Tendon Profile Layout Impact on the Shear Capacity of Unbonded Post-Tensioned Prestressed Concrete Bridge I-Girders

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Reviewer comments:

1.    The introduction should be more focused on the topic of the manuscript. Currently, the literature review covers more topics and, in reviewers' opinion, is a bit too long. 
   2.    Page 3, lines 99-102 and Page 6, lines 255-258. These parts of the text contradict each other. Additionally, in reviewers' opinion, there should be more experimental data in the literature on the shear capacity of prestressed flexural members with different profiles of post-tensioned tendons. 
   3.    Figs. 1-3 are not necessary in the manuscript as everything is described in the text, and these figures do not present any new and valuable information.
   4.    The manuscript needs to be checked for spelling, grammar, and punctuation mistakes.
   5.    In Fig. 5, Sec. C-C, it is written that there are 4Ø12 steel bars. However, there are only two. Additionally, it is not clear what the steel reinforcement and strand position are in the cross-section. Additional dimensions and explanation in the text should be added.
   6.    Page 10, lines 349-359. The information in the text is repeated.
   7.    The resolution of Fig. 6 should be higher.
   8.    Page 10, line 364. Figure 1a should be substituted with Figure 7a.
   9.    Page 10, lines 365-367. The moist curing process should be explained in more detailed manner in the text.
   10.    Page 14, line 420. Figure 1ia should be substituted with Figure 10a.
   11.    Fig. 11 and Fig. 12. The description of specimens “Specimen 1”, “Specimen 2”… does not exist in the manuscript in earlier Sections.
   12.    The names of the specimens should be checked and corrected as it is not the same as in Table 3 and Table 4, Table 5, and Fig. 11, and in the text.
   13.    Pages 18-20. The descriptions of the results of each specimen and the differences of the results from the reference specimen are very monotonic, repeating. The comparison of the results should be presented more interestingly to the readers.
   14.    The manuscript should be supplemented with a comparison of the results between different prestressed reinforcement distributions (trapezoidal, parabolic, and harped), not only a comparison with the straight distribution of the strand with respect to the angle of inclination. Additional graphical comparison also should be introduced (trapezoidal vs parabolic, parabolic vs harped and so on).
   15.    Page 23, lines 614. Figure 11 should be substituted with Figure 12.

Author Response

Response to Reviewer 1 Comments
Summary
Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

 

Comments 1: The introduction should be more focused on the topic of the manuscript. Currently, the literature review covers more topics and, in reviewers' opinion, is a bit too long.

 

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have deleted some references to be more focused on the topic of the manuscript and because the introduction was too long. These are the deleted references:

1.[Jiang et al. [14] they presented a simplified design formula for the shear capacity of prestressed concrete (PC) beams reinforced in steel plates. Using equilibrium equations, the shear contribution of the steel plates was determined taking into account shear compression failure. A parametric investigation Situated by using test data and a validated finite-element program. The formula with consideration of strength-reduction factor 0.494 accurately predicts the shear resistance of PC beams strengthened by steel plates and is consistent with the experimental results]. This change can be found on page 3, paragraph, line 135-141.

2. [Hillebrand et al. [16] they studied the fatigue behavior of 10 T-shaped prestressed concrete beams with shear reinforcement is questioned and compared by means of experimental load cycles to the prediction of the German approach based on the Eurocode 2. The study findings were beneficial for the evaluation of existing bridges and the design and construction of new bridges.]. This change can be found in on page 4, paragraph 1, line 148-153.
3. [Eisa et al. [17]They investigated static response of prestressed reinforced concrete beams externally reinforced with steel plates and woven carbon fiber fabric (WCFF). Results of testing 20 large-scale beams showed that both techniques enhanced the flexural and shear strength. U-shaped steel plates provided the highest load capacity and deflection reduction, while WCFF wrapping produced increase in shear strength]. This change can be found in on page number 4, paragraph 1, line 153-158.
4. [Qi et al. [18] they evaluated the shear performance of reinforced concrete beams with externally prestressed Carbon fiber reinforced polymer (CFRP) tendons The results indicate that CFRP tendons with stirrups increase yield and ultimate load capacities, delay diagonal cracks and provide considerable shear resistances, the levels of improvement related to preload stresses. Although initially damaged in the shear zone, the shear capacity is not much affected as load is increased. The results, along with predictive model with an error of less than 10% provide useful ideas to composite design]. This change can be found in on page 3, paragraph 1, line 158-164.
5. [Zhao et al. [19] they studied the shear behavior of 16m span prestressed hollow slabs test and numerical simulation. results show of shear-compression failure, cracks are formed at 1.35m to 1.95m from beam ends, finite element model reliability quasi-authenticated by ABAQUS simulation]. This change can be found in on page 4, line 165-168.
6. [Jancy et al. [20]they presented a new method of modelling post-tensioned beams, calibrating a finite element model versus load capacity and post-critical response until experimental evidence is matched. Two different beams with dissimilar tendons arrangement have been analyzed under the purview of Abaqus/Explicit and Hyper mesh, ensuring crack patterns & behavior at various loading stage are accurately addressed]. This change can be found in on page 4, line 168-173.
7. [Mohamed et al. [22] they explore enhancing the structural behavior of reinforced concrete beams using external pre-stressing tendons to increase load capacity and resistance. Seven RC beams were tested with different tendon configurations, showing significant improvements in load-carrying capacity, deflection, and ductility. The straight-line tendon with inner deviators proved most effective]. This change can be found in on page 4, line 176-181.
8. [Yaqub et al. [23] they investigated the performance of PC I-girders strengthened with iron-based shape memory alloy (Fe-SMA) strips and ribbed rebar and their shear capacity using experimentation and numerical modelling. Fe-SMA can recover pre-induced strains during heating, leading to enhanced shear properties and 40-47% capacity recovery. Crack control and serviceability of active Fe-SMA shear strengthening are better than those of passive systems]. This change can be found in on page 4, line 181-186.

------------------------------------------------------------------------------------------------------------------------------

Comments 2: Page 3, lines 99-102 and Page 6, lines 255-258. These parts of the text contradict each other. Additionally, in reviewers' opinion, there should be more experimental data in the literature on the shear capacity of prestressed flexural members with different profiles of post-tensioned tendons. 

Response 2: [Numerous experimental and numerical studies were performed on the shear strength of unbonded prestressed concrete girder in the last few decades. In addition, several numerical studies have looked into the effects of different tendon profile arrangements on the overall functionality of such systems] and [The tendon profile layout plays a vital role in the design of post-tensioned concrete bridges. However, most research focuses on the numerical analysis of its impact on the structural performance of prestressed concrete beams and slabs. Experimental studies are not existed, and if they do exist, there are very few]

 

Thank you for pointing this out. We agree with this comment. Both sections highlight numerous studies that have explored the shear strength of concrete beams, considering various variables. However, there is a limited number of studies that examine the effect of tendon profile layout on the shear strength of post-tensioned prestressed concrete, both numerically and experimentally. We add two more reference on the effect of the tendon profile layout of post-tensioned tendons in the literature. As follow:

1) [Ma et al. [30] examined shear design in prestressed concrete beams, due to lacking a standardized procedure. They compiled 266 test results to evaluate the accuracy of five de-sign codes and two models. The findings showed that Marí et al.'s method was the most ac-curate but had a higher coefficient of variation. A new simplified shear strength formula based on a truss-arch model was proposed, offering improved prediction accuracy and consistency, making it a promising alternative for shear strength analysis in prestressed concrete beams.]

This change can be found in on page 5, line 219-224.

2) [Mihaylov et al. [36] conducted an experimental study on eight post-tensioned concrete beams at the University of Toronto, examining the size effect on shear behavior and tendon layout variations. The beams, ranging from 250 mm to 1000 mm in depth, had unbonded tendons arranged in straight or harped configurations with varying eccentricities. Under a three-point bending test without stirrups, the beams showed arch action and size effects. The study found that shear strength increased with tendon eccentricity. A strut-and-tie model based on AASHTO guidelines accurately predicted results, while a kinematic-based approach explained the high shear resistance of smaller beams].

This change can be found in on page 5, line 259-266.

--------------------------------------------------------------------------------------------------------------

 Comments 3: Figs. 1-3 are not necessary in the manuscript as everything is described in the text, and these figures do not present any new and valuable information.

Response 3: Thank you for pointing this out. We agree with this comment. Therefore, we have deleted the figures 1-3.

------------------------------------------------------------------------------------------------------------------------------

 Comments 4: The manuscript needs to be checked for spelling, grammar, and punctuation mistakes.

