Mechanical performance and flexural behavior of reinforced concrete beams modified with nano-cellulose and steel fibers

ABSTRACT

Fiber-reinforced concrete (FRC) offers several benefits, including improved tensile strength, greater ductility, enhanced energy absorption, and superior impact resistance. In the present study, experimental investigations were carried out on high-performance fiber-reinforced concrete (HPFRC) containing rice husk ash (RHA), crimped steel fibers, and Nanocellulose fibrils (NCF). The NCFs were added to the concrete mixtures in percentages of 0.4 and 0.6 of the binder composition. The volume of crimped steel fibers was kept constant as 1.5% for better comparison. The laboratory experimental program involved a total of seven mixes with three samples per mix for compressive strength, flexural strength, elastic modulus, scanning electron microscopy. The flexural performance was tested for seven FRC beams. Additionally, finite element method (FEM) based numerical analysis was conducted for further investigation. Ductility parameters, including energy ductility and deflection ductility, were assessed using the load–deflection behavior of the FRC beams. Results from the experimental program indicate that the addition of NCF showed marginal improvement on the early age compressive strength, whereas the 28-day strength improved significantly. At 28 days, the mix containing RHA, 0.4% NCF exhibited the highest compressive strength, approximately 68 MPa, compared to the other mixes. Adding 0.4% NCFs increased the flexural strength up to 40.6% compared to the control mix due to the crack-bridging mechanism. Morphology analysis reveals a dense matrix aggregate interface due to the formation of hydration crystals. The addition of steel fibers and NCFs led to a notable enhancement in ductility performance. The HPFRC beam with RNCSF (1.5:0.4) showed the highest deflection ductility ratio, 58% higher than the control RC beam. Similarly, the peak energy ductility ratio for the same mix showed a 65% increase. The numerical simulation of load–deflection behavior and crack patterns of fiber-reinforced RC beams closely matched the experimental results.

Keywords:
Rice husk ash; Nano-cellulose fibrils; Steel fibers; Flexural behavior of beams; Morphology

1. INTRODUCTION

Sustainability in construction has become the top priority in recent times due to the rapid growth in the construction sector, directly linking with the economic growth of a nation. Determining the sustainability of the concrete mixes is vital to understanding the impact of production and usage of building materials on human health and the environment [¹, ²]. Also, this rising demand for raw materials has led to the overexploitation of natural resources around the world, with China and India making up more than 50% of the annual usage [³]. Such rising concerns over the depletion of natural resources due to the rapid urbanization call for the urgent search for alternative raw materials for concrete production [⁴, ⁵].

The production of clinkers is considered carbon intensive and energy consuming process [⁶]. Hence, supplementary cementitious materials (SCMs) have emerged as viable alternatives to traditional cement in concrete formulations. Especially, the incorporation of agricultural by-products as fillers in cementitious composites has garnered attention for its sustainability and cost-effectiveness [⁷, ⁸]. India relies heavily on the agricultural sector, which contributes to 15% of its GDP and produces around 126 million tonnes of rice husk. Most of which are burned in the fields due to the lack of affordable and profitable methods for utilizing rice straw [⁹,¹⁰,¹¹]. This practice contributes to air pollution and the emission of greenhouse gases (CO, SO₂, NO_x) [¹², ¹³]. Rice husk ash (RHA) is a form of highly reactive pozzolan obtained from controlled incineration of rice husk. The fine particle size and the high amount of silica content make the material highly reactive compared to silica fume (SF) [¹⁴]. Numerous past studies have reported the reactivity and strength benefits of RHA depending on its specific surface area [¹⁵,¹⁶,¹⁷]. The replacement of SF by RHA in concrete showed similar characteristics in the production of hydration products and also, the rate of consumption of portlandite was observed to be high when compared to SF, which ultimately improved the strength and durability properties of concrete [¹⁸]. Higher replacement levels of RHA have shown low heat release during the hydration process of mass concrete [¹⁹]. A maximum 50% replacement by weight of cement has shown beneficial results in terms of strength and shrinkage properties in the early stages of curing [²⁰]. The structure of RHA plays a vital role in strength development. The amorphous particles with high surface area are preferred compared to crystalline particles in concrete mixes, which can be achieved by a controlled burning process with a temperature ranging between 500–700 °C [²¹]. Studies have reported the dilution of strength properties due to the usage of RHA with bigger particle sizes as a replacement of cement in concrete [²²]. Past studies have reported that sustainable waste-based concrete design yields higher strength and durability, of which nanomaterial additives boost both early and long-term concrete strength and durability [²³, ²⁴]. Particularly, nanosilica fibre concrete sharply improves flexural, compressive strength, and stability [²⁵]. SHANKAR et al. [²⁶] reported that nanosilica enhances abrasion resistance and strength retention in HPFRC. PARTHASAARATHI et al. [²⁷] observed that coconut shell fibres in concrete show greater ductility and crack resistance.

