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Applied Sciences
, Volume 8 (10) – Sep 29, 2018

/lp/multidisciplinary-digital-publishing-institute/post-tensioning-steel-rod-system-for-flexural-strengthening-in-damaged-i1ku7mHUJy

- Publisher
- Multidisciplinary Digital Publishing Institute
- Copyright
- © 1996-2019 MDPI (Basel, Switzerland) unless otherwise stated
- ISSN
- 2076-3417
- DOI
- 10.3390/app8101763
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- See Article on Publisher Site

applied sciences Article Post-Tensioning Steel Rod System for Flexural Strengthening in Damaged Reinforced Concrete (RC) Beams 1 2 2 , Swoo-Heon Lee , Kyung-Jae Shin and Hee-Du Lee * School of Convergence & Fusion System Engineering, Kyungpook National University, 2559 Gyeongsang-daero, Sangju-si, Gyeongsangbuk-do 37224, Korea; ﬁnksnow@knu.ac.kr School of Architectural Engineering, Kyungpook National University, 80 Daehak-ro, Buk-gu, Daegu 41566, Korea; shin@knu.ac.kr * Correspondence: lhdza@knu.ac.kr; Tel.: +82-53-950-5591 Received: 6 September 2018; Accepted: 26 September 2018; Published: 29 September 2018 Abstract: In this study, a post-tensioning method using externally unbonded steel rods was applied to pre-damaged reinforced concrete beams for ﬂexural strengthening. Nine simply-supported beams, three reference beams and six post-tensioned beams, were subjected to three-point bending. The design parameters observed in this study were the amount of tension reinforcements (3-D19, 4-D19, and 2-D22 + 2-D25; “D” indicates the nominal diameter of the rebar) and the diameters of the external rod (j22 mm and j28 mm). A V-shaped proﬁle with a deviator at the bottom of the mid-span was applied to the pre-damaged beams, and a post-tensioning force was added to overcome the low load resistance and deﬂection already incurred in the pre-loading state. The post-tensioning force caused by tightening the nuts at the anchorage corresponded to a strain of 2000 " in the external rods; this value was approximately equal to the strain caused by torque that two adults can apply conveniently. The post-tensioning system increased the load-carrying capacity and ﬂexural stiffness by approximately 40–112% and 28–73%, respectively, when compared with the control beams. However, the external rods did not yield in the post-tensioned beam with larger steel reinforcements and external steel rods. The external rod with the larger diameter increased the ﬂexural strength more effectively. Keywords: post-tensioning system; damaged reinforced concrete; ﬂexural strength; external rods 1. Introduction Concrete is the principal component of reinforced concrete (RC) and is the most widely used structural material in modern society because of its remarkable economic value and durability [1–3]. Nonetheless, the aging of concrete in concrete structures gradually deteriorates their performance. Therefore, periodic inspections are very important for restoring the performance of concrete structures prior to performance degradation. As the importance of maintenance and rehabilitation of aged RC structures is being emphasized, the rehabilitation and reinforcement of existing structures are attracting immense interest in South Korea. Accordingly, various studies on structural materials and techniques are being pursued actively [1,4–6]. The most common strengthening techniques include new section enlargement [7–10], external plate bonding [11–17], and post-tensioning [18–21]. Sectional reinforcement involves the addition of an RC jacket section and the bonding of high-strength materials such as steel plate or carbon ﬁber. Steel plate and carbon ﬁber reinforcement methods face challenges due to low bonding reliability and unsatisfactory deﬂection recovery. In an effort to resolve this problem, Nardone et al. [22] suggested Appl. Sci. 2018, 8, 1763; doi:10.3390/app8101763 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 1763 2 of 17 a mechanical fastening technique that uses steel anchors to secure ﬁber-reinforced polymer components to the concrete substrate. However, a post-tensioning method using tensile structural materials is advantageous because the reinforcement effect is more assured and reliable, the restoration of deﬂection is more convenient, and ductile failure can occur. A post-tensioning technique can be conveniently used while the affected structure is in service [23–26]. It is commonly used overseas and is highly economical in comparison with other reinforcement methods. However, its use in South Korea has been severely limited to a certain group of structural engineers owing to its low recognition and the uncertainty regarding its maintenance and rehabilitation. It is likely that the construction cost of reinforcement will be signiﬁcantly reduced if the post-tensioning reinforcement method is used more widely [27–29]. Pre-stressing with tendons involves applying tendon pre-stressing to a concrete structure both internally and externally [30]. This method has a long history of application and is the most effective repair and reinforcement method for existing concrete beams. Moreover, it is a popular technique for constructing long-span bridges because of its short construction time and low cost [30–32]. The advantages of internal or external tendon systems compared with bonding techniques have been widely studied and are enumerated as follows [2,3,18,28–30,32,33]: more economical construction method; shorter construction time; higher convenience and freedom in the layout of the tendon and its consolidation of the concrete. The system for reinforcing the outside of existing structures with tendons is fundamentally different from the traditional method of embedding the tendon inside the concrete. The tendons embedded in the design of a concrete bridge function as the main reinforcing material (e.g., rebar). On the other hand, the tendons used as external reinforcing materials function only as a part of the total ﬂexural strengthening material, while the internal rebar, internal pre-stressing steel, or both contribute to the remaining reinforcement [18]. This study aims to examine the strengthening effect of the tensile rebar ratio and the quantity of reinforcement by using a reinforcing system comprised of external reinforcing steel rods and a deviator. This system was introduced in “Reinforcing Method of Architectural Structures Using High-strength Bars and Tensile-force Measurement Device,” as reported by Molti and Kaia [27]. This study was motivated by previous experiments that have investigated the strength capacities of continuous RC beams reinforced by externally prestressed steel bars relative to those of RC beams without external reinforcement [4,6]. Theoretical analyses have also been performed [5]. In addition, the effect of distance between stirrups and boundary conditions [28], the diameter of steel rods and the ratio of tension reinforcement [29], and the loading condition [34] have been examined. However, these investigations had difﬁculties verifying the effect of external steel rods on the damaged RC beam because they started the experiments after installing the external steel rods. The scope of the current study included (1) damage to the RC beam due to repetitive fatigue loading; (2) restoration of the deﬂection through post-tensioning; (3) strengthening effect with respect to the external strengthening quantity; and (4) evaluation of the increases in strength and stiffness. 2. Experimental Plan 2.1. Specimen Fabrication Test specimens of total length 4400 mm were prepared according to design parameters in order to evaluate the ﬂexural behavior of an RC beam externally strengthened with post-tensioning steel rods. The section size of the basic RC beam was 270 400 mm (width height), and the rebar material was SD400 grade with a tensile strength of 400 MPa. As shown in Figure 1, 3-D13 was used as the compression rebars, and 3-D19, 4-D19, and 2-D22 + 2-D25 were used as the tension rebars (“D” indicates the nominal diameter of the rebar). Transverse reinforcements of D10 were laid out at intervals of 65 mm. The design parameters for strengthening the nine test specimens are as follows: Appl. Sci. 2018, 8, 1763 3 of 17 Strengthening material: high-strength steel rod; Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 17 Diameter of steel rods: j22 mm, j28 mm; Layout shape of steel rod: V-proﬁle with deviator at mid-span; • Diameter of steel rods: φ22 mm, φ28 mm; • Layout shape of steel rod: V-profile with deviator at mid-span; Strengthening effective depth at deviator: 435 mm; • Strengthening effective depth at deviator: 435 mm; Anchorage type: penetrated anchor pin; • Anchorage type: penetrated anchor pin; Loading pattern: three-point bending; and • Loading pattern: three-point bending; and Amount of tensile reinforcements: 3-D19, 4-D19, and 2-D22 + 2-D25. • Amount of tensile reinforcements: 3-D19, 4-D19, and 2-D22 + 2-D25. 