Structural Performance of Symmetric and Asymmetric Plan Irregular Building Structures: A Comparative Analysis of Conventional and Grid Slab Systems

Structural Performance of Symmetric and Asymmetric Plan Irregular Building Structures: A Comparative Analysis of Conventional and Grid Slab Systems | 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 Structural Performance of Symmetric and Asymmetric Plan Irregular Building Structures: A Comparative Analysis of Conventional and Grid Slab Systems Samrat Poudel, Tek Raj Gyawali This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5572077/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 12 May, 2025 Read the published version in Bulletin of Earthquake Engineering → Version 1 posted 6 You are reading this latest preprint version Abstract Rapid urbanization and increasingly complex building designs have led to a rise in structural irregularities, significantly affecting seismic performance. Plan irregularities often induce torsional effects, placing additional stress on structural elements. Slabs play a crucial role in load distribution and stability, particularly in irregular buildings where conventional slabs may not be optimal. Grid slabs, known for their lightweight structure and efficient load transfer, offer a promising solution for enhancing seismic resilience. However, limited research has explored their interaction with irregular building configurations. This study investigates the seismic performance of grid slabs in buildings with varying symmetries, including symmetric, single-axis symmetric, and asymmetric structures. Numerical simulations under dynamic loading conditions were conducted to assess the impact of different grid slab configurations on deflection, shell stresses, interstorey displacement, drift, and torsional irregularities. The findings reveal that optimized grid slab configurations can significantly reduce slab deflections and improve overall seismic performance, particularly in asymmetric buildings. While grid slabs enhance seismic resilience, symmetric buildings inherently offer better structural balance due to their uniform stiffness and load distribution. These insights contribute to the efficient design of earthquake-resistant structures with complex geometries. Grid slab Diaphragm Deflection Displacement Torsional Irregularities Seismic Performance 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 Figure 14 Figure 15 Figure 16 Figure 17 1. Introduction The evolution of architectural and structural design in modern construction has been driven by the need to balance functionality, cost-efficiency, resilience and sustainability (Szolomicki and Golasz-Szolomicka 2019; Simona et al. 2022; Ilgın 2024). As urban spaces become increasingly complex, buildings are often designed to meet diverse site-specific needs, aesthetic goals, and practical requirements, leading to deviations from regular, symmetric layouts. As buildings evolve to accommodate complex designs and specific functions, they often feature discontinuities in geometry, mass, or stiffness distribution, which can significantly affect how the structure responds to lateral forces (Naveen E et al. 2019). When the center of mass does not coincide with the center of stiffness, eccentricities develop, inducing torsional effects and increasing the potential for structural damage. These challenges are particularly prominent in irregular buildings, which may have uneven load distribution due to irregular floor plans or variations in structural elements resulting in increased displacements and torsional effects that significantly influence the structure’s response, particularly under seismic forces (Özmen and Ünay 2007; Gokdemir et al. 2013). These plan irregularities, whether symmetric or asymmetric, introduce unique challenges for structural performance, particularly under dynamic loads, such as those generated by seismic events (Keertan et al. 2024; Vielma-Quintero et al. 2024). Structural pathologies, such as weak beam-column connections, out-of-plane failures of infill panels, and torsional effects due to mass eccentricity, play a critical role in causing localized and widespread damage. As seismic forces propagate through these structures, areas where load paths are disrupted or elements are poorly connected tend to experience more severe damage. Furthermore, outdated seismic codes and insufficient detailing of structural components often fail to prevent such failures, highlighting the need for updated standards and careful consideration of building design to mitigate risks. The progressive nature of seismic damage, particularly in multi-story buildings, underscores the importance of thorough assessments to better understand and prevent such vulnerabilities in future construction (Nascimbene 2024). The selection of a building plan configuration plays a vital role in seismic-resistant structural design. In real-world scenarios, perfectly regular structures are rare, and the nature of structural irregularities is challenging to define precisely (Wood L. 1992). Research confirms that irregular buildings experience more damage than their regular counterparts, highlighting the importance of studying and imposing restrictions on irregular structures to prevent abrupt changes in geometry, mass, load-paths and stiffness (Haque et al. 2016). The presence of asymmetries plan in a structure often results in imbalance, leading to significant displacement amplification and concentrated forces within resisting elements. Consequently, buildings with plan irregularities are more susceptible to damage during earthquakes due to the complex interactions between translations and rotations (Abdel Raheem et al. 2018). This imbalance can also results in severe damages and, in some cases, the collapse of structures (Patil et al. 2017). Despite the various challenges posed by irregular buildings, they cannot be disregarded entirely due to modern urban layouts and current construction practices. Proper classification and analysis of irregular buildings are essential to address their unique challenges effectively. One critical aspect in this process is the axis of symmetry, which significantly influences the dynamic response of a building under seismic forces. By examining irregular buildings based on their axis of symmetry, they can be categorized into symmetric and asymmetric plan irregular structures. As illustrated in Fig. 1, the axis of symmetry serves as a defining factor in distinguishing the response characteristics of symmetric and asymmetric irregular structures. Plan irregular structures can be classified based on the presence or absence of symmetry in their layout. Symmetric plan irregular structures exhibit irregularities that are evenly distributed around a central axis, maintaining balance in their overall geometry. In contrast, single-axis symmetric plan irregular structures display symmetry along only one axis, with irregularities confined to one direction while the other remains balanced. While asymmetric plan irregular structures are characterized by unevenly distributed irregularities with no discernible axis of symmetry, leading to significant imbalances in their structural configuration and dynamic behavior (Pandian et al. 2024). This is particularly critical in seismically active regions, where irregularities significantly increase the susceptibility to damage, as observed in various earthquake damage histories (Alavi and Rao 2013). Consequently, the design of irregular building structures necessitates planning to address these inherent vulnerabilities. These deviations from a regular, symmetric layout in a building’s horizontal projection, often caused by torsional irregularity, re-entrant corner, diaphragm discontinuity, out of plane offsets, non-parallel systems etc. and current seismic design practices focus on mitigating risks associated with irregularities by employing advanced analysis techniques and incorporating structural systems that minimize the adverse effects of imbalances (Ravikumar et al. 2012). These practices aim to enhance resilience, ensuring that irregular structures can effectively respond to seismic demands and reduce the likelihood of severe damage or collapse (IS 1893 (Part-1) 2016; NBC 105 2020). In addition to irregularities, urban densification has also led to the widespread adoption of high-rise structures as a solution to accommodate growing populations within limited urban spaces. They present unique engineering challenges due to their significant slenderness and extended vibration periods, making them highly susceptible to dynamic forces, particularly seismic and wind loads (Li et al. 2006; Ilgın 2023). Their structural stability depends on multiple factors, including mass distribution, stiffness, and the efficiency of lateral load-resisting systems. Several prior studies have conducted to examine the dynamic behavior of high-rise structures under seismic conditions, emphasizing the critical role of structural configurations in ensuring overall stability. In seismically active regions, integrating considerations of plan irregularity into the design of high-rise buildings is essential for maintaining structural integrity, resilience occupant safety, and serviceability (Jia et al. 2022; Blasi et al. 2024). Extensive research has also been conducted on the stability of irregular high-rise buildings, highlighting the effectiveness of various vertical structural elements, such as shear walls, outriggers, bracing systems, and core walls, in resisting lateral forces (Lu et al. 2013; Brunesi et al. 2016b; Iman 2018). Mazzotta et al. (2017) investigated the seismic performance of 180-meter and 300-meter-tall steel buildings equipped with outrigger and bracing systems. Their findings demonstrated the effectiveness of these systems in limiting drift and displacement but also revealed that they induce high floor accelerations, which could compromise non-structural components, equipment, furnishings, and occupant safety. Similarly, Brunesi et al. (2016a) conducted a seismic analysis of high-rise mega-braced frame core buildings, obtaining comparable results that underscore the trade-offs associated with these structural systems. Brunesi and Nascimbene (2014) investigates the contribution of secondary frame systems to the seismic performance of high-rise buildings, demonstrating their potential to significantly enhance the structural response by stiffening and strengthening the building and recommend the study of redistribution capabilities of detailed floor slab system on seismic performance of building structures. While lateral force-resisting elements such as bracing and shear wall systems remain fundamental in high-rise structures, recent studies have also explored the influence of slab systems on seismic response. Floor slabs contribute to the lateral stiffness and overall dynamic behavior of buildings, particularly in asymmetric structures, where irregular mass and stiffness distributions can lead to amplified deformations (Latha and Pratibha 2021). To determine the response of high-rise buildings to seismic loads, dynamic analysis techniques such as response spectrum analysis are used. This method incorporates ground acceleration records to develop response spectra based on seismic loads and site-specific parameters (Sujith and Kumar 2023). The eigenmodes derived from dynamic analysis provide insight into how mass and stiffness distribution affect overall seismic performance (Guleria 2014). By capturing the interplay of various vibrational modes, this approach enables precise predictions of structural responses (Sivakumar et al. 2023), facilitating the optimization of structural systems to enhance resilience against seismic events. Conventional slab design practices typically involve the use of reinforced concrete slabs, which are horizontal structural elements essential for supporting floors, ceilings, and roofs in a building (Jabir et al. 2021). These slabs distribute the loads, such as live and dead loads, from the structure above to the beams, columns, or walls below (Gupta and Singh 2020; Yılmaz et al. 2022). The design of conventional slabs comprising up to two-thirds of the total volume, are commonly used and its selection is influenced by factors such as span length, load-carrying capacity, shear stress distribution, bending moments and the intended use of the building (Kayastha and Debbarma 2019). The most common types of conventional slabs are one-way slabs and two-way slabs as shown in Fig. 2. One-way slabs are supported by beams on two opposite sides and bend in one direction, making them ideal for buildings with smaller spans or where loads are concentrated in one direction. Two-way slabs, on the other hand, are supported on all four sides, bending in two perpendicular directions, and are more suitable for buildings with square or nearly square layouts, allowing for better load distribution (Hoffman et al. 1998a, b). The thickness of conventional slabs is determined by several factors, including the span length, the loads they need to support, and the deflection limits specified by design codes (Gardner 2011). For residential buildings, slab thickness typically ranges from 100 mm to 150 mm, while in commercial or industrial buildings, slabs may be thicker, ranging from 200 mm to 300 mm, to accommodate heavier loads. Design codes also provide deflection limits to ensure the structural integrity and serviceability of slabs. As architectural requirements evolve, slab spans often increase, leading to challenges in meeting deflection criteria. In the case of very large-span structures, using conventional solid slabs, which can be either one-way or two-way, often necessitates a proportional increase in thickness to control excessive deflection (Tiwari et al. 2025). However, increasing slab thickness in large-span structures has a cascade effect. Since slabs typically consume a significant amount of concrete in building construction, increasing the thickness not only increases the concrete volume but also results in a higher dead load. This, in turn, increases the size of beams, columns, and foundations, making the structure less efficient and more expensive (Sagadevan and Rao 2021). The additional weight of the structure, driven by the increased thickness, can make the building design less economical. Therefore, while conventional slabs may be effective for smaller spans, they are often impractical for large spans, where alternative solutions must be explored to ensure both functionality, cost-effectiveness and sustainability in the design of the building (Ibrahim et al. 2013). Increasing material consumption in construction leads to greater energy use and higher carbon emissions, straining resources and conflicting with global sustainability goals. Thus, the environmental cost of inefficient design practices must be carefully considered in the context of sustainability (Heeren et al. 2015; Sanglier Contreras et al. 2022). This limitation of conventional slabs, particularly in large-span structures, underscores the need for alternative slab systems, such as grid slabs, which can effectively address deflection concerns while optimizing the overall material use and reducing the impact on the building’s structural efficiency and sustainability. On the other hand, grid slabs are innovative structural systems characterized by a thin flat plate supported by grid beams spanning in two