Simulation and Experimental Analysis of L-Section in Reinforced Cement Concrete: Uncertainties in Performance and Strength ^†

Abstract

The design and construction of reinforced cement concrete (RCC) flooring play a crucial role in the overall stability of a structure, particularly in regions prone to tectonic activity. RCC floors comprise various beams, including intermediate T-sections and specific L-sections at critical points such as corners and around staircases or lift openings. This paper identifies a key challenge in building frameworks to resist tectonic loads. It further explores the components of the structure that provide potential for interruption, capability, and the safe transfer of tectonic loading to the array connection, all while maintaining sufficient strength. The L-sections were experimented on using various grades of concrete and sizes to reinforce connections under diverse loading conditions. L-sections contribute to reducing floor height, solving economic and technical problems, and creating advanced composite connections that integrate the proposed structural system. The analysis was conducted both analytically and experimentally to assess methods to resist earthquake forces based on stiffness, building strength, and elasticity capacity. These approaches have been identified to safeguard buildings during substantial seismic events. The development of the L-section is detailed, highlighting the loading process and the capacity to overcome various structural challenges.

1. Introduction

In specific instances, openings are essential in the architecture of pre-stressed inverted L-shaped concrete frameworks. Earlier research indicates that integrating these openings in the web part of a pre-stressed concrete beam compromises its rigidity and complicates its performance [1]. Evaluating the influence of these openings on the structural durability and functionality during the design stage is vital. Although abundant research exists on reinforced concrete sections featuring openings, there has also been some focus on pre-stressed beams with web openings [2]. Nevertheless, the literature is scarce when it comes to reinforcing the areas around these web openings with glass fiber reinforced polymer (GFRP). This paper aims to address this significant research gap. Columns in reinforced concrete (RC) structures are pivotal elements and can have various cross-sectional forms, although rectangular and square shapes are most prevalent. In certain configurations, there are aesthetic inconsistencies at the intersections between walls and columns, resulting in protrusions.

To circumvent these protrusions, inverted L-sections can serve as an alternative, providing a comparable concrete surface area. The thickness of the flange or web in these L-sections can be aligned with the wall thickness to maintain uniformity. While there is scant experimental evidence concerning the behavior of T-shaped RC members under solo axial bending, guidelines for the design of L-shaped columns exposed to axial forces and biaxial moments are offered by the limit state method in accordance with IS 456:1978 [3]. Prior research has delved into the ideal configurations for rectangular columns, and biaxial interaction charts have been scrutinized for alternative forms [4]. These interaction charts play a critical role in optimizing designs, thus highlighting the necessity for additional advancements in the optimal design techniques for L-sections. This methodology could feasibly be adapted for different column shapes and integrated into digital design utilities [5,6].

1.1. L-Section Design

The L-section is employed to meet specific compressive space requirements within a predefined layout. The aim is to maintain uniformity across half of the designated widths, while capping the boundary width at a maximum of four times the grid width. Additionally, the effective boundary width should not surpass 1/12th of the overall span, and the slab’s uniformity should be at least six times that of this effective boundary width [7]. The L-section can also be modified to act as an arch, with the restriction that the thickness of the reinforcing arch should not exceed five times the uniformity of the boundary.

1.2. Determining Effective Flange Width

Basic flexural theory posits that stress conforms to the flange width. However, when this uniformity of width becomes excessive, it fails to fully engage with the bending moment, leading to non-uniform stress distribution [8]. To counteract this, a refined stress distribution model is employed, adhering to the principle of constant equivalency. This simplifies both the design and analytical procedures for L-sections. Figure 1 elucidates the crucial role of flexural and bending stresses in the curvature of an L-shaped beam. Mathematically, the relationship between the bending moment (M, in N·m), the applied force (C, in N), and the distance from the applied force to the point of interest (d, in m) is expressed as follows:

$$M=C·d$$

(1)

This formula is cited from a work accomplished by Mitra and Bindu [9].

The effective uniformity of an L-section is regulated by ACI 8.12.2 along with additional factors like $bw+16t$, the spacing between beams measured center-to-center, and $L/4$ [9]. Further guidelines for the configuration of L-shaped beams are provided by ACI 8.12.3 and ACI 8.12.4 [10].

