Flexural design of lightweight concrete-infilled hollow flange CFS beams with web openings

Abstract

Concrete-filled hollow flange cold-formed steel (CF-HFCFS) beams have recently gained attention in the construction industry due to their structural benefits and improved performance by reducing buckling instability. However, current literature does not adequately address the challenges associated with CF-HFCFS beams containing web openings, which are essential for service integration. Therefore, this study aims to investigate, for the first time, the flexural behaviour of lightweight concrete (LWC) infilled CF-HFCFS beams with web openings. Experimentally validated three-dimensional finite element (FE) models are developed for a detailed analytical investigation. The study evaluates the influence of key parameters such as, dimensions and strength of CF-HFCFS beams and web opening sizes on the ultimate moment capacity. A total of 120 FE models were developed and analysed, comprising 24 without openings and 96 with openings. Results show that CF-HFCFS beams with large web openings experience a capacity reduction of up to 13.8% compared to those without openings. However, when the web opening is below 30% of the section height, the reduction in capacity is generally negligible, particularly in smaller sections. Additionally, beams with higher yield strength demonstrate improved resistance to capacity loss due to web openings. Based on the parametric study results, a simplified design equation is proposed to predict the ultimate moment capacity (M_ult) of CF-HFCFS beams with web openings. The proposed equation demonstrates high accuracy, with a mean value of 1.00, a coefficient of variation (COV) of 0.036, and a reliability index of 0.917, indicating excellent predictive performance. Therefore, this can be implemented in in modular construction systems, service-integrated floor systems and lightweight composite beams in low-to-mid-rise buildings.

Research Highlights

• Flexural behaviour of lightweight concrete-infilled HFCFS beams with web openings investigated using validated FE models.

• 120 FE models developed assessing key design parameters, including web opening ratio, steel thickness and yield strength.

• Web opening reduced ultimate moment capacity by up to 13.8%, especially evident beyond the web opening ratios above 0.3.

• Concrete strength provided minimal effect on ultimate strength, while yield strength and thickness were more influential.

• A simplified design approach was proposed and validated to predict the capacity of CF-HFCFS beams with web opening.

Introduction

Using cold-formed steel (CFS) structural elements are becoming increasingly popular in the construction sector due to their exceptional performance and economic benefits. Replacing standard hot-rolled sections with CFS sections has resulted in significant decreases in steel consumption, construction time, and overall costs for construction projects (Szewczak et al., 2021). The other benefits of using CFS elements include their lightweight nature, compatibility with conventional joining techniques, dimensional stability, easy fabrication, and higher flexibility of element shapes leading to more efficient use of resources (Macdonald et al., 2008; Mojtabaei et al., 2019). However, due to small thickness of these elements compared to their hot-rolled counterparts, CFS beams under flexural loading are susceptible to different types of buckling modes such as distortional buckling, local buckling, web crippling and lateral torsional buckling (Meza et al., 2020; Siahaan et al., 2018). To overcome this problem, hollow flange cold-formed steel (HFCFS) profiles have been introduced offering enhanced structural efficiency.

There are many studies investigating the influence of concrete infill inside steel tube (Abadel et al., 2024; Hamoda et al., 2025a) and beams with opening (Hamoda et al., 2025b). The concept of infilling concrete inside CFS beams has been initially proposed to provide stiffness stability, as well as enhancement of ductility and energy dissipation (Gao et al., 2014). Since HFCFS beams are in general prone to lateral torsion buckling, the concept of inclusion of concrete in the hollow flanges can postpone both local and global buckling modes, leading to a considerable enhancement in their load-bearing capacity (Gao et al., 2021). Consequently, concrete-filled hollow flange cold-formed steel (CF-HFCFS) beams have found more applications in building and bridge construction due to their enhanced structural properties and economic efficiency when compared to conventional structural elements (Sifan et al., 2021).

