Anti-Impact Performance Enhancement of Two-Way Spanning Slab through the Implementation of Steel Trussed Bars

Al-Dala’ien, Rayeh Nasr; Anas, S. M.; Kodrg, Abdel-Fattah Jamal

doi:https://doi.org/10.1155/2024/8126150

Journal of Engineering

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Research Article | Open Access

Volume 2024 | Article ID 8126150 | https://doi.org/10.1155/2024/8126150

Anti-Impact Performance Enhancement of Two-Way Spanning Slab through the Implementation of Steel Trussed Bars

Rayeh Nasr Al-Dala’ien,^1,2S. M. Anas,³and Abdel-Fattah Jamal Kodrg⁴

Academic Editor: Vijayanandh Raja

Received23 Jan 2024

Revised21 Mar 2024

Accepted26 Mar 2024

Published12 Apr 2024

Abstract

Reinforced concrete (RC) slabs represent integral structural components extensively employed in architectural and infrastructural frameworks owing to their inherent robustness and longevity. In contemporary times, there has been a pronounced surge in endeavors aimed at comprehensively elucidating the anti-impact properties inherent in RC slabs. This surge is propelled by a compelling necessity to fortify these structures against the deleterious effects of low-velocity impacts, thereby ensuring their steadfastness and resilience. Consider the thorough investigation into the anti-impact characteristics of RC slabs, which has been rigorously pursued through both experimental and computational methodologies. A plethora of scholarly discourse on this topic is readily available, providing invaluable insights into the structural dynamics governing slabs subjected to low-velocity impacts. However, there is a noticeable gap in research concerning the strengthening of slabs through shear reinforcement, particularly through economical, easily fabricated, and efficient systems such as fabricated trussed bars. The primary objective of this study is to explore the structural behavior of RC slabs fortified with custom-designed trussed bars under the influence of low-velocity impacts. To accomplish this, the Abaqus software platform is explicitly employed for analysis. The slab without any shear reinforcement is experimentally tested and serves as a reference model for numerical verification. Its anti-impact performance is compared with numerical findings. Following validation, simulations are conducted for square slabs strengthened by fabricated trussed bars in orthogonal and diagonal layouts. The results demonstrate that employing fabricated truss bars shear reinforcement with a 3 mm diameter in orthogonal and diagonal layouts enhances the resistance of slabs to damage, resulting in a 28.41% and 47.06% decrease in damage, respectively. The utilization of engineered truss bars as shear reinforcement yields significant improvements in strength, rigidity, and ductility when compared to control samples lacking such reinforcement. This enhancement is particularly evident when the engineered truss bars are arranged in orthogonal and diagonal configurations.

1. Introduction

Impacts, explosions, plummeting objects, or the relentless assault of oceanic surges possess the potential to inflict considerable harm upon concrete edifices, thereby precipitating potentially catastrophic incidents [1]. These occurrences subject structures to a gamut of forces, ranging from abrupt to gradual, or a combination thereof, thereby engendering diverse effects on their constituent elements. Concrete structures, especially those fortified with reinforcements, confront both localized and extensive deterioration in the face of such exigencies, their manifestation influenced by a confluence of variables such as the magnitude of the force exerted and the inherent vibrational properties of the structure [2]. Pioneering experiments conducted on concrete elements, encompassing beams [3–12], columns [12–14], bridge piers [15], and slabs [16] have provided the foundational framework for comprehending the manner in which structures react to unanticipated and formidable forces [17]. Emphasizing the mechanisms of failure and resistance inherent to these components, historical studies have often adopted scaled-down replicas for pragmatic purposes, thereby facilitating practical insights into the behavior of concrete structures under duress.

It is crucial to reinforce slabs to prevent disastrous outcomes from sudden, intense forces caused by heavy objects or collisions. Enhancing the strength of slabs involves using stronger materials, additional reinforcement, or specific designs to counter these forces effectively. This not only prevents potential hazards but also improves the structure’s durability against such unforeseen impacts, making it a wise investment for both safety and longevity.

Various methodologies and materials have been employed to enhance the durability of slabs under both static and dynamic loading conditions. These include shear studs [18], basalt fiber-reinforced polymer (FRP) strips [19], hybrid fibers comprising hooked-end steel, polypropylene, and Kevlar [20], high-performance fiber-reinforced cementitious composites (HPFRCCs) [21], prestressed concrete [22, 23], ferrocement [24], internal anchorage stirrups [25–27], W-shaped stirrups [28], truss shear reinforcement [29–31], steel plates and slurry-infiltrated mat concrete (SIMCON) laminates [32, 33], polypropylene fiber [33], geogrids [34], and carbon textiles [35]. Increasing the thickness of the slab has demonstrated efficacy in reducing damage and altering failure modes [36], while employing higher-grade concrete has shown some advantages in mitigating slab puncture [37–41].

