Exploring the Bond, Flexure, and Shear Behaviour of Bundled Bars in Concrete Structures

Exploring the Bond, Flexure, and Shear Behaviour of Bundled Bars in Concrete Structures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Exploring the Bond, Flexure, and Shear Behaviour of Bundled Bars in Concrete Structures M Ponni, Shobha Rajkumar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4697426/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 18 Mar, 2025 Read the published version in Iranian Journal of Science and Technology, Transactions of Civil Engineering → Version 1 posted 14 You are reading this latest preprint version Abstract Bundled bars, also known as bundled reinforcement, involve grouping multiple steel bars together to form a single unit, which is then embedded within concrete structures. We aim to comprehensively understand the behavior of bundled bars in reinforced concrete structures. This study investigates the behavior of bundled reinforcement bars in concrete beams, aiming to assess their influence on structural performance. A series of experiments were conducted, including pullout tests on bundled bars and flexural and shear tests on concrete beams with and without stirrups. The study evaluated various parameters such as peak load, displacement, ductility, stiffness, and energy absorption capacity for different bundling configurations. Results indicate that bundling enhances the peak load capacity and energy absorption of beams, with minimal impact on displacement and stiffness. However, beams without stirrups exhibit higher stiffness compared to those with stirrups, suggesting a trade-off between shear capacity and structural rigidity. Overall, the findings provide insights into the behavior of bundled reinforcement bars in concrete structures, informing design practices for enhanced structural performance and resilience. Contrary to IS code recommendations, findings from this study indicate that such recommendations are not essential and could even be counterproductive. Bundled Bars Bond Strength Bond-slip Behavior Flexural and Shear Behaviour Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 1. INTRODUCTION In beam design, bundled bars refer to the practice of using multiple reinforcing bars (rebars) grouped together within a single cross-sectional area of the beam. This approach is often employed to meet the required reinforcement ratio or to provide additional strength and ductility in heavily loaded or seismic-resistant structures. By bundling bars together, engineers can effectively increase the total area of reinforcement within the beam without significantly altering its dimensions. The research area of bundled bars in reinforced concrete structures has seen significant development and interest in recent years, driven by the need for more efficient and sustainable construction solutions. With increasing demands for high-performance and cost-effective structural solutions, engineers and designers are exploring innovative reinforcement strategies like bundled bars to optimize structural efficiency and meet project requirements. Abreha et al. (2021) [ 1 ] conducted numerical simulations using explicit finite element analysis to explore the behavior of bundle reinforced concrete (BRC) columns in comparison to traditionally reinforced columns. The results revealed that bundling longitudinal reinforcement not only improves the impact capacity of BRC columns but also stabilizes their response to fluctuating loads. Giovanni et al. (2021) [ 7 ] recommended the use of equivalent area rather than equivalent perimeter for bundled bars. Walujodjati (2021) [ 14 ] observed an increase in flexural capacity with bundling. Francisco et al. (2018) [18] found a reduction in the development length for bundled bars based on their pullout test study. Liu et al. (2017) [ 10 ] observed a decrease in average bond-anchoring strength as the number of steel bars and anchorage length increased. John (2013) [ 9 ] concluded that bond strength is not reduced when an individual bar within a pair or bundle of three bars is lap-spliced, provided appropriate allowance is made for differences in confinement and the proportion of bars spliced at a section. Daniel (1994) [ 4 ] conducted experiments on pullout tests in bundled bars and compared various existing equations. He concluded that the equation proposed by Orangun et al. (1977) [ 11 ] is best suited for predicting the behavior of bundled bars in pullout tests. 2. RESEARCH SIGNIFICANCE Understanding the behavior of bundled bars remains an area with significant gaps in knowledge. Research significance lies in the exploration of bundled bars' behavior under different bundling configurations, such as single, double, triple, and quadruple arrangements, through pullout tests and subsequent analysis in beams. Understanding how bundling affects pullout strength provides insights into the bond performance of bundled bars in concrete structures, crucial for ensuring structural integrity and safety. Moreover, investigating the flexural and shear behavior of beams reinforced with longitudinally bundled bars offers valuable data for optimizing reinforcement design and enhancing structural performance. This research contributes to advancing knowledge in reinforced concrete design and construction practices, ultimately leading to more efficient and resilient structural systems. 3. PULLOUT TESTING Pullout tests are a fundamental method used to evaluate the bond strength between reinforcing bars and concrete. In a pullout test, a steel bar is embedded in a concrete specimen, and a tensile force is applied to the bar until it pulls out from the concrete. This test provides crucial information about the bond characteristics. 3.1 Specimen Preparation The pullout specimens were prepared following established standards, with traditional cylindrical specimens measuring 150 mm in diameter and 300 mm in height. The steel reinforcement was embedded into the cylinder up to a depth of 200 mm, with an additional 200 mm extending outside the cylinder. While IS2770 (Part 1) − 1967 (Reaffirmed 2007) recommends using cube specimens for pullout tests, it limits the maximum embedding depth to 150 mm. Recognizing this constraint, the decision was made to utilize cylindrical specimens to achieve deeper embedment depths, thus allowing for a more comprehensive evaluation of bond strength and behavior. This approach ensures adherence to testing standards while maximizing the depth of embedding, as illustrated in Fig. 1. Four different bundling configurations were examined in the pullout tests conducted as part of the study. The configurations included single bundling with a single 16 mm diameter rod, bundling with one 12 mm rod and one 10 mm rod, bundling with two 10 mm rods and one 8 mm rod, and bundling with four 8 mm rods. These variations were chosen to investigate the influence of the number and diameter of rods within the bundle on pullout strength and behavior. Table 1 Reinforcement Configuration Details All the bundling configurations shown in Table 1 were designed to maintain approximately the same cross-sectional area, ensuring consistency in the total amount of reinforcement across the different specimens. A total of 12 specimens were cast, with three specimens for each bundling configuration. These specimens were designed to provide a comprehensive understanding of the pullout behavior of bundled bars under different configurations. The arrangement of these specimens is depicted in Fig. 2. 3.2 Specimen Testing Pullout testing was conducted using a Universal Testing Machine (UTM) at the Government College of Engineering, Salem. Each specimen was set up with the protruding rod securely held at the top, allowing the concrete cylinder to hang freely. The UTM applied a pushing force to the cylinder, simulating the pullout of the inserted rod as shown in Fig. 3. Load-deflection data were recorded using computerized equipment integrated with the UTM. For each bundling configuration, three specimens were tested, and the lowest recorded value from each configuration was reported, ensuring conservative reporting of results. Moreover, minimal variation was observed among the three specimens tested for each configuration, indicating consistency in the pullout behavior across replicates. 