Several studies in the past have examined the structural performance of CF-HFCFS members (Gao et al., 2014; Li et al., 2019). To address the issue of increased self-weight of concrete leading to web instability in CF-HFCFS beams, some studies have focused on investigating the structural performance of lightweight concrete (LWC) infilled HFCFS beams (Abou-Rayan et al., 2020; Al Zand et al., 2021). LWC is defined as concrete with a density below 2000 kg/m³ and it can provide higher economic efficiency compared to conventional normal weigh concrete (Li et al., 2021; Zhang et al., 2021), making it especially suitable for applications where high concrete strength is not required, such as acting as a filler in composite sections to prevent buckling. Various normal strength and high strength LWC variants have been developed in the past, with a maximum aggregate size of 4.75 mm, allowing them to easily fill small steel sections (Sifan et al., 2023a, 2023b).

In practical applications, CFS beams are often produced with web openings to accommodate various services, including electrical, plumbing, and heating systems (Chen et al., 2020). These openings allow for the integration of essential utilities, ensuring efficient functionality and practicality within the structure (see Figure 1). Tsavdaridis and D’Mello (2012) comprehensively investigated the effect of different types of web opening, including circular and non-standard shapes, using FE analysis, and proposed simplified design guidelines for engineering practices.

Figure 1.

Integration of services through openings in the web (adopted from (SteelConstruction, 2022)).

Previous studies on CFS sections with various standard and innovative non-standard web opening arrangements demonstrated that the web openings could be effectively applied in various construction fields with enhanced structural performance without adding any stiffeners (Powell et al., 2023; Zhao et al., 2019). Several research studies have been also conducted on evaluating the effect of web stiffening on the structural performance and ultimate load bearing capacity of CFS elements. For instance, in a numerical investigation conducted by Yu et al. (Yu, 2012), the impact of edge-stiffened web holes on ultimate moment capacity (M_ult) was examined. The results showed that, on average, edge-stiffened web holes can enhance the M_ult of CFS channel beams by 14% compared to plain channel beams. In another study, Yu et al. (2019) introduced an analytical method to assess the distortional buckling capacity of CFS sections with circular web openings. Their method was developed based on pure bending analysis conducted by Hancock (1997), who originally proposed a computational method to calculate the distortional buckling stress in CFS without any web opening. Classen et al. (2019) investigated the structural behaviour of members with web opening and proposed a mechanical design model to predict the capacity of steel-concrete composite members with web opening. However, to the authors best of knowledge, a comprehensive study on the effect of web opening on CF-HFCFS beams is absent in the literature.

To address the above-mentioned research gaps, this study was aimed to investigate the flexural behaviour of LWC filled CF-HFCFS beams with and without web opening. First a series of detailed 3D finite element (FE) models were created and validated against the existing experimental results. The models exhibited a high level of agreement with the experiments, enabling an accurate evaluation of the structural response and M_ult of the elements in the presence of web opening. Using the validated FE models, a detailed parametric study was then conducted to investigate the effect of influential parameters such as web opening ratio, plate thickness, web height, yield strength of steel (f_y) and compressive strength of concrete. In total, 120 FE models including 96 with web opening and 24 without opening were created for parametric studies. A flowchart summarising the structure of the manuscript is shown in Figure 2. A detailed explanation of the model development, validation, and parametric study is provided, followed by a discussion of the results in the subsequent sections.

Figure 2.

Methodology chart.

Development of FE models

Three-dimensional nonlinear finite element (FE) models were developed using ABAQUS (2021) to simulate the flexural behaviour of CF-HFCFS beams with and without circular web openings. The modelling strategy was selected to accurately capture local buckling, distortional buckling, material yielding, and composite interaction mechanisms observed in thin-walled cold-formed steel members. The CF-HFCFS beam models were constructed by positioning the steel frame and solid concrete parts in their respective accurate locations. Three different circular web openings (at 300 mm intervals) were created: One web opening at the midspan of the beam and two web openings on either side of the element (see Figure 3).

Figure 3.

Mesh refinement of CF-CFCFS beams with web opening. Section 250 × 150 × 25 with an opening ratio of 0.6.

The steel section was modelled using four-node reduced integration shell elements (S4R), which are widely adopted for thin-walled CFS members due to their computational efficiency and capability to capture local and distortional buckling modes (Lifsey et al., 2025a, 2025b; Thirunavukkarasu et al., 2025). The concrete infill was modelled using eight-node reduced integration solid elements (C3D8R) to properly represent confinement effects and nonlinear compressive behaviour (Elkhouly et al., 2025; Mohamed et al., 2020; Sifan et al., 2021).