directions, resting on main beams at the boundary. Designed for cost-effective construction over long spans, often reaching up to 20 meters, these slabs have gained popularity in modern construction for their ability to reduce dead weight and improve lateral load distribution (Alraie and Barik 2017). Distinguished by large square voids between ribs, grid slabs combine structural efficiency and material optimization as depicted in Fig. 3. This design minimizes self-weight by strategically removing concrete below the neutral axis, a process facilitated by using molds like dirt pots during casting (Nithyambigai et al. 2021). The resulting ribbed structure is lighter and stiffer than traditional solid slabs, allowing for substantial reductions in dead load, thinner slabs, and improved load distribution. They exhibit significant advantages in construction projects requiring large spans, such as parking areas, halls, ramps, auditoriums, and amphitheaters, where intermediate columns are undesirable (Nishanth et al. 2020). Their lighter weight and superior structural performance reduce the risk of excessive deflection and cracking often associated with conventional solid slabs over large spans (Olawale and Ayodele 2014; Sancheti et al. 2021). These characteristics make grid slabs particularly efficient in seismic zones, as their reduced weight positively impacts the seismic behavior of structures while also lowering construction costs and promotes sustainability. By incorporating steel bar reinforcement, grid slabs enhance elasticity and durability, further ensuring structural reliability. Architecturally, grid slabs provide flexibility and are aesthetically pleasing, making them suitable for diverse applications. However, their hybrid behavior—combining features of plate slabs, beam grillages, and shell structures—presents analytical challenges, particularly under dynamic loading conditions (Thakor and Patel 2019). Despite these complexities, their benefits, including higher stiffness, reduced material usage, and efficient load transfer, make them a preferred choice in contemporary construction (Abdul-Wahab and Khalil 2000; Samson O. et al. 2023). Overall, grid slabs exemplify a balance between functionality, cost-efficiency, resilience and sustainability addressing the demand for sustainable and robust construction solutions in modern architectural designs. The design and performance of grid slabs are highly influenced by various parametric factors, with span of grid ribs, spacing between grid ribs and the depth-to-breadth (d/b) ratio of the ribs being the most critical parameters. The spacing of the grid ribs significantly impacts the structural behavior, as closer spacing leads to more frequent load distribution, improving stiffness and reducing deflections, though it may increase material usage and construction costs. On the other hand, wider spacing may reduce material costs but could lead to larger deflections and decreased load-carrying capacity, requiring an optimal balance. Similarly, the depth-to-breadth ratio of grid ribs affects their resistance to bending and shear forces. A higher d/b ratio increases stiffness and bending resistance, but also results in more material usage, making it essential to determine an efficient ratio that optimizes both structural performance and cost. Several studies have investigated the impact of these parameters on grid slab behavior. For instance, Yoosaf K.T. et al. (2013) explored how the spacing of transverse beams and the span-to-depth ratio influence deflections and bending moments in grid floor slabs, suggesting that optimizing these parameters can improve performance while minimizing material use. Similarly, Halkude and Mahamuni (2014) examined the effect of the grid beam depth on peripheral beams, noting that reducing the depth of grid beams could optimize bending moments and shear forces in peripheral beams, particularly when paired with appropriate spacing. Tripathi et al. (2021) focused on grid size variations and their effect on stress parameters, concluding that smaller grid sizes lead to increased bending moments and shear forces, while square grids provided more uniform stress distribution similar to two-way slabs. Furthermore, Prasad et al. (2005) conducted an analytical study on waffle slabs, proposing optimal rib spacing, depth, and width for improved load distribution and structural efficiency without requiring additional shear reinforcement. Building upon these findings, our research focuses on investigating the influence of spacing between grid ribs and the depth-to-breadth ratio on the performance of grid slabs, particularly in terms of load distribution, deflection, and bending resistance. By varying these parameters, we aim to identify optimal configurations that provide a balance between structural efficiency and cost-effectiveness, especially for large-span structures such as auditoriums, parking areas, and public halls, where intermediate columns are undesirable. Increased complexities in structures often lead to higher vulnerabilities during seismic events, resulting in more severe structural failures. These failures necessitate extensive retrofitting and rehabilitation, which in turn escalate energy consumption, financial costs, and structural demands (Cavalieri et al. 2023). Therefore, when irregularities cannot be avoided, it is crucial to assess the optimal configuration of the structure. Optimization not only mitigates seismic risks but also makes the rehabilitation process more cost-effective and energy-efficient, ensuring structural integrity during such events (Jebelli et al. 2022; Demir 2025). While seismic performance remains a critical concern in structural design, the increasing environmental impact of construction cannot be overlooked (Berrón Ferrer 2003; Cavalieri et al. 2023). The industry’s intensive resource consumption and high carbon emissions contribute significantly to the global climate crisis, exacerbated by unchecked industrialization. Structural components such as slabs, beams, and lateral load-resisting systems, structural configurations play a crucial role in ensuring structural integrity, yet they are also major contributors to buildings’ carbon footprints (Paik and Na 2019; Auburtin et al. 2023). Concrete, particularly due to cement production, remains one of the highest emitters of CO 2 , underscoring the challenge of optimizing structural systems without compromising performance (Bohorquez et al. 2024). The primary structural elements such as columns, beams, shear walls and slabs play a critical role in managing the loads and stresses generated by irregularities (Balendra 1993; Hussain et al. 2024). However, the performance of slabs, often seen as secondary structural elements, is sometimes overlooked in such buildings. In fact, the role of slabs in ensuring stability and load distribution is vital, particularly in irregular buildings where uneven geometries, load paths and eccentricities can affect the overall behavior of the structure (Zhang 2024). The choice of slab system—whether it be conventional slabs, flat slabs, or grid slabs—becomes integral to addressing the challenges posed by complex architectural layouts. These slab systems not only help distribute loads efficiently but also contribute to the overall stiffness and stability of the building, ensuring it performs effectively even under dynamic and lateral forces (Pradhana et al. 2019; Pang et al. 2021). The interaction between high-rise structures and slab types in buildings with plan irregularities is a critical consideration in structural engineering. By addressing the challenges posed by plan irregularities and optimizing structural systems beyond conventional approaches, engineers can design high-rise structures that are both resilient, safe and sustainable, effectively responding to dynamic forces in seismically active regions. In the study of the structural performance of irregular building structures with different slab systems, there remains a significant opportunity to explore the combined influence of grid slabs and plan irregularities of high-rise buildings. Existing studies have primarily focused on two separate areas: the analysis of irregular buildings using conventional slabs and the parametric variations of grid slab systems. However, limited attention has been given to how the interaction between slab type—particularly grid slabs with varying parameters such as depth-to-breadth ratio and rib spacing—and the irregularities in building plans affects the overall structural performance. Previous work has largely concentrated on either the dynamic response of buildings with conventional slabs or the performance of grid slabs in isolation, with minimal research on their combined effects. This issue is especially crucial in the context of seismic performance, as the dynamic response of irregular buildings depends on both the configuration of the building and the slab system in use. Despite the extensive study of grid slab behavior, the impact of optimized grid slab parameters, such as rib spacing and depth, on the performance of irregular buildings has not been fully explored. The interplay between these slab configurations and the seismic response of buildings with plan irregularities, such as torsional effects and stability under dynamic loading, has yet to be adequately addressed. By focusing on the relationship between these two elements—irregular building structures and grid slab systems—this study aims to advance understanding in this area. It seeks to investigate how varying parameters of grid slabs, such as rib spacing and depth-to-breadth ratio, can influence the overall structural performance of both symmetric and asymmetric plan irregular buildings. This work will provide valuable insights into optimizing grid slab configurations to enhance the stability and cost-efficiency of buildings in seismic zones, ultimately contributing to more effective design strategies for irregular structures. The findings will help bridge the gap between slab system design and irregular building performance, an area that remains under-explored in current literature. 2. Methodology In this study, G+9 buildings each with a floor-to-floor height of 3.5 meters, and incorporates different plan irregularities were analyzed to evaluate the performance of optimized grid slabs in comparison to conventional slabs. The grid slab optimization was conducted based on deflection criteria and shell stress. Various configurations were examined by varying the depth-to-breadth (d/b) ratio of ribs from 1 to 5 and adjusting rib spacing between 1000 mm and 4000 mm to identify the most effective design for enhanced structural efficiency and seismic performance. Using ETABS version 20 (Computers and Structures, Inc. 2022), models of the buildings were created—one incorporating the optimized grid slab and another with a conventional slab. Both models were analyzed under seismic conditions using the Response Spectrum Method. Key parameters, such as base shear, modal time period, interstorey displacement, interstorey drift, torsional irregularities, and torsional diaphragm rotations, were evaluated. This comparative analysis provided insights into the structural efficiency and seismic performance of the two slab systems, with results aiding in the selection of the most effective slab type for similar high-rise structures. The methodology is designed to ensure the study’s replicability and to provide clear insights into the building design, modeling, analysis, and optimization steps undertaken. A flowchart of the methodology is provided in Fig. 4 . The building models for the study include H-shaped, T-shaped, and L-shaped configurations, representing symmetric, single axis symmetric and asymmetric buildings, respectively. H-shaped buildings were modeled as symmetric in both axes, while T-shaped and L-shaped buildings were considered asymmetric about one and both axes, respectively. Each building was modeled with both conventional slabs and grid slab systems. The total slab area for all models remained constant, ensuring consistency in comparison. The buildings were modeled with five spans of 12 meters in both the X and Y directions, with slab configurations optimized based on rib depth and spacing. In all models, both conventional and grid slab systems were modeled as rigid diaphragms. The structural parameters and design details of the buildings, including material properties, geometry, and design specifications, are summarized in Table 1. Additionally, the parametric variations of grid rib dimensions are listed to highlight the key design variables. Table 1. Parameters of building Parameters General Description Structural System SMRF Concrete Grade M40 Reinforcements Fe 500 Importance Factor 1.5 Zone Factor (Zone V) Shape of Building H, T and L-shaped Slab Thickness 100 mm Floor to Floor Height 3.5 m Width of Grid Ribs 125 mm Parametric Variation: Depth of Grid Ribs 250 mm, 375 mm, 500 mm, 625 mm Spacing of Grid Ribs 1000 mm, 1500 mm, 2000 mm, 3000mm, 4000 mm The loading conditions applied to the buildings in this study were designed to represent realistic structural loads, including live loads, floor finishes, and roof loads. These loads are crucial for assessing the building's performance under both static and dynamic conditions, particularly in the context of seismic analysis. The specifics of the loading conditions, as summarized in Table 2, were incorporated into the building models to simulate real-world conditions and ensure the accuracy of the analysis. These applied loads are essential for evaluating the building's ability to resist both gravity loads and seismic forces, ultimately guiding the design to enhance structural safety and performance. Table 2. Loading on building Description Loads Live Load Floor 4 kN/m 2 Live Load Roof 1.5 kN/m 2 Floor Finish 1 kN/m 2 The building models were created using ETABS software that caters to multi-story building analysis and design (Computers and Structures, Inc. 2022), and finite element analysis was conducted to evaluate dynamic responses under seismic loading. The models of the buildings, incorporating both conventional and grid slab systems, are represented in Fig. 5 and Fig. 6. In these figures, H-shaped, T-shaped, and L-shaped buildings with conventional slab systems are denoted as HCB, TCB, and LCB, while those with grid slab systems are denoted as HGB, TGB, and LGB. The seismic performance of the buildings was evaluated through response spectrum analysis. The choice of a G+9 story building is based on its relevance as a mid-rise structure commonly found in seismic-prone urban areas. The study examines buildings with different plan irregularities (H, T, and L shapes) to represent typical real-world challenges. These buildings were selected for their variety in symmetry and asymmetry, which play a crucial role in the seismic response. The grid slab system was included in the study to assess its effectiveness in improving the seismic performance of the buildings, particularly in reducing deflections and enhancing torsional stability. The study aims to evaluate the impact of the grid slab system on overall building performance, focusing on the optimization of rib depth and spacing for enhanced structural resilience. 