3.3 Pull-out Test Results The load-slip curves depicted in Fig. 4 reveal several insights into the behavior of the bundled bar specimens during pullout testing. It is evident that the maximum slip occurs at approximately 3 mm for all specimens. Furthermore, all specimens exhibit a similar trend with slight variations. The consistent trend observed across all specimens implies that the bundling configurations tested have a similar influence on the load-slip behavior during pullout testing. This suggests that variations in bundling, such as the number and diameter of bars, do not significantly affect the development length or bond behavior in the pullout test setup under the given experimental conditions. The analysis of bundled bars, categorized into configurations 1#, 2#, 3#, and 4#, reveals significant variations in their mechanical performance. Configurations with a higher number of bars in the bundle generally exhibit superior peak strength, with configuration 4# demonstrating the highest peak strength of 60.15 kN, followed closely by configuration 2# at 57.9 kN. Conversely, configurations with fewer bars, such as 1# and 3#, display comparatively lower peak strengths of 54.8 kN and 46.35 kN, respectively. However, this trend is accompanied by differences in peak slip, where configurations with fewer bars tend to experience lower peak slip values. For instance, configuration 2# exhibits the lowest peak slip at 2.868 mm, while configuration 3# demonstrates the highest peak slip at 3.59 mm as shown in Table 2 . These findings suggest that while increasing the number of bars in a bundle enhances peak strength, it may also result in higher displacement before failure. Table 2 Analysis Results of Pull-out Test Analysis Parameters 1# 2# 3# 4# Peak Strength (kN) 54.80 57.90 46.35 60.15 Peak Slip (mm) 3.19 2.87 3.59 3.11 Secant Stiffness (kN/mm) 16.96 21.58 13.5 19.92 Total Energy Absorbed (kN-mm) 72 82 81 102 The analysis of secant stiffness provides insights into the structural stiffness of bundled bars at different load levels. Secant stiffness, calculated at 80% of the peak load. Configurations with higher secant stiffness values, such as 2# and 4#, demonstrate greater, suggesting their ability to maintain structural integrity under high load levels. Conversely, configurations with lower secant stiffness values 3# may exhibit more significant deformations or displacements for the same increase in load, indicating reduced stiffness and potentially compromising structural stability. On the other hand, the analysis of total energy absorbed provides insights into the ductility and energy dissipation characteristics of bundled bars during loading. Configurations with higher total energy absorbed values, such as 4#, demonstrate enhanced ductility or toughness, indicating their ability to absorb greater amounts of energy before failure occurs. The normalized bar chart is shown in Fig. 5 for better understanding. The findings from this study challenge the conventional perception prescribed by IS456:2000 regarding the increase in development length for bundled bars. According to Cl. 26.2.1.2 of the code, the development length can be increased by 10% for two bars in contact, 20% for three bars in contact, and 33% for four bars in contact. However, the results of this study suggest that such increases in length may not be necessary and could potentially be counterproductive. The study reveals that bundled bars actually outperform single bars in terms of development length, indicating that the additional bars in the bundle contribute positively to bond strength rather than diminishing it. Specifically, the findings show that configurations with bundled bars exhibit similar or even improved development lengths compared to single bars, despite having multiple bars in contact. This suggests that the presence of bundled bars enhances bond strength between the steel reinforcement and the surrounding concrete, leading to more efficient load transfer and improved structural performance. Bundling indeed increases the surface area of contact between the bundled bars and the surrounding concrete. This increased contact area allows for more effective transfer of forces between the reinforcement and the concrete, enhancing the bond strength. With more bars bundled together, there are more points of contact with the concrete, resulting in a denser and more interconnected interface. As a result, the mechanical interlock between the steel reinforcement and the concrete is strengthened, leading to improved load transfer and greater resistance to slippage or pullout. The comparison of predicted to experimental ratios for bond strength predicting equations as shown in Table 3 , including those from ACI Committee 408, IS456:2000, Orangun et al. (1977), Darwin et al. (1977), and Zuo et al. (2000), reveals notable insights into their predictive accuracy. The ACI equation demonstrates a moderate overestimation (predicted ratio: 1.44), while the IS456:2000 equation significantly underestimates bond strength (predicted ratio: 0.84). Conversely, the Orangun et al. equation shows a considerable overestimation (predicted ratio: 1.55), indicating potential conservatism. The Darwin et al. equation moderately overestimates (predicted ratio: 1.37), and the Zuo et al. equation exhibits similar behavior (predicted ratio: 1.42). These discrepancies highlight the necessity of validation against experimental data and potential adjustments to enhance the accuracy of bond strength predicting equations. Table 3 Bond Strength S. No. Code/Literature Bond Strength (T b ) Predicted (kN) \(\:\frac{\varvec{P}\varvec{r}\varvec{e}\varvec{d}\varvec{i}\varvec{c}\varvec{t}\varvec{e}\varvec{d}}{\varvec{E}\varvec{x}\varvec{p}\varvec{e}\varvec{r}\varvec{i}\varvec{m}\varvec{e}\varvec{n}\varvec{t}\varvec{a}\varvec{l}}\) 1 ACI Committee 408 (FPS) [ 2 ][ 3 ] \(\:{f}_{c}^{1/4}\left[59.9{l}_{d}\left({C}_{min}+0.5{d}_{b}\right)+2400{A}_{b}\right]\left(0.1\frac{{C}_{max}}{{C}_{min}}+0.9\right)\) 78.94 1.44 2 IS456:2000 [ 8 ] \(\:{\tau\:}_{bd}{l}_{d}\pi\:{d}_{b}\) 45.84 0.84 3 Orangun et al. (1977) (FPS ) [ 11 ] \(\:{f}_{c}^{1/2}\left[3\pi\:{l}_{d}\left(3{C}_{min}+0.4{d}_{b}\right)+200{A}_{b}\right]\) 85.146 1.55 4 Darwin et al. (1996) (FPS) [ 5 ] \(\:{f}_{c}^{1/2}\left[6.67{l}_{d}({c}_{min}+0.5{d}_{b})\left(0.08\frac{{C}_{max}}{{C}_{min}}+0.92\right)+300{A}_{b}\right]\) 75.4 1.37 5 Zuo et al. (2000) (FPS) [ 15 ] \(\:{f}_{c}^{1/4}\left[58.8{l}_{d}\left({C}_{min}+0.5{d}_{b}\right)+2350{A}_{b}\right]\left(0.1\frac{{C}_{max}}{{C}_{min}}+0.9\right)\) 78.366 1.42 In the experimental calculations, the design bond stress specified by IS456:2000, Clause 26.2.1.1 was utilized, with an additional factor of 1.5 applied. In accordance with IS456:2000, the design bond stress is provided with an inherent safety margin already incorporated. Therefore, when conducting experimental calculations, this safety factor is taken into consideration by directly using the specified design bond stress without any additional multiplication factor. 4. FLEXURAL AND SHEAR BEHAVIOUR Extending the study of bundled bars to include flexural and shear behavior is a logical progression, considering the potential benefits observed in pullout tests. 4.1 Specimen Preparation The planned experimental setup involves testing beams with bundled bars to study both flexural and shear behavior. For the flexural study, four beams are designated as 1S, 2S, 3S, and 4S. Each beam will be reinforced with bundled bars in configurations as single, double, triple, and quadruple arrangements. The beams will have dimensions of 150 mm x 200 mm x 2000 mm, with hanger bars consisting of two 12 mm diameter rods. Stirrups, spaced at 150 mm centers, provided using 8 mm diameter bars. In addition to the flexural study, four beams without stirrups are planned to investigate shear behavior. These beams are denoted as 1#, 2#, 3#, and 4#. Similar to the flexural beams, each shear beam will be reinforced with bundled bars in configurations of one, two, three, and four bundles, respectively. The dimensions of these shear beams will also be 150 mm x 200 mm x 2000 mm, with hanger bars comprising two 12 mm diameter rods as shown in Fig. 6. By conducting experiments on these beams with varying configurations of bundled bars, researchers aim to comprehensively evaluate their performance in both flexural and shear loading conditions. The planned setup allows for the investigation of the influence of bundling on the structural behavior of reinforced concrete beams, providing valuable insights for structural design and engineering practice. 4.2 Test Set-Up For the experimental study, a four-point loading setup will be employed to apply loads to the beams as shown in Fig. 7. To ensure that the beams exhibit beam behavior according to Kani's valley, the shear span to depth ratio (a/d) will be maintained at a value higher than 2.5. Specifically, a shear span of 600 mm will be chosen, with a beam span of 1800 mm. As a result, the shear span to depth ratio (a/d) for the beams will be approximately 3.43. By selecting appropriate shear span to depth ratios, the experimental setup aims to replicate realistic beam behavior, ensuring that the beams undergo primarily flexural failure rather than shear failure. These approaches allows for the study of the beams’ response to loading conditions typical of structural applications, providing valuable insights into their flexural and shear behavior under practical circumstances. 4.3 Experimental Results 4.3.1 Failure Pattern Beams subjected to four-point loading exhibit distinct failure patterns depending on the presence or absence of shear reinforcement, commonly provided in the form of stirrups. Beams with stirrups show a ductile failure mode characterized by yielding and deformation of the reinforcement before ultimate failure. Initially, small cracks may appear at the bottom near the supports as the load is applied, propagating diagonally towards the loading points. Stirrups play a crucial role by providing additional shear resistance, delaying crack propagation and redistributing shear forces along the beam's length. As the load increases, the stirrups prevent cracks from widening, maintaining beam integrity. However, if the load surpasses stirrup capacity, cracks may propagate vertically, leading to ductile failure with significant plastic deformation. Conversely, beams without stirrups are prone to brittle failure due to the absence of shear reinforcement. Cracks initiated at the bottom tend to propagate rapidly and vertically towards the top surface, without any restraint. The absence of shear reinforcement exacerbates crack widening and extension, culminating in sudden and catastrophic failure along a diagonal shear plane. The failure mode in such beams is characterized by abrupt collapse, resulting in severe damage. It has been shown in Fig. 8. 