Flexural and shear performance of concrete beams reinforced with macroscopic carbon nanotubes using finite element modelling

Abstract

Carbon nanotubes (CNTs) are one among many materials that are used to reinforce concrete alongside steel bars. They are known for their exceptional mechanical properties which have been found to improve the mechanical performance and crack resistance of cementitious materials Although CNTs are usually incorporated into concrete as nano-fillers, fibres, or powders, this study aimed at using CNTs in a macroscopic form as bars to replace steel bars in reinforcing concrete. Numerical investigation on the flexural and shear performance of concrete beams reinforced with macroscopic CNT bars was carried out using Finite element method (FEM) in ANSYS 17.2. Six simply supported beams each of RCC and macroscopic CNTs comprising Concrete Grades 40, 60, 120, 200, 300, 400 making a total of twelve beams were designed in accordance with ACI 318-19, simulated and analyzed under four-point bending. The results show that the CNT–reinforced beams in comparison to RCC beams had a higher load–carrying capacity which was up to 720 kN in difference and approximately 1.84 times that of RCC beams and this increased with higher concrete grades. From the load–deflection response, CNT–reinforced beams experienced enhanced deformation capacity at most concrete grades, ductility improved as much as 62.7%, while elastic stiffness was consistently higher than RCC beams at all grades, with improvements up to 14.4%. The flexural and shear performances as well outweighed that of RCC beams at most grades with flexural and shear capacities increasing from 496.84kNm to 912.15kNm and from 432.04kN to 793.18 kN respectively representing an improvement of 83.6%. However, when compared to the designed flexure and shear capacities, the CNT–reinforced beams performed better in flexure than shear. Failure in all RCC and macroscopic CNT–reinforced beams was governed by a combined flexure-shear action, but CNT beams had more distributed cracks indicating improved load redistribution before failure.

Introduction

Steel has been one of the oldest and major material used to reinforce concrete because it has a high tensile strength, ductility and energy absorption, and when compared to other reinforcing materials, it is readily available and cost effective. In the early 20th century, steel reinforcement in concrete was introduced, transforming concrete from a compression-only material to structural elements that have the ability to resist tensile stresses, maintain structural integrity under service loads, improves the load-carrying capacity and possess better crack control (ACI Committee 318, 2019). These advantages of steel supplement the brittle nature and low tensile strength of concrete. There are some limitations of steel some of which include corrosion that can be rated between 0.1 and 1 mm/year in chloride environments, high density of 7850kg/m3, high maintenance and life-cycle cost (often 2 to 3 times the life-cycle expenses) (fib Bulletin 49, 2009; Allwood et al., 2011; Rabi et al., 2022). Also, the Carbon dioxide (CO₂) emissions from steel production have been on the rise since 2015, as stated in the Breakthrough Agenda Report 2023 by the IEA, IRENA & UN Climate Change High-Level Champions (2023).

Over the years, researchers have been discovering and trying new materials that could be used as alternatives to steel reinforcement in concrete, either used alongside it or as full replacements. These materials include fibres (steel, synthetic, glass, carbon), fibre-reinforced polymers (glass, carbon, basalt, aramid), natural fibres (bamboo), shape memory alloys and recently, nanomaterials (ACI Committee 440, 2015; Hensher, 2016; Ashby 2012). Among the emerging nanomaterials are carbon nanotubes (CNTs) which have mechanical properties that stand out and superceeds all other materials, and they are of two types: single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs). Their tensile strengths could exceed 50 GPa and their elastic moduli as high as 1 TPa, their densities are about one-quarter of steel, thus making them ideal for lightweight, corrosion-free reinforcement (Salvetat et al., 1999; Babu, 2017; Sindu and Sasmal, 2017; Carriço et al., 2018).