100 Symmetry As = 3-D13 22 mm or 28 mm steel rod Stirrups D10 @ 65 A = 3-D19, 4-D19 or 2-D22 + 2-D25 300 1900 1900 300 28 34 R45 R45 R37.5 R47.5 37.5 47.5 t=20 t=22 ▲ Plate for 22 mm rod ▲ Plate for 28 mm rod Figure 1. Details of reinforcements (all dimensions are in mm). Figure 1. Details of reinforcements (all dimensions are in mm). Table 1 lists the test specimens by the design parameters as shown in Figures 1 and 2. S1-No, Table 1 lists the test specimens by the design parameters as shown in Figures 1 and 2. S1-No, S2-No, and S3-No are basic unstrengthened RC beam specimens with tension rebars of 2-D22 + 2-D25, S2-No, and S3-No are basic unstrengthened RC beam specimens with tension rebars of 2-D22 + 4-D19, and 3-D19 design, respectively. “R22” and “R28” in the specimen name denote the diameter of 2-D25, 4-D19, and 3-D19 design, respectively. “R22” and “R28” in the specimen name denote the the external post-tensioning steel rods. The nine specimens were subjected to three-point bending tests. diameter of the external post-tensioning steel rods. The nine specimens were subjected to three-point bending tests. Table 1. Specimen lists. Table 1. Specimen lists. A’ f’ /f’ A f /f A f /f d d d Section s y u s y u ps py pu p v h Specimen No. 2 2 2 (mm ) (MPa) (mm ) (MPa) (mm ) (MPa) (mm) (mm) (mm) (mm) A’s f’y/f’u As fy/fu Aps fpy/fpu dp dv dh Section 1 S1-No 2-D22 n/a n/a n/a n/a n/a b = 270 No. Specimen 3-D13 2 2 2 (mm ) (MPa) (mm ) (MPa) (mm ) (MPa) (mm) (mm) (mm) (mm) 544/655 + 2-D25 500/640 2-j22 h = 400 2 S1-R22 (380.1) 655/805 435 125 100 (1787.6) (760.3) d = 352 1 S1-No n/a n/a n/a n/a n/a 2-j28 3 S1-R28 625/765 435 125 100 2-D22 2-φ22 b = 270 (1231.5) 2 S1-R22 3-D13 544/ 500/ 655/805 435 125 100 + 2-D25 (760.3) h = 400 4 S2-No n/a n/a n/a n/a n/a b = 270 (380.1) 655 640 3-D13 4-D19 (1787.6) 2-φ28 d = 352 544/655 493/630 2-j22 h = 400 5 S2-R22 (380.1) (1146.0) 655/805 435 125 100 3 S1-R28 625/765 435 125 100 (760.3) d = 354 (1231.5) 2-j28 6 S2-R28 625/765 435 125 100 4 S2-No n/a n/a n/a n/a n/a (1231.5) 2-φ22 b = 270 7 S3-No n/a n/a n/a n/a n/a b = 270 5 S2-R22 3-D13 544/ 4-D19 493/ 655/805 435 125 100 3-D13 3-D19 2-j22 544/655 493/630(760.3) h h= 40 = 400 0 8 S3-R22 (380.1) (859.5) 655/805 435 125 100 (380.1) 655 (1146.0) 630 (760.3) d = 354 2-φ28 d = 354 2-j28 6 S2-R28 625/765 435 125 100 9 S3-R28 625/765 435 125 100 (1231.5) (1231.5) 7 S3-No n/a n/a n/a n/a n/a Notes: A’ , A , and A are the total sectional areas of the compression reinforcements, tension reinforcements, and s s ps external post-tensioning steel rods, respectively; f’ /f’ , f /f , and f /f are the yield/ultimate strengths of the y u y u py pu 2-φ22 b = 270 8 S3-R22 3-D13 544/ 3-D19 493/ 655/805 435 125 100 compression reinforcements, tension reinforcements, and external post-tensioning steel rods, respectively; d is the (760.3) h = 400 effective depth at the deviator; d is the vertical distance between the top of the beam and center of the anchorage; (380.1) 655 (859.5) 630 d is the horizontal distance between the support and center 2-φ of28 the anchorage; b is the beam width; h is the beam d = 354 9 S3-R28 625/765 435 125 100 height; d is the effective depth for tension reinforcement; n/a = not applicable. (1231.5) Notes: A’s, As, and Aps are the total sectional areas of the compression reinforcements, tension reinforcements, and external post-tensioning steel rods, respectively; f’y/f’u, fy/fu, and fpy/fpu are the yield/ultimate strengths of the compression reinforcements, tension reinforcements, and external post-tensioning steel rods, respectively; dp is the effective depth at the deviator; dv is the vertical distance between the top of the beam and center of the anchorage; dh is the horizontal distance between the support and center of the anchorage; b is the beam width; h is the beam height; d is the effective depth for tension reinforcement; n/a = not applicable. 170 Appl. Sci. 2018, 8, 1763 4 of 17 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 17 Effective depth d =435mm d =115mm Connection plate between saddle and clevis d =100mm Clevis Saddle pin Figure 2. Details of the strengthening specimen. Figure 2. Details of the strengthening specimen. 2.2. Material Properties 2.2. Material Properties The compressive strength tests of concrete cylindrical specimens of dimensions j100 200 mm The compressive strength tests of concrete cylindrical specimens of dimensions φ100 × 200 mm were carried out according to the speciﬁcations of KS F 2405 [35]. The longitudinal displacement and were carried out according to the specifications of KS F 2405 [35]. The longitudinal displacement and strain were simultaneously measured using two linear variable differential transformers (LVDTs) of strain were simultaneously measured using two linear variable differential transformers (LVDTs) of capacity 10 mm and two concrete strain gauges of gauge length 60 mm. The load was measured using capacity 10 mm and two concrete strain gauges of gauge length 60 mm. The load was measured a load cell mounted in a universal testing machine (UTM). The tensile tests of the rebar and steel using a load cell mounted in a universal testing machine (UTM). The tensile tests of the rebar and rod were performed in accordance with KS B 0802 [36]. The elongated displacement and strain were steel rod were performed in accordance with KS B 0802 [36]. The elongated displacement and strain measured using an extensometer of gauge length 50 mm and two strain gauges of gauge length 5 mm, were measured using an extensometer of gauge length 50 mm and two strain gauges of gauge length respectively. Table 2 and Figure 3 present the material test results. The average compressive strength 5 mm, respectively. Table 2 and Figure 3 present the material test results. The average compressive of concrete at 28 d was 30 MPa, and the D13 compression rebar exhibited a yield strength of 544 MPa strength of concrete at 28 d was 30 MPa, and the D13 compression rebar exhibited a yield strength of and tensile strength of 655 MPa. The D19, D22, and D25 tension rebars exhibited yield strengths of 493, 544 MPa and tensile strength of 655 MPa. The D19, D22, and D25 tension rebars exhibited yield 530, and 445 MPa, respectively, and tensile strengths of 631, 658, and 628 MPa, respectively. The j22 strengths of 493, 530, and 445 MPa, respectively, and tensile strengths of 631, 658, and 628 MPa, mm and j28 mm external rods exhibited yield strengths of 655 and 625 MPa, respectively, and tensile respectively. The φ22 mm and φ28 mm external rods exhibited yield strengths of 655 and 625 MPa, strengths of 805 and 765 MPa, respectively. respectively, and tensile strengths of 805 and 765 MPa, respectively. Table 2. Material test results. Table 2. Material test results. Diameter Sectional Area f or f f or f # or # y py u pu y py Diameter Sectional Area fy or fpy fu or fpu εy or εpy Type Contents Type Contents (mm) (mm ) (MPa) (MPa) (") (mm) (mm) (MPa) (MPa) (με) Reinforcements D13 126.7 544 655 2720 Reinforcements D13 126.7 544 655 2720 D19 286.5 493 631 2465 D19 286.5 493 631 2465 Mild steel D22 387.1 530 658 2650 Mild steel D22 387.1 530 658 2650 D25 506.7 445 628 2232 D25 506.7 445 628 2232 External rod j22 380.1 655 805 5196 High-strength steel External rod φ22 380.1 655 805 5196 j28 615.8 625 765 5050 High-strength steel φ28 615.8 625 765 5050 Concrete f’ = 30 MPa E = 4730 f’ = 25.9 GPa by ACI318-14 [37] Concrete f’c = 30 MPa c c Ec = 4730√f’c = 25.9 GPa by ACI318-14 [37] Notes: f and f are the yield and tensile strengths, respectively, of the mild steel reinforcements; f and f are the y u py pu yield and tensile strengths, respectively, of the external rods; # and # are the yield strains of the reinforcement y py Notes: fy and fu are the yield and tensile strengths, respectively, of the mild steel reinforcements; fpy and external rods, respectively; f’ and E are the compressive strength and modulus of elasticity, respectively, c c and fpu are the yield and tensile strengths, respectively, of the external rods; εy and εpy are the yield of the concrete. strains of the reinforcement and external rods, respectively; f’c and Ec are the compressive strength and modulus of elasticity, respectively, of the concrete. Appl. Appl. Sci. Sci. 2018 2018, , 8 8,, x FO 1763R PEER REVIEW 5 of 5 of 17 17 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 17 φ 22 φ 28 φ 28 D25 D22 D25 D22 D19 D13 D19 D13 0 150,000 300,000 0 150,000 300,000 0 150,000 300,000 0 150,000 300,000 Strain (με) Strain (με) Strain (με) Strain (με) Figure 3. Tensile test results of reinforcements (left) and external rods (right). Figure 3. Tensile test results of reinforcements (left) and external rods (right). Figure 3. Tensile test results of reinforcements (left) and external rods (right). 