4.3.2 Load – Displacement Response In order to monitor displacement during testing, Linear Variable Differential Transformers (LVDTs) will be installed at the center bottom of each beam. LVDTs are highly sensitive devices capable of accurately measuring linear displacement. By fixing LVDTs at the specified locations, the experimental setup will capture precise displacement data throughout the loading process. This information is essential for analyzing the deformation behavior of the beams under various loading conditions, contributing to a comprehensive understanding of their structural performance. The load displacement response is displayed in Fig. 9. The Equivalent Energy Elastic Plastic (EEEP) curve serves as a valuable tool for assessing various mechanical properties of materials, including yield stress, ductility, stiffness, and energy absorption capacity. By plotting load-displacement data obtained from experimental tests, the EEEP curve as shown in Fig. 10 provides insights into the material's response to applied loads, particularly in the elastic and plastic deformation regimes. 4.3.3 Analysis and Discussion [12][13] For beams with Stirrups, the peak load values for beams with different bundling configurations (1S, 2S, 3S, 4S) are relatively consistent, ranging from 106 kN to 112 kN as shown in Table 4. This indicates that the bundling configuration has a minimal effect on the peak load capacity of the beams. Similarly Peak displacement ranging from 17 mm to 22 mm indicating minimal effect. Ductility values increase with the number of bundled bars, with beam 2S demonstrating the highest ductility (3.47) among the tested configurations. Stiffness values for beams with different bundling configurations show relatively minor variations, indicating that the bundling configuration has limited influence on the overall stiffness of the beams. The energy absorbed by the beams increases with the number of bundled bars, with beam 2S absorbing the highest energy (1579 kN-mm) among the tested configurations. Table 4 Analysis Results of Beam Test 1S 1# 2S 2# 3S 3# 4S 4# Peak load (kN) 112 74 107 89 106 81 107 88 Peak Displacement (mm) 20 6.2 22 7.4 19 7.1 17 9.5 Ductility 2.76 1.82 3.47 1.85 3.28 2.09 2.39 2.07 Stiffness (kN/mm) 12.47 17.46 13.85 17.8 14.57 19.06 12.19 15.34 Energy absorbed (kN-mm) 1463 267 1579 384 1364 350 1127 508 Energy Ductility Index 4.53 2.65 5.94 2.7 5.57 3.18 3.77 3.13 For beams without Stirrups, The peak load values for beams without stirrups and with different bundling configurations (1#, 2#, 3#, 4#) vary between 74 kN and 89 kN. This indicates that the presence of bundled bars influences the peak load capacity of the beams, with higher peak loads observed for beams with increased bundling. The peak displacement remains relatively consistent across the tested configurations, suggesting that the presence of bundled bars has a limited impact on the deformability of the beams. Ductility values show a gradual increase with the number of bundled bars. Stiffness values for beams without stirrups and with bundled bars demonstrate minor variations, indicating that the presence of bundled bars has a limited influence on the overall stiffness of the beams. with beam 3# exhibiting the highest ductility (2.09) among the tested configurations. The energy absorbed by the beams increases with the number of bundled bars, with beam 4# absorbing the highest energy (508 kN-mm) among the tested configurations. This indicates that increasing the number of bundled bars enhances the energy absorption capacity of the beams, resulting in improved resilience and structural performance and can be seen from Fig. 11. Bundled bars enhance the ductility and energy absorption capacity of both beams with and without stirrups, contributing to improved structural performance and resilience. The presence of bundled bars has a minimal effect on peak load capacity and stiffness, indicating that they can provide comparable structural integrity to traditional reinforcement methods. The bar chart shown in Fig. 12 displaying the percentage change in values between beams without stirrups and beams with stirrups provides a comprehensive visualization of the impact of bundling on beam behavior. Bundling improves various aspects of beam performance, as evidenced by the positive percentage changes across different parameters. Bundling improves various aspects of beam performance, as evidenced by the positive percentage changes across different parameters. Stiffness of the beam without stirrups is higher for all cases. Beams with stirrups typically have additional reinforcement in the form of vertical stirrups placed along the length of the beam to resist shear forces. While stirrups enhance the beam's shear capacity and ductility, they may also introduce additional flexibility to the structure, leading to a reduction in overall stiffness. 6. CONCLUSION In this study, the focus is directed towards comprehending the behavior of bundled bars within concrete structures. Through systematic experimentation and analysis, the aim is to gain insights into how the bundling of reinforcement bars influences the mechanical properties and performance of concrete elements. Some concluding remarks are as follows. Increasing bundling of bars enhances contact surface area, thereby potentially improving bond behavior in reinforced concrete structures. However, conventional design codes recommend increasing the development length by 10% for two bars in contact, 20% for three bars, and 33% for four bars. Contrary to these recommendations, findings from this study indicate that such increases in length may not be essential and could even be counterproductive. The bond strength estimated by IS456:2000 significantly underestimates the actual bond strength by approximately 16%. Beams with Stirrups exhibit consistent peak load values across different bundling configurations (1S, 2S, 3S, 4S), ranging from 106 kN to 112 kN, suggesting minimal impact of bundling on peak load capacity. Peak displacement remains relatively consistent (17 mm to 22 mm) across the tested configurations, indicating limited influence of bundling on beam deformability. Energy absorption increases with the number of bundled bars, with beam 2S absorbing the highest energy (1579 kN-mm) among the configurations, indicating improved resilience with increased bundling. Beams without Stirrups and with different bundling configurations (1#, 2#, 3#, 4#) show varying peak load values ranging from 74 kN to 89 kN, indicating an influence of bundled bars on peak load capacity, with higher loads observed for beams with increased bundling. Energy absorption increases with the number of bundled bars, with beam 4# absorbing the highest energy (508 kN-mm), suggesting enhanced resilience and structural performance with increased bundling. Bundling improves various aspects of beam performance, as evidenced by the positive percentage changes across different parameters. However, the stiffness of beams without stirrups is higher for all cases. While stirrups enhance the beam's shear capacity and ductility, they may also introduce additional flexibility to the structure, leading to a reduction in overall stiffness. NOTATIONS A b Area of Bar b Breadth of the beam C min, C min Minimum and Maximum Cover Distance d Effective Depth of the Beam D Overall Depth of Beam d b Diameter of Bar f c Cylinder Compressive Strength of Concrete f y Yield Strength of Steel l d Development Length τ bd Bond Shear Strength Declarations Author Contribution Ponni M and Shobha Rajkumar D contributed equally to the conceptualization of the research. Ponni M conducted all experimental work, performed analytical tasks, and prepared the manuscript as part of her thesis. Shobha Rajkumar D provided critical insights and guidance throughout the research process. Both authors have read and approved the final manuscript. References Abreha, A. and Temesgen, W (2021) Numerical Investigation of Bundled RC Column under Impact Load. Advances in Civil Engineering, pp. 1-18. ACI 318 (2019) Building Code Requirements for Structural Concrete. American Concrete Institute , Rarmington Hill, Michigan. ACI 408R-03 Bond and Development of Straight Reinforcing Bars in Tension. Daniel B G (1994) Bond and Development of Bundled Reinforcing Steel. Thesis submitted at University of Texas at Austin. Darwin D, Tholen M L, Idun, E K., and Zuo J 1996a Splice Strength of High Relative Rib Area Reinforcing Bars. ACI Structural Journal, V. 93, No. 1, Jan.-Feb., pp. 95-107. Francisco A. G. and Juan F. C. (2018) Anchorage of Bundled Bars Grouted in Ducts. ACI Structural Journal , V-115, No. 2, March, pp. 415 – 424. Giovanni M, John C, Antonio C. and Giovanni A. P. (2021) Local bond behavior of bundled bars: Experimental investigation, Proc. of the 13th fib International PhD Symposium in Civil Engineering , pp. 2322 – 2337. IS 456: 2000 - Plain and Reinforced Concrete - Code of Practice. John C (2013) Lap Splices of Bars in Bundles. ACI Structural Journal , V-110, No. 2, March-April, pp. 1-10. Liu Q, Tang B, Subesh B. and Gao C. (2017) Research on the Bond-anchorage Behavior of HRB500 Bundled Bars. Advances in Engineering Research , V-120, pp. 1498-1501. Orangun C O, Jirsa J O, and Breen J E (1977) Reevaluation of Test Data on Development Length and Splices. ACI Journal, Proceedings V. 74, No. 3, Mar., pp. 114-122. Sivaguru V and Appa Rao G (2021) Strength and Behaviour of RC Squat Shear Walls With Openings Under Cyclic Loading ACI Structural Journal Vol. 118, No. 5, pp. 235-250. Sivaguru, V., and Appa Rao, G. (2019) Behaviour of reinforced concrete squat shear walls with utility openings, Proc. of 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS – X), Bayonne, France, June 24 – 26. Walujodjati E, Tjondro J A, Permana S., and Johari, G. J. (2020) Study of Flexural Strength on Concrete Bundled Bars Beams. The 5th Annual Applied Science and Engineering Conference (AASEC 2020) , IOP Publishing , pp. 1-5. Zuo, J., and Darwin, D., 2000, Splice Strength of Conventional and High Relative