Mechanical performance and flexural behavior of beams with different types of randomly distributed fibers have been widely documented [²⁸, ²⁹]. Cellulose fibers are obtained from plants through intricate extraction processes. The utilization of cellulose fibers in products such as papers, textiles, and other applications dates way back [³⁰]. Also, the utilization of cellulose has advantages in terms of environmental sustainability, circularity, and recyclability. The usage of cellulose in concrete has been of great interest for research communities in recent times due to the improvements it imparts on the mechanical, durability, and microstructural properties [³¹]. Advancements in processing technologies have leveraged the cellulose characteristics, which, when added to concrete, can provide resistance to microcracking, shrinkage, and chemical ingress [³²]. Three different forms of cellulose are being used in concrete, such as bacterial nano-cellulose, cellulose nanofibrils, and cellulose nanocrystals, based on the varying production processes through bacterial, mechanical, and chemical means [³³]. SINGH and GUPTA [³⁴] in their study with concrete containing ultra-cellulose fiber observed an increase in fresh and hardened properties due to the water-holding ability of the fibers, which assisted in self-curing and formation of hydration products in the later stages. MEJDOUB et al. [³⁵] studied the concrete properties containing nano fibrillated cellulose in the ranges of 0% to 1.5%, and observed significant improvement in hydration products. Furthermore, the study also reported a reduction in the thermal conductivity compared to normal concrete. Some studies have also reported a negative impact on the mechanical properties of concrete due to the addition of cellulose fibers. ARBELAIZ et al. [³⁶] investigated the effects of cellulose microfibers in mortar and observed a drop in strength properties. However, the study concluded that the negligible changes in materials density can be advantageous in reinforcement applications. Nano cellulose fibers have been proven advantageous in concrete due to their reduced unit weight, compact interface between fiber and matrix, resistance to alkaline environment and resistance to corrosion, and durability, which were some of the limitations of commercial fibers such as steel fibers, glass, and synthetic fibers [³⁷]. The flexural strength and compressive strength improvement of upto 55% and 40% were observed from the addition of 0.2% fibrillated nanocellulose in concrete [³⁸]. Apart from that, the water holding capacity and reduction in drying and autogenous shrinkage were some of the key advantages essential for the early age crack resistance of the high-performance concrete [³⁹]. Some studies have also established the influence of the aspect ratio of NCFs on the hydration [⁴⁰], flexural performance [⁴¹] and pore volume [⁴²] of the concrete. Beams made with steel fibre have improved strength and now perform better overall. SRINIVASAN et al. [⁴³] observed that silica-fortified concrete beams with steel fibres experienced improved strength, with improvements reflected in their first crack load, yield load, deflection ductility, and energy absorption. HASGUL et al. [⁴⁴] indicated that adding steel fibres to FRC beams improves their deflection and bending resistance, moment capacity, flexibility, and cracking behaviour. Interestingly, the combined addition of steel fibers with natural and synthetic fibers has shown positive improvements. SALMAN et al. [⁴⁵] analysed GFRP reinforced concrete beams containing steel fibres and carbon nanotubes (CNTs). As a result, the crack width grew smaller, the load-carrying strength increased, and deflection dropped by 25% for the same specimens when compared to those from the reference mix. Nano Cellulose inclusion in cement composites improves how particles arrange and reduces the development of nano-sized cracks. Higher linkage between cement hydration products is formed due to the high surface area of nano-ellulose, which results in better mechanical properties [⁴⁶]. When the required nano-cellulose (0.35%) was introduced, the tensile strength increased by approximately twice that of the control mix. Also, Nano silica and Nano Cellulose have interacted synergistically when brought together. Further, nano silica helps generate a larger amount of calcium-silicate-hydrate gel and improves the bond between the cement fibres and the matrix.

From the literature survey, it was observed that the performance evaluation of NCFs together with SCMs is a major research gap. Over the past several decades, numerous studies have explored the flexural behavior of RC/FRC beams. However, research focusing on the combined use of steel fibers and nano-cellulose in this context remains limited. Hence, the aim of the present study is to determine the mechanical performance of the high-performance concrete containing CSF and NCF. The research also aims to understand the developments of the morphology and ITZ for the most suitable mix combinations.

2. MATERIALS AND METHODS

2.1. Materials

Ordinary Portland cement (OPC) of 53-grade, conforming to the IS: 12269 [⁴⁷] standard code was used. RHA was obtained in powder form from Astraa chemicals. Figure 1a shows the RHA employed in this investigation. The scanning electron microscopy (SEM) analysis of RHA is shown in Figure 1b. The physical properties of OPC and RHA tested in accordance with IS codes are given in Table 1. The chemical composition of OPC and RHA is also given in Table 1. NCFs were obtained from Deep Polychem Pvt. Ltd. The physical and mechanical properties of CSF and NCF are tabulated in Table 2. The SEM images of the NCF are displayed in Figure 2. Manufactured sand was used that meets the zone II specifications of IS 383 [⁴⁸]. The fine aggregate’s fineness modulus, specific gravity, and water absorption were measured as 2.70, 2.67, and 1.96%, respectively. The coarse aggregate used was crushed stone with a maximum size of 12.5 mm. The physical properties of the coarse aggregate include a fineness modulus of 7.22, water absorption of 0.78%, and a specific gravity of 2.72. A commercially available polycarboxylate ether-based high-range water reducer, which complies with IS: 9103-1999 [⁴⁹], was used as a superplasticizer. The chemical admixture had a specific gravity of 1.2 ± 0.05 with an estimated water content of about 30%.

Figure 1
Appearance of RHA.

Table 1
Properties of OPC and RHA.

PROPERTIES	OPC	RHA
Chemical
Silicon dioxide, SiO2	21.07	92.03
Alumina (Al2O3)	5.54	0.18
Ferric Oxide (Fe2O3)	5.16	1.10
Titanium Oxide (TiO2)	0.9	0.15
Calcium Oxide (Cao)	64.26	0.70
Magnesium Oxide (Mgo)	0.86	2.10
Potassium Oxide (K2O)	0.37	0.10
Sodium Oxide (Na2O)	1.2	0.10
Loss on ignition	1.54	3.75
Physical properties
Appearance	Grey	Grey powder
Specific gravity, Sg	3.14	2.3
Pack density, D pack	1.5 gm/cc	0.86 gm/cc
B.E.T Fineness	250 m2/kg	18500 m2/kg
Greater than 90 microns	3.5 percent	1.0 percent
Moisture content	0.086 percent	0.058 percent
Consistency	31	–
Initial setting time	45 min	–
Final setting time	420 min	–

Table 2
Physical and mechanical properties of NCF.

FIBER	LENGTH (µm)	DIAMETER (µm)	ASPECT RATIO	ULTIMATE TENSILE STRENGTH (MPa)	DENSITY (kg/m3)	IMAGES
NCF	400	4	100	8000	700
CSF	33	0.5	66	1100	7850

Figure 2
Scanning Electron Microscopic images of NCF (a) Longitudinal; (b) Cross-sectional.

2.2. Mixture proportions

The mix design was conducted following the guidelines recommended by ACI 211.4R-93 [⁵⁰]. The reference mix was designed for a water-to-binder ratio of 0.4, which corresponds approximately to M50 grade concrete. The mixes contained RHA with cement replacement of 20%. Fine aggregate adjustments were carried out for the replacement of cement with RHA. In the mixes, the NCF fiber volume fractions are varied from 0.4 to 0.6%. The dosage of superplasticizer was kept constant to determine the influence of fibers on the fresh concrete properties. The details of the mix are presented in Table 3. Three samples were cast for each mix, and the average results of these samples were used as the final result for all the experimental investigations from the present study. For each mix, fine and coarse aggregates were dry-blended for 30 seconds. Then, half of the cementitious materials, half of the fibers (NCF/CSF), and half of the water were added and mixed for 1 minute. The remaining materials were added and mixed for 2 minutes before placing the fresh concrete into moulds. Samples, after being removed from the moulds, were water cured at 27 ± 2°C and 95% relative humidity. The casted samples are shown in Figure 3.