2.3. Loading and Measurement 2.3. Loading and Measurement 2.3. Loading and Measurement The specimens were subjected to three-point bending with a span length of 3800 mm. Two LVDTs The specimens were subjected to three-point bending with a span length of 3800 mm. Two The specimens were subjected to three-point bending with a span length of 3800 mm. Two of capacity 100 mm were installed at the center of the beam. Five crack gauges of capacity5 mm were LVDTs of capacity 100 mm were installed at the center of the beam. Five crack gauges of capacity ±5 LVDTs of capacity 100 mm were installed at the center of the beam. Five crack gauges of capacity ±5 installed such that the gauge length of each one was 430 mm. The gauge length of the original crack mm were installed such that the gauge length of each one was 430 mm. The gauge length of the mm were installed such that the gauge length of each one was 430 mm. The gauge length of the gauge device was 100 mm; however, it was extended using a dummy plate. The LVDTs measured the original crack gauge device was 100 mm; however, it was extended using a dummy plate. The original crack gauge device was 100 mm; however, it was extended using a dummy plate. The deﬂection at the front and back of the beam center, and the crack gauges were installed to measure the LVDTs measured the deflection at the front and back of the beam center, and the crack gauges were LVDTs measured the deflection at the front and back of the beam center, and the crack gauges were strain change and curvature of the beam section, as shown in Figure 4. installed to measure the strain change and curvature of the beam section, as shown in Figure 4. installed to measure the strain change and curvature of the beam section, as shown in Figure 4. Compression 1 Compression h φ h φ Tension Tension Figure 4. Curvature calculation using crack gauges. Figure 4. Curvature calculation using crack gauges. Figure 4. Curvature calculation using crack gauges. The method of computing the curvature from the displacements measured using the crack gauges The method of computing the curvature from the displacements measured using the crack The method of computing the curvature from the displacements measured using the crack is expressed by Equation (1): gauges is expressed by Equation (1): gauges is expressed by Equation (1): ε = Δl / l ， ε = Δl / l ， φ =() ε − ε / h # = Dl /l , # = Dl /l , j = (# # )/h (1) 2 1 g (1) 11 11 1 1 2 2 2 2 2 2 2 1 g ε = Δl / l ， ε = Δl / l ， φ =() ε − ε / h (1) 1 1 1 2 2 2 2 1 g where l1 and l2 are the gauge lengths at the top and bottom crack gauges, respectively; Δl1 and Δl2 where l and l are the gauge lengths at the top and bottom crack gauges, respectively; Dl and Dl 1 2 1 2 where l1 and l2 are the gauge lengths at the top and bottom crack gauges, respectively; Δl1 and Δl2 represent the displacements measured at the top and bottom gauges, respectively; ε1 and ε2 are the represent the displacements measured at the top and bottom gauges, respectively; # and # are the 1 2 represent the displacements measured at the top and bottom gauges, respectively; ε1 and ε2 are the strains in the compression and tension extreme fibers, respectively; hg is the vertical distance strains in the compression and tension extreme ﬁbers, respectively; h is the vertical distance between strains in the compression and tension extreme fibers, respectively; hg is the vertical distance between the two gauges; and φ represents the curvature. the two gauges; and j represents the curvature. between the two gauges; and φ represents the curvature. The steps of the experimental procedure used to simulate the actual rehabilitation and The steps of the experimental procedure used to simulate the actual rehabilitation and The steps of the experimental procedure used to simulate the actual rehabilitation and reinforcement of the RC specimens are as follows (see Figure 5): reinforcement of the RC specimens are as follows (see Figure 5): reinforcement of the RC specimens are as follows (see Figure 5): Stress (MPa) Stress (MPa) Appl. Sci. 2018, 8, 1763 6 of 17 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 17 0 50 100 150 Deflection (mm) (b) (a) 400 400 500 Begining of PT 300 300 End of PT 100 100 0 0 0 5 10 15 20 25 0 5 10 15 20 25 010 20 30 40 Deflection (mm) Deflection (mm) Deflection (mm) (c) (d) (e) Figure Figure 5. 5. Exp Experimental erimental procedure: ( procedure: a () t a) e testing sting of contr of controol l beam beam;; (( b b) ) drill ho drill hole le for for anchorag anchorage; e; ((c c)) preloa preloading; ding; ((d d)) post- post-tensioning tensioning (PT); an (PT); and d ((e e)) reload reloading. ing. (1) First, bending tests of the unstrengthened control RC beams were carried out to determine their (1) First, bending tests of the unstrengthened control RC beams were carried out to determine their yield strength, ultimate strength, and the corresponding deﬂections (Figure 5a). yield strength, ultimate strength, and the corresponding deflections (Figure 5a). (2) The specimens used for strengthening were prepared and the anchor holes at the end of the beam (2) The specimens used for strengthening were prepared and the anchor holes at the end of the beam wer were drilled e dprior rilledto prior the t loading o the lo test adrather ing test than rath pr er efabricated than prefa so brica as to ted simulate so as to si the m real-world ulate the condition of the beam (Figure 5b). real-world condition of the beam (Figure 5b). (3) Preloading was applied to the unstrengthened beam through displacement control. Several (3) Preloading was applied to the unstrengthened beam through displacement control. Several repeti repetitive tive lloads oads were a were applied pplied unti untill the the loa loaddexceeded exceeded the the yield yield l load oad in in or or der de to r to induce induc damage e damag to e to the beam (Figure 5c). the beam (Figure 5c). (4) The external unbonded member was post-tensioned after reducing the load (i.e., from the load (4) The external unbonded member was post-tensioned after reducing the load (i.e., from the load exceeding yield load down to the service load of approximately two-thirds of the ultimate exceeding yield load down to the service load of approximately two-thirds of the ultimate strength; Figure 5d). Since damage to the measuring device and measurement error can occur if strength; Figure 5d). Since damage to the measuring device and measurement error can occur if the strengthening system were installed during the loading test, the system was prepared prior the strengthening system were installed during the loading test, the system was prepared prior to the loading test and tensioned after the beam was damaged. to the loading test and tensioned after the beam was damaged. (5) Tensioning was applied while monitoring the load–deflection curve and strain of the unbonded (5) Tensioning was applied while monitoring the load–deﬂection curve and strain of the unbonded steel rod. The post-tensioning (PT) level was set at the first of two strengths: recovery of the steel rod. The post-tensioning (PT) level was set at the ﬁrst of two strengths: recovery of the deflection at the service load of the unstrengthened beam or attainment of a strain of 2000 με in deﬂection at the service load of the unstrengthened beam or attainment of a strain of 2000 " in the steel rod, which is approximately the force converted from torque that two adult men can the steel rod, which is approximately the force converted from torque that two adult men can apply using a wrench. At this time, an actuator was used to maintain the service load level by apply using a wrench. At this time, an actuator was used to maintain the service load level by load control. load control. (6) After the tensioning was completed, the test specimens were subjected to re-loading using the (6) After the tensioning was completed, the test specimens were subjected to re-loading using the displacement control method until their final failure (Figure 5e). displacement control method until their ﬁnal failure (Figure 5e). Applied Load (kN) Applied Load (kN) Applied Load (kN) Applied Load (kN) Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 17 Appl. Sci. 2018, 8, 1763 7 of 17 3. Experimental Results 3. Experimental Results 3.1. Unstrengthened Beams 3.1. Unstrengthened Beams Figure 6 indicates the typical crack distributions in an RC beam. Generally, the cracking Figure 6 indicates the typical crack distributions in an RC beam. Generally, the cracking behavior behavior of an RC beam can be described as composed of three stages: the first is the initiation of of an RC beam can be described as composed of three stages: the ﬁrst is the initiation of cracking, cracking, the second is the yield of the tensile rebar, and the third is the concrete crushing collapse the second is the yield of the tensile rebar, and the third is the concrete crushing collapse [38]. Similarly, [38]. Similarly, in this test, flexural cracking occurred from the bottom of the beam center upon in this test, ﬂexural cracking occurred from the bottom of the beam center upon attaining the crack attaining the crack load. The gradual loading resulted in a wider crack and the propagation of the load. The gradual loading resulted in a wider crack and the propagation of the crack toward the crack toward the support. As the propagation of the cracks involved simultaneous shear cracking support. As the propagation of the cracks involved simultaneous shear cracking and ﬂexural cracking, and flexural cracking, diagonal cracking was observed toward the support. After the tensile rebar diagonal cracking was observed toward the support. After the tensile rebar yielded, a plastic hinge yielded, a plastic hinge occurred around the loading point, causing the cracking to propagate occurred around the loading point, causing the cracking to propagate further, and the collapse of further, and the collapse of the concrete around the loading point started. Moreover, at this point of the concrete around the loading point started. Moreover, at this point of tensile rebar yielding, the tensile rebar yielding, the increase in load was not significant and only the deflection increased. increase in load was not signiﬁcant and only the deﬂection increased. Upon attaining the ﬁnal failure Upon attaining the final failure of the specimens, the compressive collapse of concrete in the of the specimens, the compressive collapse of concrete in the specimens S1-No, S2-No, and S3-No was specimens S1-No, S2-No, and S3-No was observed at the distances of 1200, 1000, and 600 mm, observed at the distances of 1200, 1000, and 600 