Employing TRM strips [41] for fortifying concrete slabs against low-velocity impacts can enhance their resilience, diminish surface deterioration, modify the flexural behavior and fracture patterns of the slab, and optimize the absorption and dispersion of energy across the entirety of the structure. Similarly, CFRP can offer improvements in resisting impacts, managing surface damage, and enhancing the structural resilience, with strategic placement and orientation of CFRP strips [42] yielding even better protection. These methods not only offer structural benefits but also provide design flexibility and potential cost savings, especially in retrofitting projects or new constructions aimed at better impact resistance [43–45].

Ultrahigh-performance fiber-reinforced concrete (UHPFRC) stands out due to its superior mechanical properties, promising significant improvements in impact resilience, reduced surface wear, and better managed shape changes during slow-speed impacts. A [45] research effort focuses on identifying the optimal mixtures or fiber ratios in UHPFRC to maximize its dynamic efficiency. This research is crucial for advancing structural design techniques for buildings exposed to slow-speed impacts, potentially broadening UHPFRC’s utility in various contexts.

The research endeavors to examine and juxtapose the structural reactions of conventional normal strength concrete (NSC), ultrahigh-performance concrete (UHPC), and steel fiber-reinforced ultrahigh-performance concrete (SFR-UHPC) [46] across varying stress scenarios. Using computational models to mimic the concrete types’ behavior, the study examines aspects such as strength, shape alteration, crack development, and modes of failure. The documented improvements in both the robustness and durability of SFR-UHPC and UHPC align with prior research, presumably attributable to the incorporation of steel fibers. The research approach includes a detailed comparison through computational simulations, essential for guiding design decisions in particular structural settings. Following the implementation of these reinforcement techniques [32–37], there was a noticeable transition in the primary failure mechanism from direct crushing to bending. Additionally, certain strategies have been shown to combine bending with specific localized crushing effects, as noted in earlier investigations [25–27, 29].

The arrangement and direction [47] of bending reinforcement significantly influence the damage patterns in concrete slabs, especially concerning punching or localized damage within the areas of impact. The strategic amalgamation of three tiers of tensioned steel, each positioned with distinct orientations [48], markedly mitigates impact-induced harm, underscoring the pivotal significance of reinforcement alignment in upholding slab integrity. Utilization of diverse dimensions and arrangements of steel bars alongside a welded wire mesh has evidenced that steel structural integrity often deteriorates prior to reaching peak load-bearing capacity. A lack of adequate steel reinforcement can lead to sudden concrete failure, whereas too much reinforcement might cause localized shear fractures.

Research by Hrynyk and Vecchio [49] points out that the rigidity of slabs improves with a higher steel content, suggesting that an increase in reinforcement can bolster slab stiffness and enhance overall structural behavior. This improvement is likely to result in better load management, crack reduction, and structural durability. Similarly, Yilmaz et al.’s [50] research on reinforced slabs underlines the positive impacts of a higher reinforcement ratio, including better bending strength, stiffness, and resilience, alongside reduced deformation.

These observations emphasize the pivotal significance of reinforcement in enhancing the efficacy and durability of slabs when subjected to diverse stressors. Such insights are invaluable for structural engineers, providing practical guidelines for optimizing RC slab designs and construction practices to meet specific project demands. The paramount importance of detailed reinforcement planning cannot be overstated in the pursuit of elevated structural integrity in concrete slabs, providing a cornerstone for the development of more durable and streamlined architectural solutions [17, 39, 40, 51–55].

Stirrups [56] play a pivotal role in bolstering a structure’s resilience against impacts through a multifaceted approach, namely, by mitigating cracking, enhancing lateral stability, and augmenting ductility. This allows structures to absorb and distribute the forces from impacts more effectively. Stirrups are essential for preventing cracks, maintaining the structural framework, and ensuring an even distribution of forces across the structure. The careful design of stirrup arrangements, coupled with dynamic evaluations and considerations of material characteristics, is key to achieving the optimal impact resistance in RC structures. Stirrups enhance a structure’s defense against dynamic pressures by improving resistance to punching shear and reducing displacements through the strategic increase of shear reinforcement [57].

Shear reinforcement is vital for fortifying slabs against impact forces, boosting their capacity to handle diagonal stresses, and preventing structural failures. Common shear reinforcement elements include stirrups [58], links [57, 59, 60], and shear studs. Stirrups, typically shaped in U or rectangles, are positioned perpendicularly to the principal reinforcement bars to contain and reinforce the concrete against diagonal shear. Internal anchors [25–27, 29–66], situated within the flexural reinforcement’s upper and lower bounds, enhance structural integrity. Links, forming closed loops [67], offer similar advantages and are often utilized in columns [12, 13, 68] and beams [69–71]. Shear studs [72], found in composite constructions, ensure an effective shear connection between the steel and concrete components. Inclined shear reinforcements, such as angled stirrups or truss systems [29–31], counter diagonal tension and inhibit crack growth. The choice of shear reinforcement configuration is shaped by factors such as load parameters, structural design considerations, and precise engineering mandates. This underscores the pivotal significance of shear reinforcement in augmenting both the resilience and operational efficacy of RC elements when subjected to dynamic loads.