Rib Area Bars in Normal and High-Strength Concrete, ACI Structural Journal, V. 97, No. 4, July-Aug., pp. 630-641. Additional Declarations No competing interests reported. Supplementary Files SUPPLEMENTARYDETAILS.docx Cite Share Download PDF Status: Published Journal Publication published 18 Mar, 2025 Read the published version in Iranian Journal of Science and Technology, Transactions of Civil Engineering → Version 1 posted Editorial decision: Revision requested 09 Nov, 2024 Reviewers agreed at journal 09 Nov, 2024 Reviewers agreed at journal 08 Nov, 2024 Reviews received at journal 07 Nov, 2024 Reviewers agreed at journal 07 Nov, 2024 Reviews received at journal 20 Jul, 2024 Reviewers agreed at journal 17 Jul, 2024 Reviewers agreed at journal 17 Jul, 2024 Reviewers agreed at journal 14 Jul, 2024 Reviewers agreed at journal 13 Jul, 2024 Reviewers invited by journal 12 Jul, 2024 Editor assigned by journal 08 Jul, 2024 Submission checks completed at journal 08 Jul, 2024 First submitted to journal 06 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Slip of Bundled Bars\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/275fc1503433c6d590284c6f.png"},{"id":61474845,"identity":"5eb3d82c-43b4-41c3-905f-b4bed42be075","added_by":"auto","created_at":"2024-07-31 07:32:07","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":48248,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized Values of Pull-Out Test\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/8342b47c967869772425fa62.png"},{"id":61475305,"identity":"cec8da8e-d3f5-44bd-9c79-dd1d7e590736","added_by":"auto","created_at":"2024-07-31 07:40:07","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":346063,"visible":true,"origin":"","legend":"\u003cp\u003eLongitudinal and Sectional View\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/61e3b6e40b622d6439c9b749.png"},{"id":61473666,"identity":"e1fb2bec-5a51-46ac-869b-bb4a40873b95","added_by":"auto","created_at":"2024-07-31 07:16:07","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":4916498,"visible":true,"origin":"","legend":"\u003cp\u003eBeam Preparation and Test Set-Up\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/a68a62ff7c12f3ba436c4ca8.png"},{"id":61473676,"identity":"2df8503a-2ec7-44d9-b26e-029727ae0742","added_by":"auto","created_at":"2024-07-31 07:16:07","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":7081909,"visible":true,"origin":"","legend":"\u003cp\u003eBeam Failure\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/215be78895fb17b0a606865e.png"},{"id":61474842,"identity":"e65ac523-8ca0-48cb-ad63-baa9843bc740","added_by":"auto","created_at":"2024-07-31 07:32:07","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":282313,"visible":true,"origin":"","legend":"\u003cp\u003eLoad - Displacement Response\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/35e3b618a5f2537265a01583.png"},{"id":61475304,"identity":"9550396e-8cc8-4632-a845-19889f1a3a5a","added_by":"auto","created_at":"2024-07-31 07:40:07","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":266526,"visible":true,"origin":"","legend":"\u003cp\u003eEEEP Curves\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/8d8d4a6cc8c166a6614415f2.png"},{"id":61474232,"identity":"abbc0f19-52d8-4f5b-a485-3c596190371b","added_by":"auto","created_at":"2024-07-31 07:24:07","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":203016,"visible":true,"origin":"","legend":"\u003cp\u003eBar Charts from Beam Analysis\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/af14745541dc4c171f0fa253.png"},{"id":61475306,"identity":"0646f815-97a3-45c0-b935-0fd7e62a3f6b","added_by":"auto","created_at":"2024-07-31 07:40:07","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":60751,"visible":true,"origin":"","legend":"\u003cp\u003e% Change of Beam Without Stirrups than With Stirrups\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/ef2a6c473bd0e8fb1c22f9be.png"},{"id":61474228,"identity":"787ef0ba-b3db-4e30-adcb-af76cd843382","added_by":"auto","created_at":"2024-07-31 07:24:07","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":1603739,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Test Results\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/16f9e45bcdc764caec4db37d.png"},{"id":79120474,"identity":"81500936-aa27-4b72-9a34-02911b778477","added_by":"auto","created_at":"2025-03-24 16:08:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":34389215,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/4b4295cf-905c-43d1-97e8-3f3bed017422.pdf"},{"id":61473665,"identity":"17fb5132-a4ff-416b-854f-8c57676d6c27","added_by":"auto","created_at":"2024-07-31 07:16:06","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":15213,"visible":true,"origin":"","legend":"","description":"","filename":"SUPPLEMENTARYDETAILS.docx","url":"https://assets-eu.researchsquare.com/files/rs-4697426/v1/a35ff3e18f5325e45d75baf5.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eExploring the Bond, Flexure, and Shear Behaviour of Bundled Bars in Concrete Structures\u003c/p\u003e","fulltext":[{"header":"1. INTRODUCTION","content":"\u003cp\u003eIn beam design, bundled bars refer to the practice of using multiple reinforcing bars (rebars) grouped together within a single cross-sectional area of the beam. This approach is often employed to meet the required reinforcement ratio or to provide additional strength and ductility in heavily loaded or seismic-resistant structures. By bundling bars together, engineers can effectively increase the total area of reinforcement within the beam without significantly altering its dimensions. The research area of bundled bars in reinforced concrete structures has seen significant development and interest in recent years, driven by the need for more efficient and sustainable construction solutions. With increasing demands for high-performance and cost-effective structural solutions, engineers and designers are exploring innovative reinforcement strategies like bundled bars to optimize structural efficiency and meet project requirements. Abreha et al. (2021)\u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e conducted numerical simulations using explicit finite element analysis to explore the behavior of bundle reinforced concrete (BRC) columns in comparison to traditionally reinforced columns. The results revealed that bundling longitudinal reinforcement not only improves the impact capacity of BRC columns but also stabilizes their response to fluctuating loads. Giovanni et al. (2021)\u003csup\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/sup\u003e recommended the use of equivalent area rather than equivalent perimeter for bundled bars. Walujodjati (2021)\u003csup\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e observed an increase in flexural capacity with bundling. Francisco et al. (2018)\u003csup\u003e[18]\u003c/sup\u003e found a reduction in the development length for bundled bars based on their pullout test study. Liu et al. (2017)\u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e observed a decrease in average bond-anchoring strength as the number of steel bars and anchorage length increased. John (2013)\u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e concluded that bond strength is not reduced when an individual bar within a pair or bundle of three bars is lap-spliced, provided appropriate allowance is made for differences in confinement and the proportion of bars spliced at a section. Daniel (1994)\u003csup\u003e[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/sup\u003e conducted experiments on pullout tests in bundled bars and compared various existing equations. He concluded that the equation proposed by Orangun et al. (1977)\u003csup\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e is best suited for predicting the behavior of bundled bars in pullout tests.\u003c/p\u003e"},{"header":"2. RESEARCH SIGNIFICANCE","content":"\u003cp\u003eUnderstanding the behavior of bundled bars remains an area with significant gaps in knowledge. Research significance lies in the exploration of bundled bars' behavior under different bundling configurations, such as single, double, triple, and quadruple arrangements, through pullout tests and subsequent analysis in beams. Understanding how bundling affects pullout strength provides insights into the bond performance of bundled bars in concrete structures, crucial for ensuring structural integrity and safety. Moreover, investigating the flexural and shear behavior of beams reinforced with longitudinally bundled bars offers valuable data for optimizing reinforcement design and enhancing structural performance. This research contributes to advancing knowledge in reinforced concrete design and construction practices, ultimately leading to more efficient and resilient structural systems.\u003c/p\u003e"},{"header":"3. PULLOUT TESTING","content":"\u003cp\u003ePullout tests are a fundamental method used to evaluate the bond strength between reinforcing bars and concrete. In a pullout test, a steel bar is embedded in a concrete specimen, and a tensile force is applied to the bar until it pulls out from the concrete. This test provides crucial information about the bond characteristics.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Specimen Preparation\u003c/h2\u003e \u003cp\u003eThe pullout specimens were prepared following established standards, with traditional cylindrical specimens measuring 150 mm in diameter and 300 mm in height. The steel reinforcement was embedded into the cylinder up to a depth of 200 mm, with an additional 200 mm extending outside the cylinder. While IS2770 (Part 1) \u0026minus;\u0026thinsp;1967 (Reaffirmed 2007) recommends using cube specimens for pullout tests, it limits the maximum embedding depth to 150 mm. Recognizing this constraint, the decision was made to utilize cylindrical specimens to achieve deeper embedment depths, thus allowing for a more comprehensive evaluation of bond strength and behavior. This approach ensures adherence to testing standards while maximizing the depth of embedding, as illustrated in Fig.