mm, respectively, on the left and right sides of the respectively, on the left and right sides of the loading point. The more the number of tensile rebars in loading point. The more the number of tensile rebars in the test specimen, the fewer were the hairline the test specimen, the fewer were the hairline cracks and the narrower were the cracks observed. cracks and the narrower were the cracks observed. S1-No S2-No S3-No Figure 6. Experimental crack pattern of unstrengthened beams. Figure 6. Experimental crack pattern of unstrengthened beams. Figure 7a shows the load–deﬂection curves of the control specimens. The yield load for the Figure 7a shows the load–deflection curves of the control specimens. The yield load for the specimen S1-No was 331 kN, and the corresponding mid-span deﬂection was 24.8 mm. This specimen specimen S1-No was 331 kN, and the corresponding mid-span deflection was 24.8 mm. This manifested ductility until the strain of the compressive concrete extreme ﬁber attained 0.013 with no specimen manifested ductility until the strain of the compressive concrete extreme fiber attained indication of rapid load decrease. The specimen S2-No yielded at the deﬂection of 20.3 mm and load 0.013 with no indication of rapid load decrease. The specimen S2-No yielded at the deflection of 20.3 of 228 kN. The specimen S3-No started to yield at the deﬂection of 18.2 mm and load of 181.2 kN. mm and load of 228 kN. The specimen S3-No started to yield at the deflection of 18.2 mm and load of Moreover, the two beams exhibited sufﬁcient ductility until the strain of the compressive concrete 181.2 kN. Moreover, the two beams exhibited sufficient ductility until the strain of the compressive extreme ﬁber attained 0.016 and 0.007, respectively, with no indication of load decrease. concrete extreme fiber attained 0.016 and 0.007, respectively, with no indication of load decrease. The mid-span curvature curves in Figure 7b are plotted with the strain of the section as measured The mid-span curvature curves in Figure 7b are plotted with the strain of the section as using the crack gauges installed as illustrated in Figure 4. The curvature of S1-No could not be measured using the crack gauges installed as illustrated in Figure 4. The curvature of S1-No could computed until the completion of the experiment owing to an early debonding of the crack gauge not be computed until the completion of the experiment owing to an early debonding of the crack caused by the compressive collapse of the extreme concrete ﬁber. gauge caused by the compressive collapse of the extreme concrete fiber. Table 3 summarizes the experimental results such as the stiffness, load capacity, and corresponding deﬂection of the unstrengthened control specimens. All the specimens exhibited similar crack load P cr and deﬂection d of approximately 50 kN and 2.3 mm, respectively. The initial stiffness K of about cr initial 30 kN/mm decreased to the post-stiffness K of 16.5 kN/mm for S1-No and 12.5 kN/mm for S2-No. post For S3-No, the initial stiffness was 26.0 kN/mm, and the post-stiffness after cracking was 10.1 kN/mm. Comparing the deﬂections, when the compressive strains # of the extreme concrete ﬁber were 0.003 cu or 0.005, as measured using the crack gauges, the deﬂection tended to decrease with a higher number of tensile rebars. The strain of 0.003 represents the maximum strain (or ultimate strain or failure strain) of the compressive extreme ﬁber as assumed during the typical ﬂexural design of the RC beam [37]. Appl. Sci. 2018, 8, 1763 8 of 17 The strain of 0.005 refers to the maximum value of the strain of the compressive concrete as used more practically in the rehabilitation and reinforcement of RC structures [39,40]. This study investigated the stepwise Appl. Sci. 2018 change , 8, x FO at R P strains EER REexceeding VIEW 0.003 in the compressive extreme ﬁber. 8 of 17 400 300 □ * S1-No □ ◇ 250 S1-No ◇ ○ S2-No ◇ ○ S2-No * ◇ ○ S3-No 200 S3-No 150 □ Notes: Notes: □ : At yielding ＊ : At ε = 0.003 □ : At yielding ＊ : At ε = 0.003 cu cu ◇ : At ε = 0.005 ○ : Test End ◇ : At ε = 0.005 ○ : Test End cu cu 0 0 0 50 100 150 200 0.00 0.05 0.10 0.15 0.20 0.25 Deflection (mm) Curvature (1/m) (a) (b) Figure Figure 7 7.. Resu Results lts of c of contr ontrol ol RC RC beams: beams: ( (a)ameasur ) measured total load v ed total load versus ersus mid-span mid-span def deﬂection lection and and (b) calculated (b) calculated mid-span mid-sp moment an moment vers versus curvatur us curvature rel e relationship. ationship. Table 3. Summary of measured results of control RC beams. Table 3 summarizes the experimental results such as the stiffness, load capacity, and correspondinBefore g deflect Cracking ion of the After unstre Cracking ngthened Atco Yielding ntrol spec Atim # ens. = 0.003 All the At # specimens ex = 0.005 At Phibited cu cu max Specimen similar crack load Pcr and deflection δcr of approximately 50 kN and 2.3 mm, respectively. The initial K Decrease K Decrease P d P d P d P d initial post y y 0.003 0.003 0.005 0.005 max max (kN/mm) (%) (kN/mm) (%) (kN) (mm) (kN) (mm) (kN) (mm) (kN) (mm) stiffness Kinitial of about 30 kN/mm decreased to the post-stiffness Kpost of 16.5 kN/mm for S1-No and S1-No 30.3 n/a 16.5 n/a 331.3 24.8 333.4 32.8 326.6 43.9 335.6 30.1 12.5 kN/mm for S2-No. For S3-No, the initial stiffness was 26.0 kN/mm, and the post-stiffness after S2-No 29.4 2.9 12.5 24.2 228.2 20.3 242.9 53.1 252.3 78.0 255.0 93.4 cracking was 10.1 kN/mm. Comparing the deflections, when the compressive strains εcu of the S3-No 26.0 14.1 10.1 38.5 181.2 18.2 203.9 98.1 205.5 129.2 205.9 137.0 extreme concrete fiber were 0.003 or 0.005, as measured using the crack gauges, the deflection Notes: # is the compressive strain of the extreme concrete measured using crack gauges; K is the initial stiffness cu initial before cracking; K is the post-stiffness after cracking; P and d are the yield load and its corresponding deﬂection, post y y tended to decrease with a higher number of tensile rebars. The strain of 0.003 represents the respectively; P and P are the loads and d and d are the corresponding deﬂections when # attained 0.003 0.005 0.003 0.005 cu maximum strain (or ultimate strain or failure strain) of the compressive extreme fiber as assumed 0.003 and 0.005, respectively; P and d are the maximum load and its corresponding deﬂection, respectively; max max n/a = not applicable. during the typical flexural design of the RC beam [37]. The strain of 0.005 refers to the maximum value of the strain of the compressive concrete as used more practically in the rehabilitation and 3.2. Strengthened Beams reinforcement of RC structures [39,40]. This study investigated the stepwise change at strains exceeding 0.003 in the compressive extreme fiber. Figure 8a shows the crack distribution of the S1 beams strengthened with steel rods of diameters j22 mm and j28 mm. These strengthened specimens exhibited signiﬁcantly fewer and narrower Table 3. Summary of measured results of control RC beams. cracks in comparison to the unstrengthened specimens. However, in comparison with the S2-type specimens, the tensile ﬂexural cracking was signiﬁcantly reduced. Furthermore, the concrete collapse Before Cracking After Cracking At Yielding At εcu = 0.003 At εcu = 0.005 At Pmax was Specideeper men than Kinitialthat Decrease of the S2 specimens Kpost Decrease (reaching P the y deepened δy P0.003neutral δ0.003 axis) P0.005due δ0.005 to the Pmax relative δmax increase in the (kN/tension mm) reinfor (%) cements. (kN/mm) (%) (kN) (mm) (kN) (mm) (kN) (mm) (kN) (mm) S1-N The o distribution 30.3 of cracks n/a after16. applying 5 n load /a on331. the3 S224. specimens 8 333.4 str32. engthened 8 326.6 with 43.9 steel 335.r6 ods30. of 1 diameters S2-No 29. j22 mm4 and −j2. 289 12. mm is shown5 in−24. Figur 2 e 228. 8b.2 The 20.two 3 242. specimens 9 53.1 manifested 252.3 78.0 a signiﬁcant 255.0 93.4 S3-No 26.0 −14.1 10.1 −38.5 181.2 18.2 203.9 98.1 205.5 129.2 205.9 137.0 decrease in the number and width of cracks in comparison to the unstrengthened control specimen Notes: εcu is the compressive strain of the extreme concrete measured using crack gauges; Kinitial is the S2-No. Although further reinforcement resulted in wider and deeper concrete collapse owing to initial stiffness before cracking; Kpost is the post-stiffness after cracking; Py and δy are the yield load the deepened neutral axis, the number and propagation of the ﬂexural cracks observed at the beam and its corresponding deflection, respectively; P0.003 and P0.005 are the loads and δ0.003 and δ0.005 are the bottom were relatively less. The specimen strengthened with a steel rod of diameter j28 mm (S2-R28) corresponding deflections when εcu attained 0.003 and 0.005, respectively; Pmax and δmax are the cracked around the anchorage on top of the support upon attaining the ultimate strength. However, maximum load and its corresponding deflection, respectively; n/a = not applicable. the anchorage did not fail until the completion of the test. Figure 8c indicates the crack patterns of the strengthened S3 beams. When compared to the basic 3.2. Strengthened Beams beam, the width and number of the cracks decreased. At the cracking load, ﬂexural cracks occurred near the loading point, and they grew to a height of 260–300 mm in the section at the completion of the Figure 8a shows the crack distribution of the S1 beams strengthened with steel rods of test. In S3-R22, while the load increased