 Response 4:

Paragraph 1 [In prestressed concrete beams, two factors play an important role in minimizing the magnitude of diagonal tensile stresses under service load, as compared to conventional reinforced concrete that develops stresses without applying any prestress force to the concrete section. The first factor results from the mixture of longitudinal compressive stress and shearing stress. The second factor surrounds the tendon's slope, which usually creates a shear force due to the prestress that opposes the shear force induced by the load. This opposing shear reduces diagonal tension in the beam during service. It should be noted that while prestressed beams deflect satisfactorily under service loads, checking diagonal tensile stresses at these loads is not necessarily sufficient for safety against failure. A small reduction in compressive stress or increase in shear stress, especially if a beam is overloaded, may result in an immoderate increase of principal tension. As well, when inclined tendons are employed to resist shear, their contribution does not increase proportionally with load, implying small increments in shear can pose substantial design issues. Therefore, diagonal tension design in prestressed beams should be based on factored loads rather than service loads, as principal stress analysis enables you to predict the load where the first diagonal crack will occur [1]. ]

Thank you for pointing this out. We agree with this comment and we have made the following adjustments:

1. The word [tendons] has been changed to [tendon's]. This change can be found on page 3, paragraph 2, line 103.
2. the sign comma [,] has been added. This change can be found on page 3, paragraph 2, line 110.
3. the full stop [.] has been added. This change can be found on page 3, paragraph 2, line 114.

------------------------------------------------------------------------------------------------------------------------------

Paragraph 2 [Numerous experimental and numerical studies were performed on the shear strength of unbonded prestressed concrete girders in the last few decades. In addition, several numerical studies have looked into the effects of different tendon profile arrangements on the overall functionality of such systems.]

Thank you for pointing this out. We agree with this comment and we have changed the word” girder” to “girders”. This change can be found on page 3, paragraph 3, line 116.

------------------------------------------------------------------------------------------------------------------------------

Paragraph 3 [In their study, Rupf et al. [10]  examined the behavior of post-tensioned beams with low shear reinforcement and flanges. Experimental data from twelve reinforced concrete beams are studied, with emphasis on shear strength, failure modes, and comparison with design codes and elastic–plastic stress field analysis. In their study, Huber et al. [11] emphasized the important influence of arching action on the shear resistance of slender post-tensioned beams. It has been found that the shear design models used in the assessment are excessively conservative, especially near interior supports. In particular, the flexural-shear crack model provides encouraging predictions of the shear capacity for post-tensioned beams with low shear reinforcement ratios. Ruiz et al. [12] examined the load-carrying mechanisms and strength of thin-webbed post-tensioned beams failing due to web crushing. It explores how cracking and stress disruptions from prestressing tendons reduce shear strength, using results from six full-scale tests on prestressed beams. Rana et al.[13] proposed a cost optimization technique for a post-tensioned PC I-girder bridge focused on reducing material, fabrication, and installation costs. The optimization includes girder spacing, tendon arrangement and reinforcement of variables, utilizing Evolutionary Operation (EVOP) to result in cost efficient and feasible designs in their study, they presented experimental testing the shear behavior of aging post-tensioned concrete bridges, that frequently have low shear reinforcement. Testing four full scale beams of varying tendon profiles and transverse reinforcement, the research investigated shear mechanisms of aggregate interlock, stirrups and dowel action. Results indicated that stirrups alone could not account for load-carrying behavior and aggregate interlock had only a small effect. Experimental results were compared to estimates from new and existing design codes in order to understand the current design practice.]

Thank you for pointing this out. We agree with this comment and we have made the following adjustments:

1. The word [with] has been added. This change can be found on page 3, paragraph 4, line 121.
2. The word [filed] has been changed to [field]. This change can be found on page 3, paragraph 4, line 122.
3. The word [to] has been changed to [on]. This change can be found on page 3, paragraph 4, line 123.
4. The word [beam] has been changed to [beams]. This change can be found on page 3, paragraph 4, line 124.
5. The word [at] has been changed to [on]. This change can be found on page 3, paragraph 4, line 132.
6. The word [they] has been deleted in three positions. This change can be found on page 3, paragraph 4, line 122, 127, 131.

------------------------------------------------------------------------------------------------------------------------------

Paragraph 4 [Huber et al. [15] in their study, they presented experimental testing of the shear behavior of aging post-tensioned concrete bridges that frequently have low shear reinforcement. Testing four full-scale beams of varying tendon profiles and transverse reinforcement, the research investigated shear mechanisms of aggregate interlock, stirrups, and dowel action. Results indicated that stirrups alone could not account for load-carrying behavior, and aggregate interlock had only a small effect. Experimental results were compared to estimates from new and existing design codes in order to understand the current design practice.]

Thank you for pointing this out. We agree with this comment and we have made the following adjustments:

1. The word [of] has been added. This change can be found on page 3, paragraph 4, line 142.
2. The word [full scale] has been changed to [full-scale]. This change can be found on page 3, paragraph 4, line 144.
3. the sign comma [,] has been added. This change can be found on page 4, paragraph 1, line 145 and 146.

------------------------------------------------------------------------------------------------------------------------------

Paragraph 5 [Jaing et al. [27] study provided a simplified design equation for the shear strength of prestressed concrete (PC) beams reinforced with steel plates. The formula, developed from the assumption of equilibrium equations, is based on a shear compression failure. Test data and a validated 3D finite element analysis showed the effectiveness of steel plates in increasing shear strength with a proposed strength-reduction factor of 0.494. The formula closely predicts experimental outcomes.]

Thank you for pointing this out. We agree with this comment and we have deleted the word” study. This change can be found on page 5, paragraph 2, line 201.

------------------------------------------------------------------------------------------------------------------------------

Paragraph 6 [The tendon profile layout plays a vital role in the design of post-tensioned concrete bridges. However, most research focuses on the numerical analysis of its impact on the structural performance of prestressed concrete beams and slabs. Experimental studies do not exist, and if they do exist, there are very few.]

Thank you for pointing this out. We agree with this comment and we have changed the phrase” are not exist” do not exist “it's”. This change can be found on page 6, paragraph 3, line 290-291.

------------------------------------------------------------------------------------------------------------------------------

Paragraph 7 [For all tested beams, the primary reinforcement comprised a single seven-wire, low-relaxation strand with a diameter of 15.24 mm (Grade 270). The strand served as the unbonded prestressing steel and was placed inside a plastic duct with an inner diameter of 20 mm. This configuration ensured the proper placement and protection of the prestressing steel during testing, contributing to the overall structural behavior and performance of the beams. The strand eccentricity for all tendon profiles at mid-span, or section C-C, was consistently 180 mm from the neutral axis (N.A.). In contrast, the strand eccentricity at sections B-B and A-A varied across different tendon profiles. At the beam’s end anchorages, the eccentricity values ranged from -80 mm to 0 to 80 mm for each tendon profile shape (trapezoidal, parabolic, and harped), while for the straight tendon profile, the eccentricity remained constant at 180 mm from the neutral axis (N.A.). The longitudinal reinforcement consisted of deformed steel bars with diameters of 12 mm. To ensure the beams were designed to resist flexural failure, two longitudinal 16 mm bars were added at the bottom of the beam, and 4 mm steel wires were used for the vertical stirrups. The stirrups were spaced 200 mm along the beam's length, with a tighter arrangement of 125 mm spacing within the anchorage zone. The reinforcement details for the post-tensioned I-beams, including the end blocks, are provided in Figure 2]

Thank you for pointing this out. We agree with this comment and we have made the following adjustments:

1. The phrase [bar 16 mm] has been changed to [16 mm bars]. This change can be found on page 10, paragraph 1, line 373.
2. The word [and] has been added. This change can be found on page 10, paragraph 1, line 374.

------------------------------------------------------------------------------------------------------------------------------------

 

 

 

 

Paragraph 8 [The mechanical properties, including dimensions and material specifications, of the strands and steel reinforcement used in the experimental program are summarized in the Table 2]

Thank you for pointing this out. We agree with this comment and we have made the following adjustments:

1. The phrase [summarizes] has been changed to [summarized]. This change can be found on page 10, paragraph 1, line 382.
2. the sign comma [,] has been added. This change can be found on page 10, paragraph 2, line 381.
3. the sign comma [,] has been deleted. This change can be found on page 10, paragraph 2, line 382.

------------------------------------------------------------------------------------------------------------------------------

Paragraph 9 [Tests were performed at the Civil Engineering Laboratory at Salahaddin University at Erbil, and four-point loading was used to measure the shear capacity of the beams. Beams were subjected to four-point loading with supports at both ends. The load was carried out by a testing machine with a capacity up to 2500 kN, as presented in Fig.10 b, the load was exerted using a hydraulic jack. A 100-ton load cell was used to measure and record load data, and the force was transferred to the specimen through a steel beam, which facilitates the accurate and uniform load application in the test. The steel beam, which has distributed the loads, divides it into two areas 1000 mm apart, as shown in Figure 10a. To measure the mid-span deflection of the beam, two linear variable displacement transducers (LVDTs) with the gauge length of 300 mm were used. The LVDTs were mounted at the midspan of the beam, with the]

 

Thank you for pointing this out. We agree with this comment and we have made the following adjustments:

1. The phrase [four point] has been changed to [four-point]. This change can be found on page 14, paragraph 2, line 441.
2. The sign comma [,] has been added. This change can be found on page 14, paragraph 2, line 442.
3. The phrase [transfer] has been changed to [transferred]. This change can be found on page 14, paragraph 2, line 444.
4. The phrase [even loading distribution] has been changed to [distributed the loads]. This change can be found on page 14, paragraph 2, line 446.