3. Results And Discussion This study analyzes the d/b ratio and spacing of grid ribs to optimize their configuration, focusing on deflection and other local factors. The building's structural response was assessed through linear static and dynamic evaluations. Key parameters such as torsional irregularity, modal time period, inter-storey displacement, inter-storey drift ratio, and maximum diaphragm rotations were examined. 3.1. Slab Deflection Both conventional and grid slabs were analyzed under gravity loading to evaluate their deflection behavior. The study, extending beyond IS 456:2000 recommendations, provided valuable insights into the influence of depth-to-breadth (d/b) ratios and rib spacings on structural performance. For a 12 m span with a permissible deflection of 48 mm (span/250) (IS 456 2000), deflection at a d/b ratio of 4 remained within permissible limits for rib spacings of 1000 mm (43.59 mm) and 1500 mm (45.93 mm). However, increasing the rib spacing to 2000 mm and 3000 mm results in deflections of 48.7 mm and 54.28 mm, respectively, thereby exceeding the allowable limit. Larger rib spacings compromise load distribution and exacerbate bending and shear effects and closely spaced ribs increase the reinforcement ratio which ultimately increases slab strength (Silva et al. 2020). Additionally, while lower depth-to-breadth (d/b) ratios of 2 and 3 may provide sufficient compressive strength, they fail to offer the necessary effective depth to resist bending and shear forces. Concrete and steel have low strain rates due to the premature failure of the ribs by shearing (Sacramento et al. 2018). As the grid thickness increases, the primary mode of failure transitions from pure flexural failure to a combined action of moment and shear, indicating that greater grid thickness significantly enhances the beam’s flexural bearing capacity while also influencing its shear resistance (Li et al. 2024). Moreover, the depth of grid ribs is governed by the effective span; for larger span structures, greater rib depth is essential to ensure adequate resistance to deflection (Fahmi and Saber 2020; Adamu et al. 2024). Insufficient depth compromises the slab’s ability to distribute loads effectively, ultimately leading to compromised structural performance. On the other hand, increasing the d/b ratio to 5 significantly improved structural performance. For a rib spacing of 2000 mm, deflection was reduced to 40.13 mm, well within permissible limits, establishing this configuration as both efficient and reliable. Although a rib spacing of 3000 mm with a d/b ratio of 5 resulted in a deflection of 43.62 mm, which is within the permissible limit, the design does not account for accidental loadings (Prasad et al. 2005). Considering these factors, the rib spacing of 2000 mm with a d/b ratio of 5 is preferred, offering a more robust and safe solution (Fig. 7). Fig. 8. illustrates the comparison of deflection between the optimized grid slab and the conventional slab. The conventional slab exhibited a deflection of 139.14 mm, while the optimized grid slab with a rib spacing of 2000 mm and a d/b ratio of 5 showed a deflection of 40.13 mm. This represents a substantial reduction of approximately 71.1% in deflection, highlighting the structural benefits of the grid slab in terms of load redistribution and stress mitigation. 3.2. Shell Stress In grid-reinforced slabs, shell stresses arise due to the combined effects of bending and in-plane forces induced by external loads and boundary conditions (Ibrahim et al. 2011; Guo et al. 2017; Jain and Hussain 2024). These stresses can be categorized into top shell stresses (compression in the top fibers) and bottom shell stresses (tension in the bottom fibers)(Schwetz et al. 2014). The spacing of grid ribs significantly influences the distribution and magnitude of these stresses, as they provide additional stiffness and redistribute forces across the shell (Nithyambigai et al. 2021). The analysis reveals that a rib spacing of 3000 mm with a d/b ratio of 5 results in a bottom shell stress of 5.77 MPa and a top shell stress of 10.76 MPa. While this configuration satisfies normal loading requirements, it does not fully account for potential accidental loadings, such as point impact or unexpected increases in live load. These additional loads could lead to higher stresses or excessive deflections, potentially compromising the long-term structural performance. The top shell stress under parametric variations is shown in Fig. 9, and the bottom shell stress is presented in Fig. 10. In comparison, a rib spacing of 2000 mm with a d/b ratio of 5 results in a bottom shell stress of 5.81 MPa and a top shell stress of 11.34 MPa, offering enhanced robustness against accidental loadings. The increase in bottom shell stress is only 0.7%, while the top shell stress increases by approximately 5.4%. These minor increases in stress are outweighed by the significant improvement in structural stiffness, ensuring better resistance to accidental load scenarios. When compared to the conventional slab (rib spacing = 0 mm), the 2000 mm rib spacing with a d/b ratio of 5 achieves a 74.2% reduction in bottom shell stress (from 22.48 MPa to 5.81 MPa) and a 76.6% reduction in top shell stress (from 48.41 MPa to 11.34 MPa). These reductions emphasize the efficiency of ribs of the grid slabs in redistributing stresses and optimizing overall structural performance. Although the 3000 mm rib spacing configuration results in the lowest recorded stresses (5.77 MPa for bottom shell stress and 10.76 MPa for top shell stress), the design with 2000 mm rib spacing is preferred. It offers a more robust and safer solution under both standard and accidental loading conditions, ensuring long-term structural integrity. Thus, the 2000 mm rib spacing with a d/b ratio of 5 is the optimal configuration, providing a balance between reduced stresses, improved structural robustness, and enhanced safety against accidental loading. The comparison of shell stresses between the conventional slab system and the grid slab system with the optimum rib parameters is depicted in Fig. 11. 3.3. Base Shear In this study, the base shear values for H-shaped, L-shaped, and T-shaped buildings were analyzed to compare the seismic performance of grid slabs and conventional slabs in both the X and Y directions. The results consistently show that grid slabs exhibit higher base shear values compared to conventional slabs across all building configurations and load cases (RSX, RSY) ash shown in Fig.12. Base shear reflects the total horizontal force a structure is expected to resist during seismic events, which is influenced by factors such as mass, stiffness, and the building's fundamental period (Khan 2013). In the X-direction, the base shear values for buildings with grid slabs were consistently higher than those with conventional slabs. The H-shaped building exhibited the highest base shear, with a value of 15170.42 kN for grid slabs, representing a 20.89% increase over the conventional slab value of 12549.14 kN. The L-shaped building showed a 22.75% increase in base shear, with a value of 14037.46 kN for grid slabs compared to 11435.83 kN for conventional slabs, while the T-shaped building experienced a 21.80% increase, with grid slabs yielding a base shear of 14559.78 kN, higher than the 11953.70 kN observed for conventional slabs. In the Y-direction, grid slabs again provided higher base shear values than conventional slabs. The H-shaped building recorded the highest base shear in this direction as well, with 15965.68 kN for grid slabs, reflecting an 18.45% increase compared to the conventional slab value of 13479.24 kN. The L-shaped building demonstrated a 21.61% increase in base shear, with grid slabs yielding 14569.68 kN compared to 11980.84 kN for conventional slabs, while the T-shaped building showed a 20.42% improvement, with a base shear of 14615.13 kN for grid slabs, in contrast to 12136.33 kN for conventional slabs. When comparing the maximum base shear values across both directions, the H-shaped building consistently demonstrated the highest base shear values, with 15170.42 kN in the X-direction and 15965.68 kN in the Y-direction. The T-shaped building exhibited a 4.04% lower base shear in the X-direction (14559.78 kN) and an 8.6% lower value in the Y-direction (14615.13 kN) compared to the H-shaped building. The L-shaped building recorded the lowest values, with 7.45% lower base shear in the X-direction (14037.46 kN) and 9.7% lower in the Y-direction (14569.68 kN) compared to the H-shaped building. These findings align with previous research Pandian et al. (Pandian et al. 2024) which observed that symmetric building configurations, such as square and U-shaped buildings, generally exhibit higher base shear values. In contrast, while the L-shaped building demonstrated lower base shear, there was no significant difference between the base shear values of the L-shaped and T-shaped buildings. Ultimately, symmetric buildings consistently showed higher base shear compared to their asymmetric counterparts 3.4. Modal Time Period In seismic design, a structure's compliance with safety standards relies on its fundamental time period, a key factor influencing the horizontal base shear coefficient. According to IS 1893 (IS 1893 (Part-1) 2016), the formula for the fundamental lifespan (T a ) is given by T a =0.075h 0.75 Eq. (1) where 'h' represents the total building height. Empirical application of this formula resulted in a natural time period of 1.08 seconds. Simultaneously, Fig. 13 displays fundamental time periods based on the first mode shape obtained through finite element analysis providing a comprehensive comparison for seismic assessment. The time period for the 1 st fundamental mode through finite element analysis is HCB (1.969 sec.), HGB (1.945), TCB (1.963 Sec.), TGB (1.956 Sec), LCB (1.986 Sec.), and LGB (1.972 Sec.). The grid slab systems (HGB, TGB, and LGB) demonstrate a clear reduction in the first fundamental period compared to the conventional slab systems (HCB, TCB, and LCB), with HGB exhibiting a decrease of 1.22%, TGB a decrease of 0.36%, and LGB a decrease of 0.71%. This reduction in the time period suggests that grid slab systems may offer a more favorable dynamic response, potentially improving the seismic performance of structures by reducing the oscillatory behavior and enhancing stiffness during dynamic loading. Significantly, finite element analysis yielded basic time periods ranging from 1.945 to 1.986 seconds, approximately 80–83% higher than empirical codal formula results. This stark contrast exposes a substantial flaw in code-based methods, emphasizing their tendency to underestimate building vibration time periods. These inaccuracies, crucial for lateral force procedures, align with previous studies (Khanal and Chaulagain 2020), emphasizing the need for advanced analytical methods. The study contributes to seismic design practices, shedding light on the limitations of traditional empirical approaches. Additionally, in comparing modal times for the first fundamental mode, the L-Shaped Building exhibits longer times than the grid slab system building, which, in turn, has shorter time periods than the traditional slab system. 3.5. Inter-Storey Displacement The analysis of diverse building types and seismic response methods reveals distinct trends in displacement characteristics. Maximum top storey displacements of models considered were HCB (115.96 mm), HGB (114.09 mm), TCB (136.07 mm), TGB (124.57 mm), LCB (143.83 mm) and LGB (138.08 mm). L-shaped buildings exhibited higher displacement than their H-shaped and T-shaped counterparts. Symmetric buildings, such as those with H-shaped configurations and conventional or grid slab systems, displayed similar maximum top storey displacements. However, for T-shaped and L-shaped buildings, the grid slab system resulted in less displacement compared to conventional slab systems (Fig.14). Notably, the grid slab system emerged as more efficient in reducing maximum top storey displacement, emphasizing its potential advantages in enhancing structural resilience during seismic events (Latha and Pratibha 2021). The choice of building shape and slab system, specifically favoring the grid slab system, plays a pivotal role in seismic analysis, contributing to optimized structural performance and reduced displacement. The incorporation of a grid floor system has demonstrated notable advantages in mitigating maximum displacements across different building configurations. In particular, the inclusion of grid floors resulted in a reduction of maximum displacement by 1.63% for H-shaped buildings, 4.17% for L-shaped buildings, and 9.23% for T-shaped buildings. The percentages of reduction signify a tangible improvement in the building's ability to withstand seismic forces, emphasizing the grid floor's role in contributing to a sound and resilient structural design. 3.6. Inter-Storey Drift Ratio The evaluation of the inter-storey drift ratio, a crucial parameter in seismic design, revealed significant variations among different building shapes. L-shaped structures consistently exhibited the highest drift ratios, contrasting with H-shaped structures which consistently showed the lowest (Fig.15). The accuracy of calculating inter-storey drift ratios was found to be superior in response spectrum analysis compared to static analysis. Notably, buildings with pronounced irregularities displayed higher deformations, particularly in regions characterized by elevated seismic activity, validating earlier research findings. Asymmetrical buildings, particularly those with asymmetry along a specific axis, demonstrated greater displacement along their respective axes (Naveen E et al. 2019). Interestingly, symmetric buildings constructed with grid slab and conventional slab systems demonstrated identical maximum inter-storey drift ratios, emphasizing the potential equivalence of these systems in controlling drift. The maximum inter-storey drift ratios for the models considered were HCB (0.00163), HGB (0.00153), TCB (0.00188), TGB (0.00165), LCB (0.00198) and LGB (0.00181). However, a pivotal discovery emerged when comparing asymmetric building designs. The maximum inter-storey drift ratio in L-shaped structures with grid slab and conventional slab systems was 21% and 25% higher, respectively, than that of H-shaped buildings with grid floors. Similarly, T-shaped buildings exhibited 8% and 17% higher maximum inter-storey drift ratios with grid slab and conventional slab systems compared to H-shaped buildings with grid floors. Notably, the inter-storey drift ratio in H-shaped buildings with a conventional slab system closely resembled that of structures with grid floors. Introducing grid floor systems as an alternative to conventional slabs led to a reduction in maximum inter-storey drift ratios: H-shaped buildings by 0.72%, L-shaped buildings by 3.19%, and T-shaped structures by 8.16%. Moreover, it was observed that elastic analysis tends to underestimate storey drift, particularly as the structure reaches nonlinear levels. 