Figure 3 shows the mesh refinement of the developed FE models. Based on the results of a sensitivity analyses, a 10 × 10 mm mesh was assigned for both steel and concrete parts to provide a balance between accuracy and convergence speed (Sifan et al., 2021). This provided stable results with minimal change (<2%) in ultimate moment capacity compared to finer meshes. However, a finer mesh size of 10 × 3 mm was assigned to the corner regions of both the steel beams and concrete, to capture stress concentration effects and curvature accurately. To minimise the mesh distortion around the circular opening, ‘Median axis’ option was chosen and ‘Minimize the mesh transition’ was enabled in ABAQUS (2021).

Steel was modelled as elastic–perfectly plastic with Young’s modulus of 200 GPa and Poisson’s ratio of 0.3. This modelling approach is consistent with established FE investigations on CFS flexural members and provides reliable prediction of yielding-dominated failure modes (Lifsey et al., 2025a, 2025b; Sifan et al., 2021). Strain hardening was not included to maintain conservative strength estimation and consistency with design-based modelling assumptions.

Concrete behaviour was simulated using the Concrete Damage Plasticity (CDP) model in ABAQUS. This approach was selected over smeared crack models due to its capability to represent both tensile cracking and compressive crushing under confined conditions. However, the reliability of these models relies on the accuracy of the input parameters. Therefore, for modelling LWC, the confined stress-strain model proposed by Lim and Ozbakkaloglu (2014) was employed in this study, considering a Poisson’s ratio of 0.2 (Mohamed et al., 2020). The values for modulus of elasticity and confined stress-strain relationship were also derived from equations (1)–(3). A comprehensive explanation of the confined stress-strain relationship and the definition of the parameters used in these equations can be found in (Lim and Ozbakkaloglu, 2014; Sifan et al., 2021, 2022). This confined stress-strain model was successfully utilised in modelling both the flexural (Sifan et al., 2021) and shear (Sifan et al., 2022) performance of CF-HFCFS beams without opening, providing confidence in its suitability for the present study.

$E_c=4400\sqrt{f_{co}^{\prime }}{\left(\frac{{\rho }_{c,f}}{2400}\right)}^{1.4}$

(1)

$f_c=\frac{f_{cc}^{*}\hspace{0.17em}\left({\epsilon }_c/{\epsilon }_{cc}^{*}\right)r}{r-1+{\left({\epsilon }_c/{\epsilon }_{cc}^{*}\right)}^r}\hspace{1em}if\hspace{1em}0\le {\epsilon }_c\le {\epsilon }_{cc}^{*}$

(2)

$f_c=f_{cc}^{*}-\frac{f_{cc}^{*}-f_{c,res}}{1+{\left(\frac{{\epsilon }_c-{\epsilon }_{cc}^{*}}{{\epsilon }_{c,i}-{\epsilon }_{cc}^{*}}\right)}^{-2}}\hspace{1em}if\hspace{1em}{\epsilon }_c\ge {\epsilon }_{cc}^{*}$

(3)

Due to geometric and loading symmetry, half of the beam was modelled to reduce computational cost (Mohamed et al., 2020; Sifan et al., 2021). Symmetry boundary conditions were applied at the mid-span section. The load was applied as a displacement-controlled line load on the web to ensure stable post-peak response capture. The degrees of freedom restrained at each location are illustrated in Figure 4. Adjacent span length was selected to prevent premature shear buckling (Yu and Schafer, 2003). To prevent lateral torsional buckling (LTB), movement in the ‘x’ direction and rotation about the ‘z’ direction were restrained at regular 300 mm intervals on both the top and bottom of the beam (see Figure 4).

Figure 4.

Boundary conditions of CF-HFCFS beams with web opening.