Table 3
Mixture proportions.

MIX	CONSTITUENT MATERIALS (kg/m3)								SLUMP (mm)
	OPC	RHA	WATER	FA	CA	NCF	CSF	SP
Phase I
Control	450	–	180	690	1178	–	–	2.8	98
RNCF-0	360	90	180	622	1178	–	–	2.8	91
RNCF-0.4	360	90	180	622	1178	1.8	–	2.8	89
RNCF-0.6	360	90	180	622	1178	2.7	–	2.8	88
Phase II
RCSF-1.5	360	90	180	622	1178	–	117.5	2.8	84
RNCSF (1.5:0.4)	360	90	180	622	1178	1.8	117.5	2.8	82
RNCSF (1.5:0.6)	360	90	180	622	1178	2.7	117.5	2.8	80

Figure 3
Figures showing casted samples for the experimental program.

2.3. Casting of RC/FRC beams

This experimental program contained a total of 11 RC beam specimen with RC beam (B1-Control) as the control beam. The control beams mix and reinforcement details were designed as a representative of the actual structural beam, and the observed beam behaviour corresponds to the actual behaviour of the field beams. Each beam had an effective span of 900 mm and an overall length of 1000 mm. The rectangular section was 100 mm in width and 150 mm in depth [⁵¹]. A four-point loading system was applied statically to all the specimens until they failed. The experimental investigation included two NCF beams [B3, B4]; one CSF beam [B5]; and two hybrid NCF and CSF beams [B6 and B7]. The mixes were carefully chosen to assess the changes in flexural behaviour due to NCF and CSF. All beams maintained a consistent steel reinforcement ratio, adhering to IS 456:2000 recommendations. The reinforcement detailing of the beam is shown in Figure 4.

Figure 4
Reinforcement detailing of RC beams, showing both elevation and section.

2.4. Tests on concrete specimens

The compressive strength test was carried out on 100 mm cube specimens at 7 and 28 days in accordance with the recommendations of IS 516-2021 [⁵²]. The compressive strength test was carried out on a universal testing machine loaded uniaxially with a loading capacity of 2000. The flexural strength was carried out on prism specimens of size 100 × 100 × 500 mm under a four-point bending setup with a simply supported loading span of 400mm. The tests were conducted based on the specifications provided by ASTM C78-2002 [⁵³]. The modulus of elasticity test was conducted on 150 × 300 mm cylindrical specimens after 28 days of curing, following ASTM C469 M-14 guidelines [⁵⁴]. The surface morphology of the mixes was determined using back-scattering electron microscopy. The initial preparation of the sample involved cleaning the debris, mounting the sample in a vent chamber with carbon tape, followed by gold coating for uniform electron emissions to get high-resolution images. The sample was analyzed using Zeiss model equipment.

2.5. Tests on RC/FRC beam specimens

The final casted beam specimens are shown in Figure 5a. The behavior of R.C beams in flexure under the applied static loading was studied. In this study, each beam was tested up to failure in a loading frame of capacity 1000 kN; the load increased incrementally by 2.5 kN. The beam was placed on a two-point roller support with a roller braced I-section having a two-point loading arrangement at the top, as shown in Figure 5b. The supports were adjusted for an effective span of 900 mm. The loading rate was maintained throughout the testing period of the beam specimen until the beam completely failed. A unidirectional LVDT was positioned at the mid-span of the beam to monitor flexural behavior under static loading. The LVDT was connected to a data logger to record mid-span deflections with a precision of 0.001 mm. The observations recorded were first crack load, yield load, and ultimate load. The load and the corresponding deflections were recorded through the data logger. The test setup is shown in Figure 5c. First crack load and failure load crack patterns were carefully recorded to plot the load-deflection graphs from the inception of load to the point of failure.

Figure 5
Experimental program for testing the flexural behaviour of RC beams.

3. RESULTS AND DISCUSSION

3.1. Fresh concrete properties

The slump values of all the mixes studied in the present research is shown in Figure 6. From the figure, it can be seen that the slump value for the control mix was higher compared to all other mixes. For the mix containing RHA 20%, the slump decreased up to 11.22% due to the increased surface area of RHA particles that demanded more water. The addition of NCF into the mix containing RHA further reduced the slump values. Even though the slump values reduced for the mixes containing NCF with 0.4% and 0.6%, they were still workable. The reduction in the workability for the mixes containing NCF was primarily due to the absorption of moisture by the cellulose fibers themselves. This mechanism has been frequently pointed out in past literature. The hydrophilicity of the NCF has been reported to combine with water with the hydroxyl groups of the fibers, which increases the water-holding capacity of the fibers [⁵⁵, ⁵⁶]. Such absorption of water helps in the internal curing in later ages. The addition of CSF 1.5% reduced the slump up to 14.2% compared to the control mix. The hybridization of NCF and CSF further reduced the slump value. The mix containing 1.5% CSF and 0.6% NCF showed the least workability and was moderately workable. NCF has an advantage over metallic and synthetic fibers by providing workability to the HPC, preventing drying shrinkage in the initial phases, and providing internal curing over the later stages.

Figure 6
Slump values of the mixtures.

3.2. Compressive strength

The 7 and 28-day compressive strength results of the mixes from the present study are shown in Figure 7. From the figure, a significant improvement in all the mixes can be seen when compared to the control mix. The mix containing RHA 20% and 0% NCF showed improvement of about 1.8% and 9.5% for 7 and 28 days of curing. The addition of NCF increased the compressive strength of all the mixes, with respective increments of upto 12.9% and 7.3 for 7-day mixes containing 0.4% and 0.6% fibers. Whereas, the 28-day strength increment were observed to be 21.7% and 12.3% for mix containing 0.4% and 0.6% fibers compared to the control mix. The addition of RHA made the HPC more brittle. The inclusion of NCFs in such densely packed matrices provides ductility and a crack-bridging mechanism. The compressive strength of RNCF-0.4 mix was 14.7% higher compared to RNCF-0 mix. The increase in compressive strength due to NCF addition may be linked to its higher aspect ratio and denser network-building capacity, which forms a fiber-bridging effect to arrest the microcrack initiation and accumulation of hydration products [⁵⁷, ⁵⁸]. Even though inconsistencies in the fiber dispersion have been reported to occur in mixes containing fiber volume more than 0.2% [⁵⁹], the results of the present study indicate a maximum compressive strength gain up to 0.4% addition of fibers. The compressive strength of mixes containing 0.6% NCF gradually decreased due to higher water retention from the fibers and an increase in the pore volume surrounding the fibers, leading to crack propagation. The hybridization of NCF and CSF further improved the crack resistance mechanism during failure. The long CSF arrested the crack propagation at the macro level, whereas the NCFs prevent crack initiation at the micro level. Positive synergy was observed between NCF and CSF in terms of strength performance for mic containing 1.5% CSF and 0.6% NCF. Studies have also reported that higher fiber concentration has also been reported in agglomeration, which hinders the homogeneity of the concrete and can lead to poor fiber-matrix bonding [⁶⁰, ⁶¹].