3.7. Torsional irregularity ratio According to IS 1893:2016, a building is considered torsionally irregular if the greatest horizontal displacement of any floor exceeds 1.5 times the minimum horizontal displacement in the opposite direction at the opposite end of the same level. The study notes that the values of equivalent static torsion and maximum dynamic torsion are typically similar, except for irregularly shaped L-shaped structures (Ahmed et al. 2016; Soltani et al. 2018). Torsional irregularities lead to poor seismic performance, causing lateral deflections to increase in the weak direction and decrease in the strong direction during torsion (Gokdemir et al. 2013; Krishnan and Thasleen 2020). The torsional irregularity ratios are as follows: HCB (1.00), HGB (1.00), TCB (1.3), TGB (1.14), LCB (1.52), LGB (1.41). These ratios offer insights into the impact of asymmetricity on torsional behavior. In H-shaped buildings, the torsional irregularity ratio consistently remains at 1 in both X and Y directions. Maximum torsional irregularity ratio increases with the increase in asymmetricity and reaches TCB (1.3) and TGB (1.14) but within permissible limits. This indicates excellent torsion resistance in both X and Y directions for T-shaped and H-shaped buildings, highlighting their favorable structural characteristics. Contrastingly, L-shaped structures with conventional slab systems exhibit torsional irregularity LCB (1.52) in dynamic studies, challenging the applicability of equivalent static analysis for such structures. The introduction of grid floors in L-shaped buildings restores torsional regularity LGB (1.41), demonstrating the efficacy of grid slabs in mitigating torsional irregularities (Fig. 16). This further accentuates the correlation between asymmetricity and torsional irregularity, as indicated by the observed torsional irregularity ratios. Graphical representations underscore the superior torsional performance of grid slab systems compared to traditional slab systems. The rigidity of L-shaped and T-shaped buildings increases by 30% and 27%, respectively, while the rigidity of H-shaped buildings remains the same when utilizing grid slabs instead of conventional slabs. 3.8. Torsional Diaphragm Rotation In Fig. 17, the graphical representation of torsional diaphragm rotation reveals variations along the building height in both X and Y directions. The observed pattern aligns with Özmen et al.'s findings (Özmen et al. 2014) , peaking at the top level. H-shaped structures exhibit minimal torsional rotation in both X and Y directions, while T-shaped buildings display greater rotation along the X-direction and negligible rotation along the Y-direction. In contrast, L-shaped buildings, characterized by asymmetry in both axes, exhibit maximum torsional rotation along both axes, with the X-direction rotation surpassing that of the Y-direction. This suggests that buildings symmetric along the considered axis tend to have lower torsional diaphragm rotation values compared to the axis about which they are asymmetric. The reported maximum demands are as follows: HCB (0), HGB (0), TCB (0.00086), TGB (0.000447), LCB (0.001431), and LGB (0.001225). This data-driven analysis highlights the torsional behavior of different configurations, including H-shaped buildings with both conventional and grid slabs, T-shaped buildings with conventional and grid slabs, and L-shaped buildings with conventional and grid slabs. The results confirm that H-shaped buildings, characterized by symmetry about both axes, exhibit robust stability with minimal torsional rotation. In comparison, T-shaped buildings, with single-axis symmetry, show higher torsional rotation values but fall within a moderate range, while L-shaped buildings, being asymmetric about both axes, display the highest torsional rotation. Overall, this comparative assessment emphasizes the influence of building geometry and symmetry on torsional behavior, underscoring the potential of grid slab systems to minimize torsional diaphragm rotation across diverse building types. 4. Conclusion Both conventional slab systems and grid slab systems have been used in the investigation, which was conducted on a range of building types. A comparison has been performed between conventional slab systems and grid slab systems with respect to overall structural performance. The results show that irregularity significantly affects the structural response. In all the examples that were looked at, there is a change in reaction for frames that have one or more irregularities in comparison to the typical arrangement. After analyzing these kinds of buildings, the following conclusions were drawn: The study reveals that a rib spacing of 2000 mm with a d/b ratio of 5 optimally balances deflections, reducing them by approximately 71.1% compared to conventional slabs while keeping deflections within permissible limits. The grid slab with a rib spacing of 2000 mm and a d/b ratio of 5 is optimal, reducing shell stresses by over 74% compared to conventional slabs while ensuring enhanced robustness and safety under both standard and accidental loading. This configuration balances stress reduction and long-term structural performance effectively. Although grid slabs result in higher base shear values, they significantly reduce interstorey displacement and drift, especially in buildings with plan asymmetries. This makes grid slabs more efficient in single-axis symmetric and asymmetric buildings, improving seismic performance, while the benefits are less pronounced in symmetric buildings with already balanced stiffness and load distribution. Grid slabs effectively mitigate torsional diaphragm rotation, particularly in complex L-shaped configurations, offering a scientifically grounded solution to address torsional irregularities and improve the overall structural stability under dynamic loading conditions. The grid slab system demonstrated superior structural performance over conventional slabs, showcasing its efficacy in enhancing building stability. Furthermore, the study revealed that symmetrical building designs consistently outperformed asymmetrical structures, emphasizing the importance of balanced configurations between asymmetric structure and grid slab in achieving optimal structural outcomes. Declarations CRediT authorship contribution statement Samrat Poudel : Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Tek Raj Gyawali : Writing – review & editing, Validation, Supervision, Investigation, Formal analysis, Mentorship. Conflict of Interest The authors declare that they do not have any conflict of interest. References Abdel Raheem S, Ahmed M, Ahmed M, Abdel-shafy A (2018) Evaluation of plan configuration irregularity effects on seismic response demands of L-shaped MRF buildings. Bull Earthq Eng 16:. https://doi.org/10.1007/s10518-018-0319-7 Abdul-Wahab HMS, Khalil MH (2000) Rigidity and Strength of Orthotropic Reinforced Concrete Waffle Slabs. 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Springer Nature Singapore, Singapore, pp 619–630. https://doi.org/10.1007/978-981-97-6067-1_59 Tripathi N, Dubey S, Shrivastava V (2021) Analysis Of Grid Floor And Its Parametric Study. Int J Sci Adv Res Technol 7:69–75 Vielma-Quintero JC, Diaz-Segura EG, Vielma JC (2024) Influence of the Plan Structural Symmetry on the Non-Linear Seismic Response of Framed Reinforced Concrete Buildings. Symmetry (Basel) 16:. https://doi.org/10.3390/sym16030370 Wood L. S (1992) Seismic Response of R/C Frames with Irregular Profiles. J Struct Eng 118:545–566. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:2(545) Yılmaz T, Anil Ö, Tuğrul Erdem R (2022) Experimental and numerical investigation of impact behavior of RC slab with different opening size and layout. Structures 35:818–832. https://doi.org/10.1016/j.istruc.2021.11.057 Yoosaf K.T. M, Ramadass S, Ramanujan J (2013) Finite element analysis and parametric study of grid floor slab. Am J Eng Res 3:20–27 Zhang X (2024) Design optimization of irregularity RC structure based on ANN-PSO. Heliyon 10:e27179. https://doi.org/10.1016/j.heliyon.2024.e27179 Supplementary Files Reviewercommentandadjustment.docx Cite Share Download PDF Status: Published Journal Publication published 12 May, 2025 Read the published version in Bulletin of Earthquake Engineering → Version 1 posted Editorial decision: Accept as is 15 Apr, 2025 Reviewers agreed at journal 28 Mar, 2025 Reviewers invited by journal 21 Mar, 2025 Editor invited by journal 20 Mar, 2025 Editor assigned by journal 20 Mar, 2025 First submitted to journal 20 Mar, 2025 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5572077","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":431980731,"identity":"4afad9b1-6e97-4ea9-b992-49c5aba771d8","order_by":0,"name":"Samrat Poudel","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYPACGx4Yi7GBOB0JaaRrOQxnEtYi33467cPPH+dl+Nl7D378wWAju+EA77EH+LQYnMndPLMn4TaPZM+5ZGkehjTjDQf40g3wamHI3czAA9RicCPHQJqB4XDihgM8ZhJ4Hdb/djPjn4RzPAb33xj//MHwn7AWhhu5m5l5Eg4AbQGq5GE4QFiLwY23m5ll0pKBfslLs+YxSDaeeZjHHK9f5PtzNzO+sbGz52c/e/jmjwo72b7jPWYP8DoMAUCxCTKemYGNSB0M8ARAvJZRMApGwSgYGQAA/LtHB2uwMo8AAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0006-3077-2257","institution":"Tribhuvan University Institute of Engineering","correspondingAuthor":true,"prefix":"","firstName":"Samrat","middleName":"","lastName":"Poudel","suffix":""},{"id":431980732,"identity":"8bf4aff3-cab8-47ff-8e42-747585fe1b71","order_by":1,"name":"Tek Raj Gyawali","email":"","orcid":"","institution":"Pokhara University","correspondingAuthor":false,"prefix":"","firstName":"Tek","middleName":"Raj","lastName":"Gyawali","suffix":""}],"badges":[],"createdAt":"2024-12-03 12:03:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5572077/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5572077/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10518-025-02179-w","type":"published","date":"2025-05-12T15:57:56+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":79104777,"identity":"245eef8c-4bd8-4a4e-8a6b-ad11691ff618","added_by":"auto","created_at":"2025-03-24 13:04:24","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":18153,"visible":true,"origin":"","legend":"\u003cp\u003eClassification of plan irregular building structures based on axis of symmetry: (a) symmetric plan irregular structure (b) single-axis symmetric plan irregular structure (c) asymmetric plan irregular structure\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/47df233ed05c5830c4103ae3.png"},{"id":79105626,"identity":"259c38a5-ff42-443d-a68f-a49186e9f31e","added_by":"auto","created_at":"2025-03-24 13:12:24","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":104106,"visible":true,"origin":"","legend":"\u003cp\u003eConventional solid slab (a) One-way slab (b) Two-way slab (Engineering Discoveries 2024)\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/d59eb53e0531818121b9f512.png"},{"id":79105625,"identity":"d3876444-dc65-4e99-85c9-6ed3650af37c","added_by":"auto","created_at":"2025-03-24 13:12:24","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":127053,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Plan of a grid slab system showing the arrangement of grid beams, peripheral beams, and supporting columns (Halkude and Mahamuni 2014) (b) Architectural view of a constructed grid slab highlighting its ribbed structure and voided design (Harish et al. 2017)\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/1a6c6fd78f47845f9043174f.png"},{"id":79104780,"identity":"2e3affc7-f3d6-453d-b28c-debe88e65b92","added_by":"auto","created_at":"2025-03-24 13:04:24","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":43485,"visible":true,"origin":"","legend":"\u003cp\u003eFlow chart for methodology\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/34d6fa4b6b08421cfbb278a0.png"},{"id":79104782,"identity":"e991d128-6702-475e-9320-3da25f869aa1","added_by":"auto","created_at":"2025-03-24 13:04:24","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":92523,"visible":true,"origin":"","legend":"\u003cp\u003eFinite element models of the studied building plans: a. Symmetric (HCB), b. Single-axis symmetric (TCB), and c. Asymmetric (LCB) configurations for conventional slabs; d. Symmetric (HGB), e. Single-axis symmetric (TGB), and f. Asymmetric (LGB) configurations for grid slabs.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/ca50846d2cb3188b47916b94.png"},{"id":79105628,"identity":"a7bd18cb-a250-4bb6-95d1-f21d10b22226","added_by":"auto","created_at":"2025-03-24 13:12:24","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":271419,"visible":true,"origin":"","legend":"\u003cp\u003eFinite element models of the studied building elevations: a. Symmetric (HCB), b. Single-axis symmetric (TCB), and c. Asymmetric (LCB) configurations for conventional slabs; d. Symmetric (HGB), e. Single-axis symmetric (TGB), and f. Asymmetric (LGB) configurations for grid slabs.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/cdad8dcd4cd05b4e0c2d80ba.png"},{"id":79107429,"identity":"9393b477-6f40-4f85-9276-c8b1b0f04150","added_by":"auto","created_at":"2025-03-24 13:36:24","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":24411,"visible":true,"origin":"","legend":"\u003cp\u003eSlab deflection under different parametric variations\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/26295255050d7d588911a703.png"},{"id":79107125,"identity":"39ba2674-9619-4379-9b7f-d35633e9493c","added_by":"auto","created_at":"2025-03-24 13:28:24","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":12290,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of slab deflection between optimized grid slab and conventional slab\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/82b3bcc9bdece567f849b14a.png"},{"id":79104784,"identity":"fa416c79-0566-4340-8422-103ab196e8d3","added_by":"auto","created_at":"2025-03-24 13:04:24","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":26483,"visible":true,"origin":"","legend":"\u003cp\u003eTop shell stress developed in grid slab under parametric variation\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/12e30e33ea8c8d5d326a458d.png"},{"id":79104792,"identity":"b18ae21a-ebc0-4fdb-9f77-cd4bc2e63b45","added_by":"auto","created_at":"2025-03-24 13:04:25","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":24862,"visible":true,"origin":"","legend":"\u003cp\u003eBottom shell stress developed in grid slab under parametric variation\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/daa5f82955677b54490b5450.png"},{"id":79104795,"identity":"91176ecf-aa72-4a0b-87e9-8340303a8077","added_by":"auto","created_at":"2025-03-24 13:04:25","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":13062,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of shell stress between optimized grid slab and conventional slab\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/982bf4b213ff59782a1247b1.png"},{"id":79105634,"identity":"b216e8d4-5157-472a-8e12-3b10e15d88d2","added_by":"auto","created_at":"2025-03-24 13:12:25","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":29546,"visible":true,"origin":"","legend":"\u003cp\u003eBase Shear of buildings in (a) X-direction (b) Y-direction\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/e02feeb80b8fbd31ca04965c.png"},{"id":79105894,"identity":"c17fc5a1-b47f-4d26-a56d-e17852fe0cef","added_by":"auto","created_at":"2025-03-24 13:20:24","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":18278,"visible":true,"origin":"","legend":"\u003cp\u003eModel Time Period of Building for First Fundamental Mode\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/b36cb096ed65cc17df1c5f7b.png"},{"id":79104797,"identity":"fd3b1db9-6fe9-4d29-bb7c-22926bb51fad","added_by":"auto","created_at":"2025-03-24 13:04:25","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":94090,"visible":true,"origin":"","legend":"\u003cp\u003eInter-Storey displacement of different models (a) X-direction response (b) Y-direction