from the yield load to the ultimate load, concrete crushing diameters φ22 mm and φ28 mm. These strengthened specimens exhibited significantly fewer and started on the left side of the loading point. In S3-R28, concrete crushing occurred over a wider range narrower cracks in comparison to the unstrengthened specimens. However, in comparison with the than in R22. S2-type specimens, the tensile flexural cracking was significantly reduced. Furthermore, the concrete collapse was deeper than that of the S2 specimens (reaching the deepened neutral axis) due to the relative increase in the tension reinforcements. The distribution of cracks after applying load on the S2 specimens strengthened with steel rods of diameters φ22 mm and φ28 mm is shown in Figure 8b. The two specimens manifested a significant decrease in the number and width of cracks in comparison to the unstrengthened control specimen S2-No. Although further reinforcement resulted in wider and deeper concrete collapse Applied Load (kN) Moment (kNm) Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 17 owing to the deepened neutral axis, the number and propagation of the flexural cracks observed at the beam bottom were relatively less. The specimen strengthened with a steel rod of diameter φ28 mm (S2-R28) cracked around the anchorage on top of the support upon attaining the ultimate strength. However, the anchorage did not fail until the completion of the test. Figure 8c indicates the crack patterns of the strengthened S3 beams. When compared to the basic beam, the width and number of the cracks decreased. At the cracking load, flexural cracks occurred near the loading point, and they grew to a height of 260–300 mm in the section at the completion of the test. In S3-R22, while the load increased from the yield load to the ultimate load, concrete crushing started on the left side of the loading point. In S3-R28, concrete crushing occurred Appl. Sci. 2018, 8, 1763 9 of 17 over a wider range than in R22. S1-R22 S1-R28 (a) S2-R22 S2-R28 (b) S3-R22 S3-R28 (c) Figure 8. Crack pattern of strengthened beams: (a) S1 beams; (b) S2 beams; and (c) S3 beams. Figure 8. Crack pattern of strengthened beams: (a) S1 beams; (b) S2 beams; and (c) S3 beams. Figure 9a shows the load–deﬂection and load–rod strain curves of S1-R22 strengthened with Figure 9a shows the load–deflection and load–rod strain curves of S1-R22 strengthened with a a steel rod of diameter j22 mm. Prior to the post-tensioning, the measured stiffness after cracking steel rod of diameter φ22 mm. Prior to the post-tensioning, the measured stiffness after cracking K was 17.5 kN/mm. The stiffness of the strengthened specimen after post-tensioning K was before after Kbefore was 17.5 kN/mm. The stiffness of the strengthened specimen after post-tensioning Kafter was 23.2 23.2 kN/mm. Post-tensioning was carried out after reducing the load from that at the state when it kN/mm. Post-tensioning was carried out after reducing the load from that at the state when it damaged the unstrengthened beam (P = 342.7 kN and d = 21.9 mm), to 226 kN. Post-tensioning 1st 1st damaged the unstrengthened beam (P1st = 342.7 kN and δ1st = 21.9 mm), to 226 kN. Post-tensioning aided the recovery of the deﬂection of approximately 4.1 mm at the center, and the tension strain aided the recovery of the deflection of approximately 4.1 mm at the center, and the tension strain applied to the steel rod # was measured as 2163 ". The beam specimen attained the maximum se applied to the steel rod εse was measured as 2163 με. The beam specimen attained the maximum load load P and corresponding deﬂection d of 469.4 kN and 55.5 mm, respectively, upon continuous 2nd 2nd P2nd and corresponding deflection δ2nd of 469.4 kN and 55.5 mm, respectively, upon continuous reloading after post-tensioning. The deﬂection continued to increase without a signiﬁcant increase reloading after post-tensioning. The deflection continued to increase without a significant increase in in the load until the maximum load, followed by a decrease in the load. Although the strain of the the load until the maximum load, followed by a decrease in the load. Although the strain of the concrete compressive-extreme ﬁber had already reached 0.003 prior to attaining the maximum strength, concrete compressive-extreme fiber had already reached 0.003 prior to attaining the maximum the strain of the concrete compressive extreme ﬁber could not be measured subsequently owing to the strength, the strain of the concrete compressive extreme fiber could not be measured subsequently debonding of the top crack gauge, which was caused by crushing of the concrete. However, it was likely to have exceeded 0.005, considering the linearity of strains measured by crack gauges. The external rod strain of 2163 " with post-tensioning reached 2763 " and 5582 " when the compressive strain of the concrete extreme ﬁber # and the maximum load reached 0.003 and 469.4 kN, respectively. The steel cu rod yielded at a load of 463 kN and deﬂection of 71.0 mm between the time the compressive strain of the concrete extreme ﬁber reached 0.003 and the maximum load reached 469.4 kN. The test ended at the rod strain of 6260 ". Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 17 owing to the debonding of the top crack gauge, which was caused by crushing of the concrete. However, it was likely to have exceeded 0.005, considering the linearity of strains measured by crack gauges. The external rod strain of 2163 με with post-tensioning reached 2763 με and 5582 με when the compressive strain of the concrete extreme fiber εcu and the maximum load reached 0.003 and 469.4 kN, respectively. The steel rod yielded at a load of 463 kN and deflection of 71.0 mm between the time the compressive strain of the concrete extreme fiber reached 0.003 and the maximum load reached 469.4 kN. The test ended at the rod strain of 6260 με. Figure 9b depicts the load–deflection and load–rod strain curves of S1-R28. The initial stiffness of 17.5 kN/mm immediately before post-tensioning increased to 22.3 kN/mm after strengthening with the steel rods. The mid-span deflection recovered by post-tensioning was approximately 6.4 mm; at this point, the measured steel rod strain was 1841 με. The beam specimen attained the maximum load of 521.4 kN and deflection of 59.3 mm after post-tensioning. The strains of the concrete compressive extreme fiber were 0.003 and 0.005 at the deflection stages of 26.0 and 32.5 mm, respectively, prior to attaining the maximum strength. The load continued to increase beyond the yield strength up to the maximum strength and gradually decreased after the maximum load. The test ended at the point of deflection of 100 mm at the beam center. The external rod strain of 1841 με reached 2400, 2572, and 3536 με at εcu = 0.003, εcu = 0.005, and P2nd = 521.4 kN, respectively. The strain of the steel rod did not yield, even after attaining the maximum strength, until the completion of the Appl. Sci. 2018, 8, 1763 10 of 17 experiment. w/o strengthening w/o strengthening 600 600 P after PT ma x after post-tensioning after post-tensioning P after PT ma x ε = 0.005 cu 500 ε = 0.003 ε = 0.003 500 cu cu = 0.003 ε cu P after PT ma x 400 400 ε = 0.003 or 0.005 P after PT cu ma x P prior to PT P prior to PT ma x ma x Begining of PT Begining of PT ε =2163με se ε =1841με 200 se End of PT End of PT 0 2040 6080 100 0 2000 4000 6000 8000 0 20 40 60 80 100 0 1000 2000 3000 4000 5000 Deflection at midspan (mm) Strain in external rod (με) Deflection at midspan (mm) Strain in external rod (με) (a) (b) Figure 9. Figure 9. Defle Deﬂection ction and rod and rodstrain with resp strain with respect ect to to applie applied d load: ( load:a() S1-R22 a) S1-R22 and ( andb() S1-R28 b) S1-R28. . Figure 9b depicts the load–deﬂection and load–rod strain curves of S1-R28. The initial stiffness of Figure 10a shows the load–deflection and load–rod strain curves for S2-R22 strengthened with a 17.5 kN/mm immediately before post-tensioning increased to 22.3 kN/mm after strengthening with steel rod of diameter φ22 mm. The stiffness prior to the post-tensioning of 12.5 kN/mm increased to the steel rods. The mid-span deﬂection recovered by post-tensioning was approximately 6.4 mm; at this 17.9 kN/mm after post-tensioning, which was performed after reducing the load from P1st = 230.2 kN point, the measured steel rod strain was 1841 ". The beam specimen attained the maximum load to 154 kN. The post-tensioning recovered a deflection of approximately 5.7 mm, and the effective of 521.4 kN and deﬂection of 59.3 mm after post-tensioning. The strains of the concrete compressive strain applied to the steel rod was 2153 με. The continuous reloading resulted in a maximum load of extr 419.eme 0 kN ﬁber and def werleect 0.003 ion o and f 660.005 .0 mm at . Th thee def deﬂection lections stages were 3 of026.0 .4 mand m and 32.5 41 mm, .5 mm respectively at the me,as prior uredto attaining strain of 0. the 003 an maximum d 0.005str , re ength. spectiv The ely, i load n thcontinued e concrete compressive extreme fiber; these d to increase beyond the yield strength eflection up to the s maximum occurred wstr ellength before and atta gradually ining the m decr axieased mum lo after ad c the apa maximum city. Although the decrea load. The test ended se in the at the loapoint d was of deﬂection not evident af of 100 ter the ma mm atximum l the beam oad, the experi center. The external ment was termin rod strain atof