Some studies and comprehensive reviews have shown CNTs to improve the mechanical performance and crack resistance of cementitious materials as well as refine the microstructure of concrete when there are properly incorporated (Chousidis and Zeris, 2025; Reales and Toledo Filho, 2017; Zhang et al., 2023), although most existing studies focus on CNTs as nanofillers dispersed in cement paste or mortar rather than using CNTs as structural reinforcement elements in concrete beams (Zhang et al., 2020; Bogas et al., 2021; Chousidis, 2025). The CNTs generally used in concrete to enable improvement in its compressive strength, flexural strength, tensile strength, and durability, have been in the form of fibre or powder (Mohsen et al., 2017; Mohammadyan-Yasouj, and Ghaderi, 2020). They are typically added in small amounts (about 0.01%–2% of the cement weight) and have been seen to improve the mechanical properties of concrete by about 20%–52% (Carriço et al., 2018; Song et al., 2017). There is a limitation to its effectiveness though because CNT particles tend to stick together due to van der Waals forces, thus making proper dispersion difficult. So to overcome this, researchers often modify the CNT surface through functionalization (for example, by adding carboxyl groups) to improve their distribution within the concrete matrix (Li et al., 2005; Tamimi et al., 2016).

The application of macroscopic CNT bars designed to replace conventional reinforcement bars remains limited in existing literature and so this research represents a clear gap in studies addressing structural performance using CNT bars as principal longitudinal reinforcement. Earlier studies have however demonstrated the possibility of producing macroscopic CNT assemblies from nanoscale structures. Zhang et al. (2015) reported the fabrication of macroscopic CNT bundles and fibres from spinnable CNT arrays produced using chemical vapour deposition (CVD). Through this process, aligned CNT arrays were drawn and assembled into larger bundles and cords with high tensile strength, suggesting their potential use in structural applications such as prestressing and suspension systems (Babu, 2017; Chandran, 2020). A pilot study conducted by (RameshBabu, 2021) was on a finite element analysis of high-strength concrete columns reinforced with macroscopic CNT bars. The macroscopic CNT-reinforced columns demonstrated significant strength improvements, as they gained 12%–35% higher axial capacity when compared to traditional steel-reinforced columns. These findings show the potential of CNT bars to carry substantial structural loads in columns and create an opportunity for further research assessing the structural behaviour of beam elements reinforced with macroscopic CNT bars under service and ultimate load conditions. Overall, this pilot study suggests the feasibility of structural applications of CNTs at larger scales beyond nano-filler effects alone.

Because experimental studies can be expensive and time-consuming, computational modelling, especially the finite element method (FEM), becomes invaluable for studying advanced reinforcement systems. FEM helps in a detailed simulation of nonlinearities of materials, cracking, and interactions between concrete and reinforcements, which makes it suitable for studying structural behaviour under flexure and shear. Several studies (Tawfik et al., 2021; Pandimani et al., 2022; Mohammad et al., 2025) have demonstrated the effectiveness of nonlinear FEM procedures for predicting load–deflection response, crack patterns, and ultimate capacities of reinforced concrete beams using commercial software platforms. ABAQUS and ANSYS software, for example, makes use of concrete damaged plasticity (CDP) and SOLID 65 elements respectively to make predictions of these load-deflection responses and capacities as per Kent-Park stress-strain laws (Kent and Park, 1971; Genikomsou and Polak, 2015; Abdulrahman, 2025; Movchan, 2025). These models can be validated against experimental results or available standards and then used for parametric studies across a wide range of material and geometric configurations.

In the context of CNT-reinforced concrete, the FEM approach typically models CNT effects either through equivalent mechanical property enhancement or as discrete reinforcement elements. When properly calibrated, such models can replicate observed structural responses and facilitate significant performance comparisons without extensive physical testing. Since most past research treated CNTs as dispersed additives rather than as primary longitudinal reinforcement equivalent to steel bars, and little or no studies have specifically addressed the flexural and shear behaviour of beams reinforced solely with macroscopic CNT bars and how these responses compare with reinforced concrete beams, this research thus addresses that gap and therefore becomes a pilot study. By integrating CNT bars into the beam models and analysing the resulting load-deflection behaviour, stiffness, ductility, crack and failure loads, flexural and shear capacities, this work aims to provide insight into the potential structural advantages and limitations of using CNT reinforcement at the macro scale. The outcomes will contribute to advancing high-performance concrete design using emerging nanostructured reinforcement technologies and demonstrate the practical value of finite element modelling for evaluating next-generation composite reinforcement systems.