response\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/10bed3eb74d8d41d89d35acc.png"},{"id":79104794,"identity":"e175cdc8-9c3e-4665-ab91-6c5061544316","added_by":"auto","created_at":"2025-03-24 13:04:25","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":69727,"visible":true,"origin":"","legend":"\u003cp\u003eInter-Storey drift ratio (a) X-direction response (b) Y-direction response\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/e976bdfa3873b6076f154698.png"},{"id":79104798,"identity":"616eba89-8607-414d-ae3b-9eec6e9e7741","added_by":"auto","created_at":"2025-03-24 13:04:25","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":24512,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum Torsional irregularity ratio for various models\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/1209d845959ccadaa62aab48.png"},{"id":79105633,"identity":"4033d7c8-367c-4b28-87bf-a01546d4cf60","added_by":"auto","created_at":"2025-03-24 13:12:25","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":57006,"visible":true,"origin":"","legend":"\u003cp\u003eTorsional Diaphragm Rotation (a) X-direction response (b) Y-direction response\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/3124dcb0f3cc5531c2b1af81.png"},{"id":83067985,"identity":"7cf719a1-088f-492a-a861-c11e7da7e80e","added_by":"auto","created_at":"2025-05-19 16:09:00","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1616943,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/049f272e-8f0a-49c2-a7e2-6c53b7c1fbd4.pdf"},{"id":79104779,"identity":"d42964d5-dbd5-4052-bc98-c538642976d0","added_by":"auto","created_at":"2025-03-24 13:04:24","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":48495,"visible":true,"origin":"","legend":"","description":"","filename":"Reviewercommentandadjustment.docx","url":"https://assets-eu.researchsquare.com/files/rs-5572077/v1/7973325b4e0d50aad6ecbeff.docx"}],"financialInterests":"","formattedTitle":"Structural Performance of Symmetric and Asymmetric Plan Irregular Building Structures: A Comparative Analysis of Conventional and Grid Slab Systems","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe evolution of architectural and structural design in modern construction has been driven by the need to balance functionality, cost-efficiency, resilience and sustainability\u0026nbsp;(Szolomicki and Golasz-Szolomicka 2019; Simona et al. 2022; Ilgın 2024). As urban spaces become increasingly complex, buildings are often designed to meet diverse site-specific needs, aesthetic goals, and practical requirements, leading to deviations from regular, symmetric layouts. As buildings evolve to accommodate complex designs and specific functions, they often feature discontinuities in geometry, mass, or stiffness distribution, which can significantly affect how the structure responds to lateral forces\u0026nbsp;(Naveen E et al. 2019). When the center of mass does not coincide with the center of stiffness, eccentricities develop, inducing torsional effects and increasing the potential for structural damage. These challenges are particularly prominent in irregular buildings, which may have uneven load distribution due to irregular floor plans or variations in structural elements resulting in increased displacements and torsional effects that significantly influence the structure\u0026rsquo;s response, particularly under seismic forces (\u0026Ouml;zmen and \u0026Uuml;nay 2007; Gokdemir et al. 2013). These plan irregularities, whether symmetric or asymmetric, introduce unique challenges for structural performance, particularly under dynamic loads, such as those generated by seismic events\u0026nbsp;(Keertan et al. 2024; Vielma-Quintero et al. 2024). Structural pathologies, such as weak beam-column connections, out-of-plane failures of infill panels, and torsional effects due to mass eccentricity, play a critical role in causing localized and widespread damage. As seismic forces propagate through these structures, areas where load paths are disrupted or elements are poorly connected tend to experience more severe damage. Furthermore, outdated seismic codes and insufficient detailing of structural components often fail to prevent such failures, highlighting the need for updated standards and careful consideration of building design to mitigate risks. The progressive nature of seismic damage, particularly in multi-story buildings, underscores the importance of thorough assessments to better understand and prevent such vulnerabilities in future construction (Nascimbene 2024).\u003c/p\u003e\n\u003cp\u003eThe selection of a building plan configuration plays a vital role in seismic-resistant structural design. In real-world scenarios, perfectly regular structures are rare, and the nature of structural irregularities is challenging to define precisely (Wood L. 1992). Research confirms that irregular buildings experience more damage than their regular counterparts, highlighting the importance of studying and imposing restrictions on irregular structures to prevent abrupt changes in geometry, mass, load-paths and stiffness (Haque et al. 2016). The presence of asymmetries plan in a structure often results in imbalance, leading to significant displacement amplification and concentrated forces within resisting elements. Consequently, buildings with plan irregularities are more susceptible to damage during earthquakes due to the complex interactions between translations and rotations (Abdel Raheem et al. 2018). This imbalance can also results in severe damages and, in some cases, the collapse of structures (Patil et al. 2017). Despite the various challenges posed by irregular buildings, they cannot be disregarded entirely due to modern urban layouts and current construction practices. Proper classification and analysis of irregular buildings are essential to address their unique challenges effectively. One critical aspect in this process is the axis of symmetry, which significantly influences the dynamic response of a building under seismic forces. By examining irregular buildings based on their axis of symmetry, they can be categorized into symmetric and asymmetric plan irregular structures. As illustrated in Fig. 1, the axis of symmetry serves as a defining factor in distinguishing the response characteristics of symmetric and asymmetric irregular structures. Plan irregular structures can be classified based on the presence or absence of symmetry in their layout. Symmetric plan irregular structures exhibit irregularities that are evenly distributed around a central axis, maintaining balance in their overall geometry. In contrast, single-axis symmetric plan irregular structures display symmetry along only one axis, with irregularities confined to one direction while the other remains balanced. While asymmetric plan irregular structures are characterized by unevenly distributed irregularities with no discernible axis of symmetry, leading to significant imbalances in their structural configuration and dynamic behavior (Pandian et al. 2024). This is particularly critical in seismically active regions, where irregularities significantly increase the susceptibility to damage, as observed in various earthquake damage histories (Alavi and Rao 2013). Consequently, the design of irregular building structures necessitates planning to address these inherent vulnerabilities. These deviations from a regular, symmetric layout in a building\u0026rsquo;s horizontal projection, often caused by torsional irregularity, re-entrant corner, diaphragm discontinuity, out of plane offsets, non-parallel systems etc. and current seismic design practices focus on mitigating risks associated with irregularities by employing advanced analysis techniques and incorporating structural systems that minimize the adverse effects of imbalances (Ravikumar et al. 2012). These practices aim to enhance resilience, ensuring that irregular structures can effectively respond to seismic demands and reduce the likelihood of severe damage or collapse (IS 1893 (Part-1) 2016; NBC 105 2020).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn addition to irregularities, urban densification has also led to the widespread adoption of high-rise structures as a solution to accommodate growing populations within limited urban spaces. They present unique engineering challenges due to their significant slenderness and extended vibration periods, making them highly susceptible to dynamic forces, particularly seismic and wind loads (Li et al. 2006; Ilgın 2023). Their structural stability depends on multiple factors, including mass distribution, stiffness, and the efficiency of lateral load-resisting systems. Several prior studies have conducted to examine the dynamic behavior of high-rise structures under seismic conditions, emphasizing the critical role of structural configurations in ensuring overall stability. In seismically active regions, integrating considerations of plan irregularity into the design of high-rise buildings is essential for maintaining structural integrity, resilience occupant safety, and serviceability (Jia et al. 2022; Blasi et al. 2024). Extensive research has also been conducted on the stability of irregular high-rise buildings, highlighting the effectiveness of various vertical structural elements, such as shear walls, outriggers, bracing systems, and core walls, in resisting lateral forces (Lu et al. 2013; Brunesi et al. 2016b; Iman 2018). Mazzotta et al. (2017) \u0026nbsp; investigated the seismic performance of 180-meter and 300-meter-tall steel buildings equipped with outrigger and bracing systems. Their findings demonstrated the effectiveness of these systems in limiting drift and displacement but also revealed that they induce high floor accelerations, which could compromise non-structural components, equipment, furnishings, and occupant safety. Similarly, Brunesi et al. (2016a) conducted a seismic analysis of high-rise mega-braced frame core buildings, obtaining comparable results that underscore the trade-offs associated with these structural systems. Brunesi and Nascimbene (2014) investigates the contribution of secondary frame systems to the seismic performance of high-rise buildings, demonstrating their potential to significantly enhance the structural response by stiffening and strengthening the building and recommend the study of redistribution capabilities of detailed floor slab system on seismic performance of building structures. While lateral force-resisting elements such as bracing and shear wall systems remain fundamental in high-rise structures, recent studies have also explored the influence of slab systems on seismic response. Floor slabs contribute to the lateral stiffness and overall dynamic behavior of buildings, particularly in asymmetric structures, where irregular mass and stiffness distributions can lead to amplified deformations (Latha and Pratibha 2021). To determine the response of high-rise buildings to seismic loads, dynamic analysis techniques such as response spectrum analysis are used. This method incorporates ground acceleration records to develop response spectra based on seismic loads and site-specific parameters (Sujith and Kumar 2023). The eigenmodes derived from dynamic analysis provide insight into how mass and stiffness distribution affect overall seismic performance (Guleria 2014). By capturing the interplay of various vibrational modes, this approach enables precise predictions of structural responses (Sivakumar et al. 2023), facilitating the optimization of structural systems to enhance resilience against seismic events.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eConventional slab design practices typically involve the use of reinforced concrete slabs, which are horizontal structural elements essential for supporting floors, ceilings, and roofs in a building (Jabir et al. 2021). These slabs distribute the loads, such as live and dead loads, from the structure above to the beams, columns, or walls below (Gupta and Singh 2020; Yılmaz et al. 2022). The design of conventional slabs comprising up to two-thirds of the total volume, are commonly used and its selection is influenced by factors such as span length, load-carrying capacity, shear stress distribution, bending moments and the intended use of the building (Kayastha and Debbarma 2019). The most common types of conventional slabs are one-way slabs and two-way slabs as shown in Fig. 2. One-way slabs are supported by beams on two opposite sides and bend in one direction, making them ideal for buildings with smaller spans or where loads are concentrated in one direction. Two-way slabs, on the other hand, are supported on all four sides, bending in two perpendicular directions, and are more suitable for buildings with square or nearly square layouts, allowing for better load distribution (Hoffman et al. 1998a, b). The thickness of conventional slabs is determined by several factors, including the span length, the loads they need to support, and the deflection limits specified by design codes (Gardner 2011). For residential buildings, slab thickness typically ranges from 100 mm to 150 mm, while in commercial or industrial buildings, slabs may be thicker, ranging from 200 mm to 300 mm, to accommodate heavier loads. Design codes also provide deflection limits to ensure the structural integrity and serviceability of slabs. As architectural requirements evolve, slab spans often increase, leading to challenges in meeting deflection criteria. In the case of very large-span structures, using conventional solid slabs, which can be either one-way or two-way, often necessitates a proportional increase in thickness to control excessive deflection (Tiwari et al. 2025). However, increasing slab thickness in large-span structures has a cascade effect. Since slabs typically consume a significant amount of concrete in building construction, increasing the thickness not only increases the concrete volume but also results in a higher dead load. This, in turn, increases the size of beams, columns, and foundations, making the structure less efficient and more expensive (Sagadevan and Rao 2021). The additional weight of the structure, driven by the increased thickness, can make the building design less economical. Therefore, while conventional slabs may be effective for smaller spans, they are often impractical for large spans, where alternative solutions must be explored to ensure both functionality, cost-effectiveness and sustainability in the design of the building (Ibrahim et al. 2013). Increasing material consumption in construction leads to greater energy use and higher carbon emissions, straining resources and conflicting with global sustainability goals. Thus, the environmental cost of inefficient design practices must be carefully considered in the context of sustainability (Heeren et al. 2015; Sanglier Contreras et al. 2022). This limitation of conventional slabs, particularly in large-span structures, underscores the need for alternative slab systems, such as grid slabs, which can effectively address deflection concerns while optimizing the overall material use and reducing the impact on the building\u0026rsquo;s structural efficiency and sustainability.