------------------------------------------------------------------------------------------------------------------------------

Comments 5: In Fig. 5, Sec. C-C, it is written that there are 4Ø12 steel bars. However, there are only two. Additionally, it is not clear what the steel reinforcement and strand position are in the cross-section. Additional dimensions and explanation in the text should be added.

Response 1:   Figure 2. Detail of reinforcement [For all tested beams, the primary reinforcement comprised a single seven-wire, low-relaxation strand with a diameter of 15.24 mm (Grade 270). The strand served as the unbonded prestressing steel and was placed inside a plastic duct with an inner diameter of 20 mm. This configuration ensured the proper placement and protection of the prestressing steel during testing, contributing to the overall structural behavior and performance of the beams. The strand eccentricity for all tendon profiles at mid-span, or section C-C, was consistently 180 mm from the neutral axis (N.A.). In contrast, the strand eccentricity at sections B-B and A-A varied across different tendon profiles. At the beam’s end anchorages, the eccentricity values ranged from -80 mm to 0 to 80 mm for each tendon profile shape (trapezoidal, parabolic, and harped), while for the straight tendon profile, the eccentricity remained constant at 180 mm from the neutral axis (N.A.). The longitudinal reinforcement consisted of deformed steel bars with diameters of 12 mm. To ensure the beams were designed to resist flexural failure, two longitudinal 16 mm bars were added at the bottom of the beam, and 4 mm steel wires were used for the vertical stirrups. The stirrups were spaced 200 mm along the beam's length, with a tighter arrangement of 125 mm within the anchorage zone. The reinforcement details for the post-tensioned I-beams, including the end blocks, are provided in Figure 2.]   Thank you for pointing this out. We agree with this comment. Therefore, we have made the following adjustments: 1. For fig. 2, Sec C-C, we corrected number of longitudinal steel bar from [4Ø12] to [2Ø12] steel bars and we add the position of tendon in the fig. 2. (fig. 5 would be fig. 2 after deleting figures 1-3). This change can be found on page 10, line 379-380. 2. The position of the steel reinforcement and strands within the cross-section has been revised for clarity. Additionally, we have included further dimensions and explanations within the text to ensure a comprehensive understanding. This change can be found on page 9, 10, paragraph 3, 1, line 366-371. ---------------------------------------------------------------------------------------------------------------------------

Comments 6: [Page 10, lines 349-359. The information in the text is repeated].

Response 6: [The reinforcement preparation process is shown in Figure 6a. One strand is cut to a length of 3.70 m for every beam. These strands were then placed inside plastic ducts with an inner diameter of 20 mm, which had been pre-embedded in the specimen body, as shown in Figure 6b. Additionally, spiral reinforcement was incorporated into the end block, particularly in the anchorage zone, as illustrated in Figure 6c. This reinforcement arrangement ensured proper prestressing and structural integrity during testing.]

 

Thank you for pointing this out. We agree with this comment. Therefore, we have deleted the repeated paragraph. This change can be found on page 11, paragraph 1, line 387-391.

 

----------------------------------------------------------------------------------------------------------------------------

Comments 7: [The resolution of Fig. 6 should be higher].

Response7:

(a)
(b)	(c)

Figure 3. Specimen preparation detail: (a) Specimen preparation detail, (b) plastic duct, and (c) End block spiral.

 

Thank you for pointing this out. We agree with this comment. Therefore, we changed with higher resolution. This change can be found on page 11, line 398-399.

----------------------------------------------------------------------------------------------------------------------------

Comments 8: [Page 10, line 364. Figure 1a should be substituted with Figure 7a.].

 

Response 8: [ Molds made from steel and plywood were employed to cast the reinforced beams in distinct batches. A total of ten reinforced concrete beams were produced at the Kirkuk Limited Company for Concrete Girders, as shown in Figure 4a. After casting, the beams underwent a moist curing process, which commenced 15 hours later and continued for 7 days, as presented in Figure 4b. This curing procedure was crucial to ensuring the proper hydration of the concrete, contributing to the beams' strength and durability for the subsequent testing.]

 

Thank you for pointing this out. We agree with this comment. Therefore, we changed Figure 1a should be substituted with Figure 4a. Because we delete figures 1-3. This change can be found on page 11, paragraph 3, line 402.

----------------------------------------------------------------------------------------------------------------------------

Comments 9: [Page 10, lines 365-367. The moist curing process should be explained in more detailed].

Response 9: [ Molds made from steel and plywood were employed to cast the reinforced beams in distinct batches. A total of ten reinforced concrete beams were produced at the Kirkuk Limited Company for Concrete Girders, as shown in Figure 4a. After casting, the specimens were covered with wet cloths to ensure they remained damp. The curing process began after 15 hours of casting and continued for a duration of 7-days, as presented in Figure 4b. This curing procedure was crucial to ensuring the proper hydration of the concrete, contributing to the beams' strength and durability for the subsequent testing.]

 

Thank you for pointing this out. We agree with this comment. Therefore, we explain the moist curing in more detail. This change can be found on page 11, paragraph 4, line 402-405.

------------------------------------------------------------------------------------------------------------------------------

Comments 10: [Page 14, line 420. Figure 1ia should be substituted with Figure 10a.].

 

Response 10: [ Universal testing machine was used for testing the beams, as illustrated in Figure 7a. The following procedure was carefully followed to ensure the consistency and accuracy of the experiment. To begin, the load cell and the LVDTs were connected to a data logger, which was tasked with recording the load and deflection of the specimen, as presented in Figure 7a. Next, the computer was linked to the data logger, to record the data automatically, ensuring comprehensive data management.]

 

Thank you for pointing this out. We agree with this comment. Therefore, we explain the moist curing in more detail. This change can be found on page 15, paragraph 1, line 461.

------------------------------------------------------------------------------------------------------------------------------

Comments 11: [Fig. 11 and Fig. 12. The description of specimens “Specimen 1”, “Specimen 2”… does not exist in the manuscript in earlier Section.]

Response 10:  

Table 3. List of specimens with tendon profile layouts.

Number of specimens	Name of the specimens	Name of tendon profile	Tendon Profile Layout, Units in (mm)
Specimen 1	GS-1 ST	Straight Tendon Profile With e = 180 mm
Specimen 2	GS-2 TR	Trapezoidal Tendon Profile With ee = +80 mm
Specimen 3	GS-3 TR	Trapezoidal Tendon Profile With ee = 0 mm
Specimen 4	GS-4 TR	Trapezoidal Tendon Profile With ee = −80 mm
Specimen 5	GS-5 PR	Parabolic Tendon Profile With ee = +80 mm
Specimen 6	GS-6 PR	Parabolic Tendon Profile With ee = 0 mm
Specimen 7	GS-7 PR	Parabolic Tendon Profile With ee = −80 mm
Specimen 8	GS-1 HA	Harped Tendon Profile With ee = +80 mm
Specimen 9	GS-2 HA	Harped Tendon Profile With ee = 0 mm
Specimen 10	GS-3 HA	Harped Tendon Profile With ee = −80 mm

 

Thank you for pointing this out. We agree with this comment. Therefore, we explain the discretion of specimens in table 3. Therefore, we changed word [beam] to [specimens] in table 3 to and we add a new column for specimens’ number be clearer. This change can be found on page 13, table 3, line 430.

----------------------------------------------------------------------------------------------------------------------------

Comments 12: [The names of the specimens should be checked and corrected as it is not the same as in Table 3 and Table 4, Table 5, and Fig. 11, and in the text.].

 

Response 12:

Table 3. List of specimens with tendon profile layouts.

 

Number of specimens	Name of the specimens	Name of tendon profile	Tendon Profile Layout, Units in (mm)
Specimen 1	GS-1 ST	Straight Tendon Profile With e = 180 mm
Specimen 2	GS-2 TR	Trapezoidal Tendon Profile With ee = +80 mm
Specimen 3	GS-3 TR	Trapezoidal Tendon Profile With ee = 0 mm
Specimen 4	GS-4 TR	Trapezoidal Tendon Profile With ee = −80 mm
Specimen 5	GS-5 PR	Parabolic Tendon Profile With ee = +80 mm
Specimen 6	GS-6 PR	Parabolic Tendon Profile With ee = 0 mm
Specimen 7	GS-7 PR	Parabolic Tendon Profile With ee = −80 mm
Specimen 8	GS-1 HA	Harped Tendon Profile With ee = +80 mm
Specimen 9	GS-2 HA	Harped Tendon Profile With ee = 0 mm
Specimen 10	GS-3 HA	Harped Tendon Profile With ee = −80 mm

 

Thank you for pointing this out. We agree with this comment. Therefore, we checked all the name in the tables and we correct the names in table 3.

