the stress of 475.2 MPa. The response of the specimens in G3 for the vertical forces were similar for NSC, HSF, HSS and VHS, and they had parallel curves 8

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minimum tensile strain in all top strands was recorded for CTRL specimen, which was (-18 μs), so the top strand had lost 3.54 MPa (or 0.35 kN) of the prestressing stress. The specimen 35P has a balanced condition between vertical forces and the horizontal force until the load level of 200 kN, after that the tensile strains gradually won the conflict to have a strain of 23 μs at load level of 560 kN, a moment later, the additional tensile strains were released and the strains were returned to the balanced condition, which was followed by failure. Mechanically the situation can be justified by the lower total tensile force (at the top fiber) of the specimen of 240 kN compared to 320 kN of other specimens. The tensile forces of strands located at the top slabs of the specimens could be considered as unchanged for VHS specimen, as the strains were not tolerated by more than −8 and +14 μs. The case of the NSC is similar except of the failure point at which the tensile strain was reached 37 μs. Specimen 00KE was different from others; initially the tensile strain was increased to 33 μs at load level of 160 kN, and then started to decrease in the tensile strain to 17 μs for load level of 260 kN. After that, it was again increased to have 46 μs at vertical load level of 482.6 kN, which was the failure load (beyond the ultimate load), and failure had happened by sliding of the segments.

until the load level of 500 kN, which means, the shear reinforcing steel bars were all subjected to similar stresses in the elastic range, whereas their plastic behavior was different. The same principles were true for G2, of which they have similar behavior until the load level of 400 kN. When comparing specimens for understanding influence of epoxy, a complex relationship was found, the specimens having 6 shear keys were behaving similarly; however, the specimens with 10 keys have similar behavior until the load level of 400 kN, later an opposite action was started for 10Kd, which was gradually releasing the stresses over the shear reinforcing bars. This phenomenon can be justified by releasing the webs from high stresses produced by resistance provided from shear keys; so after they were destroyed, prestressing dowel action and the frictional forces provided by the confining pressure were less effective for transferring the shear stresses. 4.3. Relationships of load and strains in the strands The prestressing strands were working under two horizontal and vertical loading actions at the same time. The bending stresses of the girders were putting the top strands under compression forces, i.e. loss of the tensile force; and the bottom strands were under additional tensile forces. At the same time the vertical displacement was pushing both top and bottom strands to act as dowels, which was an additional tensile force on the top and bottom strands. When the epoxy was crushed, a gap was produced and the tensile forces of the strands again lose an amount of its magnitude. Cracking of concrete, spalling of cover and crushing sharp corners have also a role in decreasing the tensile forces. Opening of the joints was decreasing the tensile force at the top strands, and increasing the tensile force at the bottom strands. All parameters were working simultaneously; therefore a complex behavior of strains should be expected.

4.3.2. Load – Bottom strand strains (P2) The relationship between vertical applied load and the tensile strains on the bottom strands are shown in Fig. 14. All specimens had similar general shapes of the relations. The maximum tensile strain again was for 1.5P specimen, which was 168 μs (i.e. +33.0 MPa or +3.28 kN), and no negative strains were recorded. The low bottom tensile strains are proofing that the visible opening of joint bottom was not occurred until failure had happened. Small fluctuations were returned to local crushes of concrete, crush of the shear key corners, debonding of the epoxy, and the large ranged fluctuations are due to the crushes at the concrete top flange, propagation of the diagonal cracks at the webs, and failure of shear keys.

4.3.1. Load – Top strand strains (P1) The relationship between applied vertical force on the girders and the strains of the top strands were shown in Fig. 13, the recorded strains were for seven specimens only. The maximum recorded strain for the specimens was in case of SP3-1.5P, which was only 99 μs, in addition to the tensile strain in the posttensioning process (6184 μs). Taking the elastic modulus of the strands as 196.6 GPa (AASHTO LRFD-17 [25]), hence the gained tensile stress was 19.46 MPa (or 1.93 kN). The

4.4. Relationships between load and concrete strains Relationship between the vertical applied load and the strains of concrete was determined using 80 mm strain gauges. The inaccuracy which must be expected in this section is in that; the cracks may not pass through the line of strain gauges; on the other side the strain gauges that attached to the top flange of the girders were one-way strain readers, so the transverse strains were not obtained. In addition

Fig. 13. Load – strain (P1) relationship for the top strands.