Figure 7
Compressive strength results of the mixtures.

3.3. Flexural strength

The 28-day flexural strength results of the mixes from the present study are shown in Figure 8. The flexural strength increased for all the mixes when compared to the control mix. The improvement in flexural strength due to NCF addition was not compared to the compressive strength. This phenomenon has also been reported in previous studies. The reduction in the flexural strength in mixes due to an increase in the NCF content has been attributed to the agglomeration and porous fiber-matrix interface [³⁰, ³⁵, ⁶²]. The 28-day flexural strength improvement of 22.6% was noted for the mix containing RHA 20% and 0% NCF when compared to the control mix. The addition of NCF in the volumetric ranges of 0.4% and 0.6% improved the flexural strength up to 40.6% and 8.4%, respectively. In the present study, a mix containing 0.6% NCF, apart from agglomeration, the flexural strength must also have been reduced from the improper hydration mechanism, due to the hydrophilic nature of the NCFs [⁶³]. Some studies have also recorded the ineffectiveness of cellulose fiber compared to steel and synthetic fibers in the improvement in flexural results due to cellulose fiber addition, giving only comparable results to those of the control mixes. The maximum optimum NCF dosage for obtaining the best flexural result was observed to be 0.4%. As expected, the CSF fibers performed better compared to NCFs; an improvement of 114% and 52% was observed when compared to the control mix and RNCF-0.4 mix. The hybridization was found to be effective in the flexural strength. The results are consistent with the compressive strength results, and a similar trend is also observed.

Figure 8
Flexural strength results of the mixtures.

3.4. Modulus of elasticity

The extent of the elastic deformation was determined for all the mixes at a curing period of 28 days. The maximum stress and corresponding strain values for the mixes are shown in Figure 9. As expected, the stress-strain relationship results indicated a brittle mode of failure for the control mix. A crushing mode of failure was observed for the control mix. The incorporation of RHA 20% improved the maximum load-carrying capacity; however, the failure mode was more brittle compared to the control mix, accompanied by a sudden failure. The addition of NCF has a significant effect on the strain values. All the mixes containing NCF showed load-carrying capacity with the least amount of strain. This ultimately increased the elastic modulus. The elastic modulus (secant modulus) obtained for the control and RNCF-0 mixes were 28.7 and 30.12 GPa. Whereas, the elastic modulus results for mixes containing 0.2%, 0.4%, 0.6%, and 0.8% NCF were obtained as 31.4, 32.3, 32.1, and 30.3 GPa, respectively. Invariably, the addition of cellulose fibers increased the elastic modulus with an increase in volume fractions. The optimum concentration of NCF was observed to be 0.4% for the best results. A study by KAMASAMUDRAM et al. [⁶⁴] containing nanocellulose fibers in a cementitious matrix observed a 200% improvement in the modulus of elasticity with 0.5% fiber volume fractions. The cementitious matrix plays an important role in the fiber dispersion, compatibility, and crack-bridging mechanism of the fiber [⁵⁸]. The RHA particles in the cementitious matrix provide a denser microstructure in the ITZ of fiber-matrix, thereby resisting the propagation of microcracks. The same has been observed by CLARAMUNT et al. [⁶⁵] where the cellulose nanofibers performed better in the calcium aluminate cement matrix compared to ordinary portland cement. The elastic modulus of SFRC/HyFRC was in the range of 29.40 – 34.24 GPa. The modulus of elasticity of CS-FRC mix was higher because of the hooking effect of the steel fibers while debonding. MOE improvements of 3.48% and 10.84% were obtained for RNCSF (1.5:0.6) and RNCSF (1.5:0.4) mixes compared to RCSF-1.5. The MOE of hybrid fiber reinforced concrete increased due to the reduction in pores and stronger fiber matrix bond, with a confinement effect in the transverse direction of the loading. A maximum of 22.09% improvement in MOE was obtained for Hy-FRC mix containing CS = 1.5% and NCF = 0.4% compared to the reference mix. Table 4 shows the peak strain values of all the mixes investigated in the study. It can be seen from the table that all the peak strain values are well within the 0.0035 peak strain recommended for plain concrete and 0.0035 to 0.6 recommended for FRC, as per IS 456 and ACI 544.

Figure 9
SEM micrographs of the mixtures.

Table 4
Peak strain of HPC/HPFRC mixes.

MIX DESIGNATION	PEAK STRESS	PEAK STRAIN (approx.)
Control	45.22	0.0020
RNCF-0	49.56	0.0020
RNCF-0.4	51.86	0.0027
RNCF-0.6	51.60	0.0026
RCSF-1.5	52.99	0.0030
RNCSF (1.5:0.4)	55.43	0.0033
RNCSF (1.5:0.6)	52.36	0.0034

3.5. Scanning electron microscope

The SEM images of the control mix revealed porous morphology, with wider gaps in the interfaces of aggregate and matrix, seen in Figure 9a. The microstructure of RNCF-0.4 mix reveals a denser matrix with pores filled with hydration products shown in Figure 9c. The dense pore-filling mechanism and crack-bridging effect of the NCFs were evident from the figure. A decline in Ca, and the increase in Si/Al were responsible for the formation of C-S-H and C-A-S-H. The clusters were composed mainly of Ca and Si, similar observations have been noted in a study containing crystalline additive minerals as an additive in concrete [⁶⁶]. The hydrophilicity of the cellulose fibers provides good compatibility between NCF and the cementitious matrix due to the adherence of the hydration products with the hydroxyl groups present in the fiber. This results in the formation of hydration products surrounding the fibers that form interconnections with the cement matrix, causing homogeneity and providing crack crack-bridging effect. The large amount of embedded hydration products forms a larger surface area can be seen in Figure 9c. The NCF has been reported to act as micro-level nucleation sites for the formation of C-S-H and other hydration products [⁶⁷, ⁶⁸]. Figure 9d shows the CS-FRC mix, with the dark rims indicating voids left by the steel fibers. The void surfaces show a smooth texture that might make it easier for the fibers to separate during bending. In the RNCSF (1.5:0.4) mix, the area between the fiber and matrix had some hydration products filling it moderately. The mixes with RHA and NCF did a better job at refining pores compared to the reference mix, as shown in Figure 9b and 9c. Likewise, the mixture with both CS and NCF demonstrated a strong ability to fill pores, which is evident in the steel fiber voids seen in Figure 9e. The high space-filling ability of RHA hydration products, combined with the intense hydration from RHA and NCF, led to significant microstructural improvements. This enhanced the bond between the matrix and steel fibers, boosting energy absorption.