ed when the measured de 1841 " reached 2400, 2572, flection and was 87 mm because brittle failure by concrete crushing was predicted. The initial strain of the 3536 " at # = 0.003, # = 0.005, and P = 521.4 kN, respectively. The strain of the steel rod did not cu cu 2nd post-tensioning rod (εse = 2153 με) increased to 3141, 3805, and 5411 με at εcu = 0.003, εcu = 0.005, and yield, even after attaining the maximum strength, until the completion of the experiment. P2nd = 419.0 kN, respectively. The external rod yielded at the load and deflection of 417 kN and 62.6 Figure 10a shows the load–deﬂection and load–rod strain curves for S2-R22 strengthened with mm, respectively; this occurred immediately prior to attaining the maximum load. a steel rod of diameter j22 mm. The stiffness prior to the post-tensioning of 12.5 kN/mm increased The measured load–deflection and rod strain curves for S2-R28 are shown in Figure 10b. The to 17.9 kN/mm after post-tensioning, which was performed after reducing the load from P = 230.2 1st stiffness prior to post-tensioning of 13.8 kN/mm increased to 19.8 kN/mm after post-tensioning, kN to 154 kN. The post-tensioning recovered a deﬂection of approximately 5.7 mm, and the effective which resulted in a deflection recovery of approximately 8.5 mm. The initial strain in the external strain applied to the steel rod was 2153 ". The continuous reloading resulted in a maximum load of rod was 2035 με. Reloading was applied at a deflection of 8.2 mm, which was less than the deflection 419.0 kN and deﬂection of 66.0 mm. The deﬂections were 30.4 mm and 41.5 mm at the measured strain 11.3 mm of the unstrengthened specimen owing to the deflection recovery. In this beam, a maximum of 0.003 and 0.005, respectively, in the concrete compressive extreme ﬁber; these deﬂections occurred well before attaining the maximum load capacity. Although the decrease in the load was not evident after the maximum load, the experiment was terminated when the measured deﬂection was 87 mm because brittle failure by concrete crushing was predicted. The initial strain of the post-tensioning rod (# = 2153 ") increased to 3141, 3805, and 5411 " at # = 0.003, # = 0.005, and P = 419.0 kN, se cu cu 2nd respectively. The external rod yielded at the load and deﬂection of 417 kN and 62.6 mm, respectively; this occurred immediately prior to attaining the maximum load. The measured load–deﬂection and rod strain curves for S2-R28 are shown in Figure 10b. The stiffness prior to post-tensioning of 13.8 kN/mm increased to 19.8 kN/mm after post-tensioning, which resulted in a deﬂection recovery of approximately 8.5 mm. The initial strain in the external rod was 2035 ". Reloading was applied at a deﬂection of 8.2 mm, which was less than the deﬂection 11.3 mm of the unstrengthened specimen owing to the deﬂection recovery. In this beam, a maximum load and the corresponding strain of 513.8 kN and 61.1 mm, respectively, were recorded after post-tensioning and reloading. The deﬂections at the measured strains of 0.003 and 0.005 were 26 and 29 mm, respectively. The compressive strain at the concrete extreme ﬁber reached 0.005 prior to the maximum load. Although the strain of the external rod reached 4592 " at the maximum load, the yield strain was not attained at this point. Applied Load (kN) Applied Load (kN) Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 17 load and the corresponding strain of 513.8 kN and 61.1 mm, respectively, were recorded after post-tensioning and reloading. The deflections at the measured strains of 0.003 and 0.005 were 26 and 29 mm, respectively. The compressive strain at the concrete extreme fiber reached 0.005 prior to the maximum load. Although the strain of the external rod reached 4592 με at the maximum load, Appl. Sci. 2018, 8, 1763 11 of 17 the yield strain was not attained at this point. w/o strengthening w/o strengthening 600 600 after post-tensioning after post-tensioning P after PT ma x ε = 0.003 cu ε = 0.005 cu 500 500 P after PT ma x P after PT ε = 0.003 ma x cu ε = 0.003 ε = 0.003 cu cu after PT P ma x ε = 0.005 400 400 cu ε = 0.005 cu ε = 0.005 cu P prior to PT ma x P prior to PT ma x 200 200 ε =2153με Begining of PT se ε =2035με se Begining of PT 100 100 End of PT End of PT 0 2040 6080 100 0 2000 4000 6000 8000 020 40 60 80 100 0 2000 4000 6000 Deflection at midspan (mm) Strain in external rod (με) Deflection at midspan (mm) Strain in external rod (με) (a) (b) Figure 10. Figure 10. Deflection and rod Deﬂection and rodstrain with re strain with respect spect to to applie applied d load: ( load: a (a ) S2-R2 ) S2-R22 2 and ( and b (b ) S2-R2 ) S2-R28. 8. The changes in the deﬂection and strain of the external rod with increasing applied load for the The changes in the deflection and strain of the external rod with increasing applied load for the S3-R22 beam are plotted in Figure 11a. The stiffness of 10.4 kN/mm prior to post-tensioning reduced S3-R22 beam are plotted in Figure 11a. The stiffness of 10.4 kN/mm prior to post-tensioning reduced to 17.5 kN/mm afterwards. The ﬁrst maximum load prior to post-tensioning was 182.4 kN, and the to 17.5 kN/mm afterwards. The first maximum load prior to post-tensioning was 182.4 kN, and the post-tensioning was conducted after unloading to 120 kN. Post-tensioning achieved a deﬂection post-tensioning was conducted after unloading to 120 kN. Post-tensioning achieved a deflection recovery of 6.0 mm, and the initial strain of the steel rod was 2148 " at the end of post-tensioning. recovery of 6.0 mm, and the initial strain of the steel rod was 2148 με at the end of post-tensioning. In In this beam, the load marginally decreased after the maximum load of 409 kN and, thereafter, this beam, the load marginally decreased after the maximum load of 409 kN and, thereafter, the the compressive strain of the concrete extreme ﬁber reached 0.003. compressive strain of the concrete extreme fiber reached 0.003. Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 17 Figure 11b shows the load–deflection and load–rod strain plots of S3-R28. In this specimen, w/o strengthening w/o strengthening 500 500 because of an operational error that caused the UTM to act abruptly on the beam immediately prior P after strengthening after post-tensioning ma x after strengthening ε = 0.003 cu P after PT ma x to the post-tensioning, the initial strain of the rod and the deflection recovery were zero. The P after PT ma x 400 400 stiffnesses before and after post-tensioning were calculated as 10.4 kN/mm and 18.0 kN/mm, P after ma x ε = 0.003 cu strengthening respectively. The load was plotted as 281.9 kN a ε = 0.005 t the concrete extreme fiber strain of 0.005, and the ε = 0.005 cu cu 300 300 maximum load was recorded as 436.9 kN. ε = 0.005 cu ε = 0.005 cu 200Table 4 summarizes the test results of the strengthened specime 200 ns. The stiffness-strengthening P prior to PT ma x effects for the S1-, S2-, and S3-type specimens were approximately 30, 43, and 70%, respectively. The Begining of PT 100 100 ε =2148με se specimens with a higher number of tensile rebars exhibited less stiffness-strengthening effects. Begining of strengthening End of PT Begining of strengthening Additionally, based on the maximum load, the strengthening effect was observed to be 0 0 approximately two times for the S3-type specimens, approximately 40 and 55% for the S1-type 0 20 40 60 80 100 0 2000 4000 6000 8000 0 30 60 90 120 150 0 2000 4000 6000 Deflection at midspan (mm) Strain in external rod (με) Deflection at midspan (mm) Strain in external rod (με) specimens, and 64 and 101% for the S2-type specimens. The strengthening effect was more than 37% at the compressive concre (a) te strain of 0.003 or 0.005 except for S3-28, which (b wa ) s not post-tensioned owing to the aforementioned operational error. Figure 11. Figure Deflection and rod 11. Deﬂection and strain with re rod strain with spect to respect applie to applied d load: ( load: a) S3-R2 (a) S3-R22 2 and (b and ) S3-R2 (b) S3-R28. 8. Figure 11b shows the load–deﬂection and load–rod strain plots of S3-R28. In this specimen, Table 4. Summary of measured results in post-tensioned beams. because of an operational error that caused the UTM to act abruptly on the beam immediately prior to Before & after PT At First Peak At Second Peak At εcu = 0.003 At εcu = 0.005 the post-tensioning, the initial strain of the rod and the deﬂection recovery were zero. The stiffnesses Kafter P2nd P0.003 P0.005 before and after post-tensioning were calculated as 10.4 kN/mm and 18.0 kN/mm, respectively. Specim. Kbefore Kafter P1st δ1st P2nd δ2nd P0.003 δ0.003 P0.005 δ0.005 /Kbefore /Pmax /Pmax /Pmax The load was plotted as 281.9 kN at the concrete extreme ﬁber strain of 0.005, and the maximum load (kN/mm) (kN/mm) (%) (kN) (mm) (kN) (%) (mm) (kN) (%) (mm) (kN) (%) (mm) was recorded as 436.9 kN. S1-R22 17.5 23.2 1.33 342.7 21.9 469.4 1.40 55.5 464.0 1.38 26.3 n.d. n.d. n.d. Table 4 summarizes the test results of the strengthened specimens. The stiffness-strengthening S1-R28 17.5 22.3 1.28 344.1 24.5 521.4 1.55 59.3 469.8 1.40 26.4 484.9 1.45 32.7 effects for the S1-, S2-, and S3-type specimens were approximately 30, 43, and 70%, respectively. S2-R22 12.5 17.9 1.43 230.2 21.6 419.0 1.64 66.0 409.8 1.61 30.4 401.5 1.57 41.5 The specimens with a higher number of tensile rebars exhibited less stiffness-strengthening effects. S2-R28 13.8 19.8 1.43 238.4 20.0 513.8 2.02 61.1 467.5 1.83 25.9 473.0 1.86 29.3 Additionally, based