Fig. 14. Load – Strain (P2) relationship for the bottom strands. 9

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Fig. 15. Load – strain relationship, top surface of the top slab for male segments (C1).

Fig. 16. Load – strain relationship, bottom surface of the bottom slab for male segments (C2).

to the cases of when the concrete top cover of which the strain gauge was attached, was spall out between the two regions of the concentrated loads.

469 μs to 2671 μs. Whereas, the minimum recorded strain at failure was for 10Kd specimen, which was only 251 μs. Generally, the specimens have a low compressive strain values, for example, the first group strains at the load level of 400 kN, were 174 (+23), 202 (+45) and 168 (+68) μs, respectively for 0.5P, 1.0P and 1.5P specimens; noting that the values in the brackets were pre-load strains coming from prestressing. The girders at the second group were also had similar behavior until the load level of 400 kN, thereafter they behaved differently when they were finished their elastic limit and entered their plastic behavior.

4.4.1. Load–strain relation, top slab of male segments (C1) Fig. 15 is showing relationship between the vertical applied load and the strain at the top surface of the top slab of male segments in longitudinal direction. The maximum strain recorded for the top fiber was in CTRL specimen at failure, and it was suddenly changed from 10

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dimensional combined shear and axial stresses; the confining pressure was as expected increasing the tensile strength of the concrete at the web regions. For proofing of this explanation, the best example is the ultimate shear strength of 1.5P, that when compared to 1.0P and 0.5P, it is much higher, although the three specimens have similar overall configurations, and the same mode of failure. Another phenomenon which was noted for flat specimens is that, releasing of the tensile stresses had happened for both 00KE and 00Kd girders. The tension to compression conversions behavior of both girders was happened at different load levels, but the source of the action was only slipping of the segments, from which tensile stresses were stored, and then released gradually.

The G3 also behaved similar reactions against the load until the load level of 440 kN, after that the strain rate of the VHS specimens was accelerated to a higher rate due to its brittle behavior, for which finally an explosion in the top slab covers had happened, and a concrete pieces of more than 200 cm2 were breaking out. In the other side using epoxied joints have a role of transferring stresses to the surrounding concrete and contribution of a larger number of elements to resist the shear and compression stresses. 4.4.2. Load–strain relation, bottom slab of male segments (C2) The relationship between vertical applied load and the strains at the bottom surface of the male segments in longitudinal direction is shown Fig. 16. The tensile strains at the bottom fiber of the specimens were not like of that expected for non-prestressed girders, and they were recorded relatively small strain values. Tensile stress at the bottom of the segmental girders shall firstly overcome the compressive force on the bottom of the specimen, and then start to produce tensile stresses. The maximum recorded tensile strain was 941 μs for 35P specimen, of which 176 μs of prestressing must be subtracted to have pure tensile strain of 765 μs. In Fig. 16, several specimens like 53P, HSF, 1.5P have a midway shift, which refers to propagation of non-visible cracks at the bottom of specimens, a sudden vertical displacement due to smoothening of the shear key corners, crushing one of the shear keys and/or loss of the adhesion bond. In case of specimen 00KE, the tensile strains were produced by the vertical displacement, and they were gradually increased. Subsequently the epoxy bond allowed slip of the segments; the tensile strain was gradually released to have only 14 μs. Eventually, the pure strain was returned to compressive strain of −116 μs, which was exactly equivalent to 5.3 MPa, and too close to the initial stress of 5.4 MPa on the bottom of the specimen. The recovery of some specimens was not happening as there were broken or crushed shear key segments at the joints.

4.5. Damage figures and crack patterns The concrete stress–strain relation exhibits nearly linear elastic response up to a specific portion of its compressive strength depending on the strength class of the concrete. This is followed by gradual softening up to the concrete compressive strength, when the material stiffness drops to zero. Beyond the compressive strength the concrete stress strain relation exhibits strain softening until failure takes place by crushing. Showing crack patterns for structures or any common structural members are helpful in understanding or analyzing the causes of a failure. However, analyzing the state of stresses and the root causes of cracks, size and shape of damage for box sections, is always more difficult and complex, according to the applied loading model, and the loading characteristics.