3.6. Load-deflection behavior of RC beams

This section presents the findings and discussions regarding the impact of adding NCF and steel fibers on the flexural behavior of RC/FRC beams. It also examines the ductility performance, energy absorption capacity, and crack patterns of RC/FRC beams. Lastly, it compares the experimental investigations with finite element modelling.

The capacity of a structure to absorb energy during flexural loading is crucial for designing against blasts and earthquakes. The load-deflection behavior of RC/FRC beams was examined from the onset of loading until the beam specimens failed. Deflections corresponding to a load at an interval of 1 kN were recorded using LVDT. The complete load–deflection values for all the beams tested in the present study are provided in the supplementary file (Supplementary Material 1) for reference. Key observations were made at the initiation of the first crack and at the point of ultimate failure. Table 5 presents the load and corresponding deflection values for all the RC beams tested at the first crack stage and at the ultimate stage. The deflection values given in the table indicate the mid-span deflection at the given loads. Figure 10 displays the yield and ultimate load-carrying capacities of FRC beams. Analysis of the load-deflection behavior of RC/FRC beams was conducted to comprehend the changes resulting from the inclusion of steel fibers and NCF. The impact of steel fiber addition and hybridization of fibers, and the flexural behavior of the RC beams, can be observed from the load-deflection curves shown in Figure 11. From Figure 12, it is evident that all RC beam specimens undergo three primary stages. The initial stage is characterized by linear elasticity, where the relationship between beam load and deflection is proportional. The second stage commences with the initiation of cracking, and crack propagation follows a nonlinear trajectory up to the ultimate load. The third stage begins with the ultimate load and extends to the point of failure. The load-deflection behavior of FRC beams depends on the volume fractions and type of fibers present in the concrete. Figure 12 illustrates that for both FRC and hybrid FRC beams, the beams sustained higher loads even within the elastic region. Specifically, the beam containing crimped steel fiber (B5) showed a sharp increase in flexural behavior during the second stage. The beam with NCFs demonstrated favorable performance primarily in the initial stage, effectively delaying crack initiation. Conversely, the beam (B6) incorporating a hybrid combination of crimped steel (CSF) and NCFs exhibited remarkable performance in the second and third stages, with a gradual increase in deflection leading to enhanced energy absorption capacity. These findings suggest that the hybridization of steel fibers has beneficial effects on both the ultimate load and energy absorption capacity of RC beams.

Table 5
Load and deflection results of RC/FRC beams.

BEAM NO.	BEAM ID	FIRST CRACK STAGE		ULTIMATE STAGE
		LOAD (Pcr) (kN)	DEFLECTION (Δy) (mm)	LOAD (Pu) (kN)	DEFLECTION (Δmax) (mm)
B1	Control	47.01	4.20	66.06	7.27
B2	RNCF-0	55.06	3.76	65.92	6.75
B3	RNCF-0.4	61.22	4.06	78.66	8.96
B4	RNCF-0.6	55.13	3.86	74.57	8.02
B5	RCSF-1.5	79.93	3.04	101.25	8.47
B6	RNCSF (1.5:0.4)	92.83	3.13	116.27	8.54
B7	RNCSF (1.5:0.6)	91.66	2.64	112.31	7.03

Figure 10
First crack and ultimate crack loads of RC/FRC beams.

Figure 11
Load-deflection curves of RC/FRC beams -B1, B2, B3, and B4.

Figure 12
Load-deflection curves of RC/FRC beams- B5, B6, and B7.

The flexural behavior of RC beams, the area under the load-deflection curve, was evaluated as an indicator of the energy absorption capacity of FRC composites. The addition of steel fibers and NCF resulted in a significant enhancement of flexural ductility compared to the control concrete mix. The influence of SCM addition on the fiber-reinforced concrete (FRC) beams is evident from Figures 11 and 12. It is apparent from the figure that the addition of both CSF and NCF significantly enhances the ultimate load-carrying capacity of FRC beams. The toughness and energy absorption capacity of FRC beams B6 and B7, which contain CSF and NCF, showed marked improvement compared to the control beam B1. Particularly, the inclusion of 1.5% CSF led to a remarkable enhancement in the second stage of the load-deflection response. This improvement in flexural behavior can be attributed to the formation of a stronger fiber-matrix bond due to the development of more robust interfacial components. The load-deflection curve of beam B7 exhibited a steeper slope, indicating enhanced crack resistance due to the presence of NCFs.

3.7. Ductility results of RC beams

Ductility refers to the capacity of the beam to endure inelastic deformation without experiencing a reduction in its load-carrying capability before reaching failure. Ductility is commonly represented by a ratio known as the ductility index or factor.

3.7.1. Deflection ductility

The ductility index measures deflection flexibility and is determined by the ratio of the deflection at the point of failure to the deflection at which the tensile reinforcement begins yielding. Adding the displacement ductility index offers another factor, along with strength, to predict the performance of RC/FRC beams. This ductility index is essential for the effectiveness of structures designed to withstand earthquakes, seismic activity, and blasts. The expression for measuring the deflection ductility of the beams is given in Eqa. 1.

(1) $${\mu }_u={\mathrm{\Delta }}_{max}\text{/}{\mathrm{\Delta }}_{\text{y}}$$

Where µ_u is the deflection ductility index, Δ_y is the deflection at first crack, and Δ_max is the deflection at ultimate load. The deflection ductility index of a standard RC beam is primarily influenced by its size and the amount of reinforcement incorporated. Therefore, maintaining a consistent reinforcement ratio can help predict the improvement in ductility due to the addition of fibers. For beams, the deflection ductility index has been observed to range from 1 to 5, with 1 indicating elastic responsiveness and 5 representing greater ductility [⁶⁹]. Considering that numerous factors influence the deflection at peak load, the most reliable evaluation would be based on the ductility enhancement ratio relative to the control beam. A ductility improvement ratio ranging from 1.5 to 3 suggests that a structural element possesses sufficient energy absorption capacity and can sustain deformations before reaching failure.