on the maximum load, the strengthening effect was observed to be approximately S3-R22 10.4 17.5 1.69 182.4 20.6 409.0 1.99 35.8 399.3 1.94 48.0 369.9 1.80 91.3 two times for the S3-type specimens, approximately 40 and 55% for the S1-type specimens, and 64 S3-R28 10.4 18.0 1.73 171.0 15.2 436.9 2.12 104.9 118.5 0.58 10.3 281.9 1.37 27.3 and 101% for the S2-type specimens. The strengthening effect was more than 37% at the compressive Notes: εcu is the compressive strain of the extreme concrete measured using the crack gauge; Kbefore concrete strain of 0.003 or 0.005 except for S3-28, which was not post-tensioned owing to the and Kafter are the stiffnesses prior to and after post-tensioning (PT), respectively; P1st and δ1st are the aforementioned operational error. first peak load and its corresponding deflection, respectively, before PT is applied to the beam; P2nd and δ2nd are the second peak load and its corresponding deflection, respectively, after PT is applied to the beam; P0.003 and P0.005 are the loads and δ0.003 and δ0.005 are the corresponding deflections when εcu attained 0.003 and 0.005, respectively; Pmax is the maximum load of the unstrengthened beam as summarized in Table 3; n.d. = no data. 3.3. Flexural Strength Analysis Flexural strength analyses were performed for the mid-span section of the tested beams. The analysis performed in this study was different from that performed for a beam with internal tendons since the internal tendons remain in place relative to the surrounding concrete under varying deflection. However, in this study, the deflection of the external unbonded steel along the beam length is different from that of the surrounding concrete [41–44]. Therefore, the analysis required the calculation of the elongation of the external rod, which was dependent on the deflection at the deviator point [41]. The elongation (Δεps) of the external rod was obtained from Equations (2)–(4) and Figure 12, as reported by Lee et al. [5]. Applied Load (kN) Applied Load (kN) Applied Load (kN) Applied Load (kN) Appl. Sci. 2018, 8, 1763 12 of 17 Table 4. Summary of measured results in post-tensioned beams. Before & after PT At First Peak At Second Peak At # = 0.003 At # = 0.005 cu cu Specim. K K K /K P d P P /P d P P /P d P P /P d before after after before 1st 1st 2nd 2nd max 2nd 0.003 0.003 max 0.003 0.005 0.005 max 0.005 (kN/mm) (kN/mm) (%) (kN) (mm) (kN) (%) (mm) (kN) (%) (mm) (kN) (%) (mm) S1-R22 17.5 23.2 1.33 342.7 21.9 469.4 1.40 55.5 464.0 1.38 26.3 n.d. n.d. n.d. S1-R28 17.5 22.3 1.28 344.1 24.5 521.4 1.55 59.3 469.8 1.40 26.4 484.9 1.45 32.7 S2-R22 12.5 17.9 1.43 230.2 21.6 419.0 1.64 66.0 409.8 1.61 30.4 401.5 1.57 41.5 S2-R28 13.8 19.8 1.43 238.4 20.0 513.8 2.02 61.1 467.5 1.83 25.9 473.0 1.86 29.3 S3-R22 10.4 17.5 1.69 182.4 20.6 409.0 1.99 35.8 399.3 1.94 48.0 369.9 1.80 91.3 S3-R28 10.4 18.0 1.73 171.0 15.2 436.9 2.12 104.9 118.5 0.58 10.3 281.9 1.37 27.3 Notes: # is the compressive strain of the extreme concrete measured using the crack gauge; K and K are cu before after the stiffnesses prior to and after post-tensioning (PT), respectively; P and d are the ﬁrst peak load and its 1st 1st corresponding deﬂection, respectively, before PT is applied to the beam; P and d are the second peak load and 2nd 2nd its corresponding deﬂection, respectively, after PT is applied to the beam; P and P are the loads and d 0.003 0.005 0.003 and d are the corresponding deﬂections when # attained 0.003 and 0.005, respectively; P is the maximum 0.005 cu max load of the unstrengthened beam as summarized in Table 3; n.d. = no data. 3.3. Flexural Strength Analysis Flexural strength analyses were performed for the mid-span section of the tested beams. The analysis performed in this study was different from that performed for a beam with internal tendons since the internal tendons remain in place relative to the surrounding concrete under varying deﬂection. However, in this study, the deﬂection of the external unbonded steel along the beam length is different from that of the surrounding concrete [41–44]. Therefore, the analysis required the calculation of the elongation of the external rod, which was dependent on the deﬂection at the deviator point [41]. The elongation (D# ) of the external rod was obtained from Equations (2)–(4) and Figure 12, ps Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 17 as reported by Lee et al. [5]. L/2 dh Neutral axis Figure 12. Elongation of external rod after deformation. Figure 12. Elongation of external rod after deformation. L0 L p p L′ − L D# = (2) ps p p Δε = L ps p (2) 2 2 L = (L/2 d ) + (d d ) (3) p h p v 2 2 L =() L / 2 − d +() d − d (3) p h p v 2 2 L0 = fL/2 d (y d )qg + (d d + d) (4) p h v p v 2 2 ′ () L ={} L / 2 − d −() y − d θ + d − d + δ (4) p h v p v where L and L’ are the rod lengths before and after deformation, respectively; L is the span length; p p d is the horizontal distance from the support to the center of the anchorage; d is the effective depth where h Lp and L’p are the rod lengths before and after deformation, respectively; L is the span length; of the post-tensioning rod at the deviator; d is the vertical distance from the top of the beam to the dh is the horizontal distance from the support to v the center of the anchorage; dp is the effective depth center of the anchorage; y ¯ is the neutral axis depth; q is the rotational angle; and d is the deﬂection at of the post-tensioning rod at the deviator; dv is the vertical distance from the top of the beam to the the deviator. center of the anchorage; ȳ is the neutral axis depth; θ is the rotational angle; and δ is the deflection at To obtain the value of the elongation (L’ ) at a particular loading state, the deﬂection the deviator. (d) and rotation (q) at that state in Equation (4) should be calculated. At a speciﬁc ultimate To obtain the value of the elongation (L’p) at a particular loading state, the deflection (δ) and rotation (θ) at that state in Equation (4) should be calculated. At a specific ultimate state, these parameters can be determined using Equations (5)–(7) and the ultimate curvature of Figure 13 [5,45]. L/2 L/2 Solid: idealized Dashed: actual L0 L0 Figure 13. Curvature distribution at ultimate state. L L LL L 0 0 0 δ =() φ L −() φ L = − φ (5) u u 0 u 0 u 2 2 2 2 θ = φ L (6) u u 0 φ = ε / c (7) u cu where δu is the ultimate deflection, L is the span length, L0 is the plastic hinge length extended on either side of the beam from the beam center (note that it is considered as 0.5d), d is the effective depth of the tension reinforcing bar, φu is the ultimate curvature (= εcu/c), and c is the neutral axis depth at the ultimate state. To calculate the deflection and rotation in Equations (5) and (6), the neutral axis depth c in Equation (7) is required. These interrelated values (δ, θ, c, and Δεps) should be obtained by an iteration procedure until all the conditions, including the strain compatibility, force equilibrium, δ d p φ u y-dv dv Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 17 L/2 dh Neutral axis Figure 12. Elongation of external rod after deformation. L′ − L p p Δε = (2) ps 2 2 L =() L / 2 − d +() d − d (3) p h p v 2 2 L ={} L / 2 − d −() y − d θ +() d − d + δ (4) p h v p v where Lp and L’p are the rod lengths before and after deformation, respectively; L is the span length; dh is the horizontal distance from the support to the center of the anchorage; dp is the effective depth of the post-tensioning rod at the deviator; dv is the vertical distance from the top of the beam to the center of the anchorage; ȳ is the neutral axis depth; θ is the rotational angle; and δ is the deflection at the deviator. Appl. Sci. 2018, 8, 1763 13 of 17 To obtain the value of the elongation (L’p) at a particular loading state, the deflection (δ) and rotation (θ) at that state in Equation (4) should be calculated. At a specific ultimate state, these parameters can be determined using Equations (5)–(7) and the ultimate curvature of Figure 13 state, these parameters can be determined using Equations (5)–(7) and the ultimate curvature of [5,45]. Figure 13 [5,45]. L/2 L/2 Solid: idealized Dashed: actual L0 L0 Figure 13. Curvature distribution at ultimate state. Figure 13. Curvature distribution at ultimate state. L L L L LL LL L L 0 0 0 0 0 δ =() φ L −() φ L = − φ d = (j L ) (j L ) = j (5 (5) ) u u 0 u 0 u u u 0 u 0 u 2 2 2 2 2 2 2 2 q θ= = φj L L (6) u u 0 (6) u u 0 j = # /c (7) φ u = ε cu / c (7) u cu where d is the ultimate deﬂection, L is the span length, L is the plastic hinge length extended on u 0 where δu is the ultimate deflection, L is the span length, L0 is the plastic hinge length extended on either side of the beam from the beam center (note that it is considered as 0.5d), d is the effective depth either side of the beam from the beam center (note that it is considered as 0.5d), d is the effective of the tension reinforcing bar, j is the ultimate curvature (= # /c), and c is the neutral axis depth at u cu depth of the tension reinforcing bar, φu is the ultimate curvature (= εcu/c), and c is the neutral axis the ultimate state. depth at the ultimate state. To calculate the deﬂection and rotation in Equations (5) and (6), the neutral axis depth c To calculate the deflection and rotation in Equations (5) and (6), the neutral axis depth c in in Equation (7) is required. These interrelated values (d, q, c, and D# ) should be obtained by Appl. Sci. 2018, 8, x FOR PEER REVIEW ps 14 of 17 Equation (7) is