Trussed bars represent a highly effective means of augmenting shear resistance within slabs, owing to their adeptness in proficiently managing diagonal tensile stresses. The triangular configuration of these bars allows for the effective distribution and redirection of shear forces, thereby enhancing the slab’s resilience to such stresses. This geometrically favorable design ensures optimal reinforcement material usage, reducing the need for excess steel while maximizing shear resistance. Trussed bars’ adaptability to various slab geometries enhances their utility across a range of structural applications. Additionally, their ease of installation presents a cost-effective reinforcement solution, compliant with industry standards and construction practices. The empirical evidence supporting the use of trussed bars in concrete reinforcement underscores their proven efficacy in enhancing slab shear resistance [29–31].

However, the literature reveals significant research gaps in the application of trussed bars for slab reinforcement. Despite the reliance on computational modeling, there is a marked scarcity of empirical and numerical data, highlighting the imperative for thorough experimental validation. Real-world data are crucial for a reliable assessment of trussed bars’ effectiveness and practical utility. Moreover, a detailed exploration of design variables, such as the shape and spacing of truss bars, is necessary to fully understand their impact on performance. The interaction dynamics between the concrete slabs and trussed bars, particularly under impact loading conditions, warrant an exhaustive investigation to uncover their behavior and potential for performance improvement. It is imperative to address these lacunae in research in order to acquire a thorough comprehension of the operational efficacy of trussed bars. Such understanding is pivotal as it serves to elucidate and refine their utilization in bolstering the durability and resilience of RC slabs against the rigors of impact stresses.

2. Experimental Arrangement and Specimen Configuration

In pursuit of conducting rigorous examinations, three RC solid slabs measuring 800 × 800 × 90 mm have been fabricated. Subsequent sections will meticulously scrutinize the testing methodologies employed in this investigation.

2.1. Experimental Samples and Constituents

The slabs were fabricated utilizing 6 mm steel rods as primary and ancillary reinforcement, boasting a yield strength of 560 MPa, adhering rigorously to the guidelines set forth by the ASTM E8/E8M standards. The consistent placement of the steel bars throughout the slab enhances its load-bearing capacity and resistance to bending moments [73].

The slab design described in Figure 1 includes specific dimensions and reinforcement details in accordance with the ACI codes. The combination of two concrete covers, with a thickness of 10 mm at the base and 20 mm at the apex, augmented by an additional 50 mm cover on each side, ensures comprehensive protection for the embedded reinforcement, thereby significantly contributing to the resilience and longevity of the slab. The flexural bars, which are uniformly sized and evenly spaced in both directions, provide reinforcement against bending moments. The steadfast steel proportions, with ρ = 0.37% allocated for flexural tension reinforcement and ρ′ = 0.37% designated for compression reinforcement, align seamlessly with the design criteria outlined in ACI 421.1R-08 for a solid slab [26, 29, 40, 74–77]. The thickness of the slab adheres to the stipulations delineated in the ACI code 9.5.3, thereby guaranteeing structural robustness and alignment with prescribed design criteria. In its entirety, the design meticulously conforms to the paramount standards of the industry and regulatory mandates, thereby safeguarding the structural robustness and operational efficacy of the slab.

The targeted compressive strength of the slabs was set at 30 MPa, prompting the formulation of a concrete mix ratio tailored to achieve this specification. Three 10 × 10 × 10 cm cube samples were taken from each batch, trowel-straightened, and vibrated to remove air voids. After curing for 28 days, the concrete’s compressive strength was determined using axial load testing [78], with results converted to cylindrical strength as per Eurocode-2 (1992-1-1) [79] recommendations. This standardized testing procedure ensures accurate evaluation of concrete strength, providing crucial data for assessing the performance of the RC slabs.

2.2. Instruments and Test Devices

The contemporary investigation employed the drop-weight impact assessment method, initially formulated by ACI Committee 544 in 1988 [80]. Crucially, it is imperative to note that the descent distance remains consistent throughout the experiment, with the apparatus capable of attaining a maximum descent height of 1200 mm. Various weights of different diameters can be released from different drop distances using this setup. The pivotal component of subjecting the test specimens to impact loading is the impactor, also referred to as the hammer. Crafted from high-strength steel, it is meticulously engineered to ensure both longevity and uniform dispersion of impact forces. Deliberately, an eccentric load is imposed, with precise coordination, positioning the targeted impact point at coordinates (20, 20) mm away from the central axis of the slab, as depicted in Figure 2.

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In the present analysis of impact testing, the magnitude of energy imparted onto the specimens is contingent upon both the mass of the steel hammer and the altitude from which it is released. In order to maintain uniformity, the experiment was structured to administer a homogeneous force of impact totaling 176.58 Joules. This was accomplished by utilizing a hammer mass of 40 kilograms and a drop height of 450 millimeters. Careful consideration was given to the parameters to accurately track specimen degradation. This included accounting for the measurement constraints of the experimental instruments when calculating the impact loading energy.