The deflection ductility ratios for the beams were calculated and are presented in Table 6. The deflection ductility index derived from this current experimental investigation varies between 1.73 and 2.78, and the ductility ratios for the beams ranged from 1 to 1.61. In fiber-reinforced RC beams with CSF, a pullout behavior was observed during fiber failure at the ultimate stage. Conversely, the inclusion of RHA enhanced the bond between the fiber and matrix, resulting in a crack-bridging effect. The inclusion of both CSF and NCF led to an enhancement in the deflection ductility improvement ratio by up to 58%. A beam with fibers of CS = 1.5% and NCF = 0.4% in the RC beam demonstrated notable improvement in the deflection ductility index. A comparison of the deflection ductility ratios of various beams is presented in Figure 13. Most of the beams achieved a deflection ductility index exceeding 2, indicating that structural elements constructed with FRC beams can sustain deformations prior to failure. The inclusion of NCF and CSF fibers significantly enhanced the deflection ductility index of RC beams, indicating improved deformation capacity under load. Hybrid fiber-reinforced beams (B6 and B7) exhibited superior ductility, with B5 showing the highest index (2.78), demonstrating effective energy dissipation. Compared to the control beam, all fiber-reinforced mixes showed increased ductility ratios, confirming the positive impact of fiber addition on structural performance.

Table 6
Deflection ductility results of FRC beams.

BEAM NO.	BEAM ID	FIRST CRACK STAGE	ULTIMATE STAGE	DEFLECTION DUCTILITY INDEX µu = Δmax/Δy	DEFLECTION DUCTILITY RATIO
		(Δy) (mm)	(Δmax) (mm)
B1	Control	4.20	7.27	1.73	1.00
B2	RNCF-0	3.76	6.75	1.80	1.04
B3	RNCF-0.4	4.06	8.96	2.21	1.28
B4	RNCF-0.6	3.86	8.02	2.08	1.20
B5	RCSF-1.5	3.04	8.47	2.78	1.61
B6	RNCSF (1.5:0.4)	3.13	8.54	2.73	1.58
B7	RNCSF (1.5:0.6)	2.64	7.03	2.67	1.54

Figure 13
Deflection ductility ratios of RC/FRC beams.

3.7.2. Energy ductility

Energy ductility is computed to assess the energy absorption capability of the RC/FRC beam from the point of yielding up to the ultimate loading. The energy ductility index serves as an indicator of the beam’s capacity to absorb fracture energy and its resistance to abrupt failure while maintaining adequate load-carrying capacity and undergoing deformations. The energy ductility index is the ratio of the energy absorbed up to the load corresponding to ultimate deflection to the energy absorbed up to the deflection at the initial cracking point. The expression given in Eqa. 2 can be used to denote the energy ductility index

(2) $$U_E=A_p\text{/}{A}_u$$

Where A_u is the area under the load-deflection curve at first crack load, and A_p is the area under the curve before the load drops to 15% of the peak load.

The energy ductility index and energy ductility ratio of FRC beams are given in Table 7. The energy ductility indices of NCF beams were in the range of 3.15 to 3.27, and for HyFRC beams, the values were in the range of 4.30 to 5.11. Figure 14 provides a graphical representation of the energy ductility indices of all the beams. RC beam with a hybrid fiber combination of CS = 1.5% and NCF = 0.4% exhibited the most significant enhancement in energy ductility, being 1.73 times higher than that of the control RC beam specimen. The energy absorption index of beam B2, containing RHA = 20%, was higher than that of beam B1. The blending of CSF and NCF in the HyFRC beam (B6) demonstrated an energy absorption that was 189.8% higher than the control beam B1, 10.98% more than the beam with RHA = 20%, 37.5% greater than beam B4 containing NCF = 0.4%, 29.2% more than beam B5 containing CS = 1.5%, and 18.3% higher than beam B7 containing CSF = 10% and NCF = 0.6%. To ensure a meaningful comparison, the energy absorption capacity of all beams was assessed up to a constant deflection point of 15mm. Table 8 presents the total energy absorption values measured up to 15mm. From the table, it is seen that the energy absorption of the hybrid FRC mix (B6) containing CS = 1.5% and NCF = 0.4% shows improvement over the NCF RC mix (B3) containing NCF = 0.4%. The HPFRC mix (B6) presented maximum energy absorption compared to all other beams from the present study. Figure 15 illustrates the improvement in energy absorption ratio up to 15mm deflection for FRC beams (Increase compared to the control beam B1). The enhanced performance of hybrid FRC beams is attributed to the complementary action of CSF and NCF, where CSF controls macro-crack propagation and NCF prevents micro-crack initiation. This dual-scale crack-bridging mechanism improves energy dissipation and overall ductility under flexural loads. Additionally, the optimized fiber content promotes a denser matrix with improved bonding and load transfer efficiency.

Table 7
Energy ductility results of RC/FRC beams.

BEAM NO.	BEAM ID	FIRST CRACK STAGE	ULTIMATE STAGE	ENERGY DUCTILITY INDEX	ENERGY DUCTILITY RATIO
		UE	UE
B1	Control	236.55	731.22	3.09	1.00
B2	RNCF-0	259.93	818.87	3.15	1.02
B3	RNCF-0.4	326.68	1068.27	3.27	1.06
B4	RNCF-0.6	275.01	882.76	3.21	1.04
B5	RCSF-1.5	312.06	1340.73	4.30	1.39
B6	RNCSF (1.5:0.4)	414.79	2119.10	5.11	1.65
B7	RNCSF (1.5:0.6)	389.90	1909.29	4.90	1.58

Figure 14
Energy ductility index of RC/FRC beams.

Table 8
Energy absorption and its improvement ratio of RC/FRC beams.