Materials and methods

Design details

Twelve (12) concrete beams comprising grades 40, 60, 120, 200, 300, and 400 were designed as simply supported beams (hinged on one end and roller at the other end) in accordance with ACI 318–19. Longitudinal and shear reinforcements were provided for all beams based on design requirements. The beams were analysed under four-point loading and loaded up to their full design moment capacity to simulate flexural behaviour. For each concrete grade, two models were developed: one reinforced with conventional steel bars (RCC) and the other reinforced with macroscopic carbon nanotube (CNT) bars, resulting in a total of twelve numerical models. The geometry, loading configuration, and reinforcement arrangement are presented schematically in Figure 1, while the detailed design parameters of the beams are given in Table 1.

FIGURE 1

Mesh, boundary conditions and loading

Nonlinear Finite Element Analysis (NLFEA) was carried out using ANSYS version 17.2 ANSYS (2016). The finite element model consisted of concrete solid elements and embedded beam elements representing the longitudinal reinforcement and stirrups. The concrete beam was discretised using a structured mesh to ensure adequate accuracy while maintaining reasonable computational cost. A typical finite element mesh of the beam model is shown in Figure 2. Simply supported boundary conditions were applied by restraining vertical and lateral displacements at the hinged support and allowing horizontal movement at the roller support. Four-point loading was applied as two equal concentrated loads placed symmetrically about the midspan to simulate pure bending in the constant moment region.

FIGURE 2

Concrete

Concrete was modelled using SOLID 65 element in ANSYS Library. This element is mostly used for modelling concrete as it permits the modelling of solids with or without reinforcing bars, allows the input of nonlinear material properties and is capable of cracking and crushing (ANSYS Manual). Linear Isotropic properties (Young’s modulus of elasticity and Poisson’s ratio) and multilinear Isotropic hardening properties were used for modelling the concrete. The Young’s modulus of elasticity E_c used was calculated for each of the concrete grades by respectively multiplying 5700 by the square root of their characteristic compressive strengths (f’_c) in accordance with ACI 318-19 provisions.

Steel and macroscopic CNT–reinforcing bars

BEAM 188 element in ANSYS Library was used to model the Steel bars, stirrups as well as the CNT bars, as this supports linear and nonlinear material models such as elasticity, plasticity, and creep. The CNTs were modelled as macroscopic bars similar to steel reinforcement, having the following geometry: three main bars of 16mm and 20 mm diameter each for concrete grades 40, 60, 120 and concrete grades 200, 300, 400 respectively as well as 2 top bars to hold the stirrups in place. The reinforcing bars were defined as discrete beam elements generated along the nodal lines corresponding to their actual locations within the concrete section. The properties of the steel and CNT reinforcing bars considered were density, Young’s modulus of elasticity Poisson’s ratio and yield strength (F_y), although the value for CNT bars is that of an assumed fracture stress seeing that CNTs display no visible yielding before fracture. See Table 2 for details. The longitudinal bars assumed the bilinear isotropic hardening model and the stirrups assumed that of the linear isotropic material properties.