2. Methodology and Materials

A critical concern was raised regarding the structural framework’s ability to endure extensive tectonic forces. This involves pinpointing specific structural elements that not only possess the potential for disruption and capability but also facilitate the secure channeling of tectonic forces to the connecting framework, while ensuring sufficient resilience [11]. The L-section’s joint was constructed with a variety of concrete grades and reinforcement sizes to test the resilience of the connection under varying load scenarios. Additionally, the L-section aids in smoothing the floor-to-floor height transitions and addresses both economic and technical issues related to connections. The investigative approach and materials in this study focus on the constituents’ physical attributes. In particular, the study made use of materials such as GFRP mesh, manufactured sand (M-sand), coarse aggregates, cement, fly ash, water, fine aggregates, substantial tensile strength elements, and superplasticizers, as elaborated in the following sections [5,12]. The schematic representation of the L-section is illustrated in Figure 2.

Fibers play an essential role in enhancing composite materials, particularly in contributing significant layers and components within the matrix. The effectiveness of fiber reinforcement is influenced by various parameters, such as the method of fiber incorporation, fiber type, volume fraction, and length in the composite structure. GFRP (polymer) bars are utilized as a key reinforcing element [13]. While GFRP materials offer strong dimensional stability, they also present challenges related to their strain behavior, often leading to compatibility issues due to the lower modulus of elasticity compared to steel. This results in elevated stress levels in GFRP structures, necessitating energy absorption in their plastic state. This variant of glass fiber, often referred to as fiberglass, comes with benefits such as being lightweight, easy to handle, cost-effective, and less brittle. The characteristics of the glass fiber mesh are elaborated in

Table 1. Attributes of Glass Fiber Mesh.

No.	Attribute	Values
1	Maximum Tensile Strength (MPa)	3390
2	Maximum Compressive Strength (MPa)	1100
3	Density of the Material (g/cm3)	2.59
4	Thermal Expansion Coefficient (µm/m°C)	4.67
5	Melting Point (°C)	850
6	Poisson’s Ratio	0.3

[14].

The product Araldite^® AW 106/Hardener HV 953 U was used for diverse functions, including bolstering material durability, delivering high-caliber adhesives, and allowing for curing at ambient temperatures.

This blend was versatile, and capable of adhering to an array of materials like rigid plastics, rubber, ceramics, metals, and glass, commonly used in various applications.

Table 2. Specifications of Araldite AW 106 and Hardener HV 953 U.

Characteristics	Araldite® AW 106	Hardener HV 953 U	Composite Mix
Color	Neutral	Light Yellow	Light Yellow
Specific Gravity	Approx. 1.15	Approx. 0.95	Approx. 1.05
25 °C Viscosity	30–50 (Pas)	20–35 (Pas)	30–45 (Pas)
Pot Life	-	-	Around 100 min
Shelf Duration	3 years	3 years	-

outlines the specifications of the resin and hardener utilized in this research (Araldite AW 106 and Hardener HV 953 U). The investigation focused on M25-grade concrete and Iron500-grade steel. The ratio of ingredients for reinforced concrete is detailed in

Table 3. Ratio of Ingredients for Reinforced Concrete.

Cement (kg)/m3	Fly Ash	Fine Aggregate (FA)	Coarse Aggregate (CA)	Water	Superplasticizer
265	112	743	1200	190	9.14
1		1.80	3.76	0.454	0.195

. Intersections between columns and beams, often termed as L-joints, nodes, or junctions, were evaluated to discern the properties of the L-section. This included examining aspects such as ductility, energy absorption capabilities, stress distribution, variations in strength, and displacement. Analysis System software was employed for both analytical and experimental evaluations.