\u0026nbsp;1.\u003c/p\u003e \u003cp\u003eFour different bundling configurations were examined in the pullout tests conducted as part of the study. The configurations included single bundling with a single 16 mm diameter rod, bundling with one 12 mm rod and one 10 mm rod, bundling with two 10 mm rods and one 8 mm rod, and bundling with four 8 mm rods. These variations were chosen to investigate the influence of the number and diameter of rods within the bundle on pullout strength and behavior.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e Reinforcement Configuration Details\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"583\" height=\"325\"\u003e\u003c/p\u003e \u003cp\u003eAll the bundling configurations shown in Table 1 were designed to maintain approximately the same cross-sectional area, ensuring consistency in the total amount of reinforcement across the different specimens. A total of 12 specimens were cast, with three specimens for each bundling configuration. These specimens were designed to provide a comprehensive understanding of the pullout behavior of bundled bars under different configurations. The arrangement of these specimens is depicted in Fig. 2.\u003c/p\u003e\u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Specimen Testing\u003c/h2\u003e \u003cp\u003ePullout testing was conducted using a Universal Testing Machine (UTM) at the Government College of Engineering, Salem. Each specimen was set up with the protruding rod securely held at the top, allowing the concrete cylinder to hang freely. The UTM applied a pushing force to the cylinder, simulating the pullout of the inserted rod as shown in Fig.\u0026nbsp;3. Load-deflection data were recorded using computerized equipment integrated with the UTM. For each bundling configuration, three specimens were tested, and the lowest recorded value from each configuration was reported, ensuring conservative reporting of results. Moreover, minimal variation was observed among the three specimens tested for each configuration, indicating consistency in the pullout behavior across replicates.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Pull-out Test Results\u003c/h2\u003e \u003cp\u003eThe load-slip curves depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e4\u003c/span\u003e reveal several insights into the behavior of the bundled bar specimens during pullout testing. It is evident that the maximum slip occurs at approximately 3 mm for all specimens. Furthermore, all specimens exhibit a similar trend with slight variations. The consistent trend observed across all specimens implies that the bundling configurations tested have a similar influence on the load-slip behavior during pullout testing. This suggests that variations in bundling, such as the number and diameter of bars, do not significantly affect the development length or bond behavior in the pullout test setup under the given experimental conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe analysis of bundled bars, categorized into configurations 1#, 2#, 3#, and 4#, reveals significant variations in their mechanical performance. Configurations with a higher number of bars in the bundle generally exhibit superior peak strength, with configuration 4# demonstrating the highest peak strength of 60.15 kN, followed closely by configuration 2# at 57.9 kN. Conversely, configurations with fewer bars, such as 1# and 3#, display comparatively lower peak strengths of 54.8 kN and 46.35 kN, respectively. However, this trend is accompanied by differences in peak slip, where configurations with fewer bars tend to experience lower peak slip values. For instance, configuration 2# exhibits the lowest peak slip at 2.868 mm, while configuration 3# demonstrates the highest peak slip at 3.59 mm as shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. These findings suggest that while increasing the number of bars in a bundle enhances peak strength, it may also result in higher displacement before failure.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAnalysis Results of Pull-out Test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnalysis Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1#\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2#\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3#\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4#\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePeak Strength (kN)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e54.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e57.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e46.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e60.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePeak Slip (mm)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSecant Stiffness (kN/mm)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e21.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e13.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e19.92\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eTotal Energy Absorbed (kN-mm)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e102\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe analysis of secant stiffness provides insights into the structural stiffness of bundled bars at different load levels. Secant stiffness, calculated at 80% of the peak load. Configurations with higher secant stiffness values, such as 2# and 4#, demonstrate greater, suggesting their ability to maintain structural integrity under high load levels. Conversely, configurations with lower secant stiffness values 3# may exhibit more significant deformations or displacements for the same increase in load, indicating reduced stiffness and potentially compromising structural stability. On the other hand, the analysis of total energy absorbed provides insights into the ductility and energy dissipation characteristics of bundled bars during loading. Configurations with higher total energy absorbed values, such as 4#, demonstrate enhanced ductility or toughness, indicating their ability to absorb greater amounts of energy before failure occurs. The normalized bar chart is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e5\u003c/span\u003e for better understanding.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe findings from this study challenge the conventional perception prescribed by IS456:2000 regarding the increase in development length for bundled bars. According to Cl. 26.2.1.2 of the code, the development length can be increased by 10% for two bars in contact, 20% for three bars in contact, and 33% for four bars in contact. However, the results of this study suggest that such increases in length may not be necessary and could potentially be counterproductive. The study reveals that bundled bars actually outperform single bars in terms of development length, indicating that the additional bars in the bundle contribute positively to bond strength rather than diminishing it. Specifically, the findings show that configurations with bundled bars exhibit similar or even improved development lengths compared to single bars, despite having multiple bars in contact. This suggests that the presence of bundled bars enhances bond strength between the steel reinforcement and the surrounding concrete, leading to more efficient load transfer and improved structural performance. Bundling indeed increases the surface area of contact between the bundled bars and the surrounding concrete. This increased contact area allows for more effective transfer of forces between the reinforcement and the concrete, enhancing the bond strength. With more bars bundled together, there are more points of contact with the concrete, resulting in a denser and more interconnected interface. As a result, the mechanical interlock between the steel reinforcement and the concrete is strengthened, leading to improved load transfer and greater resistance to slippage or pullout.\u003c/p\u003e \u003cp\u003eThe comparison of predicted to experimental ratios for bond strength predicting equations as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, including those from ACI Committee 408, IS456:2000, Orangun et al. (1977), Darwin et al. (1977), and Zuo et al. (2000), reveals notable insights into their predictive accuracy. The ACI equation demonstrates a moderate overestimation (predicted ratio: 1.44), while the IS456:2000 equation significantly underestimates bond strength (predicted ratio: 0.84). Conversely, the Orangun et al. equation shows a considerable overestimation (predicted ratio: 1.55), indicating potential conservatism. The Darwin et al. equation moderately overestimates (predicted ratio: 1.37), and the Zuo et al. equation exhibits similar behavior (predicted ratio: 1.42). These discrepancies highlight the necessity of validation against experimental data and potential adjustments to enhance the accuracy of bond strength predicting equations.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBond Strength\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS. No.