Geometric imperfections were incorporated using an eigenvalue buckling-based approach. A linear elastic eigenvalue analysis was first conducted to extract the lowest buckling mode. The corresponding mode shape was then introduced into the nonlinear model with an amplitude of 0.34 t, based on the statistically representative imperfection magnitude reported Schafer and Peköz (1998). A brief sensitivity study was conducted by varying imperfection amplitude between 0.25 t and 0.5 t. The variation in ultimate moment capacity was within approximately 3–5%, confirming that the model predictions and resulting design recommendations are not unduly sensitive to imperfection magnitude. Since all 120 parametric models incorporate this imperfection level, the resulting ultimate moment capacities inherently include the influence of realistic local buckling sensitivity and post-buckling behaviour. While measured imperfections may provide specimen-specific accuracy, they are not always available and may not represent statistically typical fabrication conditions. The eigenvalue-based approach used herein provides a consistent and reproducible framework suitable for parametric and design-oriented investigations.

Surface-to-surface contact interaction was defined between steel and concrete. A friction coefficient of 0.57 was adopted for tangential behaviour, consistent with previous calibrations (Sifan et al., 2021, 2022). Hard contact was defined in the normal direction to prevent penetration while allowing separation. The steel was assigned as the master surface to ensure numerical stability. This contact formulation allows realistic load transfer and confinement development between steel and concrete components. An alternative strategy can be the use of embedded region constraints, where concrete nodes are constrained to follow steel deformation. While this approach simplifies numerical implementation, it assumes full bond and prevents slip or local separation effects. For thin-walled composite members where confinement and contact behaviour influence local buckling response, the surface-to-surface contact formulation provides a more physically representative interaction mechanism.

This modelling framework ensures accurate representation of local buckling interaction, composite confinement effects, and web opening stress redistribution, thereby providing a reliable basis for the subsequent parametric investigation and design development.

Model validation

To ensure the reliability of the analytical results, the developed FE models were validated against the previous experimental results obtained by Perera and Mahendran (2018), Abou-Rayan et al. (2020), and Chen et al. (2020). These three validation sets were specifically selected to capture the effects of web holes (Chen et al., 2020), the hollow-flange nature (Perera and Mahendran, 2018), and concrete infill (Abou-Rayan et al., 2020), respectively. By verifying each of these parameters individually, it was possible to confirm that the chosen modelling characteristics comprehensively address the distinct behaviours of concrete-infilled, hollow-flange cold-formed steel beams with web holes.

In particular, web openings introduce local stress concentrations and can alter both the failure mode and overall stiffness (Tsavdaridis and D’Mello, 2012), hollow flanges present unique geometric constraints that influence global flexural behaviour and local buckling, and concrete infill significantly enhances capacity and stiffness while influencing load transfer mechanisms (Sifan et al., 2021). Validating these features separately ensures that the model accurately simulates each structural phenomenon, thereby establishing a robust foundation for evaluating the combined system’s flexural performance.

In each case, the FE predictions were compared against key experimental outcomes, including the observed failure pattern, ultimate moment or load-carrying capacity, and full load–displacement response. Tables 1–3 summarise the comparison of ultimate moment (or load) capacities for the three sets of tests. The coefficient of variation (COV) between the FE predictions and the experimental results were 0.067, 0.037 and 0.026 for the experimental results reported by Perera and Mahendran (2018), Abou-Rayan et al. (2020), and Chen et al. (2020), respectively.

Table 1.

Ultimate moment capacity comparison for flexural loading without concrete infill (Perera and Mahendran, 2018).

Specimen index	Ultimate moment capacity-test (kNm)	Ultimate moment capacity-FE (kNm)	MTest/MFE
HFSPG-75 × 25 × 2.5-100 × 3	27.4	25.9	1.06
HFSPG-75 × 25 × 1.6-100 × 3	16.2	15.7	1.03
HFSPG-75 × 25 × 1.6-150 × 1.6	22.2	22.3	1.00
HFSPG-75 × 25 × 1.6-200 × 1.6	28.9	29.5	0.98
HFSPG-65 × 35 × 2.5-100 × 3	31.9	27.6	1.16
Mean			1.04
COV			0.067

Table 2.

Ultimate load capacity comparison for flexural loading with concrete infill (Abou-Rayan et al., 2020).