------------------------------------------------------------------------------------------------------------------------------

Comments 13: [ Pages 18-20. The descriptions of the results of each specimen and the differences of the results from the reference specimen are very monotonic, repeating. The comparison of the results should be presented more interestingly to the readers.]

 

Response 13: [ As shown in Figure 8a, the load-deflection curve for the control specimen (GS-1 ST), demonstrated an initial linear response during the elastic stage, where load increased proportionally with deflection. Upon reaching 167.17 kN and 1.36 mm de-flection, the first cracks appeared, marking the transition to inelastic behavior in the elastoplastic stage. The load-deflection curve then showed a decrease in slope, indicating reduced beam stiffness due to cracking, with deflection increasing more rapidly than load. As the load continued to rise, the curve displayed a further reduction in slope, transitioning to a plastic response caused by the yielding of the longitudinal reinforcement, which continued until the test concluded. During this phase, the load stabilized while deflection increased sharply. The ultimate load reached 601.17 kN, with a deflection of 30.1 mm, and the Pcr/Pu ratio was 27.81%, as indicated in Table 4.

      For GS-2 TR, with eccentricity at the end of the beam (e_e) 80 mm, exhibited a different load-deflection response, as shown in Figure 8b. Its elastic stage was lower compared to the GS-1 ST; the first crack appeared at 137.98 kN and a deflection of 0.98 mm. This specimen demonstrated a higher ultimate load of 603.03 kN and a significantly greater deflection of 42.59 mm at failure. The ultimate load increased by 1.86 kN (a 0.31% increase), while the ultimate deflection increased by 12.59 mm, reflecting a 41.97% increase over the control specimen, as summarized in Table 5. The (Pcr/Pu) ratio for GS-2 TR was 22.88%, which was lower than that of the control beam, as detailed in Table 4.

      For GS-3 TR, with eccentricity at the anchorage point zero, demonstrated a dis-tinct behavior, as shown in Figure 8c. This specimen exhibited a larger elastic stage compared to the GS-1 ST, with the first crack appearing at 184.73 kN and a deflection of 0.79 mm. It reached a higher ultimate load of 613.42 kN and a lower deflection of 37.59 mm at failure. These values represent a 12.25 kN (2.04%) increase in ultimate load and a 7.49 mm (24.88%) increase in ultimate deflection compared to the control specimen, as summarized in Table 5. The (Pcr/Pu) ratio for GS-3 TR was 30.11%, higher than that of the GS-1 ST, as presented in Table 4.

 

      For Specimen GS-4 TR, with the e_e = −80 mm at the anchorage point, demonstrated unique load-deflection characteristics, as shown in Figure 8d. The elastic stage for this specimen was higher than that of the control beam, with the first cracks forming at 188.72 kN and a mid-span deflection of 1.44 mm. The specimen exhibited a larger ultimate load of 647.08 kN and a larger deflection of 42 mm at failure. Compared to the control beam, this represents an increase in ultimate load by 45.91 kN (7.64%) and an increase in ultimate deflection by 11.9 mm (39.53%), as summarized in Table 5. The (Pcr/Pu) ratio for GS-4 TR was 29.16%, which is higher than that of the GS-1 ST, as presented in Table 4.

      For GS-5 PR, with the e_e = +80 mm at the anchorage point, demonstrated distinct load-deflection behavior, as shown in Figure 8e. This specimen exhibited a higher elastic stage compared to the control beam, with the first cracks appearing at 178.6 kN, surpassing the control beam’s cracking load, and a deflection 2 mm greater than that of the control specimen. The specimen achieved a larger ultimate load of 607.43 kN, with a corresponding deflection of 37.24 mm at failure. These values reflect an increase in ultimate load by 6.26 kN (1.04%) and an increase in ultimate deflection by 6.79 mm (22.56%) over the control beam, as summarized in Table 5. The (Pcr/Pu) ratio for GS-5 PR was 29.40%, which is higher than that of the control beam, as indicated in Table 4.

      For GS-6 PR, with e_e = 0, exhibited unique load-deflection behavior, as depicted in Figure 8f. Compared to the GS1-ST, this specimen displayed a longer elastic stage, with the first cracks occurring at 183.95 kN and a deflection of 1.68 mm. It reached a larger ultimate load of 613.6 kN and a higher deflection of 42.04 mm at failure. These findings represent a 2.07% increase in ultimate load (12.43 kN) and a 39.67% increase in ultimate deflection (11.94 mm) compared to the control specimen, as summarized in Table 5. The (Pcr/Pu) ratio for GS-6 PR was 29.98%, which is lower than that of the GS-1 ST, as shown in Table 4.

       For GS-7 PR, with the e_e= −80 mm, exhibited distinct load-deflection behavior, as shown in Figure 8g. The elastic stage for this specimen was shorter than that of GS-1 ST. The first crack in the concrete appeared at a load of 151.2 kN with a deflection of 1.43 mm. It reached a larger ultimate load of 624 kN and a higher deflection of 42.26 mm at failure. These results represent a 3.80% increase in ultimate load (22.83 kN) and a 41.06% increase in ultimate deflection (12.36 mm) compared to the control specimen, as summarized in Table 5. The (Pcr/Pu) ratio for GS-7 PR was 24.23%, which is lower than that of GS-1 ST, as indicated in Table 4. These findings suggest that the eccentricity of the tendon profile contributed to an enhanced load-bearing capacity and deflection, although the ductility, as indicated by the (Pcr/Pu) ratio, was slightly reduced compared to the GS-1 ST.

      For GS-1 HA, with the e_e=+80 mm at the anchorage, displayed distinct load-deflection behavior, as shown in Figure 8h. The specimen exhibited a shorter elastic stage compared to the control beam, with the first crack appearing at 126.73 kN and a deflection of 0.86 mm. Despite this, GS-1 HA reached a larger ultimate load of 608.4 kN and a higher deflection of 35.82 mm at failure. These results correspond to a 1.20% increase in ultimate load and a 19.00% increase in ultimate deflection compared to the control beam, as detailed in Table 5. The (Pcr/Pu) was 20.83%, lower than that of the GS-1 ST, as illustrated in Table 4.

      For GS-2 HA, with e_e=0, exhibited a load-deflection behavior, as illustrated in Figure 8i. The elastic stage for this specimen was shorter compared to the GS-1 ST, with the first crack occurring at 145.88 kN and a deflection of 1.3 mm. However, this specimen reached a larger ultimate load of 615 kN and a greater deflection of 41.95 mm at failure. These results indicate a 2.30% increase in ultimate load and a 39.37% increase in ultimate deflection compared to the control beam, as summarized in Table 5. The (Pcr/Pu) for GS-2 HA was 23.72%, which is lower than that of GS-1 ST, as shown in Table 4. These findings suggest that the tendon configuration in GS-2 HA enhanced both the load-carrying capacity and deflection behavior, while slightly reducing the beam's ductility as evidenced by the (Pcr/Pu) ratio.

      For GF-3 HA, featuring (e_e) of −80 mm at the anchorage, exhibited distinct load-deflection behavior, as shown in Figure 8j. Its elastic stage was shorter compared to the GS-1 ST, with the first cracks appearing at 166.48 kN and a deflection of 1.52 mm. This specimen demonstrated a significantly greater ultimate load of 706.5 kN and a higher deflection of 43.81 mm at failure. These results indicate a 17.52% increase in ultimate load and a 45.55% increase in ultimate deflection compared to the control beam, as summarized in Table 5. The (Pcr/Pu) for GF-3 HA was 23.56%, which is lower than that of the GS-1 ST, as presented in Table 4. These findings suggest that the harped tendon profile with eccentricity significantly im-proved both the load-bearing capacity and deflection performance, although the beam's ductility, as indicated by the (Pcr/Pu) ratio, was slightly reduced.

 

When comparing all beams to the GS-1ST control, as depicted in Figures 11k8k–m, the variances in ultimate loads and corresponding deflections can be attributed to variations in tendon profile layouts (straight, trapezoidal, parabolic, and harped) and tendon end anchorage configurations. Beams with higher eccentricity at the end anchorages or steeper tendon slopes demonstrated a greater load capacity than those with lower eccentricity or straight tendons. This enhanced load capacity is primarily due to the influence of the tendon profile layout, where beams with greater eccentricity or steeper slopes experience a higher vertical component of the effective prestressing force (Vp). This increase in prestressing force results in a higher nominal shear (Vcw), which raises the point at which web-shear cracking occurs, ultimately leading to im-proved shear strength capacity and overall performance of the beams.]