Results and discussion

Cracking load and ultimate load behavior

The cracks and crushing plots were obtained to observe the cracks in the beams. The beams were observed at first cracks and at failure and the corresponding loads were recorded. First Cracks appeared in CNT beams much before RCC beams (see Figure 3A) but they occurred at loads slightly higher than RCC beams, with the difference ranging between 5 kN and 16kN, (see Figure 3B), which may be attributed to the brittle but strong nature of CNTs. It was also observed (see Figure 3B) in both beam types that the load at which first cracks appeared increased as the concrete grade increased which indicates a delay in crack formation as concrete became stronger. This behaviour can be partly explained by Hu et al. (2014), who showed that MWCNTs at 0.05 and 0.10 percent by weight (wt%) of cement can bridge cement particles and form a network that transfers load enhancing the matrix’s resistance to cracking, which may contribute to the higher ultimate load observed in CNT beams despite early cracking and the crack delay associated with higher concrete grades. The major difference between RCC beams and CNT beams appeared at failure where CNT beams had a much higher load–carrying capacity, with differences reaching up to 720 kN and about 1.84 times that of RCC beams and this increased with higher concrete grades (see Figure 3C). This highlights the high tensile capacity of macroscopic CNT reinforcement and also confirms that although CNTs might be relatively brittle than Steel, they can carry higher structural loads before failure.

FIGURE 3

Load deflection response

The load–deflection curves of macroscopic CNT-reinforced beams as seen in Figure 4 show an increasing linear trend of deflection with increasing load. The curves show that all CNT beams behaved linearly at the initial stage of loading before cracking occurred and then a not so visible change in curvature after the first cracks, which is similar to the experimental study carried out by Naji et al. (2021) when MWCNTs was used to enhance reinforced concrete beams in flexure. Beams CNT40, CNT200 and CNT400 show similar curve lengths as they failed at approximately 0.65mm–0.68 mm despite their differences in load carrying capacity. In contrast, beams CNT60, CNT120 and CNT300 showed significantly higher deflections resulting in longer load deflection curves. CNT300 beam however recorded the largest deflection of 1.266 mm and highest ultimate load carrying capacity of 1586.35 kN. All CNT beams except that of grades 40 and 200, exhibited higher deflections at failure than RCC beams as seen in Figure 5. It can be deduced from these results that macroscopic CNTs increased the ultimate deformation capacity of the concrete beams and that higher concrete grades improve the load–carrying capacity but not necessarily the deflection behavior as deflection depends on the concrete strength and the CNT reinforcement.

FIGURE 4

FIGURE 5

Principal stress, shear stress and strain behaviour

Contour plots of first principal stress (S1), third principal stress (S3), XY shear stress (SS), and total mechanical strain (TMS) were examined to evaluate the stress distribution and deformation behaviour of the beams. These parameters capture the tensile behaviour, compressive response, shear stress distribution, and strain development within the beam under loading. The results were compared for CNT-reinforced beams and RCC beams across concrete grades 40–400. The maximum and minimum values of each parameter extracted from the contour plots are noted in Table 3, while representative stress and strain distributions are shown in Figures 6–8. The S1 results shows that CNT beams consistently developed higher tensile stresses than RCC beams. It is seen where the maximum tensile stress increased from 278.72 MPa in CNT40 to 495.69 MPa in CNT300, whereas the corresponding RCC values ranged from 105.92 MPa to 118.65 MPa. Similarly, the S3 results show larger compressive stresses in CNT beams, reaching −428.69 MPa for CNT300 compared with −69.78 MPa in RCC300, indicating that the CNT-reinforced beams sustained higher internal stresses before failure. The SS contours also displayed the expected diagonal stress pattern near the supports, with CNT beams showing higher shear stress values at higher concrete grades, such as 39.38 MPa for CNT300 compared with 20.42 MPa for RCC300.

FIGURE 6

FIGURE 7

FIGURE 8

The strain contours further indicate that RCC beams developed larger tensile strains, reaching 0.001859 in RCC40, whereas CNT beams showed relatively lower tensile strain values, indicating higher stiffness and reduced deformation. According to ACI 318, the modulus of rupture of concrete is approximately f_r = 0.62SQRTf’_c, which for Grade-40 concrete corresponds to only a few megapascals of tensile capacity. The higher tensile stresses obtained from the finite element analysis therefore occur because the concrete in the tension zone has cracked and the tensile forces are primarily carried by the reinforcement. The code also assumes an ultimate concrete compressive strain of about 0.003 in flexural members. The strain contours show that the compression zone approaches the ultimate concrete compressive strain limit as loading increased, confirming that the beams reached the flexural failure state. The contour plots in all showed that CNT reinforcement allowed the beam to sustain higher tensile, compressive, and shear stresses while having lower strain levels compared with RCC beams.