Within impact assessments, the experimental framework integrates an array of sophisticated measuring apparatuses to procure vital data. The principal instruments utilized within this experimental initiative encompass accelerometers, LVDTs (linear variable differential transformers), dataloggers, steel strain gauges, and concrete strain gauge systems. These instruments are crucial for capturing important parameters such as acceleration, displacement, strain, and other dynamic responses during impact testing. Table 1 furnishes an exhaustive inventory delineating the array of tools incorporated within the experimental configuration, accentuating the breadth of instruments deployed to facilitate meticulous data collection and analysis. Concurrently, real-time data are projected onto the digital interface of the testing apparatus, while a data logger boasting 16 channels adeptly captures the measurements derived from assorted sensors. The amassed dataset encompasses temporal trajectories of displacement, acceleration, concrete strain, and steel strains.

Under hypothesized supporting conditions, C-channel steel sections securely anchor the specimens on all four sides. Impact testing ceases upon the failure of all specimens, with maximum displacement values meticulously documented. Visual inspections are conducted to assess concrete cracking and the integrity of steel reinforcements. The esteemed software developed by IMC meticulously analyzes the data, unveiling intricate failure mechanisms and structural responses under dynamic loads. The comprehensive testing protocol meticulously evaluates the impact resistance of RC slabs. Figure 3 provides a graphical depiction illustrating the strategic placement of strain gauges affixed to the primary steel during experimental procedures. Table 2 and Figure 4 present the experimental findings obtained from the instrumentation installed in the control samples.

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Since control sample 1 had an average total number of drops of 124, as shown in Table 2, the sample results were taken into consideration during the discussion.

The cumulative kinetic energy exerted upon the control specimen, designated as “N” (mgh), is computed utilizing the equation wherein “m” symbolizes the mass of the hammer, “” denotes the gravitational acceleration, “h” signifies the altitude of descent, and “N” reflects the count of successive drops.

The cumulative kinetic energy exerted on the control sample amounts to 21895.92 Joules, calculated through the formula: 124 multiplied by 40, then by 9.81, and finally by 0.45.

Upon scrutinizing the empirical findings, it became evident that the control specimens underwent significant structural compromise, characterized by slab perforation and top-face punching failure. Furthermore, sample 3 displayed the manifestations of scabbing and concrete perforation. Furthermore, there were signs of flexural bond deterioration and diagonal and intermittent cracks observed on the lower slab surface, as illustrated in Figure 5.

3. Finite Element Analysis and Verification

In this structural engineering investigation, Abaqus is employed to construct finite element representations of RC slabs. The facile simulation of both dynamic and static loads facilitates intricate numerical scrutiny. Abaqus is favored for its adeptness in exploring intricate phenomena such as high-velocity impacts, contact mechanics intricacies, and deformations in structural components. Its utilization is widespread among engineers and projects owing to its capability in utilizing advanced material models and precise failure criteria, culminating in meticulous and reliable results [81].

Concrete slabs, steel reinforcement, impactors, and C-sections (slab boundary components) are all modeled in three dimensions using Abaqus software in structural engineering. The process of modeling entails the meticulous allocation of suitable material attributes to individual components. This involves the software configuring three discernible material classifications: concrete, steel reinforcement bars crafted from HRB500 steel, and the steel hammer constructed from linear elastic steel [82].

To gain deeper insights into the stress-strain interplay in both compression and tension scenarios, scholars resort to employing the concrete damaged plasticity (CDP) model. This sophisticated model aptly captures the intricate nonlinearities inherent in concrete behavior. Detailed elucidations of the material properties pertaining to concrete and steel are meticulously documented in Tables 3 and 4, respectively.

To elucidate the interrelationship among diverse geometries, a comprehensive contact interaction, as delineated in reference [83], is employed. This interaction encompasses both tangential and rigid contact behaviors and assumes a friction coefficient of 0.02 at the contact interface, as referenced in Ref. [42]. Furthermore, the integration of an embedded region constraint fortifies the linkage between the encompassing concrete substrate and the steel reinforcements, thereby augmenting structural robustness and load-bearing capacity, as articulated in Ref. [84]. Concerning boundary conditions, the edges of the slab are wholly fixed to emulate the experimental configuration. Steel C-sections are instantiated on each periphery of the slab to emulate rigid support, as elucidated in Ref. [84], mirroring the experimental test conditions and precluding any potential motion or deformation. To mitigate energy dissipation due to steel deformation under stress, the design of the steel hammer incorporates a rigid body. Two distinct sets of boundary conditions are applied: specialized constraints for the hammer, confining its motion solely to the vertical (y) axis, and fully fixed (ENCASTRE) conditions for the supporting framework, as referenced in Ref. [81].

The numerical framework has been meticulously crafted to integrate the implementation of recurrent low-velocity impact loading, aligning precisely with the experimental test configuration. A predetermined height above the upper surface of the slab is designated for the hammer’s elevation, following which it is released, descending freely under the influence of gravitational force. This descent occurs singularly, characterized by a distinct velocity. The determination of the free-fall velocity and the duration of the descent is achieved by employing established equations that faithfully capture the specific conditions intrinsic to the experimental setup. The scrupulous application of numerical methodologies guarantees a precise depiction of the dynamic responses exhibited by RC slabs under the influence of impact load,

Within this framework, symbol “” symbolizes the gravitational acceleration (9.81 mm/s²), while “h” denotes the descent height (450 mm).