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCode/Literature\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBond Strength (T\u003csub\u003eb\u003c/sub\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePredicted (kN)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\varvec{P}\\varvec{r}\\varvec{e}\\varvec{d}\\varvec{i}\\varvec{c}\\varvec{t}\\varvec{e}\\varvec{d}}{\\varvec{E}\\varvec{x}\\varvec{p}\\varvec{e}\\varvec{r}\\varvec{i}\\varvec{m}\\varvec{e}\\varvec{n}\\varvec{t}\\varvec{a}\\varvec{l}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eACI Committee 408 (FPS)\u003c/b\u003e\u003csup\u003e[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e][\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{c}^{1/4}\\left[59.9{l}_{d}\\left({C}_{min}+0.5{d}_{b}\\right)+2400{A}_{b}\\right]\\left(0.1\\frac{{C}_{max}}{{C}_{min}}+0.9\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e78.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eIS456:2000\u003c/b\u003e\u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\tau\\:}_{bd}{l}_{d}\\pi\\:{d}_{b}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e45.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eOrangun et al. (1977) (FPS\u003c/b\u003e\u003csup\u003e\u003cb\u003e)\u003c/b\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{c}^{1/2}\\left[3\\pi\\:{l}_{d}\\left(3{C}_{min}+0.4{d}_{b}\\right)+200{A}_{b}\\right]\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e85.146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eDarwin et al. (1996) (FPS)\u003c/b\u003e\u003csup\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{c}^{1/2}\\left[6.67{l}_{d}({c}_{min}+0.5{d}_{b})\\left(0.08\\frac{{C}_{max}}{{C}_{min}}+0.92\\right)+300{A}_{b}\\right]\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e75.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eZuo et al. (2000) (FPS)\u003c/b\u003e\u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{c}^{1/4}\\left[58.8{l}_{d}\\left({C}_{min}+0.5{d}_{b}\\right)+2350{A}_{b}\\right]\\left(0.1\\frac{{C}_{max}}{{C}_{min}}+0.9\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e78.366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn the experimental calculations, the design bond stress specified by IS456:2000, Clause 26.2.1.1 was utilized, with an additional factor of 1.5 applied. In accordance with IS456:2000, the design bond stress is provided with an inherent safety margin already incorporated. Therefore, when conducting experimental calculations, this safety factor is taken into consideration by directly using the specified design bond stress without any additional multiplication factor.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. FLEXURAL AND SHEAR BEHAVIOUR","content":"\u003cp\u003eExtending the study of bundled bars to include flexural and shear behavior is a logical progression, considering the potential benefits observed in pullout tests.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e4.1 Specimen Preparation\u003c/h2\u003e\n\u003cp\u003eThe planned experimental setup involves testing beams with bundled bars to study both flexural and shear behavior. For the flexural study, four beams are designated as 1S, 2S, 3S, and 4S. Each beam will be reinforced with bundled bars in configurations as single, double, triple, and quadruple arrangements. The beams will have dimensions of 150 mm x 200 mm x 2000 mm, with hanger bars consisting of two 12 mm diameter rods. Stirrups, spaced at 150 mm centers, provided using 8 mm diameter bars. In addition to the flexural study, four beams without stirrups are planned to investigate shear behavior. These beams are denoted as 1#, 2#, 3#, and 4#. Similar to the flexural beams, each shear beam will be reinforced with bundled bars in configurations of one, two, three, and four bundles, respectively. The dimensions of these shear beams will also be 150 mm x 200 mm x 2000 mm, with hanger bars comprising two 12 mm diameter rods as shown in Fig. 6. By conducting experiments on these beams with varying configurations of bundled bars, researchers aim to comprehensively evaluate their performance in both flexural and shear loading conditions. The planned setup allows for the investigation of the influence of bundling on the structural behavior of reinforced concrete beams, providing valuable insights for structural design and engineering practice.\u003c/p\u003e\n\u003cdiv\u003e\n \u003ch2\u003e4.2 Test Set-Up\u003c/h2\u003e\n \u003cp\u003eFor the experimental study, a four-point loading setup will be employed to apply loads to the beams as shown in Fig. 7. To ensure that the beams exhibit beam behavior according to Kani\u0026apos;s valley, the shear span to depth ratio (a/d) will be maintained at a value higher than 2.5. Specifically, a shear span of 600 mm will be chosen, with a beam span of 1800 mm. As a result, the shear span to depth ratio (a/d) for the beams will be approximately 3.43. By selecting appropriate shear span to depth ratios, the experimental setup aims to replicate realistic beam behavior, ensuring that the beams undergo primarily flexural failure rather than shear failure. These approaches allows for the study of the beams\u0026rsquo; response to loading conditions typical of structural applications, providing valuable insights into their flexural and shear behavior under practical circumstances.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ch2\u003e4.3 Experimental Results\u003c/h2\u003e\n \u003ch2\u003e4.3.1 Failure Pattern\u003c/h2\u003e\n \u003cp\u003eBeams subjected to four-point loading exhibit distinct failure patterns depending on the presence or absence of shear reinforcement, commonly provided in the form of stirrups. Beams with stirrups show a ductile failure mode characterized by yielding and deformation of the reinforcement before ultimate failure. Initially, small cracks may appear at the bottom near the supports as the load is applied, propagating diagonally towards the loading points. Stirrups play a crucial role by providing additional shear resistance, delaying crack propagation and redistributing shear forces along the beam\u0026apos;s length. As the load increases, the stirrups prevent cracks from widening, maintaining beam integrity. However, if the load surpasses stirrup capacity, cracks may propagate vertically, leading to ductile failure with significant plastic deformation.\u003c/p\u003e\n \u003cp\u003eConversely, beams without stirrups are prone to brittle failure due to the absence of shear reinforcement. Cracks initiated at the bottom tend to propagate rapidly and vertically towards the top surface, without any restraint. The absence of shear reinforcement exacerbates crack widening and extension, culminating in sudden and catastrophic failure along a diagonal shear plane. The failure mode in such beams is characterized by abrupt collapse, resulting in severe damage. It has been shown in Fig. 8.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ch2\u003e4.3.2 Load \u0026ndash; Displacement Response\u003c/h2\u003e\n \u003cp\u003eIn order to monitor displacement during testing, Linear Variable Differential Transformers (LVDTs) will be installed at the center bottom of each beam. LVDTs are highly sensitive devices capable of accurately measuring linear displacement. By fixing LVDTs at the specified locations, the experimental setup will capture precise displacement data throughout the loading process. This information is essential for analyzing the deformation behavior of the beams under various loading conditions, contributing to a comprehensive understanding of their structural performance. The load displacement response is displayed in Fig. 9.\u003c/p\u003e\n \u003cdiv\u003e\n \u003cp\u003eThe Equivalent Energy Elastic Plastic (EEEP) curve serves as a valuable tool for assessing various mechanical properties of materials, including yield stress, ductility, stiffness, and energy absorption capacity. By plotting load-displacement data obtained from experimental tests, the EEEP curve as shown in Fig. 10 provides insights into the material\u0026apos;s response to applied loads, particularly in the elastic and plastic deformation regimes.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ch2\u003e4.3.3 Analysis and Discussion\u003csup\u003e[12][13]\u003c/sup\u003e\u003c/h2\u003e\n \u003cp\u003eFor beams with Stirrups, the peak load values for beams with different bundling configurations (1S, 2S, 3S, 4S) are relatively consistent, ranging from 106 kN to 112 kN as shown in Table 4. This indicates that the bundling configuration has a minimal effect on the peak load capacity of the beams. Similarly Peak displacement ranging from 17 mm to 22 mm indicating minimal effect. Ductility values increase with the number of bundled bars, with beam 2S demonstrating the highest ductility (3.47) among the tested configurations. Stiffness values for beams with different bundling configurations show relatively minor variations, indicating that the bundling configuration has limited influence on the overall stiffness of the beams. The energy absorbed by the beams increases with the number of bundled bars, with beam 2S absorbing the highest energy (1579 kN-mm) among the tested configurations.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eTable 4\u003c/strong\u003e Analysis Results of Beam Test\u003c/p\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"591\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"32.88135593220339%\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e\u003cstrong\u003e1S\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e\u003cstrong\u003e1#\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e\u003cstrong\u003e2S\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.779661016949152%\"\u003e\n \u003cp\u003e\u003cstrong\u003e2#\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e\u003cstrong\u003e3S\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.152542372881356%\"\u003e\n \u003cp\u003e\u003cstrong\u003e3#\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e\u003cstrong\u003e4S\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e\u003cstrong\u003e4#\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"32.88135593220339%\"\u003e\n \u003cp\u003e\u003cstrong\u003ePeak load (kN)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e107\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.779661016949152%\"\u003e\n \u003cp\u003e89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.152542372881356%\"\u003e\n \u003cp\u003e81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e107\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e88\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"32.88135593220339%\"\u003e\n \u003cp\u003e\u003cstrong\u003ePeak Displacement (mm)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e6.