4.5.1. Damage figures after failure of the specimens Fig. 17 is showing the final shape of three specimens after failure had happened. All specimens exhibited failure at the joints, and the damaged parts at failure were mainly, the overhangs, mid-span of the transverse section of male segments, and the webs of female segments. The damaged parts of all specimens were similar except of flat joints that have no shear keys. The pushed out concrete is clearly showing the shear stress paths of which started from the regions under loading plates, attempting to find the shortest and weakest route toward the support under female segments’ edge.

4.4.3. Load–strain relations, webs of male segments (C3) Theoretically, the outside face of the webs is under tensile strains in two ways, the first one is normally from flexural moments by the vertical force, another and the major tension source is related to the box shape nature, in which the circumferential stresses attempting to push the outside concrete cover of the webs to destroy the web-flange connection and make sectional deformation at the plastic stage. Tensile strains of the first three groups were almost similar in rate of straining, since the variable in the three groups weren’t specifically related to the section of the joints and the interlocked region, by which the strains were transferred to the webs. The maximum recorded strains for G4 were 620 μs, 637 μs and 817 μs, respectively for 00KE, 06KE and 10KE. The recorded strains were relatively smaller, when compared with the top slab strains under compression, however the direction of which the strains were taken is tangential to the web slope, and it wasn’t at the direction of the principal stresses; so it should be expected that a combined axial stress and shear stress were acting at the webs, in the direction of which strain measurements were taken. Another important point is that the 80 mm wide shear key were located at the middle of the 120 mm width of the webs, so the plane of which shear keys attached to the male segment (that are regions of maximum stresses) were covered by a 20 mm thick concrete cover, or located at the depth of at least 20 mm from web surfaces. 4.4.4. Load–strain relations, webs of female segments (C4) Propagation of the cracks at the inside face of the female keys was leading the outside 20 mm covers of female keys to work like reinforcement cover, and in most times they were pushed out like a shell, or a relatively large flat uncrushed thin concrete piece, like 10KE and 35P. In other cases the cover of female keys at the joint regions, was textured with diagonal parallel multiple cracks, and then the lower part was first pushed out, before the upper parts, clear examples of this type were NSC, 53P. Since, the outer face of the web was subjected to three-

Fig. 17. Different crack patterns and failure modes of some specimens (left: male segment, right: female segment). 11

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Fig. 18. Crack vs. load, considering time-lapse (00Kd).

Fig. 19. Crack vs. load, considering time-lapse (6Kd).

Fig. 20. Crack vs. load considering time-lapse (VHS).

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Fig. 21. Crack vs. load, considering time-lapse (35P).

4.5.2. Crack initiation zones considering time lapse When considering time-lapse regarding crack initiation, generally the specimens had behaved three different modes of crack propagation. Some specimens were cracked at a load level of approximately 90% of the ultimate load, and then the crack widths and number of cracks was increased gradually, until reaching the failure limit. When the failure was reached the released energy was mostly 10%; an example of this kind of failure is SP3-1.5P. The second main mode of crack initiation could be described by a sudden catastrophic failure, in which moments before failure visible cracks could be seen, while the joint region wasn’t disintegrated to expect failure. Within parts of a second, a very brittle failure hah happened, as in SP1. The specimens of this kind were not showing any visible surface cracks up to 99% of the ultimate load. The reason for this failure type was based on criteria that shear keys were mainly resisting joint shear failure, not letting the segments to bend at joint by epoxy adhesion bond, and it didn’t let slipping of segments at the joints. Released energy at this type of failure was too high and reaching 35% of the ultimate shear load resisted by the joint. The third type was slipping of specimens having no shear keys, in which the energy was stored step by step and then released by slipping. The process was repeated until reaching the limit of sudden failure by crushing of concrete due to combined stresses. Figs. 18–21, were explaining step by step crack propagation of the specimens considering time-lapse. The load level of which surface visible cracks were appeared is shown in Table 6. It should be noted that cracks shown in the figures were surface cracks, and when conflicting with reinforcement they were terminated or transferred by changing of their paths. However, the shape of the deep cracks was almost an arch around shear keys in the joint region. Results of the cracking load level were in a good agreement with conclusions of other researchers [3,8].

Table 6 First crack load level and released load at failure. Sr.