Ductility

The ductility results indicate that the CNT-reinforced beams exhibited superior ductile behavior compared to RCC beams across all except concrete grades 40 and 200 in which there was a 31.8% and 30.5% reduction in ductility respectively. There was a greater improvement in the ductility of CNT120 and CNT300 with the latter having the highest ductility of 2.68 signifying a 62.7% enhancement (Figure 9A), which implies the ability of CNT beams to be able to undergo larger inelastic deformation after yielding. This improved ductility may also be supported by previous studies, where functionalized SWCNT and MWCNT at 0.08 and 0.10 wt% of cement showed significantly better ductile behavior under flexural testing of notched specimens of carbon nanotube reinforced cementitious composites (Parveen et al., 2015). The increase in the ductility of CNT beams may be because of their ability to carry more load even after the initial cracks.

FIGURE 9

Stiffness

The stiffness was calculated in the elastic region and CNT beams exhibited higher elastic stiffness in comparison to RCC beams and increased consistently at all grades (see Figure 9B). This implies that the use of macroscopic CNT bars provided initial rigidity and improved the flexural stiffness in the uncracked section of the beams, which may be due to the superior modulus of CNTs. The stiffness of CNT beams was enhanced for all concrete grades by 14.4%, 11.8%, 8.8%, 7.6%, 6.3%, and 5.7% respectively. Konsta-Gdoutos et al. (2010) showed that adding short and long MWCNT fibres makes cement paste stiffer. This happened because the nanotubes helped form more C–S–H gel and reduce porosity, even at a small dosage of 0.16% by weight of water. Similarly, Parveen et al. (2015) reported that cement mixtures containing SWCNT and MWCNT at 0.08 and 0.10 wt% of cement exhibited significantly higher stiffness, fracture energy, and ductility which aligns with the higher elastic stiffness observed in CNT beams.

Flexural capacity

The flexural capacity of CNT beams was observed to be better than that of RCC beams and they improved with higher concrete grade, grade 300 showing a most balanced performance increasing from 496.84kNm in RCC beams to 912.15kNm in CNT beams indicating a performance improvement of 83.6% (see Figure 10A). This shows that macroscopic CNT bars contribute significantly to moment resistance. In comparison to the simulated flexural moment capacity, the design moment for most of the concrete grades were higher, others were same or closely matched ACI predictions as seen in Table 4. The lower simulated values could be expected because simulation accounts for cracking and nonlinear behavior of reinforced concrete. There was an observation from Saafi et al. (2013) of an increase in the flexural strength of nanocomposites after the addition of MWCNT fibres at 0.1, 0.5, and 1.0 wt% of the matrix. Konsta-Gdoutos et al. (2010) also found that short and long MWCNT fibres improved the flexural strength of cement-based materials, showing that these fibres help both the nano- and macro-level mechanical properties. Additionally, Parveen et al. (2015) reported that functionalized SWCNT improved both flexural and compressive strengths of cement mixtures, supporting the observed enhancements in CNT beam flexural capacity.

FIGURE 10

Shear performance

The shear strength of macroscopic CNT–reinforced beams was also observed to be better than that of RCC beams and they improved with higher concrete grade, grade 300 showing best behaviour as the shear strength increased from 432.04kN to 793.18 kN indicating an improvement of about 83.6% (see Figure 10B). This aligns with findings from Song et al. (2017), who reported that MWCNT addition at 0.05, 0.1, 0.15, 0.20, and 0.25 wt% of cement substantially increased interfacial shear strength (maximum 51.5%) with medium variation. But the design shear strengths of both beam types were much higher than the simulated shear strengths. This may be expected because ACI shear equations include safety factors and assume ideal conditions and also due to the fact that shear failure is brittle and FEM detects shear cracking early. The simulated shear strengths for both RCC and CNT beams are shown in Table 4. It was observed that CNT beams did not gain as much in shear as they gained in flexure and although the CNT bars improved flexure significantly, the simulated shear strengths remained much lower than the design strengths. This suggests that CNT reinforcement performs better in flexure than shear.