 

Thank you for pointing this out. We agree with this comment. Therefore, we make the comparison it in separate paragraphs and we delete the repeated paragraphs. The repetitive nature of the results description is to increase clarity in the comparison of each specimen with the reference specimen. Given the similarity in the analysis across all specimens, this detailed and organized approach ensures a good understanding of the accurate differences. While I understand the desire for a more engaging presentation, I believe that preserving this format is essential for accuracy in the comparison, and I hope you agree to keep the comparison as it was modified. I appreciate your insights and am open to any further suggestions to enhance the readability. more detail. This change can be found on page 19-21, line 484-598.

------------------------------------------------------------------------------------------------------------------------------

 

Comments 14: [ The manuscript should be supplemented with a comparison of the results between different prestressed reinforcement distributions (trapezoidal, parabolic, and harped), not only a comparison with the straight distribution of the strand with respect to the angle of inclination. Additional graphical comparison also should be introduced (trapezoidal vs parabolic, parabolic vs harped and so on.]

Response 14: [ When comparing all beams to the GS-1ST control, as depicted in Figures 8k–n, the improvement in ultimate loads and corresponding deflections can be attributed to variations in tendon profile layouts, which included straight, trapezoidal, parabolic, and harped shapes, as well as differences in tendon end anchorage. Beams with higher eccentricity at the end anchorages or steeper tendon slopes demonstrated a greater load capacity than those with lower eccentricity or straight tendons. This enhanced load capacity is primarily due to the influence of the tendon profile layout, where beams with greater eccentricity or steeper slopes experience a higher vertical component of the effective prestressing force (Vp). This increase in prestressing force results in a higher nominal shear (Vcw), which raises the point at which web-shear cracking occurs, ultimately leading to improved shear strength capacity and overall performance of the beams.]

 

 

(n) Specimen 1,4, 7 and 10

Thank you for pointing this out. We agree with this comment. Therefore, we explain and added figure 8n to make a comparison between beams with higher strength for each tendon profile shapes. This change can be found on page 19, line 503.

Comments 15: [Page 23, lines 614. Figure 11 should be substituted with Figure 12.].

Response 15: [Figure 9. Crack patterns of the specimens.]

Thank you for pointing this out. We agree with this comment and we have changed the [Figure 11] to enhance [ Figure 9]. This change can be found on page 24, line 659.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

I have evaluated the manuscript entitled "Tendon Profile layout Impact on the Shear Capacity of Un-bonded Post-Tensioned Prestressed Concrete Bridge I-Girders " submitted for potential publication in the infrastructures. I encourage the authors to carefully consider the following points, which if addressed, could help raise the manuscript's quality and impact to the standards of this journal:
1.Abstract: The abstract should more clearly reflect some of the key quantitative findings of the study.
2.Introduction: This section is somewhat redundant. It would be better to summarize and synthesize research topics rather than simply listing them. Additionally, the authors could cite relevant literature in the following: 

10.1016/j.istruc.2025.108288

3.Materials and methods: The concrete compressive strength of the first seven beams  was 62.8 MPa, while that of the last three beams was 69.7 MPa. Since concrete strength significantly influences shear capacity, how did you account for this strength disparity when analyzing the effect of tendon profiles on shear performance? 
4.Experimental programm: All specimens are reported to fail by shear failure. Did the authors observe any yielding of longitudinal reinforcement prior to shear failure? How did the authors confirm that the failure mode was purely shear-dominated (not a combination of flexure and shear)? Providing strain data from longitudinal bars or stirrups would strengthen the validity of this conclusion?
5.The experimental program focuses on varying tendon profiles and end eccentricities, but other key parameters (e.g., prestressing force magnitude, shear span-to-depth ratio, or stirrup ratio) were held constant. Have the authors considered using numerical simulations (e.g., finite element analysis) to extend your study to a broader range of parameters? This would help validate your experimental findings and enhance the generality of your conclusions about optimal tendon layouts. 

Author Response

Response to Reviewer 2 Comments
Summary
Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

 

Comments 1: [Abstract: The abstract should more clearly reflect some of the key quantitative findings of the study]

 

Response 1: [Abstract: The main objective of this research is to investigate the impact of tendon profile layout on the shear strength of unbonded post-tensioned prestressed concrete bridge I-girders. This study involves an experimental investigation where ten unbonded post-tensioned bridge girders are cast and subjected to four-point loads. The focus of the investigation is on the effect of different tendon profile layouts, including trapezoidal, parabolic, and harped shapes. The experimental results reveal that the shear behavior of the specimens progresses through three distinct stages: the elastic stage, the elastic–plastic stage, and the plastic stage, with all specimens ultimately failing due to shear. The results show that tendon profiles with higher eccentricity at the end of the beams (80 mm above the neutral axis) had the highest ulti-mate load capacity for each tendon profile shape, coupled with the largest deflection. Conversely, profiles with lower eccentricity (80 mm below the neutral axis) demonstrated the lower ultimate load capacity for each tendon profile shape and minimal deflection. Among the various tendon profile layouts that were tested, the specimen with the harped tendon profile (GF-1 HA) showed the highest ultimate load capacity, with an increasing rate of 17.52% in ultimate load and a 45.55% increase in ultimate deflection compared to the control beam (GF-1 ST) with a straight tendon profile. On the other hand, the harped tendon profile specimen (GF-1 HA) exhibited the lowest deflection among the various tendon profile shapes with an increasing rate of 5.7% in ultimate load deflection in comparison with the control beam (GF-1 ST) with a straight tendon profile. These improvements in stiffness, load capacity, and deflection are attributed to enhanced resistance, particularly at the supports. Consequently, the optimized tendon layouts offer an increase in the overall structural efficiency, leading to potential cost savings in bridge girder production.]

 

Thank you for pointing this out. We agree with this comment. Therefore, we have we have made the following adjustments:

1. The phrase [capacity for each tendon profile shape, coupled] has been added. This change can be found on page 1, paragraph 1, line 18.
2. The phrase [for each tendon profile shape] has been added. This change can be found on page 1, paragraph 1, line 20-21.
3. The sentences [, with an increasing rate of 17.52% in ultimate load and a 45.55% increase in ultimate deflection compared to the control beam (GF-1 ST) with a straight tendon profile.] has been added. This change can be found on page 1, paragraph 1, line 23-24.
4. The sentences [among the various tendon profile shapes with an increasing rate of 5.7% in ultimate load deflection in comparison with the control beam (GF-1 ST) with a straight tendon profile.] has been added. This change can be found on page 1, paragraph 1, line 26-27.

------------------------------------------------------------------------------------------------------------------------------

Comments 2: [Introduction: This section is somewhat redundant. It would be better to summarize and synthesize research topics rather than simply listing them. Additionally, the authors could cite relevant literature in the following:  10.1016/j.istruc.2025.108288]

 

Response 2:

Thank you for pointing this out. We agree with this comment. Therefore, we have deleted some references to be more focused on the topic of the manuscript, and we added two more references on shear strength and the effect of the tendon profile layout of post-tensioned tendons in the literature, and we also deleted some references to be more focused on the topic of the manuscript and because the introduction was too long. As follows:

1. The deleted references:
2. a) [Ma et al. [30] examined shear design in prestressed concrete beams, due to lacking a standardized procedure. They compiled 266 test results to evaluate the accuracy of five de-sign codes and two models. The findings showed that Marí et al.'s method was the most ac-curate but had a higher coefficient of variation. A new simplified shear strength formula based on a truss-arch model was proposed, offering improved prediction accuracy and consistency, making it a promising alternative for shear strength analysis in prestressed concrete beams.]

This change can be found in introduction of reviewed manuscript on page 5, paragraph 4, line numbers (219-224).

1. b) [Mihaylov et al. [36] conducted an experimental study on eight post-tensioned concrete beams at the University of Toronto, examining the size effect on shear behavior and tendon layout variations. The beams, ranging from 250 mm to 1000 mm in depth, had unbonded tendons arranged in straight or harped configurations with varying eccentricities. Under a three-point bending test without stirrups, the beams showed arch action and size effects. The study found that shear strength increased with tendon eccentricity. A strut-and-tie model based on AASHTO guidelines accurately predicted results, while a kinematic-based approach explained the high shear resistance of smaller beams].

This change can be found in introduction of reviewed manuscript on page 6, paragraph 2, line numbers (259-266).

2. The deleted references.

1.[Jiang et al. [14] they presented a simplified design formula for the shear capacity of prestressed concrete (PC) beams reinforced in steel plates. Using equilibrium equations, the shear contribution of the steel plates was determined taking into account shear compression failure. A parametric investigation Situated by using test data and a validated finite-element program. The formula with consideration of strength-reduction factor 0.494 accurately predicts the shear resistance of PC beams strengthened by steel plates and is consistent with the experimental results]. This change can be found on page 3, paragraph, line 135-141.