Upon finalizing the generation of finite element models, each component underwent a meticulous meshing process, whereby it was subdivided into smaller constituents. Meshing stands as a critical operation necessitating iterative exploration to ascertain the optimal mesh size that strikes a balance between precision and computational efficiency. The duration of computational processes is significantly influenced by the mesh size, thereby rendering it a pivotal factor for consideration. Table 5 elucidates the node and element counts for the specimens. Figure 6 offers a comparative depiction of acceleration-time history plots for various mesh sizes of RC slabs during the initial impact of the drop weight. The investigation concludes that a 10 mm element size closely corresponds with the experimental observations. Furthermore, Figure 6 illustrates the formation of the finite element model subsequent to the meshing process.

The process involved reviewing various finite element models and conducting dynamic explicit nonlinear analysis. This method allowed for the comparison of numerical data with experimental results obtained through measurements.

The calibration procedure stood as a pivotal endeavor, indispensable in guaranteeing the precision and dependability of the numerical model. This intricate process entailed the iterative refinement of both model parameters and input variables, meticulously constrained within permissible margins, to harmonize the numerical outputs closely with empirical observations. The paramount objective remained the cultivation of a robust numerical model, one distinguished by its faithful depiction of the slabs’ response to impinging forces.

Following the calibration process, a thorough juxtaposition of numerical results against experimental data was undertaken, with meticulous scrutiny of pivotal performance metrics and influential factors delineated in both Tables 6 and 7. This meticulous comparative analysis served to illuminate the veracity and precision of the numerical model employed (Figure 7). Furthermore, Figure 8 presents the acceleration-time profile observed during the inaugural descent, furnishing visual elucidation on the manner in which the slabs reacted to the impinging force. This graphical representation facilitated the comprehension of the alterations in velocity experienced by the slabs throughout the duration. Moreover, Figure 9 juxtaposed the authentic failure mode against the finite element model’s failure mode across specimens featuring varied scabbing concrete widths, thereby furnishing a graphical elucidation of the concordance between empirical and computational outcomes.

Tables 6 and 7 stand as exhaustive validation tools for the finite element model, showcasing its precision in prognosticating acceleration magnitudes during the onset of descent. This validation extends to the control specimen, with the model exhibiting an accuracy of 1.8% for the control sample when compared to the experimental results. The finite element model accurately predicts steel strain at failure, within an 8% margin compared to experimental data. Figure 8 shows similar peak acceleration and duration, indicating agreement between the experiments and simulations under impact loads. The model effectively captures slab behavior, bolstering confidence in its accuracy and numerical analysis results.

Moreover, in accordance with the failure mode illustrated in Figure 9, a notable concurrence emerges in the manner of failure, encompassing concrete scabs, diagonal cracks, and the lack of bending between steel and the enveloping concrete, between the experimental and FEM findings. Additionally, the extent of scabbing concrete exhibits a striking resemblance between the experimental and FEM results, differing by a mere 4% in comparison with the experimental outcomes.

The test findings from the practical examination closely paralleled the envisaged failure modalities, particularly emphasizing phenomena such as punching shear and the disintegration of the bond between steel and concrete. Mesh size limitations led to discrepancies, especially in truss bar samples’ inability to clearly show fractures. Differences between numerical predictions and real-world outcomes were attributed to concrete’s nonhomogeneous nature [85] and varying support conditions, not adequately captured by models assuming homogeneity. These variations arise from factors such as compaction and curing conditions, altering material characteristics.

Additionally, numerical analyses, though precise in addressing support conditions, might disregard pragmatic factors such as friction or displacement among supports under impact loading. The omission of strain rate effects could similarly account for variations noted in dynamically stressed concrete. The existing CDP [86] material model did not fully consider concrete’s strain rate dependence, especially under dynamic loading. The authors proposed enhancing the CDP model by integrating stress-strain characteristics dependent on the strain rate, thereby offering a more adept approach toward mitigating dynamic impacts [87].

4. Parametric Study

After the proficient validation of the finite element simulation, a parametric investigation was initiated to delve into the dynamic characteristics of RC slabs fortified with truss bars for shear reinforcement when subjected to low-velocity impact loads. This investigation sought to evaluate the influence of various parameters on the behavior of slabs, incorporating factors that may pose challenges for experimental assessment due to constraints related to time, labor, and expenses. Figures 10 and 11 delineate the structural layout parameter pertaining to the fabricated trussed bar shear reinforcement examined in this study. Despite subjecting all specimens to an identical number of loading cycles (124 drops), the parametric analysis involving slabs reinforced with trussed bar shear reinforcement enabled an exploration of the effects of this reinforcement technique and its layout parameters on structural response under controlled experimental conditions. To enhance clarity in discussing the specimens, a system of naming conventions is detailed in Table 8, while Figure 12 provides the visual representations of the finite element models employed for the parametric study specimens.