SP1 SP2 SP3 SP4 SP5 SP6 SP7 SP8 SP9 SP10 SP11 SP12 SP13

SP

CTRL 0.5P 1.5P 35P 53P NSC HSF VHS 00KE 10KE 00Kd 06Kd 10Kd

Ratio of the released load at failure to ultimate load (%)

33.89 34.50 08.82 07.13 19.32 19.69 20.36 11.33 19.49 31.21 19.74 27.57 13.22

First crack load level and its ratio to ultimate load Pcr (kN)

Pcr/Pu (%)

736.7 472.0 991.1 682.2 502.4 522.8 715.4 740.2 486.6 763.6 341.2 505.3 539.9

99.27 99.73 93.26 97.67 95.33 94.35 99.62 98.44 99.18 90.58 87.26 86.87 81.65

Crack developing mode

1 1 2 2 1 2 1 1 3 1 3a 1a 2a

Crack development modes: Mode – 1: diagonal web and flange shear cracks, sudden and brittle failure at a moment within 1/12 s. Mode – 2: diagonal web and flange shear cracks, less brittle and failed gradually. Mode – 3: sudden failure at joint combined shear-compression failure due to slip of the segments. Mode – 1a: semicircular crack around key regions and then sudden failure. Mode – 2a: semicircular crack around shear key regions, and then diagonal shear cracks, intersection of both cracks, failed gradually. Mode – 3a: no visible cracks, step by step storage of energy then released in slipping, with sudden failure.

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Fig. 22. (a) Parallel cracks initiated at shear key ordinates HSF (b) diagonal crack of male and female segments 1.5P.

Fig. 23. Crack pattern of overhanged flange portions.

Fig. 24. (a) Concrete flow due to stress conncentration (b) shear key cover pushed out in relatively large and thin portions.

of the female segment web cracks. Propagation of the male segment shear cracks was due to the higher confining stress, which resulted in a higher shear capacity, thereby, a higher shear stress was applied (26–172% higher than other specimens), and that overcomes the provided additional 20 mm concrete cover, at the base of the male shear keys. The overhangs had not had shear reinforcement, so their source of the shear resistance was come from concrete, and the dowel action by longitudinal slab reinforcement. The crack inclination angle for the overhangs was in the range of 30°−35°, for specimens with the higher prestressing force (1.5P or 53P), or those that have the alignment shear keys (10KE or 10Kd). While for relatively weaker specimens (0.5P) the crack inclination was in the range of 10° − 15°, as shown in Fig. 23. For specimens without using epoxy as adhesion bond between segments, the cracks of the top slabs were passing directly through joints, whiled

4.5.3. Analysis of the cracks and failure events The first crack for the entire specimens was started at the top of upper shear key of the webs (top flange-web connection) or top of the middle shear key, prolonged toward the support line. Fig. 22a is showing that parallel cracks with the angle of 30° were started at the top and the bottom of the shear keys in the male segment extended toward the supporting vertical line. The webs of the male segments were free of cracks (Figs. 17 and 20) because of the additional 20 mm concrete cover provided beside the encapsulted male shear keys. The only specimen that had the diagonal shear cracks at the root of the male keys, was 1.5P (Fig. 22b). However, it was not the first crack, and was appeared 20 kN later to the first crack in the female segment. When the load was increased, the width of the crack was not increased, but additional cracks were appeared at the roots of other male keys. At failure the width of the male segment web cracks was much smaller than that 14

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Fig. 25. Failure shapes of shear keys and shear deformation.

Fig. 26. Slip of segments after crushing of shear keys (6Kd).

for epoxy bonded segments, the cracks in the overhang edges were inclined to an angle according to other parameters of the specimen. The state is proofing that the adhesion epoxy bond was so strong and didn’t permit the cracks to separate the segments that resisting as a monolithic section regarding the crack and stress transfer. The flat joints were controlled by slipping, and the joint itself was the weakest path for the cracks; therefore, no web cracks or overhang cracks were appeared, except of the regions of stress concentration. A phenomenon of flowing of the crushed concrete (like a liquid) was observed for flat specimens, with and without epoxy. This was due to the high local compression stresses that restricting slip of the segments and suddenly released at failure (Fig. 24a). In many cases a large, thin concrete cover was spalled, as shown in Fig. 24b. The reason for the behavior was that when the shear keys were damaged internally, with the action of internal pressure the crushed concrete was pushing the concrete cover to be de-bonded without cracking or breaking to smaller segments. Several failure shapes were captured for shear keys. The main shapes can be seen in Fig. 25, and noting shear deformation of the shear keys. Three failure types were recognized which are: failure at shear key bases, inclined crack through shear keys, and totally crushed shear keys. It can be noted in Fig. 26, that even when all shear keys are profusely cracked or sheared off, the irregular crushed bases were still capable of resisting shearing loads, through rough surfaces of the broken shear keys.