required. These interrelated values (δ, θ, c, and Δεps) should be obtained by an an iteration procedure until all the conditions, including the strain compatibility, force equilibrium, iteration procedure until all the conditions, including the strain compatibility, force equilibrium, and compatibility between the rod elongation and deflection are satisfied. The force equilibrium is and compatibility between the rod elongation and deﬂection are satisﬁed. The force equilibrium is expressed as Equation (8) based on Figure 14. expressed as Equation (8) based on Figure 14. ε ' cu 0.85f As ε E ε' A' '' 's s s s (≤ f As) s f A ps f A cosα (≤ f A cosα) A ps ps py ps ps Figure 14. Stress and strain distribution at ultimate state. Figure 14. Stress and strain distribution at ultimate state. c − d c d 0 0 ′ ′ 0.85 0.85 f fab ab++A A E E ε# = =A A f f ++ AA f f cos cos α a (8 (8) ) s s cu s y ps ps c s s cu s y ps ps f = # + D# E f (9) ps se ps p py f = (ε + Δε )E ≤ f ps se ps p py (9) where f’ is the compressive strength of the concrete; a is the Whitney stress block depth; b is the beam where f’c is the compressive strength of the concrete; a is the Whitney stress block depth; b is the width; E is the elastic modulus of the reinforcing bar; A’ and A are the areas of the compressive s s s beam width; Es is the elastic modulus of the reinforcing bar; A’s and As are the areas of the and tensile reinforcements, respectively; # is the compressive strain of the concrete extreme ﬁber at cu compressive and tensile reinforcements, respectively; εcu is the compressive strain of the concrete the ultimate state; c is the neutral axis depth; d’ is the distance from the beam top to the centroid of extreme fiber at the ultimate state; c is the neutral axis depth; d’ is the distance from the beam top to the compression steel; f is the yield strength of the tension steel; A is the area of the external steel y ps the centroid of the compression steel; fy is the yield strength of the tension steel; Aps is the area of the rod; f is the stress acting on the external rod; a is the angle of the external rod with respect to the ps external steel rod; fps is the stress acting on the external rod; α is the angle of the external rod with horizontal axis after deformation; # and D# are the initial effective strain and increased strain on se ps respect to the horizontal axis after deformation; εse and Δεps are the initial effective strain and the external rod, respectively; and E and f are the elastic modulus and yield strength, respectively, p py increased strain on the external rod, respectively; and Ep and fpy are the elastic modulus and yield of the external rod. The values of E # (c d’)/c and f are equal to those of f’ and f , respectively, s cu ps y py strength, respectively, of the external rod. The values of Esεcu(c − d’)/c and fps are equal to those of f’y and fpy, respectively, when the compressive reinforcing bar and external rod yield. f’y is the yield strength of the compressive reinforcing bar. Finally, the flexural strength Mn is expressed by Equation (10): () c − d ′ () ′ () () (10) M = 0.85 f ab c − a / 2 + A E ε + A f d − c + A f cos α d − c n c s s cu s y ps ps p Table 5 shows a comparison between the analytical and measured moment capacities for each specimen. A sensitivity analysis was also conducted with respect to the four loading steps: εcu = 0.003, εcu = 0.005, Pmax, and at the end of the test. No significant difference in the predicted moment capacities was observed. It was recommended in previous studies [40,46] that an ultimate compression strain of 0.005 be conservatively adopted for the purpose of rehabilitation. In this sensitivity analysis, the predicted moment capacities for εcu = 0.005 were closer to the measured moment capacities than those for εcu = 0.003. The average and standard deviations between the predicted and measured capacities were 0.84 and 0.08, respectively, for εcu = 0.005. Table 5. Sensitivity analysis of moment capacities with respective to loading step. Mn_0.003/ Mn_0.005/ Mn_Pmax/ Mn_end/ Mu_test Mn_0.003 Mn_0.005 Mn_Pmax Mn_end Specimen Mu_test Mu_test Mu_test Mu_test (kN·m) (kN·m) (%) (kN·m) (%) (kN·m) (%) (kN·m) (%) S1-No 318.8 260.7 0.82 265.7 0.83 259.8 0.81 265.7 0.83 S1-R22 445.9 403.3 0.90 414.2 0.93 414.2 0.93 414.1 0.93 S1-R28 495.3 446.0 0.90 470.5 0.95 480.1 0.97 480.1 0.97 S2-No 242.3 179.4 0.74 181.7 0.75 183.2 0.76 183.2 0.76 S2-R22 398.1 347.4 0.87 352.3 0.89 352.1 0.88 351.9 0.88 S2-R28 488.1 420.9 0.86 430.3 0.88 430.0 0.88 429.8 0.88 S3-No 195.6 137.4 0.70 138.1 0.71 138.3 0.71 138.8 0.71 S3-R22 388.6 313.5 0.81 318.3 0.82 311.0 0.80 318.0 0.82 L' d p d' δ d p φ u y-dv dv Appl. Sci. 2018, 8, 1763 14 of 17 when the compressive reinforcing bar and external rod yield. f’ is the yield strength of the compressive reinforcing bar. Finally, the ﬂexural strength M is expressed by Equation (10): (c d ) 0 0 M = 0.85 f ab(c a/2) + A E # + A f (d c) + A f cos a d c (10) n s s cu s y ps ps p Table 5 shows a comparison between the analytical and measured moment capacities for each specimen. A sensitivity analysis was also conducted with respect to the four loading steps: # = 0.003, cu # = 0.005, P , and at the end of the test. No signiﬁcant difference in the predicted moment capacities cu max was observed. It was recommended in previous studies [40,46] that an ultimate compression strain of 0.005 be conservatively adopted for the purpose of rehabilitation. In this sensitivity analysis, the predicted moment capacities for # = 0.005 were closer to the measured moment capacities than cu those for # = 0.003. The average and standard deviations between the predicted and measured cu capacities were 0.84 and 0.08, respectively, for # = 0.005. cu Table 5. Sensitivity analysis of moment capacities with respective to loading step. M M M /M M M /M M M /M M M /M u _test n n u _test n n u _test n n u _test n n u _test _0.003 _0.003 _0.005 _0.005 _Pmax _Pmax _end _end Specimen (kNm) (kNm) (%) (kNm) (%) (kNm) (%) (kNm) (%) S1-No 318.8 260.7 0.82 265.7 0.83 259.8 0.81 265.7 0.83 S1-R22 445.9 403.3 0.90 414.2 0.93 414.2 0.93 414.1 0.93 S1-R28 495.3 446.0 0.90 470.5 0.95 480.1 0.97 480.1 0.97 S2-No 242.3 179.4 0.74 181.7 0.75 183.2 0.76 183.2 0.76 S2-R22 398.1 347.4 0.87 352.3 0.89 352.1 0.88 351.9 0.88 S2-R28 488.1 420.9 0.86 430.3 0.88 430.0 0.88 429.8 0.88 S3-No 195.6 137.4 0.70 138.1 0.71 138.3 0.71 138.8 0.71 S3-R22 388.6 313.5 0.81 318.3 0.82 311.0 0.80 318.0 0.82 S3-R28 415.1 299.0 0.72 318.0 0.77 401.1 0.97 401.0 0.97 Average 0.81 0.84 0.86 0.86 Standard deviation 0.08 0.08 0.09 0.09 Minimum 0.70 0.71 0.71 0.71 Maximum 0.90 0.95 0.97 0.97 4. Conclusions This study experimentally evaluated and veriﬁed the strengthening effect of post-tensioning on an RC beam using external unbonded steel rods. The objective was to examine the effect of such strengthening on damaged RC beams as a technique for rehabilitation or reinforcement. Reinforced concrete beams with different tensile rebar quantities were prepared, and three-point bending tests were performed with different diameters (j22 mm and j28 mm) of steel rods in order to evaluate the performance of the steel rods as strengthening members. The beam specimens were damaged by repetitive loading before applying the reinforcement system. Subsequently, the loading was controlled up to the service load after the yield load was attained, and post-tensioning was applied to the steel rod. Tension was applied by tightening the nut of the anchorage, and the initial tension was set to the amount of force required to recover the deﬂection up to the service load stage or about 2000 " (the strain in the steel rods that two adult men could achieve conveniently). The following conclusions were derived from the ﬂexural strength tests: (1) External post-tensioning was highly effective in strengthening the RC beams because the strengthened test specimens generally exhibited stable load–deﬂection behavior after reaching the maximum load, without a rapid decrease in strength. (2) The rehabilitation or reinforcement of the beams using external unbonded post-tensioning steel rods resulted in enhancements exceeding 28% and 40% in stiffness and strength, respectively. Furthermore, the external post-tensioning was effective in controlling the crack width and re-establishing the service load deﬂections of the RC beams. This method reduced the crack widths or closed the cracks and resulted in a stiffer load–deﬂection behavior. Appl. Sci. 2018, 8, 1763 15 of 17 (3) Comparing the effects of the external rod diameter, the maximum strength of the beams strengthened with the thicker steel rods was higher; however, the depth of concrete crushing at the ultimate strength was also higher in these beams. (4) Notably, tensioning played a highly important role in external strengthening. It was also observed that the initial tension of the steel rod was sufﬁciently effective for recovering the deﬂection up to the service load stage or approximately 2000 ". (5) The ultimate moment determined using moment capacity analysis was found to be sufﬁciently accurate and computationally efﬁcient at various loading steps, i.e., # = 0.003, 0.005, P , cu max and test completion. 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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Applied Sciences – Multidisciplinary Digital Publishing Institute

**Published: ** Sep 29, 2018

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