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Flexural tension and compression reinforcement were assessed, yielding steel ratios of ρ = 0.37% and ρ′ = 0.37%, respectively. Equation (2) was employed to calculate the transverse steel ratio, encompassing the vertical legs of the truss bars, for both inclined and vertical truss bars shear reinforcement,

In the above equation, represents the area of the shear reinforcement in the form of truss bars with two legs linked together. These truss bars are 3 mm in diameter. The variable “s” symbolizes the consistent interval between shear reinforcement elements. Furthermore, ϕ1 and ϕ2 denote the angles formed between the forefront of the truss bar reinforcement and the vertical link, as well as their alignment with the truss bar reinforcement and the axis perpendicular to the exerted shear force, respectively.

The slab adheres meticulously to the parameters delineated within the ACI code 9.5.3 concerning thickness, while the steel ratio impeccably aligns with the design constraints as articulated in ACI 421.1R-08 for RC solid slabs.

Adhering to the directives delineated in ACI 318-19 and ACI 421.1R-08, it is imperative to employ the method of uniformly distributing shear reinforcement around the pivotal section’s centroid. This approach is crucial to guaranteeing the convergence of the failure surface of the slab with the peripheries of the shear reinforcement, thereby augmenting the structural efficacy and load-bearing capacity of the edifice.

Ensuring the symmetrical placement of shear reinforcement, as depicted in Figures 10 and 11, is imperative for achieving uniform distribution of loads and forces throughout the slab. This practice fosters a well-calibrated system for transferring loads and mitigates the likelihood of localized structural failures. Notably, shear stresses tend to amplify at critical junctures, underscoring the significance of this methodology. Comprehensive analyses detailing failure modes for each variation within the parametric study are exhaustively outlined in Table 7. Furthermore, numerical findings pertaining to the study samples are comprehensively documented in Tables 8 and 9. Visual representations elucidating the numerical outcomes are vividly illustrated in Figures 12–14.

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5. Results and Discussions

The findings from the experimental, numerical, and parametric research studies conducted in this study are thoroughly covered in the following subsections.

5.1. Damage Profile

As per the findings delineated in Table 9, the degradation extends diagonally toward the peripheries of the slab, albeit manifesting in a less pronounced manifestation of the flexural mode. Concrete serves to alleviate damage in the flexural mode by circumventing diagonal fractures. The pristine slab (designated as Cϕ6) demonstrates a cumulative damage due to energy (DDE) amounting to 77.205 J at the 124th drop, whereas the specimens incorporating engineered truss bars (denoted as TBϕ3Orth and TBϕ3Dia) register cumulative DDEs of 55.2723 J and 40.8717 J, respectively, at an equivalent number of drops.

The study endeavors to ascertain whether the incorporation of shear reinforcement in orthogonal directions could mitigate the vulnerability of the slab to punching failure. The inclusion of shear reinforcement demonstrates a marked reduction in punching, flexural bond failure, and the emergence of diagonal fractures at the underside in contrast to control specimens devoid of such reinforcement. The extent of damage suffered by a slab reinforced with shear is notably inferior to that experienced by the reference control slab upon complete failure, showcasing a reduction of 28.41% (TBϕ3Orth) and 47.06% (TBϕ3Dia) relative to (Cϕ6).

Altering the configuration of shear reinforcement in truss bars, shifting from orthogonal to diagonal, results in a reduction in the dissipated energy (DDE) from 55.2723 Joules for the orthogonal configuration (denoted as TBϕ3Orth) to 40.8717 Joules for the diagonal configuration (referred to as TBϕ3Diag), representing a decrease of 26.05%, as elaborated in Table 10.

The diagonal arrangement of engineered truss bars, employed in reinforcing systems for slabs, manifests a pronounced impact on failure modalities [88]. Diagonally oriented reinforcement configurations [42, 61] have showcased remarkable efficacy in curtailing the extent of damage, encompassing phenomena such as concrete scabbing, spalling, and cracking within slabs. Notably, the slabs reinforced with diagonally oriented bars exhibit the least width and frequency of cracks.

5.2. Acceleration

In this study [41, 42, 48, 89], the evaluation predominantly relied on numerical estimations of acceleration, contrasting results primarily at the initial impact. The culmination of acceleration during impact reveals the inertia influence of the slab, intimately linked with its rigidity. The research underscores the significant impact of integrating shear reinforcement on the maximal vertical acceleration of the slab. Notably, slabs with denser reinforcement exhibit heightened accelerations compared to those with lighter reinforcement [90]. Figure 14 depicts the peak accelerations of 520.945 g (Cϕ6), 649.565 g (TBφ3Orth), and 604.0968 g (TBφ3Dia) directly beneath the hammer, reflecting an increment of 24.701% and 15.972% relative to the control sample, respectively. The presence of steel beneath the impact zone notably influences the maximum acceleration.

Furthermore, transitioning from the orthogonal (TBφ3Orth) to diagonal (TBφ3Diag) configuration of truss bars induces a significant acceleration effect, resulting in a reduction of approximately 7.00% compared to the orthogonal arrangement. The utilization of diagonal layouts in previous reinforcement systems [42, 61, 91] has exhibited a marked elevation in acceleration metrics for RC slabs in comparison with configurations with strips arranged orthogonally or unidirectionally. This particular reinforcement design has proven more efficacious in bolstering the impact resilience of RC slabs.