Failure mode

Both RCC and CNT–reinforced beams showed similar crack initiation location, however, CNT beams exhibited delayed crack propagation and were able to sustain higher loads after crack initiation. For instance, it was observed for grade 300 that CNT–reinforced beams sustained first cracks at 453.10 kN and were able to withstand loading up to failure at 1586.35 kN when compared to RCC beams which sustained first cracks at 436.89 kN and failed at 864.07 kN. At failure, RCC beams showed more localized cracking and a relatively abrupt loss of load–carrying capacity, whereas CNT–reinforced beams displayed more distributed cracking and a more gradual failure process. This behaviour suggests improved crack control and load redistribution in CNT–reinforced beams, even though the overall failure remained governed by combined flexure–shear action. Failure was primarily governed by tensile cracking in all grades except in CNT120 and CNT300 where localized compressive crushing near ultimate load was observed. All beams in this study exhibited a combined flexure–shear failure mode, although some studies reported a flexure only mode of failure as in the case of Naji et al. (2021). In all cases, inclined shear cracks initiated near the support regions before the development of flexural cracks at the midspan. As loading increased, flexural cracks began to form in the midspan region. The early initiation of shear cracks indicates a shear-influenced response, which may be attributed to the applied loading configuration, shear span-to-depth ratio, and the use of high-strength concrete. According to ACI 318-19, beams with relatively small shear spans and high compressive strength may experience critical diagonal tensile stresses prior to flexural cracking. Representative failure crack patterns are shown in Figure 11.

FIGURE 11

Conclusion

This numerical study using nonlinear finite element modelling, focused on analysing the flexural and shear performance on Concrete beams reinforced with macroscopic CNTs while comparing their performance with Steel–reinforced beams and ACI 318-19 design standard. The following conclusions were drawn. Macroscopic CNT–reinforced beams had marginally higher cracking loads than RCC beams at most grades, differences ranging from 5 kN to 16kN, but when they reached failure, they exhibited a significantly higher ultimate load–carrying capacity than RCC beams with up to 720 kN difference having improved performance of about 1.84 times that of RCC beams at higher concrete grades. There was improvement in stiffness in all grades, with percentage enhancement up to 14.4 although reductions in ductility were observed at lower and intermediate grades but CNT120 and CNT300 had higher ductility of 2.57 and 2.68 respectively. The flexural and shear capacities of CNT beams were enhanced at most grades with CNT 300 being the optimum where both capacities were improved by 83.6% compared to RCC beams. Comparative to standards, higher improvements in flexural resistance than in shear resistance were measured for CNT–reinforced beams, hence inferring the efficacy of macroscopic CNT bars in improving the resistance to flexure rather than shear in concrete beams. Also, the failure modes in all CNT beams and RCC beams were governed by flexure and shear, however, CNT beams exhibited more distributed crack patterns and were able to sustain higher loads after the first cracks. From the stress analysis, CNT beams consistently developed higher tensile stresses than RCC beams, they sustained higher internal stresses before failure, and had higher shear stress values than RCC beams at higher concrete grades, CNT300 having best performance. Overall, CNT300 beam showed higher deflection capability, had the highest ultimate load–carrying capacity, maximum tensile stress, compressive stress, ductility, flexural and shear performance. Conclusively, macroscopic CNT bars can be perceived as an effective longitudinal reinforcing material in concrete beams with clear improvements in the flexural and shear performances thus demonstrating their potential as an alternative to steel reinforcements in advanced structural applications.

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