(2)

(3) (4)

(5)

5. Conclusions

(6)

Based on the observations and analysis of the test results, the following conclusions were drawn: (1) The vertical displacement of specimens is significantly influenced 15

by the prestressing force magnitude. At the load level of 300 kN, when decreasing the prestressing force from 1.0P to 0.5P, the displacement has increased by 21.9%; while by increasing the prestressing force from 1.0P to 1.5P, the displacement has decreased by 24.1%. However, at the load level of 600 kN, when increasing the prestressing force from 1.0P to 1.5P, the displacement has decreased by 27.6%. The relative displacement of the flat and keyed dry joints is approximately double of that in the identical epoxied joints. Displacements corresponding to the ultimate load for six and ten key specimens in dry multi-key joints were higher than that of epoxied joints by 94.5% and 91.1% respectively. The linearity of the load–displacement was continued up to 65–85% for keyed joints, whereas it was 40–45% for the flat joints. The elastic stiffness of the segmental box bridges can be increased by adding as much as possible number of shear keys in the joint, and by increasing the confining stress. By decreasing the confining stress to one half, the elastic stiffness was decreased by 17%, while increasing the stress by 50%, the stiffness increased 35%. The epoxy can also increase the joint stiffness by 87.2% & 220.7% for 6 and 10 shear keys, respectively. The plastic ductility is much higher for specimens with higher prestressing values; it causes gradual crushing of concrete and slower strength degradation, instead of cracking and failure by the tensile stresses. The brittle behavior of the epoxied jointed can be made less severe, by adding more shear keys to the flanges or increasing the level of confining stress to 4.5 MPa.

Engineering Structures 206 (2020) 110151

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Declaration of Competing Interest

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] Ahmed G, Aziz O. Influence of intensity & eccentricity of posttensioning force and concrete strength on shear behavior of epoxied joints in segmental box girder bridges. Cons Build Mat 2019;197:117–29. [2] Saibabu S, Srinivas V, Sasmal S, Lakshmanan N, Iyer NR. Performance evaluation of dry and epoxy jointed segmental prestressed box girders under monotonic and cyclic loading. Cons Build Mat 2013;38:931–40. [3] Zhou X, Mickleborough N, Li Z. Shear strength of joints in precast concrete segmental bridges. ACI Struct J 2005;102(1):3–11. [4] Shamass R, Zhou X, Alfano G. Finite-element analysis of shear-off failure of keyed dry joints in precast concrete segmental bridges. J Bridge Eng 2015;20(6):04014084. [5] Ahmed G, Aziz O. Shear behavior of dry and epoxied joints in precast concrete segmental box girder bridges under direct shear loading. Eng Struct 2019;182:89–100. [6] Jiang H, Cao Q, Liu A, Wang T, Qiu Y. Flexural behavior of precast concrete segmental beams with hybrid tendons and dry joints. Cons Build Mat 2016;110:1–7. [7] Jiang H, Chen L, Ma ZJ, Feng W. Shear behavior of dry joints with castellated keys in precast concrete segmental bridges. J Bridge Eng 2015;20(2):04014062. [8] Buyukozturk O, Bakhoum MM, Beattie SM. Shear behavior of joints in precast concrete segmental bridges. ASCE J Struct Eng 1990;116(12):3380–401. [9] Yang KH, Sim JI, Kang JH, Ashour AF. Shear capacity of monolithic concrete joints without transverse reinforcement. Mag Concr Res 2012;64(9):767–79. [10] Jiang H, Wei R, Ma ZJ, Li Y, Jing Y. Shear strength of steel fiber-reinforced concrete dry joints in precast segmental bridges. J Bridge Eng 2016;04016085. [11] Issa MA, Abdalla HA. Structural behavior of single key joints in precast concrete

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