BEAM NO.	BEAM ID	ENERGY ABSORPTION UP TO 15 MM DEFLECTION (kN-m)	RATIO OF ENERGY ABSORPTION OF BEAMS
B1	Control	1428.23	1.00
B2	RNCF-0	2722.49	1.16
B3	RNCF-0.4	2334.31	1.63
B4	RNCF-0.6	2192.77	1.54
B5	RCSF-1.5	3200.12	2.24
B6	RNCSF (1.5:0.4)	3989.41	2.79
B7	RNCSF (1.5:0.6)	3666.73	2.57

Figure 15
Ratio of energy absorption up to 15mm deflection for FRC beams (increase compared to the control beam B1).

3.8. Crack pattern and failure modes of RC/FRC beams

The crack patterns and propagation mechanisms of all beam specimens are depicted below. The development of both micro and macro cracks is indicated in the respective beams up to the point of failure. The widest cracks occur at the location of the ultimate load application. The inclusion of fibers is essential for managing cracks and bridging their propagation. Hybridizing fibers results in a decrease in the number of microcracks due to the crack-bridging effect of NCF. Additionally, in hybrid fiber beam specimens, the width of the predominant crack was observed to be narrower compared to beams with a single type of fiber, as shown in Figure 16. The addition of pozzolans also affects the crack formation mechanism. When pozzolans and hybrid steel fibers are incorporated, the beam displays fewer cracks that are spaced further apart. Beams with either single or hybrid combinations of CS and NCF show decreased crack widths across all load levels and a significant reduction in the number of cracks compared to the control RC beam. The prevention of both micro and macro cracks relies on the pullout effect capability of either single-type fibers or hybrid fibers. The crack growth patterns observed for the RC/FRC beams are illustrated in Figure 16. The figure indicates that the addition of fibers, particularly NCF, reduces the occurrence of microcracks and hinders the spread of macrocracks due to a robust fiber-matrix bond. At the failure point, only a few major cracks were observed. In beams with CSF, fiber breakage was more prevalent than fiber slippage. In Beam B5 with 1,5% of SF, fiber failure occurred mainly due to slippage, resulting in a greater number of cracks compared to B6 and B7 beams, although the crack widths were minimal. FRC beam (B6) showcased the combined benefits of both CSF and NCF in terms of crack bridging and crack count. The interaction between pozzolan and fibers was found to significantly reduce crack propagation.

Figure 16
Crack pattern of RC/FRC beams.

3.9. Numerical investigations on RC/FRC beams

3.9.1. Finite element analysis of RC beams

Finite element analysis (FEA) is a methodical approach for examining complex structural and fluid problems. ABAQUS was chosen for simulating RC beam behavior in this research due to its intuitive interface and ability to handle parametric modeling effectively. ABAQUS comprises a suite of robust engineering simulation tools capable of handling a wide range of analyses, from straightforward linear ones to intricate nonlinear simulations. Each mesh of finite elements represents a portion of the structure and is linked to adjacent elements through common nodes. The mesh, composed of nodes and finite elements, defines this discretization. Mesh density refers to the ratio of elements within the mesh relative to the physical dimensions (length, area, or volume). In stress analysis, ABAQUS primarily computes node displacements as key variables. Once these displacements are determined, stress-strain values of each finite element can be computed accordingly.

3.9.2. Modeling and boundary conditions

Concrete was simulated using a 3D 8-node hexahedral element with reduced integration (C3D8R). The steel reinforcement bars and stirrups embedded in the concrete structure were modeled using B31 elements (3D linear beam). The reinforcement elements were embedded within the concrete domain using the embedded region constraint technique, which ensures a perfect bond assumption between steel and surrounding concrete. This approach effectively transfers stress and strain across the concrete–steel interface without requiring explicit contact definitions, thereby simplifying the computational model. Material attributes such as the elasticity modulus designated as EX and Poisson’s ratio (PRXY) were assigned for all the beams. In addition, appropriate stress-strain relationship was defined for the reinforcing steel to capture yielding and strain hardening characteristics. Meshing is vital in finite element analysis, as increasing element numbers improves accuracy but also increases computation time. The modeled and meshed representation of FRC beam is depicted in Figure 17a. Loads cause deformation in the physical structure, leading to the development of stress within it. Boundary conditions were utilized to restrict elements from the model from remaining stationary or to move by specified amounts, since unrestricted rigid body motion can result in a unique stiffness matrix, potentially causing issues for the solver during the solution phase and prematurely terminating the simulation. Figure 17b illustrates the specific boundary conditions applied to the RC beam.

Figure 17
(a) Meshing of beams; (b) Boundary conditions.

3.9.3. Analytical behavior of RC beams

Static analysis was employed to assess the long-term structural response under applied loads. Seven RC beams analyzed using nonlinear finite element analysis were compared and discussed with experimental findings. The experimental and analytical deflections of FRC beams at ultimate loads are detailed in Table 9, while the load versus deflection behavior is illustrated in Figs. 18 (a)-(g). For instance, experimental deflection for beam B1 at an ultimate load of 66.06 kN measured 7.27 mm, whereas the corresponding FEA-predicted load and deflection were 69.71 kN and 5.7 mm, showing a variation of 5.5% and 21.6%, respectively. Similarly, for FRC beam (B3) at 78.66 kN, experimental deflection was 8.96 mm compared to FEA’s 73.85 kN and 7.35 mm, with a maximum variation of 6.11% and 17.97%, respectively. For the Hy-FRC beam (B6) at 116.27 kN, experimental deflection was 8.54 mm compared to FEA’s 114.71 kN and 9.33 mm, with a maximum variation of 1.35% and 9.25% respectively. Analytical crack patterns of FRC beams are depicted in Figure 19. Comparing numerical results from FEM with experimental data reveals load and deflection values with a maximum error of 6.67% and 28.76%. The addition of cellulose fibers alongside steel fibers enhances crack control and improves ductility through synergistic fiber bridging. The numerical models accurately capture both pre-peak and post-peak load-deflection behaviors observed in experimental testing, demonstrating good agreement between numerical predictions and experimental results across all beams.

Table 9
Load and deflection of RC/FRC beams by numerical methods.

BEAM NO.	ULTIMATE LOAD (kN)		ERROR (%)	DEFLECTION (mm)		ERROR (%)
	EXPERIMENTAL	NUMERICAL		EXPERIMENTAL	NUMERICAL
B1	66.06	69.71	5.53	7.27	5.7	21.60
B2	65.92	70.32	6.67	6.75	5.97	11.56
B3	78.66	73.85	6.11	8.96	7.35	17.97
B4	74.57	72.33	3.00	8.02	7.57	5.61
B5	101.25	104.02	2.74	8.47	8.63	1.89
B6	116.27	114.71	1.34	8.54	9.33	9.25
B7	112.31	109.82	2.22	7.03	6.21	11.66

Figure 18
Load versus deflection behavior of RC/FRC beams.