2. [Hillebrand et al. [16] they studied the fatigue behavior of 10 T-shaped prestressed concrete beams with shear reinforcement is questioned and compared by means of experimental load cycles to the prediction of the German approach based on the Eurocode 2. The study findings were beneficial for the evaluation of existing bridges and the design and construction of new bridges.]. This change can be found in on page 4, paragraph 1, line 148-153.
3. [Eisa et al. [17]They investigated static response of prestressed reinforced concrete beams externally reinforced with steel plates and woven carbon fiber fabric (WCFF). Results of testing 20 large-scale beams showed that both techniques enhanced the flexural and shear strength. U-shaped steel plates provided the highest load capacity and deflection reduction, while WCFF wrapping produced increase in shear strength]. This change can be found in on page number 4, paragraph 1, line 153-158.
4. [Qi et al. [18] they evaluated the shear performance of reinforced concrete beams with externally prestressed Carbon fiber reinforced polymer (CFRP) tendons The results indicate that CFRP tendons with stirrups increase yield and ultimate load capacities, delay diagonal cracks and provide considerable shear resistances, the levels of improvement related to preload stresses. Although initially damaged in the shear zone, the shear capacity is not much affected as load is increased. The results, along with predictive model with an error of less than 10% provide useful ideas to composite design]. This change can be found in on page 3, paragraph 1, line 158-164.
5. [Zhao et al. [19] they studied the shear behavior of 16m span prestressed hollow slabs test and numerical simulation. results show of shear-compression failure, cracks are formed at 1.35m to 1.95m from beam ends, finite element model reliability quasi-authenticated by ABAQUS simulation]. This change can be found in on page 4, line 165-168.
6. [Jancy et al. [20]they presented a new method of modelling post-tensioned beams, calibrating a finite element model versus load capacity and post-critical response until experimental evidence is matched. Two different beams with dissimilar tendons arrangement have been analyzed under the purview of Abaqus/Explicit and Hyper mesh, ensuring crack patterns & behavior at various loading stage are accurately addressed]. This change can be found in on page 4, line 168-173.
7. [Mohamed et al. [22] they explore enhancing the structural behavior of reinforced concrete beams using external pre-stressing tendons to increase load capacity and resistance. Seven RC beams were tested with different tendon configurations, showing significant improvements in load-carrying capacity, deflection, and ductility. The straight-line tendon with inner deviators proved most effective]. This change can be found in on page 4, line 176-181.
8. [Yaqub et al. [23] they investigated the performance of PC I-girders strengthened with iron-based shape memory alloy (Fe-SMA) strips and ribbed rebar and their shear capacity using experimentation and numerical modelling. Fe-SMA can recover pre-induced strains during heating, leading to enhanced shear properties and 40-47% capacity recovery. Crack control and serviceability of active Fe-SMA shear strengthening are better than those of passive systems]. This change can be found in on page 4, line 181-186.

-----------------------------------------------------------------------------------------------------------------------------

Comments 3: [Materials and methods: The concrete compressive strength of the first seven beams was 62.8 MPa, while that of the last three beams was 69.7 MPa. Since concrete strength significantly influences shear capacity, how did your account for this strength disparity when analyzing the effect of tendon profiles on shear performance?]

 

Response 3: Thank you for pointing this out. We agree with this comment. Therefore, to account for the disparity in concrete compressive strength between the first seven beams (fcu = 62.8 MPa) and the last three beams (fcu = 69.7 MPa), we carefully analyzed the experimental results. While the ultimate load of the first two beams in the higher strength group increased by 1 to 5 kN, the significant increase in ultimate load observed in the third beam from the higher fcu group was primarily due to the tendon profile layout, which had a higher eccentricity (80 mm above the neutral axis).

The theoretical shear force calculations showed a difference of only 12 kN (representing 1.7%–2%) when using either fcu = 62.8 or fcu=69.7 kN value. This minimal difference in compressive strength (approximately 10%) had a negligible effect on shear strength, indicating that the primary factor contributing to the increase in ultimate load was the tendon profile layout.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

 

Comments 4: [Experimental program: All specimens are reported to fail by shear failure. Did the authors observe any yielding of longitudinal reinforcement prior to shear failure? How did the authors confirm that the failure mode was purely shear-dominated (not a combination of flexure and shear)? Providing strain data from longitudinal bars or stirrups would strengthen the validity of this conclusion?]

 

Response 4: Thank you for pointing this out. We agree with this comment. Therefore, In the experimental program, all specimens indeed failed due to shear failure because we designed the beam for avoiding flexural failure, and we calculated theoretically the ultimate capacity of flexural to be higher than shear capacity, and two longitudinal 16 mm bars were added at the bottom of the beam. However, no yielding of the longitudinal reinforcement was observed prior to shear failure. To confirm that the failure mode was purely shear-dominated, we closely monitored the behavior of the specimens during loading, ensuring that no flexural cracking or yielding occurred at load levels below the shear failure load. The oblique cracks appeared in the web; as the load increased, these cracks spread diagonally, both upward and downward.

------------------------------------------------------------------------------------------------------------------------------

Comments 5: [The experimental program focuses on varying tendon profiles and end eccentricities, but other key parameters (e.g., prestressing force magnitude, shear span-to-depth ratio, or stirrup ratio) were held constant. Have the authors considered using numerical simulations (e.g., finite element analysis) to extend your study to a broader range of parameters? This would help validate your experimental findings and enhance the generality of your conclusions about optimal tendon layouts.]

 

 

 

Response 5: Thank you for pointing this out. We agree with this comment. Therefore, While the experimental program focused on varying tendon profiles and end eccentricities, we acknowledge that other parameters, such as prestressing force magnitude, shear span-to-depth ratio, and stirrup ratio, were held constant. We have considered to use of numerical simulations, such as finite element analysis, to further explore the influence of these additional parameters. Incorporating these simulations would indeed help validate our experimental results and provide a broader understanding of optimal tendon layouts, enhancing the generality of our conclusions.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1.The Introduction should be reorganized and rewritten:
(1) Since the post-tensioning (PT) technology is well-known and widely used in concrete structures. The relevant technical background does not require a lengthy introduction. I think the first few paragraphs (Line 31 - Line 73) can be merged and condensed into one paragraph.
(2) This study focus on the impact of tendon profile layout on the shear strength of tested beams. Some literature reviews (Line 103 -Line 210 ) have little relevance to the objects and aims, and I think they can be briefly analyzed or deleted.
2. Line 282 - Line 285:  the average compressive strength of  the first seven beams was 62.8 MPa, while the last three beams with a harped tendon profile (GF-1 HA, GF-2 HA, GF-3 HA), the modulus of rupture was slightly higher at 5.3 MPa. I wonder  if these factors can affect their comparison results with GF-1 HA (Fig. 11m).
3. Fig. 11: Since the contents in Fig. 11a - Fig. 11j  have been included in Fig. 11k - Fig. 11m, I think Fig. 11a - Fig. 11j can be deleted.
4. It seems that there is only one tested specimen for each tendon profile layout. To improve the reliability of the results, Several sets of repeated experiments or numerical simulations may be necessary.
5. The current analysis of results is primarily a comparative analysis of data, and relevant mechanical mechanisms (such as prestress loss) have not been analyzed and explained.
6. The conclusion needs to be further refined, and the results that can provide guidance for practical engineering need to be highlighted.

Author Response

Response to Reviewer 3 Comments
Summary
Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

 

Comments 1: [The Introduction should be reorganized and rewritten:

(1) Since the post-tensioning (PT) technology is well-known and widely used in concrete structures. The relevant technical background does not require a lengthy introduction. I think the first few paragraphs (Line 31 - Line 73) can be merged and condensed into one paragraph.

(2) This study focus on the impact of tendon profile layout on the shear strength of tested beams. Some literature reviews (Line 103 -Line 210) have little relevance to the objects and aims, and I think they can be briefly analyzed or deleted.]

 

Response 1:

1. Thank you for pointing this out. We agree with this comment. Therefore, we have merged the first few paragraphs (Line 31 - Line 73) into two paragraphs, as follows:

[Recent advancements in structural engineering focus on cost-effective solutions through the use of advanced design methods and stronger materials, resulting in reduced weight and cross-sectional dimensions of structures. This is particularly important in reinforced concrete, where dead loads often contribute significantly to the total load. Despite these improvements, issues like cracking and excessive deflection, especially in high-stiffness structures, remain prevalent. Prestressed concrete addresses these challenges by introducing internal stresses that counteract external loads, improving strength, durability, and overall performance of traditional reinforced concrete [1,2].