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.779661016949152%\"\u003e\n \u003cp\u003e7.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.152542372881356%\"\u003e\n \u003cp\u003e7.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e9.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"32.88135593220339%\"\u003e\n \u003cp\u003e\u003cstrong\u003eDuctility\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e2.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e1.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e3.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.779661016949152%\"\u003e\n \u003cp\u003e1.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e3.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.152542372881356%\"\u003e\n \u003cp\u003e2.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e2.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e2.07\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"32.88135593220339%\"\u003e\n \u003cp\u003e\u003cstrong\u003eStiffness (kN/mm)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e12.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e17.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e13.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.779661016949152%\"\u003e\n \u003cp\u003e17.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e14.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.152542372881356%\"\u003e\n \u003cp\u003e19.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e12.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e15.34\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"32.88135593220339%\"\u003e\n \u003cp\u003e\u003cstrong\u003eEnergy absorbed (kN-mm)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e1463\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e267\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e1579\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.779661016949152%\"\u003e\n \u003cp\u003e384\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e1364\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.152542372881356%\"\u003e\n \u003cp\u003e350\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e1127\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e508\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"32.88135593220339%\"\u003e\n \u003cp\u003e\u003cstrong\u003eEnergy Ductility Index\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e4.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e2.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e5.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.779661016949152%\"\u003e\n \u003cp\u003e2.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e5.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.152542372881356%\"\u003e\n \u003cp\u003e3.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.966101694915254%\"\u003e\n \u003cp\u003e3.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.661016949152541%\"\u003e\n \u003cp\u003e3.13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eFor beams without Stirrups, The peak load values for beams without stirrups and with different bundling configurations (1#, 2#, 3#, 4#) vary between 74 kN and 89 kN. This indicates that the presence of bundled bars influences the peak load capacity of the beams, with higher peak loads observed for beams with increased bundling. The peak displacement remains relatively consistent across the tested configurations, suggesting that the presence of bundled bars has a limited impact on the deformability of the beams. Ductility values show a gradual increase with the number of bundled bars. Stiffness values for beams without stirrups and with bundled bars demonstrate minor variations, indicating that the presence of bundled bars has a limited influence on the overall stiffness of the beams. with beam 3# exhibiting the highest ductility (2.09) among the tested configurations. The energy absorbed by the beams increases with the number of bundled bars, with beam 4# absorbing the highest energy (508 kN-mm) among the tested configurations. This indicates that increasing the number of bundled bars enhances the energy absorption capacity of the beams, resulting in improved resilience and structural performance and can be seen from Fig. 11.\u003c/p\u003e\n \u003cp\u003eBundled bars enhance the ductility and energy absorption capacity of both beams with and without stirrups, contributing to improved structural performance and resilience. The presence of bundled bars has a minimal effect on peak load capacity and stiffness, indicating that they can provide comparable structural integrity to traditional reinforcement methods.\u003c/p\u003e\n \u003cp\u003eThe bar chart shown in Fig. 12 displaying the percentage change in values between beams without stirrups and beams with stirrups provides a comprehensive visualization of the impact of bundling on beam behavior. Bundling improves various aspects of beam performance, as evidenced by the positive percentage changes across different parameters. Bundling improves various aspects of beam performance, as evidenced by the positive percentage changes across different parameters. Stiffness of the beam without stirrups is higher for all cases. Beams with stirrups typically have additional reinforcement in the form of vertical stirrups placed along the length of the beam to resist shear forces. While stirrups enhance the beam\u0026apos;s shear capacity and ductility, they may also introduce additional flexibility to the structure, leading to a reduction in overall stiffness.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/div\u003e\n \u003c/div\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"6. CONCLUSION","content":"\u003cp\u003eIn this study, the focus is directed towards comprehending the behavior of bundled bars within concrete structures. Through systematic experimentation and analysis, the aim is to gain insights into how the bundling of reinforcement bars influences the mechanical properties and performance of concrete elements. Some concluding remarks are as follows.\u003c/p\u003e \u003cp\u003e \u003col style=\"list-style-type:lower-alpha;\"\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIncreasing bundling of bars enhances contact surface area, thereby potentially improving bond behavior in reinforced concrete structures. However, conventional design codes recommend increasing the development length by 10% for two bars in contact, 20% for three bars, and 33% for four bars. Contrary to these recommendations, findings from this study indicate that such increases in length may not be essential and could even be counterproductive. The bond strength estimated by IS456:2000 significantly underestimates the actual bond strength by approximately 16%.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eBeams with Stirrups exhibit consistent peak load values across different bundling configurations (1S, 2S, 3S, 4S), ranging from 106 kN to 112 kN, suggesting minimal impact of bundling on peak load capacity. Peak displacement remains relatively consistent (17 mm to 22 mm) across the tested configurations, indicating limited influence of bundling on beam deformability. Energy absorption increases with the number of bundled bars, with beam 2S absorbing the highest energy (1579 kN-mm) among the configurations, indicating improved resilience with increased bundling.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eBeams without Stirrups and with different bundling configurations (1#, 2#, 3#, 4#) show varying peak load values ranging from 74 kN to 89 kN, indicating an influence of bundled bars on peak load capacity, with higher loads observed for beams with increased bundling. Energy absorption increases with the number of bundled bars, with beam 4# absorbing the highest energy (508 kN-mm), suggesting enhanced resilience and structural performance with increased bundling.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eBundling improves various aspects of beam performance, as evidenced by the positive percentage changes across different parameters. However, the stiffness of beams without stirrups is higher for all cases. While stirrups enhance the beam's shear capacity and ductility, they may also introduce additional flexibility to the structure, leading to a reduction in overall stiffness.