In the research, detailed analyses were carried out on L-shaped joints connecting beams and columns. The first example, designated as CT1, was centered on understanding the basic properties of the foundational specimen [15]. The beam dimensions were 1.10 m × 1.100 m × 1.100 m, and it was affixed to a column at its middle height. The column had dimensions of $1.1\mathrm{m}\times 1.1\mathrm{m}$. The entire length of $2\mathrm{m}$ was equally divided into upper and lower parts. High-tensile steel was used for both segments of the beam and the column’s longitudinal reinforcement [16]. The beam’s main steel reinforcement had two bars, each measuring $11\mathrm{mm}$ in diameter, and the supplementary steel also had an $11\mathrm{mm}$ diameter. The column was fortified with four steel bars, each measuring $11\mathrm{mm}$ in diameter and placed at the corners of its cross-sectional layout. To emulate seismic forces, a separate connection between the beam and the column was subjected to static loads ranging between $5\mathrm{KN}$ and $22\mathrm{KN}$. As the load escalated, both tensile and compressive forces were exerted $560\mathrm{mm}$ away from the top and bottom sections of the column, respectively. The top segment experienced sustained compressive loading, while the lower part of the beam was firmly anchored to the base [17]. This loading equated to $0.3f_{\mathrm{ck}}$ of the static force applied on the column.

Displacement data were collected using reflectometers. To alleviate localized stress concentrations at load application points, a plate with a thickness of $7\mathrm{mm}$ was strategically placed.

3. Results and Discussion

A concrete L-section and HSL section were examined, with columns connected at each end of the beam. To shield the specimen from forces during testing, a wrapped rod was provided around the column. The displacement was measured using a deflectometer instrument [18]. The maximum loading capacity up to $60\mathrm{kN}$ was ascertained by inspecting the ring. Both experimental and analytical results of the test were garnered and are delineated below. During each stage of the process, the loading was increased gradually. The logical sequence of the load increments was $4\mathrm{kN}$, $8\mathrm{kN}$, $12\mathrm{kN}$, and so on. Deflection measurements were $0.45\mathrm{mm}$ for both downward and upward loads. In the downward phase, the first load step was $5\mathrm{kN}$, and during the upward phase, it was $8\mathrm{kN}$. The maximum deflection measured was $6.01\mathrm{mm}$ at a load of $78\mathrm{kN}$. A quantitative analysis of the tectonic features was articulated in depth, referencing the deformation response to loading, which consistently followed a bilinear pattern [19,20]. The ratio of the maximum deformation of a specific phase to the deflection could yield a measurement of tectonic displacement. The values of tectonic displacements obtained at the first phase of loading were $1.45$ for reverse and $0.7$ for forward.

The initial strength value, assessed at the beginning of the first cycle, was found to be $5.45\mathrm{kN}/\mathrm{mm}$. As the load increased, this strength value consistently decreased, reaching a peak load of $13\mathrm{kN}$ during the loading procedure, at which point the strength was $0.78\mathrm{kN}/\mathrm{mm}$. The cyclic behavior of the L-section, in the absence of Glass Fiber Reinforced Plastic (GFRP), is depicted in Figure 3.

The ability of the structure to absorb energy during the cyclic process was quantified by summing specific areas under the load–deflection curve. In particular, the energy absorbed in the first loading cycle was calculated to be $0.4\mathrm{kN}·\mathrm{mm}$, and in the sixth cycle, it was measured at $4.76\mathrm{kN}·\mathrm{mm}$. A comprehensive assessment of the total energy absorption capacity was conducted by aggregating the energy absorbed during each individual cycle, as tabulated in

Table 4. Experimental test results for L-section without GFRP mesh under cyclic loading.

S.No	Cycle No.	Max Load	Max Deflection	Ductility Factor	C. D.F	E.A.	C.E.A	Stiffness
Forward Cycle ($\Delta y=0.5$ mm)
1	2	4	0.98	0.90	0.40	0.50	0.50	4.45
2	4	8	1.90	3.98	3.80	1.45	2.12	1.45
3	6	12	3.89	7.30	11.56	4.77	6.84	0.68
Reverse Cycle ($\Delta y=0.23$ mm)
4	3	6	0.87	1.38	12.43	0.30	7.13	3.34
5	6	12	1.98	7.45	19.90	1.63	8.54	1.43
6	9	18	3.90	15.34	35.56	3.65	12.45	0.09

.