Figure 19
Analytical crack patterns of RC/FRC beams.

Experimental and numerical results of the analyses of RC/FRC beams demonstrate that the crack pattern and the mode of failure match well, where both techniques have been able to differentiate the sequence between microcracks and macrocracks that result in the eventual failure. As observed experimentally, the inclusion of fibers considerably narrows and decreases the count of cracks, especially in hybrid fiber beams, owing to an increase in the crack-bridging and fiber-matrix bond effects. These trends are well reproduced using numerical finite element models, which faithfully represent smaller and more limited cracks in fiber-reinforced specimens, and are also strongly similar in the location and path followed by larger cracks. The load-deflection responses are also the most consistent, with maximum errors of 6.67 percent load and 28.76 percent deflection, indicating that numerical models can be used to predict both the pre-peak and post-peak characteristics. Fiber beams: In hybrid fiber beams, the ductility and crack control improvements observed in experiments are reflected in the numerical results. Overall, the differences are small and mostly relate to the accurate measurement of crack widths and locations, which numerical models underestimate deflections somewhat, but reproduce failure modes and the general character of crack development well.

An analytical examination of related research indicates some definite benefits of the current study. First, the hybrid system (CS + NCFs with pozzolans) is a higher ultimate load and narrower cracks with broader distance between them, which is congruent with and exceeds what has been reported by others: hybrid or dual-fiber concretes are superior to single-fiber mixes in terms of post-cracking toughness and control of cracks [⁷⁰, ⁷¹]. The experimental-FEA correspondence (≤ 6.7% in ultimate load; ≤ 28.8% in deflection) is statistically consistent with other recent validations of RC beam experiments, which find that flexure is well matched experimentally-numerically by our modeling framework [⁷², ⁷³]. In comparison to steel-only or PP-only beams, the hybrids from the present study reflect the literature developments in which steel dominates post-crack stiffness with synthetics/natural fibers holding the crack open, resulting in superior balanced ductility and serviceability [⁷⁴, ⁷⁵]. It has also been found that the synergistic relationship between the addition of fibers and pozzolans enhances strength and durability–a phenomenon which our findings support when subjected to flexural loading [⁷⁶]. Moreover, previous data show that hybrid mixes increase cracking load (≈ +14%) and decrease the crack widths compared to single-fiber controls; the beams from the present study follow the same trend with further improvements by NCF-CS synergy [⁷⁷, ⁷⁸]. The present study provides a more serviceable, ductile, and numerically predictable RC/FRC beam while using fibers combined with pozzolans and validating using FEA, compared to the traditional or single-fiber solution, thereby reinforcing and enhancing the existing literature [⁷⁹].

4. CONCLUSIONS

Results from the experimental program carried out present the following conclusions:

• The addition of RHA made the HPC more brittle. The inclusion of NCFs in such densely packed matrices provides ductility and crack-bridging mechanism. The mixes RNCF-0 and RNCF-0.4 exhibited a 28-day compressive strength increment of 9.5% and 27.8% when compared to the reference mix.

• The maximum increase in flexural tensile strength due to the addition of NCFs was found to be about 40.6% with respect to the control mix,

• In HPC mixes, the role of RHA was more attributed to the particle packing and secondary C-S-H gel formation. Whereas, the NCFs contributed more towards the improvement in modulus of elasticity by minimising the transverse propagation of cracks under axial loading. The findings suggest that the static modulus of elasticity of RHA-NCF mixes showed improvement over the RHA mix.

• The observations indicated a stronger interface between the matrix and aggregate due to the addition of NCFs, resulting in enhanced toughness and energy absorption.

• The load versus displacement graph shows that fiber volume fraction and geometry play major roles in the toughness characteristics of concrete. The hybridization was effective in the early stages of deflection, as the final stage of the post-cracking toughness was dependent on the volume fraction of the steel fiber only.

• The ductility index for most of the tested beams are above 2. The inclusion of both CSF and NCF led to an enhancement in the deflection ductility improvement ratio by up to 58% compared to the reference beam.

• The RC beam with HyFRC mix containing CS = 1.5% and NCF = 0.4% exhibited the most significant enhancement in energy ductility, which was 1.73 times higher than that of the control RC beam.

• Energy ductility index assessed for the HyFRC beams showed improvement over NCF beams, which indicates the higher energy absorption capacity of hybrid fibrous concrete composites.

• The blending of CSF and NCF in the HyFRC beam (B6) demonstrated an energy absorption that was 189.8% higher than the control beam B1, 10.98% more than the beam with RHA = 20%, 37.5% greater than beam B4 containing NCF = 0.4%, 29.2% more than beam B5 containing CS = 1.5%, and 18.3% higher than beam B7 containing CSF = 10% and NCF = 0.6%.

• It was observed that CS fibers contributed to the strength, toughness, and ductility, whereas NCFs are effective in providing control of cracks.

• The energy absorption capacity of all beams assessed up to a constant deflection point of 15mm reveals that the inclusion of pozzolans enhanced the fiber bridging effect and energy absorption capacity of the RC beams. The beam B11 showed the maximum energy absorption capacity.

• Numerical models developed for the flexural behavior of FRC beams are compared with experimental load vs. deflection results. The predicted results were in agreement with the experimental values.

5. LIMITATIONS AND FUTURE SCOPE

The current research has a few limitations, which include lack of crack width and strain distribution measurements and assumption of a perfect bond between steel and concrete without specific bond-slip modeling. There were only 1 RC beam specimen per mix which can limit the statistical validity of the findings. These limitations will be addressed in the future through the provision of crack width in studies, the adoption of advanced constitutive models (damage plasticity), and an explicit way of modeling bond-slip behavior. The validation of the results will be increased by increasing the number of RC beam specimens. More precise finite element modeling will also be performed through convergence studies.

6. ACKNOWLEDGMENTS

The authors express their sincerest gratitude to the research laboratory and the personnel in the Roever Engineering College for their support in the research project.

SUPPLEMENTARY MATERIAL

The following online material is available for this article:

Table S1

Load-deflection values of beams.

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Publication Dates

• Publication in this collection
  05 Dec 2025
• Date of issue
  2025

History

• Received
  21 June 2025
• Accepted
  20 Oct 2025