Specimen index	Ultimate load-test (kNm)	Ultimate Load-FE (kNm)	PTest/PFE
Control	154.9	165.1	0.94
A-LWC-U (concrete infill)	217.3	217.1	1.00
C-LWC-UL (concrete infill)	219.2	219.3	1.00
Mean			0.98
COV			0.037

Table 3.

Ultimate moment capacity comparison of CFS beam with opening (Chen et al., 2020).

Specimen index	Hole diameter	Ultimate moment -test (kNm)	Ultimate moment-FE (kNm)	PTest/PFE
240-L4000-UH1	141.5	11.0	11.4	0.96
240-L4000-UH3	140.8	10.6	11.2	0.95
290-L4000-UH1	141.5	16.7	18.1	0.92
290-L4000-UH3	141.9	16.3	17.9	0.91
Mean				0.94
COV				0.026

Figure 5 further illustrates the load–displacement response of selected models with and without web openings, compared against experimental curves. Overall, the FE models show close agreement with the experimental data, validating both the initial stiffness and the global load-carrying capacity. Minor discrepancies observed (e.g., slightly higher stiffness in some FE simulations) can be attributed to the flexibility of the test setup and localised geometric imperfections in the experimental specimens, as noted by Perera and Mahendran (2018).

Figure 5.

Load vs displacement comparison (a) Abou-Rayan et al. (2020); (b) Perera and Mahendran (2028); (c, d) Chen et al. (2020).

Figure 6 compares failure modes observed experimentally with those predicted by the FE simulations. In each case, beams with single or multiple web openings, hollow flanges, and concrete infill, the predicted failure patterns match well with the experimental observations, confirming that local buckling, distortional buckling, and yielding zones are accurately represented in the model.

Figure 6.

Comparison of failure patten between test and FEA. (a) with one web opening and (b) with three web opening ((Chen et al., 2020)); (c, d) without web opening (Perera and Mahendran, 2018) and (Abou-Rayan et al., 2020).

The combined validation from Perera and Mahendran (2018), Abou-Rayan et al. (2020), and Chen et al. (2020) demonstrates that the selected FE modelling characteristics suitably capture the effects of web holes, the hollow-flange nature, and concrete infill in hollow flanges, respectively. This comprehensive approach supports the reliability of the FE simulations for predicting the flexural performance of concrete-infilled hollow flange cold-formed steel beams, even in the presence of web openings, and provides a robust foundation for further parametric investigations and design recommendations.

Parametric studies

By using the same modelling approach, the validated models were expanded to conduct a comprehensive parametric study to evaluate the influence of key parameters, including concrete strength (f_c), web opening ratio, yield strength (f_y), and thickness (t), on the M_ult and the associated reduction in capacity due to web openings. In total, 120 FE models, 24 without web opening and 96 with web openings, were analysed to provide better insights into how these factors interact and influence flexural behaviour of CF-HFCFS beams (see Table 4).

Table 4.

Variation of the key influential parameters in parametric study.

CF-HFCFS beams with web openings	Variable	Values
	Section (d x bf x df)	150 × 90 × 15, 200 × 120 × 20, 250 × 150 × 25
	Thickness (t)	2 mm and 3 mm
	Yield strength (fy)	350 MPa and 450 MPa
	Concrete strength (fc)	30 MPa and 50 MPa
	Web opening ratio $\left(\frac{d_w}{d_1}\right)$	0.2, 0.4, 0.6, 0.8

Three sections namely 150 × 90 × 15, 200 × 120 × 20, and 250 × 150 × 25 were considered. The section notation is defined by height of the section × width of the web × height of the flange. Four web opening ratios (0.2, 0.4, 0.6, and 0.8) were considered based on the practical construction needs and previous studies (Lifsey et al., 2025b). Here, web opening ratio is defined by $\frac{d_w}{d_1}$ , where d_w and d₁ represent the diameter of the web hole and the clear height of the web, respectively. Two different steel grades (350 MPa and 450 MPa) and two different concrete compressive strength (30 MPa and 50 MPa) were also considered for the parametric study.