Under a loading process of $13\mathrm{kN}$, the L-section, devoid of GFRP reinforcement, was found to have an energy absorption capacity of $13.47\mathrm{kN}·\mathrm{mm}$. The L-section specimen without GFRP under reverse and forward loading is elaborated in Table 4. The specimen achieved a tectonic value of $16.87$ at $13\mathrm{kN}$ and also an energy absorption of $5.45\mathrm{kN}·\mathrm{mm}$. Simultaneously, the number of the processes increased the tectonic factor, absorption of energy, strength, cumulative absorption of energy, and cumulative tectonic factor.

A maximum loading of 15 kN was enforced on the illustration, resulting in the greatest deviation of 4.98 mm. The equivalent tension for the L-section with Glass Fiber Reinforced Plastic (GFRP) was 132.89 MPa at this loading. Upon increasing the maximum loading to 27 kN, the greatest deviations were 5.34 mm and 143.89 MPa, respectively. The deformation and tension details for L-section with GFRP are included in the analysis. During the loading process, a gradual increment occurred in the following sequence: 3 kN, 6 kN, 8 kN, and so on. Deflection measurements recorded a value of 0.25 mm when a downward load was applied, and 0.29 mm under an upward load. The initial process in both directions involved a 5 kN load. In Figure 4, the cyclic loading and deflection data for the L-section are illustrated. The peak deflection reached was 5.01 mm, occurring at a 23 kN load. An examination of the deformation process exposed a correlation with tectonic shifts, resulting in a tectonic factor of 0.3 during forward loading and 0.18 during reverse loading. The compiled data for both tectonic and cumulative tectonic displacements can be found in

Table 5. Experimental test results for the given cycles.

S.No	Cycle No.	Max Load	Max Deflection	Ductility Factor	C. D.F	E.A.	C.E.A	Stiffness
Forward Cycle ($\Delta y=1.1$ mm)
1	2	4	0.23	0.34	0.78	0.34	0.09	4.98
2	4	8	1.14	1.34	1.56	1.90	1.23	3.56
3	6	12	2.91	2.45	3.09	4.09	6.45	3.27
4	8	16	3.45	3.78	7.09	5.98	11.09	2.02
5	10	20	4.13	3.90	10.98	7.56	19.23	1.09
Reverse Cycle ($\Delta y=1.5$ mm)
6	3	6	0.34	0.23	11.29	0.67	19.09	4.22
7	6	12	1.15	0.79	11.24	0.34	20.08	3.56
8	9	18	2.98	1.98	13.67	5.98	25.50	2.09
9	12	24	3.45	2.89	16.90	4.98	30.24	1.23

.

Notably, a steady escalation was identified, starting from 0.23 at the first loading process and extending to 18.23 during the ninth loading process. As depicted in Figure 4, the strength of the material altered alongside the loading sequence. It initiated at 5.34 kN/mm at the first load, and progressively lessened to 1.98 kN/mm at the highest load of 25 kN. The corresponding energy absorption values were observed to be 0.4 kN/mm at the first process, and they increased to 8.4 kN/mm at the ninth process.

Table 5 presents the values concerning the energy absorption pattern and cyclic process pertinent to the L-section. The L-section’s experimental results, when combined with GFRP, are elaborated upon for both reverse and forward loads in Table 5. At a 25 kN load, the maximum quake factor was noted as 4.89, while the apex of energy absorption was registered at 8.45 kN mm. The data reveal a multifaceted interplay among variables such as loading increments, deflection measurements, tectonic values, material strength, and cumulative energy absorption.

In this study, the L-section specimens, composed of Glass Fiber Reinforced Concrete (GFRC), were subjected to cycles of forward and reverse loading. The results of the study were comprehensive, encompassing both experimental observations and analytical assessments. Notable among these were comparisons between the first crack load and ultimate load of the specimens. Before the onset of cracking, both the strains and stress within the GFRC elements were found to be uniformly distributed along the length of the concrete member, displaying a tensional behavior. The initial phase of the loading process exhibited a harmonious interaction between the concrete and the reinforcement. This is attributed to the strain compatibility and equilibrium forces that are sustained through the linear elastic material responses between the reinforcing fibers and the concrete. In this uncracked state, the concrete and the reinforcement strains were congruent, with no slippage observed, and the load on the beam was proportionally shared based on the rigidity of each material component. However, as the tensile strength of the GFRC was approached, the first significant change, or crack, in the material was observed. This initiation of cracking marked a critical transition point in the behavior of the specimen. Subsequent to this cracking, the tensile stress within the affected concrete region reduced to zero. This phenomenon necessitated a reconfiguration of both concrete strains and reinforcement, resulting in a discontinuity in strain compatibility.