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e "},{"header":"NOTATIONS","content":"\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"383\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003eA\u003csub\u003eb\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eArea of Bar\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003eb\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eBreadth of the beam\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003eC\u003csub\u003emin,\u003c/sub\u003e C\u003csub\u003emin\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eMinimum and Maximum Cover Distance\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003ed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eEffective Depth of the Beam\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003eD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eOverall Depth of Beam\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003ed\u003csub\u003eb\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eDiameter of Bar\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003ef\u003csub\u003ec\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eCylinder Compressive Strength of Concrete\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003ef\u003csub\u003ey\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eYield Strength of Steel\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003el\u003csub\u003ed\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eDevelopment Length\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.887728459530027%\" valign=\"bottom\"\u003e\n \u003cp\u003e\u0026tau;\u003csub\u003ebd\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"79.11227154046998%\" valign=\"bottom\"\u003e\n \u003cp\u003eBond Shear Strength\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003ePonni M and Shobha Rajkumar D contributed equally to the conceptualization of the research. Ponni M conducted all experimental work, performed analytical tasks, and prepared the manuscript as part of her thesis. Shobha Rajkumar D provided critical insights and guidance throughout the research process. Both authors have read and approved the final manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAbreha, A. and Temesgen, W (2021) Numerical Investigation of Bundled RC Column under Impact Load. Advances in Civil Engineering, pp. 1-18.\u003c/li\u003e\n \u003cli\u003eACI 318 (2019) Building Code Requirements for Structural Concrete. \u003cem\u003eAmerican Concrete Institute\u003c/em\u003e, Rarmington Hill, Michigan.\u003c/li\u003e\n \u003cli\u003eACI 408R-03 Bond and Development of Straight Reinforcing Bars in Tension.\u003c/li\u003e\n \u003cli\u003eDaniel B G (1994) Bond and Development of Bundled Reinforcing Steel. \u003cem\u003eThesis\u003c/em\u003e submitted at University of Texas at Austin.\u003c/li\u003e\n \u003cli\u003eDarwin D, Tholen M L, Idun, E K., and Zuo J 1996a Splice Strength of High Relative Rib Area Reinforcing Bars. ACI Structural Journal, V. 93, No. 1, Jan.-Feb., pp. 95-107.\u003c/li\u003e\n \u003cli\u003eFrancisco A. G. and Juan F. C. (2018) Anchorage of Bundled Bars Grouted in Ducts. ACI Structural Journal\u003cem\u003e,\u0026nbsp;\u003c/em\u003eV-115, No. 2, March,\u003cem\u003e\u0026nbsp;\u003c/em\u003epp. 415 \u0026ndash; 424.\u003c/li\u003e\n \u003cli\u003eGiovanni M, John C, Antonio C. and Giovanni A. P. (2021) Local bond behavior of bundled bars: Experimental investigation, Proc. of the 13th fib International PhD Symposium in Civil Engineering\u003cem\u003e,\u0026nbsp;\u003c/em\u003epp. 2322 \u0026ndash; 2337.\u003c/li\u003e\n \u003cli\u003eIS 456: 2000 - Plain and Reinforced Concrete - Code of Practice.\u003c/li\u003e\n \u003cli\u003eJohn C (2013) Lap Splices of Bars in Bundles. ACI Structural Journal\u003cem\u003e,\u0026nbsp;\u003c/em\u003eV-110, No. 2, March-April, pp. 1-10.\u003c/li\u003e\n \u003cli\u003eLiu Q, Tang B, Subesh B. and Gao C. (2017) Research on the Bond-anchorage Behavior of HRB500 Bundled Bars. Advances in Engineering Research\u003cem\u003e,\u0026nbsp;\u003c/em\u003eV-120, pp. 1498-1501.\u003c/li\u003e\n \u003cli\u003eOrangun C O, Jirsa J O, and Breen J E (1977) Reevaluation of Test Data on Development Length and Splices. ACI Journal, Proceedings V. 74, No. 3, Mar., pp. 114-122.\u003c/li\u003e\n \u003cli\u003eSivaguru V and Appa Rao G (2021) Strength and Behaviour of RC Squat Shear Walls With Openings Under Cyclic Loading ACI Structural Journal Vol. 118, No. 5, pp. 235-250.\u003c/li\u003e\n \u003cli\u003eSivaguru, V., and Appa Rao, G. (2019) Behaviour of reinforced concrete squat shear walls with utility openings, Proc. of 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS \u0026ndash; X), Bayonne, France, June 24 \u0026ndash; 26.\u003c/li\u003e\n \u003cli\u003eWalujodjati E, Tjondro J A, Permana S., and Johari, G. J. (2020) Study of Flexural Strength on Concrete Bundled Bars Beams. The 5th Annual Applied Science and Engineering Conference (AASEC 2020)\u003cem\u003e,\u0026nbsp;\u003c/em\u003eIOP Publishing\u003cem\u003e,\u0026nbsp;\u003c/em\u003epp. 1-5.\u003c/li\u003e\n \u003cli\u003eZuo, J., and Darwin, D., 2000, Splice Strength of Conventional and High Relative Rib Area Bars in Normal and High-Strength Concrete, ACI Structural Journal, V. 97, No. 4, July-Aug., pp. 630-641.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"iranian-journal-of-science-and-technology-transactions-of-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"istc","sideBox":"Learn more about [Iranian Journal of Science and Technology, Transactions of Civil Engineering](http://link.springer.com/journal/40996)","snPcode":"40996","submissionUrl":"https://submission.nature.com/new-submission/40996/3","title":"Iranian Journal of Science and Technology, Transactions of Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Bundled Bars, Bond Strength, Bond-slip Behavior, Flexural and Shear Behaviour","lastPublishedDoi":"10.21203/rs.3.rs-4697426/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4697426/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBundled bars, also known as bundled reinforcement, involve grouping multiple steel bars together to form a single unit, which is then embedded within concrete structures. We aim to comprehensively understand the behavior of bundled bars in reinforced concrete structures. This study investigates the behavior of bundled reinforcement bars in concrete beams, aiming to assess their influence on structural performance. A series of experiments were conducted, including pullout tests on bundled bars and flexural and shear tests on concrete beams with and without stirrups. The study evaluated various parameters such as peak load, displacement, ductility, stiffness, and energy absorption capacity for different bundling configurations. Results indicate that bundling enhances the peak load capacity and energy absorption of beams, with minimal impact on displacement and stiffness. However, beams without stirrups exhibit higher stiffness compared to those with stirrups, suggesting a trade-off between shear capacity and structural rigidity. Overall, the findings provide insights into the behavior of bundled reinforcement bars in concrete structures, informing design practices for enhanced structural performance and resilience. Contrary to IS code recommendations, findings from this study indicate that such recommendations are not essential and could even be counterproductive.\u003c/p\u003e","manuscriptTitle":"Exploring the Bond, Flexure, and Shear Behaviour of Bundled Bars in Concrete Structures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-31 07:16:01","doi":"10.21203/rs.3.rs-4697426/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-11-09T17:14:32+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"207422177083099835415097270358021508955","date":"2024-11-09T15:46:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"58226296075975718472232456675004901202","date":"2024-11-08T13:18:54+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-11-08T04:05:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"81268482026484784467166881683270865775","date":"2024-11-08T01:32:53+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-20T19:43:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"118928545550454150840505643376487420900","date":"2024-07-17T23:37:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"165299948300514827157892008392727054822","date":"2024-07-17T22:28:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"319673948492961387582999028671525418202","date":"2024-07-15T00:49:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"306337220959221939890720954830241327535","date":"2024-07-13T09:13:24+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-12T22:26:44+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-08T09:20:36+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-08T09:18:54+00:00","index":"","fulltext":""},{"type":"submitted","content":"Iranian Journal of Science and Technology, Transactions of Civil Engineering","date":"2024-07-06T15:24:05+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"iranian-journal-of-science-and-technology-transactions-of-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"istc","sideBox":"Learn more about [Iranian Journal of Science and Technology, Transactions of Civil Engineering](http://link.springer.com/journal/40996)","snPcode":"40996","submissionUrl":"https://submission.nature.com/new-submission/40996/3","title":"Iranian Journal of Science and Technology, Transactions of Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d7068b91-eb04-4d0e-bc95-1d048e2dab41","owner":[],"postedDate":"July 31st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-03-24T16:01:33+00:00","versionOfRecord":{"articleIdentity":"rs-4697426","link":"https://doi.org/10.1007/s40996-025-01800-x","journal":{"identity":"iranian-journal-of-science-and-technology-transactions-of-civil-engineering","isVorOnly":false,"title":"Iranian Journal of Science and Technology, Transactions of Civil Engineering"},"publishedOn":"2025-03-18 15:57:37","publishedOnDateReadable":"March 18th, 2025"},"versionCreatedAt":"2024-07-31 07:16:01","video":"","vorDoi":"10.1007/s40996-025-01800-x","vorDoiUrl":"https://doi.org/10.1007/s40996-025-01800-x","workflowStages":[]},"version":"v1","identity":"rs-4697426","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4697426","identity":"rs-4697426","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}