\u003c/p\u003e\n\u003cp\u003eOn the other hand, grid slabs are innovative structural systems characterized by a thin flat plate supported by grid beams spanning in two directions, resting on main beams at the boundary. Designed for cost-effective construction over long spans, often reaching up to 20 meters, these slabs have gained popularity in modern construction for their ability to reduce dead weight and improve lateral load distribution\u0026nbsp;(Alraie and Barik 2017). Distinguished by large square voids between ribs, grid slabs combine structural efficiency and material optimization as depicted in\u0026nbsp;Fig. 3. This design minimizes self-weight by strategically removing concrete below the neutral axis, a process facilitated by using molds like dirt pots during casting\u0026nbsp;(Nithyambigai et al. 2021). The resulting ribbed structure is lighter and stiffer than traditional solid slabs, allowing for substantial reductions in dead load, thinner slabs, and improved load distribution. They exhibit significant advantages in construction projects requiring large spans, such as parking areas, halls, ramps, auditoriums, and amphitheaters, where intermediate columns are undesirable\u0026nbsp;(Nishanth et al. 2020). Their lighter weight and superior structural performance reduce the risk of excessive deflection and cracking often associated with conventional solid slabs over large spans\u0026nbsp;(Olawale and Ayodele 2014; Sancheti et al. 2021). These characteristics make grid slabs particularly efficient in seismic zones, as their reduced weight positively impacts the seismic behavior of structures while also lowering construction costs and promotes sustainability. By incorporating steel bar reinforcement, grid slabs enhance elasticity and durability, further ensuring structural reliability. Architecturally, grid slabs provide flexibility and are aesthetically pleasing, making them suitable for diverse applications. However, their hybrid behavior\u0026mdash;combining features of plate slabs, beam grillages, and shell structures\u0026mdash;presents analytical challenges, particularly under dynamic loading conditions\u0026nbsp;(Thakor and Patel 2019). Despite these complexities, their benefits, including higher stiffness, reduced material usage, and efficient load transfer, make them a preferred choice in contemporary construction\u0026nbsp;(Abdul-Wahab and Khalil 2000; Samson O. et al. 2023).\u0026nbsp;Overall, grid slabs exemplify a balance between functionality, cost-efficiency, resilience and sustainability addressing the demand for sustainable and robust construction solutions in modern architectural designs.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe design and performance of grid slabs are highly influenced by various parametric factors, with span of grid ribs, spacing between grid ribs and the depth-to-breadth (d/b) ratio of the ribs being the most critical parameters. The spacing of the grid ribs significantly impacts the structural behavior, as closer spacing leads to more frequent load distribution, improving stiffness and reducing deflections, though it may increase material usage and construction costs. On the other hand, wider spacing may reduce material costs but could lead to larger deflections and decreased load-carrying capacity, requiring an optimal balance. Similarly, the depth-to-breadth ratio of grid ribs affects their resistance to bending and shear forces. A higher d/b ratio increases stiffness and bending resistance, but also results in more material usage, making it essential to determine an efficient ratio that optimizes both structural performance and cost. Several studies have investigated the impact of these parameters on grid slab behavior. For instance, Yoosaf K.T. et al. (2013) explored how the spacing of transverse beams and the span-to-depth ratio influence deflections and bending moments in grid floor slabs, suggesting that optimizing these parameters can improve performance while minimizing material use. Similarly, Halkude and Mahamuni (2014) examined the effect of the grid beam depth on peripheral beams, noting that reducing the depth of grid beams could optimize bending moments and shear forces in peripheral beams, particularly when paired with appropriate spacing. Tripathi et al. (2021) focused on grid size variations and their effect on stress parameters, concluding that smaller grid sizes lead to increased bending moments and shear forces, while square grids provided more uniform stress distribution similar to two-way slabs. Furthermore, Prasad et al. (2005) conducted an analytical study on waffle slabs, proposing optimal rib spacing, depth, and width for improved load distribution and structural efficiency without requiring additional shear reinforcement. Building upon these findings, our research focuses on investigating the influence of spacing between grid ribs and the depth-to-breadth ratio on the performance of grid slabs, particularly in terms of load distribution, deflection, and bending resistance. By varying these parameters, we aim to identify optimal configurations that provide a balance between structural efficiency and cost-effectiveness, especially for large-span structures such as auditoriums, parking areas, and public halls, where intermediate columns are undesirable.\u003c/p\u003e\n\u003cp\u003eIncreased complexities in structures often lead to higher vulnerabilities during seismic events, resulting in more severe structural failures. These failures necessitate extensive retrofitting and rehabilitation, which in turn escalate energy consumption, financial costs, and structural demands (Cavalieri et al. 2023). Therefore, when irregularities cannot be avoided, it is crucial to assess the optimal configuration of the structure. Optimization not only mitigates seismic risks but also makes the rehabilitation process more cost-effective and energy-efficient, ensuring structural integrity during such events (Jebelli et al. 2022; Demir 2025). While seismic performance remains a critical concern in structural design, the increasing environmental impact of construction cannot be overlooked (Berr\u0026oacute;n Ferrer 2003; Cavalieri et al. 2023). The industry\u0026rsquo;s intensive resource consumption and high carbon emissions contribute significantly to the global climate crisis, exacerbated by unchecked industrialization. Structural components such as slabs, beams, and lateral load-resisting systems, structural configurations play a crucial role in ensuring structural integrity, yet they are also major contributors to buildings\u0026rsquo; carbon footprints (Paik and Na 2019; Auburtin et al. 2023). Concrete, particularly due to cement production, remains one of the highest emitters of CO\u003csub\u003e2\u003c/sub\u003e, underscoring the challenge of optimizing structural systems without compromising performance (Bohorquez et al. 2024).\u003c/p\u003e\n\u003cp\u003eThe primary structural elements such as columns, beams, shear walls and slabs play a critical role in managing the loads and stresses generated by irregularities (Balendra 1993; Hussain et al. 2024). However, the performance of slabs, often seen as secondary structural elements, is sometimes overlooked in such buildings. In fact, the role of slabs in ensuring stability and load distribution is vital, particularly in irregular buildings where uneven geometries, load paths and eccentricities can affect the overall behavior of the structure (Zhang 2024). The choice of slab system\u0026mdash;whether it be conventional slabs, flat slabs, or grid slabs\u0026mdash;becomes integral to addressing the challenges posed by complex architectural layouts. These slab systems not only help distribute loads efficiently but also contribute to the overall stiffness and stability of the building, ensuring it performs effectively even under dynamic and lateral forces (Pradhana et al. 2019; Pang et al. 2021). The interaction between high-rise structures and slab types in buildings with plan irregularities is a critical consideration in structural engineering. By addressing the challenges posed by plan irregularities and optimizing structural systems beyond conventional approaches, engineers can design high-rise structures that are both resilient, safe and sustainable, effectively responding to dynamic forces in seismically active regions. In the study of the structural performance of irregular building structures with different slab systems, there remains a significant opportunity to explore the combined influence of grid slabs and plan irregularities of high-rise buildings. Existing studies have primarily focused on two separate areas: the analysis of irregular buildings using conventional slabs and the parametric variations of grid slab systems. However, limited attention has been given to how the interaction between slab type\u0026mdash;particularly grid slabs with varying parameters such as depth-to-breadth ratio and rib spacing\u0026mdash;and the irregularities in building plans affects the overall structural performance. Previous work has largely concentrated on either the dynamic response of buildings with conventional slabs or the performance of grid slabs in isolation, with minimal research on their combined effects. This issue is especially crucial in the context of seismic performance, as the dynamic response of irregular buildings depends on both the configuration of the building and the slab system in use. Despite the extensive study of grid slab behavior, the impact of optimized grid slab parameters, such as rib spacing and depth, on the performance of irregular buildings has not been fully explored. The interplay between these slab configurations and the seismic response of buildings with plan irregularities, such as torsional effects and stability under dynamic loading, has yet to be adequately addressed. By focusing on the relationship between these two elements\u0026mdash;irregular building structures and grid slab systems\u0026mdash;this study aims to advance understanding in this area. It seeks to investigate how varying parameters of grid slabs, such as rib spacing and depth-to-breadth ratio, can influence the overall structural performance of both symmetric and asymmetric plan irregular buildings. This work will provide valuable insights into optimizing grid slab configurations to enhance the stability and cost-efficiency of buildings in seismic zones, ultimately contributing to more effective design strategies for irregular structures. The findings will help bridge the gap between slab system design and irregular building performance, an area that remains under-explored in current literature.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cp\u003eIn this study, G+9 buildings each with a floor-to-floor height of 3.5 meters, and incorporates different plan irregularities were analyzed to evaluate the performance of optimized grid slabs in comparison to conventional slabs. The grid slab optimization was conducted based on deflection criteria and shell stress. Various configurations were examined by varying the depth-to-breadth (d/b) ratio of ribs from 1 to 5 and adjusting rib spacing between 1000 mm and 4000 mm to identify the most effective design for enhanced structural efficiency and seismic performance. Using ETABS version 20 (Computers and Structures, Inc. 2022),\u0026nbsp;models of the buildings were created\u0026mdash;one incorporating the optimized grid slab and another with a conventional slab.\u0026nbsp;Both models were analyzed under seismic conditions using the Response Spectrum Method. Key parameters, such as base shear, modal time period, interstorey displacement, interstorey drift, torsional irregularities, and torsional diaphragm rotations, were evaluated. This comparative analysis provided insights into the structural efficiency and seismic performance of the two slab systems, with results aiding in the selection of the most effective slab type for similar high-rise structures. The methodology is designed to ensure the study\u0026rsquo;s replicability and to provide clear insights into the building design, modeling, analysis, and optimization steps undertaken. A flowchart of the methodology is provided in \u003cstrong\u003eFig. 4\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003eThe building models for the study include H-shaped, T-shaped, and L-shaped configurations, representing symmetric, single axis symmetric and asymmetric buildings, respectively. H-shaped buildings were modeled as symmetric in both axes, while T-shaped and L-shaped buildings were considered asymmetric about one and both axes, respectively. Each building was modeled with both conventional slabs and grid slab systems. The total slab area for all models remained constant, ensuring consistency in comparison. The buildings were modeled with five spans of 12 meters in both the X and Y directions, with slab configurations optimized based on rib depth and spacing. In all models, both conventional and grid slab systems were modeled as rigid diaphragms. The structural parameters and design details of the buildings, including material properties, geometry, and design specifications, are summarized in\u0026nbsp;Table 1. Additionally, the parametric variations of grid rib dimensions are listed to highlight the key design variables.\u003c/p\u003e\n\u003cp\u003eTable 1.\u0026nbsp;Parameters of building\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"542\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eParameters\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eGeneral Description\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eStructural System\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003eSMRF\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eConcrete Grade\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003eM40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eReinforcements\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003eFe 500\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eImportance Factor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eZone Factor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003col start=\"0\"\u003e\n \u003cli\u003e(Zone V)\u003c/li\u003e\n \u003c/ol\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eShape of Building\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003eH, T and L-shaped\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eSlab Thickness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003e100 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eFloor to Floor Height\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003e3.5 m\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eWidth of Grid Ribs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003e125 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eParametric Variation:\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eDepth of Grid Ribs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003e250 mm, 375 mm, 500 mm, 625 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 145px;\"\u003e\n \u003cp\u003eSpacing of Grid Ribs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 397px;\"\u003e\n \u003cp\u003e1000 mm, 1500 mm, 2000 mm, 3000mm, 4000 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe loading conditions applied to the buildings in this study were designed to represent realistic structural loads, including live loads, floor finishes, and roof loads. These loads are crucial for assessing the building\u0026apos;s performance under both static and dynamic conditions, particularly in the context of seismic analysis. The specifics of the loading conditions, as summarized in Table 2, were incorporated into the building models to simulate real-world conditions and ensure the accuracy of the analysis. These applied loads are essential for evaluating the building\u0026apos;s ability to resist both gravity loads and seismic forces, ultimately guiding the design to enhance structural safety and performance.