Table 6. Experimental Outcomes for L-Section Test Samples.

S. No	Assessment Metrics	Standard Concrete (kN)	Reinforced GFRP Concrete (kN)
1	Initial Crack Load	7	12
2	Peak Load Capacity	12	20

provides detailed data on the first crack and ultimate load for the L-section specimens, and Figure 5 graphically represents these findings. Specifically, upon placing the specimen in the loading frame, the first crack was identified at loads of $7\mathrm{kN}$ for conventional concrete and $12\mathrm{kN}$ for the specimens with GFRP mesh. This observation suggests a notable enhancement in load resistance imparted by the GFRP mesh. Moreover, the ultimate load, or the maximum load the specimen could bear before failure, was recorded as $12\mathrm{kN}$ for conventional concrete and $20\mathrm{kN}$ for GFRP mesh concrete. This represents a significant $40\%$ increase in ultimate load capacity for the L-section beams reinforced with GFRP mesh compared to those without.

In essence, the inclusion of GFRP mesh in the concrete proved to be influential, enhancing the load-bearing capacity of the L-section beams and altering the characteristics of crack formation and propagation as the axial load increased, until a state of crack stability was eventually reached.

Comparison of Results for L-Section Specimens

The results of the L-section specimens for both experimental and analytical studies were compared for various types of concrete under load, as depicted in Figure 5. The maximum load of conventional concrete was determined to be $12\mathrm{kN}$ with a deflection of $3.67\mathrm{mm}$ for the experimental assessment, similar to the analytical value of $12\mathrm{kN}$ with a deflection of $3.90\mathrm{mm}$.

Table 7. Comparison of test results of L-section (experimental and analytical).

Load (kN)	With GFRP		Without GFRP
	Exp. (mm)	Calc. (mm)	Exp. (mm)	Calc. (mm)
0	0	0	0	0
2	0.17	0.60	0.05	0.38
4	0.20	1.07	0.10	0.98
6	0.85	1.80	0.60	1.14
8	1.50	2.15	1.10	1.97
10	2.80	3.00	2.10	2.30
12	3.67	3.90	3.20	3.35
20	-	-	4.11	4.69

and Figure 6 illustrate the load versus deflection outcomes for each load increment in the L-section, both with and without GFRP mesh, based on experimental and analytical analyses. Similarly, the maximum load for GFRP mesh concrete was found to be $20\mathrm{kN}$ with a deflection of $4.11\mathrm{mm}$ for experimental testing, comparable to the analytical value of $20\mathrm{kN}$ with a deflection of $4.69\mathrm{mm}$.

4. Conclusions

In summary, the research comprehensively explored the interface of beams and columns in structural designs, particularly focusing on the use of Glass Fiber Reinforced Plastic (GFRP). Employing Analysis System software version 15 for both analytical and experimental methods, the study was conducted in adherence to the Indian Standard of M25-grade concrete. Specimens were methodically prepared, cured, and then tested under a structured loading process using a compression machine. The study affirmed the significant role of GFRP in enhancing the structural strength and resilience of the connections. It was found that under varying loading conditions, the presence of GFRP markedly influences critical parameters such as strength, maximum stress, and deflection. Without GFRP, the L-section exhibited a maximum deflection of 4.34 mm at a 14 kN load and 5.23 mm at a 25 kN load. On the other hand, the inclusion of GFRP significantly altered these values, underscoring the material’s potential for enhancing structural robustness. The study also employed a thorough analytical framework developed to examine the behavior of the L-section in both upward and downward loading scenarios. The analytical results were corroborated by experimental findings, validating the methodologies and tools used in this research. This investigation offers a substantial contribution to the existing body of knowledge in the field of structural engineering and reinforced concrete design. The insights gleaned from this study are expected to serve as valuable references for future research and real-world applications in constructing more resilient and efficient structural connections.