There are two primary types of prestressed concrete systems: pretensioned and post-tensioned. In pre-tensioning, tendons are stretched before the concrete is poured, while in post-tensioning, tendons are tensioned after the concrete has cured. Both methods aim to improve structural effectiveness by overcoming stresses caused by external loads, thus enhancing strength and stability [3–5]. Post-tensioning is particularly advantageous in bridge construction due to its material efficiency, better deflection and cracking control, longer material life, faster construction, lower costs, and greater design flexibility. The system includes prestressing strands, protective ducts, grout, and anchorages, all of which work together to enhance concrete stiffness and overall structural performance [6,7]. The durability of post-tensioning depends on the quality of materials like prestressing steel, anchorages, and ducts, as well as installation and environmental protection measures [8]. Post-tensioned concrete can be either bonded, where tendons are in contact with the concrete, or unbonded, where tendons are isolated (not in contact with the concrete), influencing the stress distribution and structural behavior in distinct ways.]

This change can be found on page number 1-2, paragraph 1-2, line numbers (35-42,52-56, 64-68, 75-77, 80-82).

 

2. Thank you for pointing this out. We agree with this comment. Therefore, we have deleted some references to be more focused on the topic of the manuscript and because the introduction was too long. These are the deleted references:

1.[Jiang et al. [14] they presented a simplified design formula for the shear capacity of prestressed concrete (PC) beams reinforced in steel plates. Using equilibrium equations, the shear contribution of the steel plates was determined taking into account shear compression failure. A parametric investigation Situated by using test data and a validated finite-element program. The formula with consideration of strength-reduction factor 0.494 accurately predicts the shear resistance of PC beams strengthened by steel plates and is consistent with the experimental results]. This change can be found on page 3, paragraph, line 135-141.

2. [Hillebrand et al. [16] they studied the fatigue behavior of 10 T-shaped prestressed concrete beams with shear reinforcement is questioned and compared by means of experimental load cycles to the prediction of the German approach based on the Eurocode 2. The study findings were beneficial for the evaluation of existing bridges and the design and construction of new bridges.]. This change can be found in on page 4, paragraph 1, line 148-153.
3. [Eisa et al. [17]They investigated static response of prestressed reinforced concrete beams externally reinforced with steel plates and woven carbon fiber fabric (WCFF). Results of testing 20 large-scale beams showed that both techniques enhanced the flexural and shear strength. U-shaped steel plates provided the highest load capacity and deflection reduction, while WCFF wrapping produced increase in shear strength]. This change can be found in on page number 4, paragraph 1, line 153-158.
4. [Qi et al. [18] they evaluated the shear performance of reinforced concrete beams with externally prestressed Carbon fiber reinforced polymer (CFRP) tendons The results indicate that CFRP tendons with stirrups increase yield and ultimate load capacities, delay diagonal cracks and provide considerable shear resistances, the levels of improvement related to preload stresses. Although initially damaged in the shear zone, the shear capacity is not much affected as load is increased. The results, along with predictive model with an error of less than 10% provide useful ideas to composite design]. This change can be found in on page 3, paragraph 1, line 158-164.
5. [Zhao et al. [19] they studied the shear behavior of 16m span prestressed hollow slabs test and numerical simulation. results show of shear-compression failure, cracks are formed at 1.35m to 1.95m from beam ends, finite element model reliability quasi-authenticated by ABAQUS simulation]. This change can be found in on page 4, line 165-168.
6. [Jancy et al. [20]they presented a new method of modelling post-tensioned beams, calibrating a finite element model versus load capacity and post-critical response until experimental evidence is matched. Two different beams with dissimilar tendons arrangement have been analyzed under the purview of Abaqus/Explicit and Hyper mesh, ensuring crack patterns & behavior at various loading stage are accurately addressed]. This change can be found in on page 4, line 168-173.
7. [Mohamed et al. [22] they explore enhancing the structural behavior of reinforced concrete beams using external pre-stressing tendons to increase load capacity and resistance. Seven RC beams were tested with different tendon configurations, showing significant improvements in load-carrying capacity, deflection, and ductility. The straight-line tendon with inner deviators proved most effective]. This change can be found in on page 4, line 176-181.
8. [Yaqub et al. [23] they investigated the performance of PC I-girders strengthened with iron-based shape memory alloy (Fe-SMA) strips and ribbed rebar and their shear capacity using experimentation and numerical modelling. Fe-SMA can recover pre-induced strains during heating, leading to enhanced shear properties and 40-47% capacity recovery. Crack control and serviceability of active Fe-SMA shear strengthening are better than those of passive systems]. This change can be found in on page 4, line 181-186.

------------------------------------------------------------------------------------------------------------------------------

Comments 2: [Line 282 - Line 285:  the average compressive strength of the first seven beams was 62.8 MPa, while the last three beams with a harped tendon profile (GF-1 HA, GF-2 HA, GF-3 HA), the modulus of rupture was slightly higher at 5.3 MPa. I wonder if these factors can affect their comparison results with GF-1 HA (Fig. 11m).]

 

Response 2: [Thank you for pointing this out. We agree with this comment. Therefore, to account for the disparity in concrete compressive strength between the first seven beams (fcu = 62.8 MPa) and the last three beams (fcu = 69.7 MPa), we carefully analyzed the experimental results. While the ultimate load of the first two beams in the higher strength group increased by 1 to 5 kN, the significant increase in ultimate load observed in the third beam from the higher fcu group was primarily due to the tendon profile layout, which had a higher eccentricity (80 mm above the neutral axis). The theoretical shear force calculations showed a difference of only 12 kN (representing 1.7%–2%) when using either fcu = 62.8 or fcu=69.7 kN value. This minimal difference in compressive strength (approximately 10%) had a negligible effect on shear strength, indicating that the primary factor contributing to the increase in ultimate load was the tendon profile layout.]

------------------------------------------------------------------------------------------------------------------------------

Comments 3: [Fig. 11: Since the contents in Fig. 11a - Fig. 11j have been included in Fig. 11k - Fig. 11m, I think Fig. 11a - Fig. 11j can be deleted]

 

Response 3: [Thank you for this pointing out. We included these figures because the elastic stage and elastic-plastic stage are not clearly distinguishable in the last three figures (Fig. 11k - Fig. 11m,) due to the overlap and interaction of the curves in these stages. I kindly request that all figures be retained to ensure greater clarity for the readers. I believe this will provide a more comprehensive understanding of the data. Thank you for your consideration.]

------------------------------------------------------------------------------------------------------------------------------

 

 

 

 

 

 

Comments 4: [It seems that there is only one tested specimen for each tendon profile layout. To improve the reliability of the results, several sets of repeated experiments or numerical simulations may be necessary.]

 

Response 4: Thank you for pointing this out. We agree with this comment. Therefore, we appreciate your observation regarding the limited number of specimens for each tendon profile layout. While the current study is based on a single specimen for each layout, we acknowledge that multiple sets of repeated experiments or numerical simulations would improve the reliability and generalizability of the results. In further research, we would like to include more experimental repetitions and explore the use of numerical models to further substantiate our results and address the intrinsic variability in structural behavior. This will give us a better idea of how tendon profiles affect the performance of prestressed concrete structures.

 

------------------------------------------------------------------------------------------------------------------------------

 

Comments 5: [The current analysis of results is primarily a comparative analysis of data, and relevant mechanical mechanisms (such as prestress loss) have not been analyzed and explained.]

 

Response 5: Thank you for pointing this out. We agree with this comment. Though the current analysis centered on comparing the experimental data, we acknowledge that it is crucial to investigate relevant mechanical mechanisms such as prestress loss. In the future we will investigate these factors, to deeply understand about their impact on performance of prestressed concrete beam. This will increase the confidence in the results and provide a deeper understanding of the mechanisms underlying behavior as observed.

------------------------------------------------------------------------------------------------------------------------------ Comments 6: [The conclusion needs to be further refined, and the results that can provide guidance for practical engineering need to be highlighted.]

 

Response 6: [

4          Among the specimens with a trapezoidal tendon profile, the greater increase in ultimate load was observed in specimen GS-4 TR, which showed a 7.64% improvement compared to the control beam. For the specimens with a parabolic tendon profile, an increase of 3.8% in ultimate load was recorded, with specimen GS-7 PR achieving a maximum increase of 22.83 kN over the control beam. Specimens featuring a harped tendon profile also demonstrated a greater increase in ultimate load, with specimen GS-3 HA showing a significant 17.52% improvement over the control beam. The specimen GS-3 HA with harped tendon profile showed the highest ultimate load in comparison with all other tendon profiles. These results highlight the beneficial impact of tendon profile layout on the load-carrying capacity of prestressed concrete beams.