5.3. Displacement and Stress

Table 10 presents a concise overview detailing the stress exerted on concrete and the subsequent displacement observed during both the initial descent and ultimate failure of the specimens under examination. Notably, when subjected to impacts at their upper and lower surfaces, both the standard sample and those augmented with custom truss bars exhibited discernible variations. Implementation of fabricated truss bars, whether in orthogonal or diagonal configurations, yielded a noteworthy reduction in concrete stress at the upper surface by 8.372% and 9.805%, respectively, compared to the unaltered sample. Conversely, there was an elevation in concrete stress at the lower surface by 12.034% and 9.879% for orthogonal and diagonal layouts, respectively, in contrast to the control sample. The transition from the orthogonal (TBφ3Orth) to diagonal (TBφ3Diag) arrangement of the truss bars precipitated a modest decrease in concrete stress at both upper and lower surfaces during the initial descent, registering reductions of 1.5637% and 1.9231%, respectively. Notably, the stress endured by the concrete core of the standard sample and the modified specimen with truss bars amounted to 26.12 MPa and 18 MPa, respectively, following 124 successive impacts culminating in structural collapse. Furthermore, upon reaching the point of complete failure after 124 iterations, the stress experienced by the concrete at the central region of the upper surface was measured at 18 MPa for TBφ3Orth, while for TBφ3Diag, it escalated to 19.286 MPa, as illustrated in Figure 12.

Table 11 reveals the conspicuous declines in the strain exhibited by the upper and lower steel components positioned 200 mm away from the point of impact, suggesting that the inclusion of truss bars as shear reinforcement effectively promoted an equitable dispersion of stress and consequentially mitigated strain levels in the primary steel elements.

In terms of displacement, when situated 2 cm away from the central point of the bottom face, the standard control sample (Cφ6) and specimens incorporating fabricated truss bars manifested displacements measuring 0.82087 mm and 0.87561 mm (TBφ3Orth), alongside 0.90107 mm (TBφ3Dia), respectively, during the initial descent. The introduction of fabricated truss bars resulted in displacement increments of 6.669% and 9.770% for both orthogonal and diagonal configurations compared to the baseline sample. Upon reaching complete failure subsequent to 124 drops, the displacement directly beneath the impactor for the control sample and those specimens featuring fabricated truss bars amounted to 26.50 mm, 9.1 mm (TBφ3Orth), and 18.787 mm (TBφ3Dia), respectively. Transitioning from an orthogonal to a diagonal arrangement of truss bars amplified the displacement at full failure by 106.4505% relative to TBφ3Orth, as depicted in Figure 13.

Ultimately, the residual displacement measured at a distance of 20 cm from the slab’s center amounted to 0.522167342 mm for the Cφ6 configuration and 0.5944608 mm for TBφ3Orth, marking a 13.876% escalation relative to the baseline sample. The introduction of diagonal truss bar alignment, denoted as TBφ3Diag, yielded a reduction in residual displacement by −3.1525% compared to the orthogonal truss bar configuration (TBφ3Orth), as visually depicted in Figure 13(b).

The discoveries herein corroborate established methodologies for enhancing structural integrity, as cited, which effectively mitigate the deleterious effects of impact loading on RC slabs. This serves to mitigate fractures and underscores the efficacy of the strengthening technique in absorbing energy. Previous methodologies employing diagonal configurations in slab reinforcement have significantly influenced stress distribution, thereby attenuating the patterns of failure severity. Diagonal reinforcement arrangements facilitate the uniform propagation of stress waves, thereby subjecting the concrete to considerable dynamic loading during impulsive impacts. Consequently, the susceptibility to damage is diminished compared to control slabs and those employing conventional orientations [38, 39, 65].

The implementation of diagonal configurations in slab reinforcement systems has yielded notable effects on both vertical displacement and stress distribution. Strengthening methodologies [38], particularly when deployed diagonally in two orthogonal directions, have exhibited substantial reductions in the maximum displacement values induced by impacts. Furthermore, this specific reinforcement scheme has effectively curtailed both the width and quantity of cracks observed in the slabs.

The deployment of diagonal shear reinforcement orientation configurations [91] has facilitated a more uniform propagation of stress waves throughout the steel reinforcement network. Such configuration exposes the concrete to heightened dynamic loading forces during impulsive impacts, thereby permitting the concrete to manifest its optimal strength. As a result, slabs reinforced with a diagonal orientation demonstrate diminished structural deterioration in contrast to both the standard slab and slabs featuring conventional orientations. The efficacy of the diagonal pattern in bolstering the structural integrity and resilience of RC slabs under dynamic loading conditions is underscored by its proficiency in mitigating damage.

6. Conclusions

The principal aim of this investigation is to scrutinize and quantify the impact of a reinforcement technique on the low-velocity capabilities of RC slabs, incorporating shear reinforcement provided by fabricated truss bars. In order to maintain consistent input energy during impact loading, a 40 kg hammer was systematically released from a height of 450 mm in a succession of trials carried out within the scope of the study. Numerous measurements of acceleration, displacement, and strain were meticulously recorded to assess both the efficacy of the reinforcement procedure and the response of the slabs to impact [74, 92–96].