\u003c/p\u003e\n\u003cp\u003eTable 2.\u0026nbsp;Loading on building\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"511\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 202px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDescription\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 308px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eLoads\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 202px;\"\u003e\n \u003cp\u003eLive Load Floor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 308px;\"\u003e\n \u003cp\u003e4 kN/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 202px;\"\u003e\n \u003cp\u003eLive Load Roof\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 308px;\"\u003e\n \u003cp\u003e1.5 kN/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 202px;\"\u003e\n \u003cp\u003eFloor Finish\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 308px;\"\u003e\n \u003cp\u003e1 kN/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe building models were created using ETABS software that caters to multi-story building analysis and design (Computers and Structures, Inc. 2022), and finite element analysis was conducted to evaluate dynamic responses under seismic loading. The models of the buildings, incorporating both conventional and grid slab systems, are represented in Fig. 5 and Fig. 6. In these figures, H-shaped, T-shaped, and L-shaped buildings with conventional slab systems are denoted as HCB, TCB, and LCB, while those with grid slab systems are denoted as HGB, TGB, and LGB. The seismic performance of the buildings was evaluated through response spectrum analysis.\u003c/p\u003e\n\u003cp\u003eThe choice of a G+9 story building is based on its relevance as a mid-rise structure commonly found in seismic-prone urban areas. The study examines buildings with different plan irregularities (H, T, and L shapes) to represent typical real-world challenges. These buildings were selected for their variety in symmetry and asymmetry, which play a crucial role in the seismic response. The grid slab system was included in the study to assess its effectiveness in improving the seismic performance of the buildings, particularly in reducing deflections and enhancing torsional stability. The study aims to evaluate the impact of the grid slab system on overall building performance, focusing on the optimization of rib depth and spacing for enhanced structural resilience.\u003c/p\u003e"},{"header":"3. Results And Discussion","content":"\u003cp\u003eThis study analyzes the d/b ratio and spacing of grid ribs to optimize their configuration, focusing on deflection and other local factors. The building\u0026apos;s structural response was assessed through linear static and dynamic evaluations. Key parameters such as torsional irregularity, modal time period, inter-storey displacement, inter-storey drift ratio, and maximum diaphragm rotations were examined.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e3.1. Slab Deflection\u003c/h2\u003e\n\u003cp\u003eBoth conventional and grid slabs were analyzed under gravity loading to evaluate their deflection behavior. The study, extending beyond IS 456:2000 recommendations, provided valuable insights into the influence of depth-to-breadth (d/b) ratios and rib spacings on structural performance. For a 12 m span with a permissible deflection of 48 mm (span/250) (IS 456 2000), deflection at a d/b ratio of 4 remained within permissible limits for rib spacings of 1000 mm (43.59 mm) and 1500 mm (45.93 mm). However, increasing the rib spacing to 2000 mm and 3000 mm results in deflections of 48.7 mm and 54.28 mm, respectively, thereby exceeding the allowable limit. Larger rib spacings compromise load distribution and exacerbate bending and shear effects and closely spaced ribs increase the reinforcement ratio which ultimately increases slab strength (Silva et al. 2020). Additionally, while lower depth-to-breadth (d/b) ratios of 2 and 3 may provide sufficient compressive strength, they fail to offer the necessary effective depth to resist bending and shear forces. Concrete and steel have low strain rates due to the premature failure of the ribs by shearing (Sacramento et al. 2018). As the grid thickness increases, the primary mode of failure transitions from pure flexural failure to a combined action of moment and shear, indicating that greater grid thickness significantly enhances the beam\u0026rsquo;s flexural bearing capacity while also influencing its shear resistance (Li et al. 2024). Moreover, the depth of grid ribs is governed by the effective span; for larger span structures, greater rib depth is essential to ensure adequate resistance to deflection (Fahmi and Saber 2020; Adamu et al. 2024). Insufficient depth compromises the slab\u0026rsquo;s ability to distribute loads effectively, ultimately leading to compromised structural performance. On the other hand, increasing the d/b ratio to 5 significantly improved structural performance. For a rib spacing of 2000 mm, deflection was reduced to 40.13 mm, well within permissible limits, establishing this configuration as both efficient and reliable. Although a rib spacing of 3000 mm with a d/b ratio of 5 resulted in a deflection of 43.62 mm, which is within the permissible limit, the design does not account for accidental loadings (Prasad et al. 2005). Considering these factors, the rib spacing of 2000 mm with a d/b ratio of 5 is preferred, offering a more robust and safe solution (Fig. 7).\u003c/p\u003e\n\u003cp\u003eFig. 8. illustrates the comparison of deflection between the optimized grid slab and the conventional slab. The conventional slab exhibited a deflection of 139.14 mm, while the optimized grid slab with a rib spacing of 2000 mm and a d/b ratio of 5 showed a deflection of 40.13 mm. This represents a substantial reduction of approximately 71.1% in deflection, highlighting the structural benefits of the grid slab in terms of load redistribution and stress mitigation.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e3.2. Shell Stress\u003c/h2\u003e\n\u003cp\u003eIn grid-reinforced slabs, shell stresses arise due to the combined effects of bending and in-plane forces induced by external loads and boundary conditions (Ibrahim et al. 2011; Guo et al. 2017; Jain and Hussain 2024). These stresses can be categorized into top shell stresses (compression in the top fibers) and bottom shell stresses (tension in the bottom fibers)(Schwetz et al. 2014). The spacing of grid ribs significantly influences the distribution and magnitude of these stresses, as they provide additional stiffness and redistribute forces across the shell (Nithyambigai et al. 2021).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe analysis reveals that a rib spacing of 3000 mm with a d/b ratio of 5 results in a bottom shell stress of 5.77 MPa and a top shell stress of 10.76 MPa. While this configuration satisfies normal loading requirements, it does not fully account for potential accidental loadings, such as point impact or unexpected increases in live load. These additional loads could lead to higher stresses or excessive deflections, potentially compromising the long-term structural performance. The top shell stress under parametric variations is shown in Fig. 9, and the bottom shell stress is presented in Fig. 10. In comparison, a rib spacing of 2000 mm with a d/b ratio of 5 results in a bottom shell stress of 5.81 MPa and a top shell stress of 11.34 MPa, offering enhanced robustness against accidental loadings. The increase in bottom shell stress is only 0.7%, while the top shell stress increases by approximately 5.4%. These minor increases in stress are outweighed by the significant improvement in structural stiffness, ensuring better resistance to accidental load scenarios. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWhen compared to the conventional slab (rib spacing = 0 mm), the 2000 mm rib spacing with a d/b ratio of 5 achieves a 74.2% reduction in bottom shell stress (from 22.48 MPa to 5.81 MPa) and a 76.6% reduction in top shell stress (from 48.41 MPa to 11.34 MPa). These reductions emphasize the efficiency of ribs of the grid slabs in redistributing stresses and optimizing overall structural performance. Although the 3000 mm rib spacing configuration results in the lowest recorded stresses (5.77 MPa for bottom shell stress and 10.76 MPa for top shell stress), the design with 2000 mm rib spacing is preferred. It offers a more robust and safer solution under both standard and accidental loading conditions, ensuring long-term structural integrity. Thus, the 2000 mm rib spacing with a d/b ratio of 5 is the optimal configuration, providing a balance between reduced stresses, improved structural robustness, and enhanced safety against accidental loading. The comparison of shell stresses between the conventional slab system and the grid slab system with the optimum rib parameters is depicted in Fig. 11.\u003c/p\u003e\n\u003ch2\u003e3.3. Base Shear\u003c/h2\u003e\n\u003cp\u003eIn this study, the base shear values for H-shaped, L-shaped, and T-shaped buildings were analyzed to compare the seismic performance of grid slabs and conventional slabs in both the X and Y directions. The results consistently show that grid slabs exhibit higher base shear values compared to conventional slabs across all building configurations and load cases (RSX, RSY) ash shown in Fig.12. Base shear reflects the total horizontal force a structure is expected to resist during seismic events, which is influenced by factors such as mass, stiffness, and the building\u0026apos;s fundamental period\u0026nbsp;(Khan 2013).\u003c/p\u003e\n\u003cp\u003eIn the X-direction, the base shear values for buildings with grid slabs were consistently higher than those with conventional slabs. The H-shaped building exhibited the highest base shear, with a value of 15170.42 kN for grid slabs, representing a 20.89% increase over the conventional slab value of 12549.14 kN. The L-shaped building showed a 22.75% increase in base shear, with a value of 14037.46 kN for grid slabs compared to 11435.83 kN for conventional slabs, while the T-shaped building experienced a 21.80% increase, with grid slabs yielding a base shear of 14559.78 kN, higher than the 11953.70 kN observed for conventional slabs.\u003c/p\u003e\n\u003cp\u003eIn the Y-direction, grid slabs again provided higher base shear values than conventional slabs. The H-shaped building recorded the highest base shear in this direction as well, with 15965.68 kN for grid slabs, reflecting an 18.45% increase compared to the conventional slab value of 13479.24 kN. \u0026nbsp;The L-shaped building demonstrated a 21.61% increase in base shear, with grid slabs yielding 14569.68 kN compared to 11980.84 kN for conventional slabs, while the T-shaped building showed a 20.42% improvement, with a base shear of 14615.13 kN for grid slabs, in contrast to 12136.33 kN for conventional slabs.\u003c/p\u003e\n\u003cp\u003eWhen comparing the maximum base shear values across both directions, the H-shaped building consistently demonstrated the highest base shear values, with 15170.42 kN in the X-direction and 15965.68 kN in the Y-direction. The T-shaped building exhibited a 4.04% lower base shear in the X-direction (14559.78 kN) and an 8.6% lower value in the Y-direction (14615.13 kN) compared to the H-shaped building. The L-shaped building recorded the lowest values, with 7.45% lower base shear in the X-direction (14037.46 kN) and 9.7% lower in the Y-direction (14569.68 kN) compared to the H-shaped building. These findings align with previous research Pandian et al. (Pandian et al. 2024) which observed that symmetric building configurations, such as square and U-shaped buildings, generally exhibit higher base shear values. In contrast, while the L-shaped building demonstrated lower base shear, there was no significant difference between the base shear values of the L-shaped and T-shaped buildings. Ultimately, symmetric buildings consistently showed higher base shear compared to their asymmetric counterparts\u003c/p\u003e\n\u003ch2\u003e3.4. Modal Time Period\u003c/h2\u003e\n\u003cp\u003eIn seismic design, a structure\u0026apos;s compliance with safety standards relies on its fundamental time period, a key factor influencing the horizontal base shear coefficient. According to IS 1893\u0026nbsp;(IS 1893 (Part-1) 2016), the formula for the fundamental lifespan (T\u003csub\u003ea\u003c/sub\u003e) is given by\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u0026nbsp;T\u003csub\u003ea\u003c/sub\u003e=0.075h\u003csup\u003e0.75\u003c/sup\u003e\u003csub\u003e\u0026nbsp;\u003c/sub\u003e\u003c/em\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; Eq. (1)\u003c/p\u003e\n\u003cp\u003ewhere \u0026apos;h\u0026apos; represents the total building height.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eEmpirical application of this formula resulted in a natural time period of 1.08 seconds. Simultaneously, Fig. 13 displays fundamental time periods based on the first mode shape obtained through finite element analysis providing a comprehensive comparison for seismic assessment. The time period for the 1\u003csup\u003est\u003c/sup\u003e fundamental mode through finite element analysis is HCB (1.969 sec.), HGB (1.945), TCB (1.963 Sec.), TGB (1.956 Sec), LCB (1.986 Sec.), and LGB (1.972 Sec.). The grid slab systems (HGB, TGB, and LGB) demonstrate a clear reduction in the first fundamental period compared to the conventional slab systems (HCB, TCB, and LCB), with HGB exhibiting a decrease of 1.22%, TGB a decrease of 0.36%, and LGB a decrease of 0.71%. This reduction in the time period suggests that grid slab systems may offer a more favorable dynamic response, potentially improving the seismic performance of structures by reducing the oscillatory behavior and enhancing stiffness during dynamic loading.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSignificantly, finite element analysis yielded basic time periods ranging from 1.945 to 1.986 seconds, approximately 80\u0026ndash;83% higher than empirical codal formula results. This stark contrast exposes a substantial flaw in code-based methods, emphasizing their tendency to underestimate building vibration time periods. These inaccuracies, crucial for lateral force procedures, align with previous studies\u0026nbsp;(Khanal and Chaulagain 2020),\u0026nbsp;emphasizing the need for advanced analytical methods. The study contributes to seismic design practices, shedding light on the limitations of traditional empirical approaches. Additionally, in comparing modal times for the first fundamental mode, the L-Shaped Building exhibits longer times than the grid slab system building, which, in turn, has shorter time periods than the traditional slab system.