To ensure accurate flexural behaviour prediction, element failure needs be due to pure bending, and hence other possible premature failure modes such as shear buckling, and LTB of the adjacent span should be avoided. Therefore, the effective span length of 4878 mm was selected with an adjacent span of 1626 mm to prevent shear buckling of the elements (Yu and Schafer, 2003). To avoid LTB, lateral torsional restraints were applied at regular 300 mm intervals.

Results and discussion

Failure modes

Figure 7 shows the typical failure mode of the CF-HFCFS beams used in this study. The predominant failure mode was in-plane flexure due to pure bending. As seen in Figure 6(c), the compression and tension flanges at midspan reached their ultimate stresses under the maximum applied load, with no evidence of other failure modes. The presence of concrete prevented or delayed local buckling, allowing the top and bottom flanges to carry more load and fail by yielding. The same behaviour was observed for CF-HFCFS beams, regardless of the selected design parameters. A similar scenario was also reported by Sifan et al. (2021) for CF-HFCFS beams without openings. Based on the 120 FE model results, a comprehensive investigation on the influential parameters is given in the following sub sections.

Figure 7.

Failure mode of section 250 × 150 × 25 with thickness = 3 mm, fc = 30 MPa, f_y = 350 MPa, and web opening ratio = 0.8.

Effect of web opening ratio

Impact on M_ult

The variations of M_ult with web opening ratios for different sections are presented in Figure 8. It is shown that the presence of web openings consistently reduces the M_ult of CF-HFCFS beams across all section sizes. When comparing beams with and without web openings, the negative effect of the openings becomes evident in some cases. In the smallest section (150 × 90 × 15) with a thickness of 2 mm and f_y of 350 MPa, the M_ult without web openings is 20.7 kN m for f_c = 30 MPa. The same beam with a web opening ratio of 0.2 retains its original capacity of 20.7 kN m, but as the web opening ratio increases to 0.8, the M_ult drops to 18.8 kN m, representing around 9% reduction. This trend is consistent across all section sizes, with higher opening ratios leading to progressively larger reductions in M_ult as shown in Figure 7. However, it can be noted that the effect of web openings below 30% of the section height is generally negligible, especially in the case of smaller sections.

Figure 8.

Variation of M_ult with web opening for different sections.

For larger sections, the difference between beams with and without openings becomes more pronounced. In the 250 × 150 × 25 section with a thickness of 3 mm and f_y of 350 MPa, the M_ult without web openings is 94.1 kNm. Introducing a web opening ratio of 0.8 reduces this capacity to 81.1 kNm, representing a 13.8% decrease.

Comparative analysis

When comparing CF-HFCFS beams with and without web openings, the overall trend shows that web openings result in a reduction of M_ult, with the degree of reduction increasing as the opening ratio increases. However, as discussed above, the extent of this reduction is influenced by other factors such as f_y and thickness. Larger sections exhibit higher moment capacities both with and without web openings, but the percentage reductions are similar across all section sizes. This indicates that while increasing the overall size of the beam improves the M_ult, it does not eliminate the adverse effects of web openings. In the 250 × 150 × 25 section with a f_y of 450 MPa, the M_ult without web openings is 113.8 kNm. At a web opening ratio of 0.8, the capacity reduces to 102.3 kNm, representing a reduction of around 10%. The magnitude of the reduction is comparable to that observed in smaller sections, confirming that the negative impact of web openings remains significant even in larger beams.

Effect of yield strength (f_y)

As expected, yield strength (f_y) plays a significant role in determining the M_ult of the beams, while higher f_y results in higher M_ult values across all sections (see Figure 9). In section 150 ×90 × 15 with a thickness of 2 mm and a web opening ratio of 0.2, increasing the f_y from 350 MPa to 450 MPa enhances the M_ult from 20.7 kNm to 26.5 kNm. The level of M_ult enhancement is proportional to the increase in the f_y, that can be justified as shear buckling and LTB modes are prevented. This trend holds true across larger specimens as well, where the M_ult for a f_y of 450 MPa is significantly higher than that for 350 MPa. The ability of beams with higher f_y to mitigate the reduction in M_ult due to web openings is particularly noteworthy. In the 250 × 150 × 25 specimen, while the reduction in M_ult due to a web opening ratio of 0.8 is 12.9% at 350 MPa, it decreases to 8.3% at 450 MPa. This indicates that beams with higher f_y can better withstand the adverse effects of larger web openings, maintaining a higher proportion of their load-bearing capacity.