The RC slabs with shear reinforcement from produced truss bars underwent both the physical inspection and incremental dynamic analysis using the Abaqus software. The accuracy of the model was checked by simulating the impact behavior using a finite element model and comparing the numerical findings to experimental data. A comprehensive analysis was conducted to ascertain the efficacy of employing truss bars as a means of augmenting the structural integrity of slabs against impact loads. This investigative inquiry adopted a parametric approach, juxtaposing various methods to discern the most potent solution. The investigation included a wide range of scenarios.

Based on the investigation conducted, a potential solution to the complexities entailed by antiquated and contemporary methods of fortifying RC slabs lies in the utilization of fabricated truss bar reinforcement. This alternative presents viable options for forthcoming strengthening systems aimed at enhancing the resilience of slabs against dynamic forces and potentially expediting the dissipation of impact loads. The primary conclusions drawn from the study are encapsulated as follows:(1)The integration of fabricated truss bars as shear reinforcement substantially enhanced the impact resistance of the slabs. Employing fabricated truss bars for shear reinforcement led to significant improvements in strength, rigidity, and ductility in contrast to specimens without such reinforcement. Notably, these enhancements were most evident when the fabricated truss bars were strategically placed in both orthogonal and diagonal configurations.(2)During impact loads, concrete crushing is the predominant failure mechanism. Implementing trussed bars as shear reinforcement, with a 3 mm diameter arranged orthogonally and diagonally, notably enhances slab resistance to damage. This reinforcement strategy results in a substantial reduction of 28.41% and 47.06% in DDE, respectively.(3)Fabricated trussed bars arranged orthogonally outperform those placed diagonally in terms of displacement and damage prevention, particularly with regard to perforation and splitting.(4)The integration of fabricated trussed bars as shear reinforcement significantly enhances the stiffness and toughness of RC slabs. Orthogonally arranged truss bars show a remarkable 24.701% increase, while diagonally placed bars exhibit a notable 15.972% enhancement compared to the control sample. Diagonally oriented truss bars notably bolster the impact resistance of RC slabs.(5)The orthogonal arrangement of fabricated truss bars for shear reinforcement significantly affects the performance of RC slabs under sudden dynamic impact loads. This configuration demonstrates reduced failure modes and increased maximum acceleration values, showing a notable improvement of about 7% compared to the diagonal layout.(6)The study shows that utilizing fabricated trussed bar shear reinforcement significantly improves the load capacity and impact resistance of slabs. This innovative reinforcement system, designed with vertically inclined links to enhance shear resistance, holds promise for enhancing overall structural ductility. Incorporating this method substantially boosts both load capacity and impact ductility of slabs, with displacement increasing by 6.669% and 9.770% in orthogonal and diagonal layouts compared to the control sample.(7)In contrast to conventional laboratory experimentation, the utilization of finite element analysis via the Abaqus tool serves to authenticate test outcomes, thereby enhancing temporal efficiency while furnishing researchers with indispensable insights into structural reactions to impact loads.

Symbols

ρ:	Flexural tension reinforcement
ρ′:	Compression reinforcement
:	Gravity acceleration
:	Microstrain
N:	Number of drops
m:	Mass
h:	Drop height
:	Poisson’s ratio
E:	Elastic modulus of material
:	Stress ratio (Abaqus User Guide, 2020)
:	Shape factor
Ψ:	Dilation angle
µ:	Viscosity parameter
:	Velocity of free fall
:	Time of free fall
:	Bar diameter
Orth:	Orthogonal
Diag:	Diagonal
TB:	Truss bars
:	Area of the shear reinforcement in the form of truss bars with two legs linked together
b:	Uniform spacing between the shear reinforcement
s:	Distance between vertical or inclined bars
ϕ₁ and ϕ₂:	Angles between the front of the truss bars reinforcement and the vertical link and positioned between the truss bars reinforcement and the axis that is perpendicular to the shear force
DDE:	Damage dissipation energy
:	Reference sample.

Data Availability

All information provided in the conclusion is presented in the full document.

Ethical Approval

This work did not report on or involve the use of any animal or human data or tissue.

All participants gave their consent for their data to be published in the journal article.

Conflicts of Interest

The authors declare that there are no conflicts of interest.

Authors’ Contributions

Rayeh Nasr Al-Dala’ien conceived the study; Rayeh Nasr Al-Dala’ien and S. M. Anas curated the data; Rayeh Nasr Al-Dala’ien, Abdel-Fattah Jamal Kodrg, and S. M. Anas contributed to the formal analysis; Rayeh Nasr Al-Dala’ien and S. M. Anas investigated the study; Rayeh Nasr Al-Dala’ien helped with methodology; Abdel-Fattah Jamal Kodrg helped with software; S. M. Anas supervised the study; Rayeh Nasr Al-Dala’ien and Abdel-Fattah Jamal Kodrg validated the study. Rayeh Nasr Al-Dala’ien wrote the original draft of the manuscript; and S. M. Anas reviewed and edited the manuscript.

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Copyright © 2024 Rayeh Nasr Al-Dala’ien et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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