5. The vertical deflection measurements of the tendon profile specimens revealed distinct variations. For the trapezoidal tendon profile, specimen GS-3 TR exhibited the smallest ultimate load deflection at 37.59 mm, which was 24.88% greater than that of the GS-1 ST. Among the parabolic tendon profile specimens, GF-5 PR showed the least ultimate load deflection at 37.24 mm, 22.56% higher than GS-1 ST, while for harped tendon profile, GS-1 HA recorded a lower ultimate load deflection of 35.82 mm, 19% greater than GS-1 ST. The specimen GS-1 HA with harped tendon profile showed the lowest ultimate load deflection in comparison with trapezoidal and parabolic tendon profiles. These findings highlight the influence of tendon profile shapes on ultimate load deflection, offering insights into their structural performance.
6. The study revealed that each tendon profile shape (trapezoidal, parabolic, harped) exhibited the highest ultimate load capacity and ultimate load de-flection when beams with higher eccentricity (80 mm above N.A.), while beams with lower eccentricity (80 mm below N.A.) resulted in the lowest load capacity and ultimate load deflection. Notably, specimen GS-3 HA, featuring the harped tendon profile, displayed the greatest ultimate load capacity, while specimen GS-1 HA, with the harped tendon profile, recorded the smallest ultimate load deflection. These findings highlight the significant influence of tendon profile shape and eccentricity on the structural performance of the specimens.
7. The experimental results of girders tested with optimized tendon profiles indicated that their performance was enhanced remarkably in comparison with the control beam and the harped tendon profile showed the beast improvements in performance in comparison with all other tendon profiles. These girders could carry higher loads, and these girders could sustain larger loads due to the more effective distribution of the prestressing forces along the girder length. The optimum tendon arrangements lead to more homogeneous distribution of stresses inside the concrete, fully utilizing a larger part of the cross-section. This study demonstrates the advantage of adopting optimized tendon profiles to enhance the performance of prestressed concrete bridge girders.]

Thank you for pointing this out. We agree with this comment. Therefore, we have refined the results. The following adjustments have also been made:

1. The name [GF-4 TR] has been changed to [ GS-4 TR]. This change can be found on page 24, line 673.
2. The ratio [12.80%] has been changed to [ 7.64%]. This change can be found on page 24, line 673.
3. The ratio [6.36%] has been changed to [ 3.8%]. This change can be found on page 24, line 675.
4. The name [GF-7 PR] has been changed to [ GS-7 PR]. This change can be found on page 24, line 676.
5. The name [GF-3 HA] has been changed to [ GS-3 HA]. This change can be found on page 24, line 678.
6. The ratio [29.36%] has been changed to [ 17.52%]. This change can be found on page 24, line 678.
7. The sentences [The specimen GS-3 HA with harped tendon profile showed the highest ultimate load in comparison with all other tendon profiles.] has been added. This change can be found on page 24, line 679-681.
8. The name [GF-2 TR] has been changed to [ GS-3 TR]. This change can be found on page 24, line 684.
9. The word [ultimate load] has been added. This change can be found on page 24, 25, line 685, 687, 689, 692, 702.
10. The deflection [35.14] has been changed to [ 37.59]. This change can be found on page 24, line 685.
11. The ratio [17.13%] has been changed to [ 24.88%]. This change can be found on page 24, line 686.
12. The ratio [22.97%] has been changed to [ 22.56%]. This change can be found on page 25, line 688.

 

13. The ratio [19.4%] has been changed to [ 19%]. This change can be found on page 25, line 689.

 

14. The sentences [The specimen GS-1 HA with harped tendon profile showed the lowest ultimate load deflection in comparison with trapezoidal and parabolic tendon profiles.] has been added. This change can be found on page 25, line 690-692.

 

15. The sentences [the eccentricity was set at e_e = -80 mm, while the eccentricity of e_e = +80 mm resulted in the lowest load capacity and deflection] has been changed to [beams had higher eccentricity (80 mm above N.A.), while beams had lower eccentricity (80 mm below N.A.) resulted in the lowest load capacity and ultimate load deflection]. This change can be found on page 25, line 696-698.
16. The name [GF-1 HA] has been changed to [ GS-3 HA]. This change can be found on page 25, line 700.
17. The name [GF-2 TR] has been changed to [ GS-1 HA]. This change can be found on page 25, line 701.
18. The sentences [and the harped tendon profile showed the beast improvements in performance in comparison with all other tendon profiles.] has been added. This change can be found on page 25, line 707-708.

 

 

 

 

 

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This manuscript is mainly based on the analysis and discussion of experimental results. The overall structure is clear; however, its novelty and research depth appear somewhat limited. My specific comments are as follows:

1. On page 6, the manuscript refers to the BS 12390-3 standard and the ACI 211.1 specification, but no corresponding references are provided. It is recommended that the authors include complete references for all standards cited at their first appearance and check the manuscript for similar issues.

2. Could Figure 8 be combined into a single figure to facilitate the presentation of the prestressing setup?

3. When the test was terminated, the load had not decreased to 80% of Pu. Please clarify the exact criterion used for stopping the test.

4. Although the title of the paper indicates an investigation into shear capacity, the manuscript does not present an in-depth analysis of shear capacity. Instead, it mainly discusses ductility comparisons.

Author Response

Response
Summary
Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

 

Comments 1: [On page 6, the manuscript refers to the BS 12390-3 standard and the ACI 211.1 specification, but no corresponding references are provided. It is recommended that the authors include complete references for all standards cited at their first appearance and check the manuscript for similar issues.]

 

Response 1: [The design concrete mix used in this study was designed based on ACI 211.1 standard and followed the recommendations of the ACI 211.1R recommendation [42]. A high-performance superplasticizer, Sika ViscoCrete 1681 as shown in Figure 1, was added to improve workability and overall performance of the mixture. The detailed mixing proportions are presented in Table 1. The compressive strength of the concrete cubes (fcu) was set to reach a minimum of 55 MPa at 28 days.] and [The concrete compressive strength was evaluated using 150 × 150 × 150 mm cubic samples, following the BS 12390-3 standard [43]. The compressive strength was determined by testing 12 concrete cubes at 28 days. For the first seven beams, which incorporated straight, trapezoidal, and parabolic tendon profiles, the average compressive strength was 62.8 MPa. In contrast, the last three beams, which featured a harped tendon profile, exhibited a higher average compressive strength of 69.7 MPa. These values were measured using a concrete compression testing machine.

Thank you for pointing this out. We agree with this comment. Therefore, we have added the references, as follow:

1. The reference of ACI 211.1 standard has been added. This change can be found on page 7, paragraph 2, line 306.
2. The reference of ACI 211.1 standard has been added. This change can be found on page 7, paragraph 3, line 314.

------------------------------------------------------------------------------------------------------------------------------

 

 

 

 

 

 

 

 

 

Comments 2: [Could Figure 8 be combined into a single figure to facilitate the presentation of the prestressing setup?]

 

Response 2: Thank you for pointing this out. We agree with this comment. There is a mistake in the name on figure 8 because there were two different figures, one for the post-tension machine and tendon jacking, and the other was a flowchart for the preparation of the test specimens. Therefore, we have corrected the figure number to be Figure 5. (a) Post-tensioning machine. (b) tendon jacking and Figure 6. Flowchart for the preparation of the test specimens. (Note: we deleted figures 1 to 3 according to one of the reviewers request. For this reason, fig.8 will be fig.5)

Comments 3: [When the test was terminated, the load had not decreased to 80% of Pu. Please clarify the exact criterion used for stopping the test.]

 

Response 3: Thank you for pointing this out. We agree with this comment. The test was terminated when the load stopped increasing and began to slightly decrease, while the displacement continuously increased significantly. The specimens exhibited signs such as significant cracking and excessive deflection, which led to concrete cracking in one of the tests.

------------------------------------------------------------------------------------------------------------------------------

 

Comments 4: [Although the title of the paper indicates an investigation into shear capacity, the manuscript does not present an in-depth analysis of shear capacity. Instead, it mainly discusses ductility comparisons.]

 

Response 4: [Thank you for pointing this out. We agree with this comment. In this study, we focused on investigating the effect of tendon profile layouts on the shear strength of unbonded post-tensioned prestressed concrete. We tested ten beams with different tendon profiles and compared their ultimate loads, ultimate load deflections, cracking loads, and cracking load deflections. Additionally, we analyzed the ratio of cracking load to ultimate load, a key parameter that defines beam ductility and overall structural performance. Our findings highlight the tendon profile that offered the greatest improvement in both ultimate load and deflections.]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have made sufficient improvements to the manuscript and can be considered for publication in the Infrastructure Journal.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper can be accepted

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have improved the quality of the manuscript, and I think it can be considered for publication. However, I encourage the authors to further conduct relevant experiments and theoretical analysis on this subject in the future.

Reviewer 4 Report

Comments and Suggestions for Authors

Thank you for submitting your revised manuscript. After careful review, I must highlight the following concerns: In this revision, you have not provided direct and substantive responses to the critical issues raised in the previous review round.