\u003c/p\u003e\n\u003ch2\u003e3.5. Inter-Storey Displacement \u003c/h2\u003e\n\u003cp\u003eThe analysis of diverse building types and seismic response methods reveals distinct trends in displacement characteristics. Maximum top storey displacements of models considered were HCB (115.96 mm), HGB (114.09 mm), TCB (136.07 mm), TGB (124.57 mm), LCB (143.83 mm) and LGB (138.08 mm). L-shaped buildings exhibited higher displacement than their H-shaped and T-shaped counterparts. Symmetric buildings, such as those with H-shaped configurations and conventional or grid slab systems, displayed similar maximum top storey displacements. However, for T-shaped and L-shaped buildings, the grid slab system resulted in less displacement compared to conventional slab systems (Fig.14). Notably, the grid slab system emerged as more efficient in reducing maximum top storey displacement, emphasizing its potential advantages in enhancing structural resilience during seismic events (Latha and Pratibha 2021). The choice of building shape and slab system, specifically favoring the grid slab system, plays a pivotal role in seismic analysis, contributing to optimized structural performance and reduced displacement. The incorporation of a grid floor system has demonstrated notable advantages in mitigating maximum displacements across different building configurations. In particular, the inclusion of grid floors resulted in a reduction of maximum displacement by 1.63% for H-shaped buildings, 4.17% for L-shaped buildings, and 9.23% for T-shaped buildings. The percentages of reduction signify a tangible improvement in the building\u0026apos;s ability to withstand seismic forces, emphasizing the grid floor\u0026apos;s role in contributing to a sound and resilient structural design.\u003c/p\u003e\n\u003ch2\u003e3.6. Inter-Storey Drift Ratio\u003c/h2\u003e\n\u003cp\u003eThe evaluation of the inter-storey drift ratio, a crucial parameter in seismic design, revealed significant variations among different building shapes. L-shaped structures consistently exhibited the highest drift ratios, contrasting with H-shaped structures which consistently showed the lowest (Fig.15). The accuracy of calculating inter-storey drift ratios was found to be superior in response spectrum analysis compared to static analysis. Notably, buildings with pronounced irregularities displayed higher deformations, particularly in regions characterized by elevated seismic activity, validating earlier research findings. Asymmetrical buildings, particularly those with asymmetry along a specific axis, demonstrated greater displacement along their respective axes\u0026nbsp;(Naveen E et al. 2019).\u0026nbsp;Interestingly, symmetric buildings constructed with grid slab and conventional slab systems demonstrated identical maximum inter-storey drift ratios, emphasizing the potential equivalence of these systems in controlling drift. The maximum inter-storey drift ratios for the models considered were HCB (0.00163), HGB (0.00153), TCB (0.00188), TGB (0.00165), LCB (0.00198) and LGB (0.00181).\u003c/p\u003e\n\u003cp\u003eHowever, a pivotal discovery emerged when comparing asymmetric building designs. The maximum inter-storey drift ratio in L-shaped structures with grid slab and conventional slab systems was 21% and 25% higher, respectively, than that of H-shaped buildings with grid floors. Similarly, T-shaped buildings exhibited 8% and 17% higher maximum inter-storey drift ratios with grid slab and conventional slab systems compared to H-shaped buildings with grid floors. Notably, the inter-storey drift ratio in H-shaped buildings with a conventional slab system closely resembled that of structures with grid floors. Introducing grid floor systems as an alternative to conventional slabs led to a reduction in maximum inter-storey drift ratios: H-shaped buildings by 0.72%, L-shaped buildings by 3.19%, and T-shaped structures by 8.16%. Moreover, it was observed that elastic analysis tends to underestimate storey drift, particularly as the structure reaches nonlinear levels.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e3.7. Torsional irregularity ratio\u003c/h2\u003e\n\u003cp\u003eAccording to IS 1893:2016, a building is considered torsionally irregular if the greatest horizontal displacement of any floor exceeds 1.5 times the minimum horizontal displacement in the opposite direction at the opposite end of the same level. The study notes that the values of equivalent static torsion and maximum dynamic torsion are typically similar, except for irregularly shaped L-shaped structures\u0026nbsp;(Ahmed et al. 2016; Soltani et al. 2018). Torsional irregularities lead to poor seismic performance, causing lateral deflections to increase in the weak direction and decrease in the strong direction during torsion\u0026nbsp;(Gokdemir et al. 2013; Krishnan and Thasleen 2020). The torsional irregularity ratios are as follows: HCB (1.00), HGB (1.00), TCB (1.3), TGB (1.14), LCB (1.52), LGB (1.41). These ratios offer insights into the impact of asymmetricity on torsional behavior.\u003c/p\u003e\n\u003cp\u003eIn H-shaped buildings, the torsional irregularity ratio consistently remains at 1 in both X and Y directions. Maximum torsional irregularity ratio increases with the increase in asymmetricity and reaches TCB (1.3) and TGB (1.14) but within permissible limits. This indicates excellent torsion resistance in both X and Y directions for T-shaped and H-shaped buildings, highlighting their favorable structural characteristics. Contrastingly, L-shaped structures with conventional slab systems exhibit torsional irregularity LCB (1.52) in dynamic studies, challenging the applicability of equivalent static analysis for such structures. The introduction of grid floors in L-shaped buildings restores torsional regularity LGB (1.41), demonstrating the efficacy of grid slabs in mitigating torsional irregularities (Fig. 16). This further accentuates the correlation between asymmetricity and torsional irregularity, as indicated by the observed torsional irregularity ratios. Graphical representations underscore the superior torsional performance of grid slab systems compared to traditional slab systems. The rigidity of L-shaped and T-shaped buildings increases by 30% and 27%, respectively, while the rigidity of H-shaped buildings remains the same when utilizing grid slabs instead of conventional slabs.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e3.8. Torsional Diaphragm Rotation\u003c/h2\u003e\n\u003cp\u003eIn Fig. 17, the graphical representation of torsional diaphragm rotation reveals variations along the building height in both X and Y directions. The observed pattern aligns with \u0026Ouml;zmen et al.\u0026apos;s findings\u0026nbsp;(\u0026Ouml;zmen et al. 2014)\u003cstrong\u003e,\u003c/strong\u003e peaking at the top level. H-shaped structures exhibit minimal torsional rotation in both X and Y directions, while T-shaped buildings display greater rotation along the X-direction and negligible rotation along the Y-direction. In contrast, L-shaped buildings, characterized by asymmetry in both axes, exhibit maximum torsional rotation along both axes, with the X-direction rotation surpassing that of the Y-direction. This suggests that buildings symmetric along the considered axis tend to have lower torsional diaphragm rotation values compared to the axis about which they are asymmetric.\u003c/p\u003e\n\u003cp\u003eThe reported maximum demands are as follows: HCB (0), HGB (0), TCB (0.00086), TGB (0.000447), LCB (0.001431), and LGB (0.001225). This data-driven analysis highlights the torsional behavior of different configurations, including H-shaped buildings with both conventional and grid slabs, T-shaped buildings with conventional and grid slabs, and L-shaped buildings with conventional and grid slabs. The results confirm that H-shaped buildings, characterized by symmetry about both axes, exhibit robust stability with minimal torsional rotation. In comparison, T-shaped buildings, with single-axis symmetry, show higher torsional rotation values but fall within a moderate range, while L-shaped buildings, being asymmetric about both axes, display the highest torsional rotation. Overall, this comparative assessment emphasizes the influence of building geometry and symmetry on torsional behavior, underscoring the potential of grid slab systems to minimize torsional diaphragm rotation across diverse building types.\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eBoth conventional slab systems and grid slab systems have been used in the investigation, which was conducted on a range of building types. A comparison has been performed between conventional slab systems and grid slab systems with respect to overall structural performance. The results show that irregularity significantly affects the structural response. In all the examples that were looked at, there is a change in reaction for frames that have one or more irregularities in comparison to the typical arrangement. After analyzing these kinds of buildings, the following conclusions were drawn:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eThe study reveals that a rib spacing of 2000 mm with a d/b ratio of 5 optimally balances deflections, reducing them by approximately 71.1% compared to conventional slabs while keeping deflections within permissible limits.\u003c/li\u003e\n \u003cli\u003eThe grid slab with a rib spacing of 2000 mm and a d/b ratio of 5 is optimal, reducing shell stresses by over 74% compared to conventional slabs while ensuring enhanced robustness and safety under both standard and accidental loading. This configuration balances stress reduction and long-term structural performance effectively.\u003c/li\u003e\n \u003cli\u003eAlthough grid slabs result in higher base shear values, they significantly reduce interstorey displacement and drift, especially in buildings with plan asymmetries. This makes grid slabs more efficient in single-axis symmetric and asymmetric buildings, improving seismic performance, while the benefits are less pronounced in symmetric buildings with already balanced stiffness and load distribution.\u003c/li\u003e\n \u003cli\u003eGrid slabs effectively mitigate torsional diaphragm rotation, particularly in complex L-shaped configurations, offering a scientifically grounded solution to address torsional irregularities and improve the overall structural stability under dynamic loading conditions.\u003c/li\u003e\n \u003cli\u003eThe grid slab system demonstrated superior structural performance over conventional slabs, showcasing its efficacy in enhancing building stability. Furthermore, the study revealed that symmetrical building designs consistently outperformed asymmetrical structures, emphasizing the importance of balanced configurations between asymmetric structure and grid slab in achieving optimal structural outcomes.\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCRediT authorship contribution statement \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSamrat Poudel\u003c/strong\u003e: Writing \u0026ndash; original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. \u003cstrong\u003eTek Raj Gyawali\u003c/strong\u003e: Writing \u0026ndash; review \u0026amp; editing, Validation, Supervision, Investigation, Formal analysis, Mentorship.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they do not have any conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbdel Raheem S, Ahmed M, Ahmed M, Abdel-shafy A (2018) Evaluation of plan configuration irregularity effects on seismic response demands of L-shaped MRF buildings. 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Heliyon 10:e27179. https://doi.org/10.1016/j.heliyon.2024.e27179\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":"bulletin-of-earthquake-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"beee","sideBox":"Learn more about [Bulletin of Earthquake Engineering](https://www.springer.com/journal/10518)","snPcode":"10518","submissionUrl":"https://submission.nature.com/new-submission/10518/3","title":"Bulletin of Earthquake Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Grid slab, Diaphragm, Deflection, Displacement, Torsional Irregularities, Seismic Performance","lastPublishedDoi":"10.21203/rs.3.rs-5572077/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5572077/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Rapid urbanization and increasingly complex building designs have led to a rise in structural irregularities, significantly affecting seismic performance. Plan irregularities often induce torsional effects, placing additional stress on structural elements. Slabs play a crucial role in load distribution and stability, particularly in irregular buildings where conventional slabs may not be optimal. Grid slabs, known for their lightweight structure and efficient load transfer, offer a promising solution for enhancing seismic resilience. However, limited research has explored their interaction with irregular building configurations. This study investigates the seismic performance of grid slabs in buildings with varying symmetries, including symmetric, single-axis symmetric, and asymmetric structures. Numerical simulations under dynamic loading conditions were conducted to assess the impact of different grid slab configurations on deflection, shell stresses, interstorey displacement, drift, and torsional irregularities. The findings reveal that optimized grid slab configurations can significantly reduce slab deflections and improve overall seismic performance, particularly in asymmetric buildings. While grid slabs enhance seismic resilience, symmetric buildings inherently offer better structural balance due to their uniform stiffness and load distribution. These insights contribute to the efficient design of earthquake-resistant structures with complex geometries.","manuscriptTitle":"Structural Performance of Symmetric and Asymmetric Plan Irregular Building Structures: A Comparative Analysis of Conventional and Grid Slab Systems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-24 13:04:19","doi":"10.21203/rs.3.rs-5572077/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accept as is","date":"2025-04-15T05:56:46+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-03-28T17:51:39+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-21T08:50:07+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Bulletin of Earthquake Engineering","date":"2025-03-20T12:56:56+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-20T11:46:48+00:00","index":"","fulltext":""},{"type":"submitted","content":"Bulletin of Earthquake Engineering","date":"2025-03-20T04:54:52+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bulletin-of-earthquake-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"beee","sideBox":"Learn more about [Bulletin of Earthquake Engineering](https://www.springer.com/journal/10518)","snPcode":"10518","submissionUrl":"https://submission.nature.com/new-submission/10518/3","title":"Bulletin of Earthquake Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"b8aaf134-8490-42c1-b8bc-5f13f816957d","owner":[],"postedDate":"March 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-05-19T16:04:58+00:00","versionOfRecord":{"articleIdentity":"rs-5572077","link":"https://doi.org/10.1007/s10518-025-02179-w","journal":{"identity":"bulletin-of-earthquake-engineering","isVorOnly":false,"title":"Bulletin of Earthquake Engineering"},"publishedOn":"2025-05-12 15:57:56","publishedOnDateReadable":"May 12th, 2025"},"versionCreatedAt":"2025-03-24 13:04:19","video":"","vorDoi":"10.1007/s10518-025-02179-w","vorDoiUrl":"https://doi.org/10.1007/s10518-025-02179-w","workflowStages":[]},"version":"v1","identity":"rs-5572077","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5572077","identity":"rs-5572077","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}