Figure 9.

Variation of M_ult with yield strength (f_y) for different sections.

Effect of thickness

As expected, thickness is another influential parameter affecting the M_ult of sections, with increased thickness leading to higher M_ult (see Figure 10). In the 150 × 90 × 15 mm specimen, for a f_y of 350 MPa and a web opening ratio of 0.2, the M_ult increases from 20.7 kNm to 30.7 kNm when the thickness is increased from 2 mm to 3 mm. This trend is consistent across all specimen sizes, highlighting the critical role of thickness in enhancing structural performance. Similar to f_y, for a given section the enhancement in M_ult is proportional to the increase in thickness, as long as the elements are designed to fail by yielding. The increased thickness also provides some resistance against the reduction in M_ult due to web openings. In the 200 × 120 × 20 mm specimen, the M_ult reduction for a web opening ratio of 0.8 is 9.7% at a thickness of 3 mm, compared to 12.1% at 2 mm (for a f_y of 350 MPa). This suggests that increasing thickness can be used as an effective strategy to counteract the negative effects of web openings in CF-HFCFS sections, especially in configurations with larger opening ratios.

Figure 10.

Variation of M_ult with thickness (t) for different sections.

Effect of concrete strength (f_c)

Concrete strength (f_c) also impacts the M_ult, though its effect is more subtle compared to f_y and thickness (see Figure 8). For the 150 × 90 × 15 mm specimen, raising f_c from 30 MPa to 50 MPa leads to a modest increase in M_ul across all configurations. The impact of f_c is more pronounced in larger specimens, such as the 250 × 150 × 25 mm specimen, where higher f_c values contribute to greater M_ult (up to 7% enhancement), especially in configurations with lower web opening ratios. Higher f_c values offer marginal improvements in resisting the reduction of M_ult due to web openings. For the 250 × 150 × 25 mm specimen with a f_y of 450 MPa and a web opening ratio of 0.8, the reduction in M_ult is 11.9% at f_c = 50 MPa compared to 12.9% at f_c = 30 MPa. However, the effect of f_c is minimal compared to the effect of f_y in reducing M_ult of CF-HFCFS elements.

Design methodology

Developing design guidelines

In this section, a practical design approach is introduced to determine the M_ult of CF-HFCFS beams with circular-shaped web openings. The baseline capacity (M_ult of the CF-HFCFS beam) can be established using the modified Han’s model developed in Sifan et al. (2021) as given below, considering all the influential parameters affecting M_ult of the CF-HFCFS beam.

$M_{com,NH}={\gamma }_m{W}_{scm}{f}_{scy}$

(4)

${\gamma }_m=1.39\hspace{0.17em}\ln \left(\xi +{\lambda }_1\right)-6.27$

(5)

$\xi =\frac{A_s{f}_y}{A_c{f}_c}$

(6)

${\lambda }_1={\left(\frac{b_f}{t_f}\right)}^{4.41}$

(7)

$f_{scy}=\left(1.90+1.91\xi \right)f_{ck}$

(8)

where, $M_{com,NH}$ is the bending capacity of CF-HFCFS beams with no circular web openings (solid web), ${\gamma }_m$ is flexural strength index, $\xi$ represents confinement ratio, ${\lambda }_1$ is slenderness ratio and $f_{scy}$ denoted the nominal yield strength of the composite beam.

M_ult of CF-HFCFS beams with web openings can be then established by adding factors to $M_{com,NH}$ considering the key influential parameters, which can reduce the M_ult of CF-HFCFS beams due to web openings. As indicated by the findings of the parametric study in the previous sections, the main influential parameter in reducing the M_ult was the web opening ratio. However, f_y and thickness also notably contributed in some cases, whereas the influence of f_c was generally negligible. Therefore, the effect of web opening ratio, thickness and yield strength of steel were considered as influential parameters in this study. Subsequently, M_ult of CF-HFCFS beams with web openings can be established as follows:

$M_{com,H}=\left[M_{com,NH}\right]\left[f_w\left(w\right)\right]\left[f_t\left(t\right)\right]\left[f_{st}\left(f_y\right)\right]$

(9)

$\left[f_w\left(w\right)\right]=1-{A.w}^B$

(10)

$\left[f_t\left(t\right)\right]=1-C.t$

(11)

$f_{st}\left(f_y\right)={\left(\frac{f_y}{350}\right)}^D$

(12)

where, $M_{com,H}$ is the bending capacity of CF-HFCFS beams with circular web openings, $f_w\left(w\right)$ is the web opening reduction factor, $f_t\left(t\right)$ and $f_{st}\left(f_y\right)$ are thickness correction factor and material strength correction factor, respectively, $w$ is web opening ratio, $t$ denotes thickness, and A, B, C and D are constant factors obtained from a systematic regression analyses using the results of this study.

As seen in Figure 8, the variation of M_ult with web opening ratio (w) can be divided into two regions. Up to w = 0.3, the reduction in M_ult is nearly linear, while beyond this point, it exhibits a non-linear trend. The constants A, B, C and D were determined for each region, as shown below.

$M_{com,H}=\{\begin{array}{l}\left(M_{com,NH}\right)\hspace{0.17em}\left(1-0.029w\right)\hspace{1em}for\hspace{0.5em}w<0.3\\ \left(M_{com,NH}\right)\hspace{0.17em}\left(1-{0.164w}^{1.612}\right)\hspace{0.17em}\left(1-0.0003t\right){\left(\frac{f_y}{350}\right)}^{0.081}\hspace{1em}for\hspace{0.17em}w>0.3\end{array}$

(13)

The mean and COV for the ratios between the predicted moment capacities, calculated using the proposed design approach, and those obtained from the parametric study were 1.00 and 0.036, respectively. Figure 11 presents a comparison between moment capacities derived from the parametric analysis and those predicted by the design approach, confirming the high accuracy and reliability of the proposed design equation.

Figure 11.

M_ult – Parametric FE analysis vs predicted using design.

Reliability analysis

Reliability analysis was performed according to AISI (2016) to calculate the reduction factor ( $Ø$ ) for the proposed design equations using equation (14).

$Ø=C_{Ø}{M}_M{F}_M{P}_M{e}^{-\mathbf{\beta }\sqrt{\left\{V_M^2+V_F^2+C_p{V}_P^2+V_Q^2\right\}}}$

(14)

where M_M = 1.1 and V_M = 0.1 represent the mean and COV of the material factor, respectively. Similarly, F_M = 1.0 and V_F = 0.05 are the mean and COV for the fabrication factor. The COV for the load effect, V_Q = 0.21, is based on the ratio between the permanent and variable actions (AISI, 2016). According to AISI (2016), the reliability index β is taken as 2.5, and the calibration coefficient $C_{\mathrm{Ø}}$ is 1.521. C_P is the correction coefficient based on the number of FE results. P_M = 1.00 and V_P = 0.036 represent the mean and COV of the ratio between the FE results and the predicted $M_{com,H}$ values obtained using equation (13). Based on the analysis, the calculated $Ø$ was 0.917.

Conclusion

This study presented a comprehensive numerical investigation into the flexural behaviour of lightweight concrete-infilled hollow flange cold-formed steel (CF-HFCFS) beams with circular web openings. A total of 120 nonlinear FE models were developed and validated against experimental data, demonstrating strong agreement in terms of ultimate capacity (mean = 1.00; COV = 0.055), load–displacement response, and failure modes. The following key findings were established.

(1) The presence of web openings reduced the ultimate moment capacity (M_ult) by up to 13.8%, with the reduction increasing nonlinearly when the web opening ratio exceeded approximately 0.3.

(2) Web openings below 30% of the web depth resulted in negligible capacity reduction, particularly for smaller sections, indicating a practical threshold for design consideration.

(3) The study demonstrated that yield strength (f_y) and thickness of steel were found to be more influential factors in enhancing the flexural capacity of CF-HFCFS beams In contrast, concrete compressive strength (f_c) had comparatively minor influence, particularly in smaller specimens.

(4) A simplified design approach incorporating a web opening reduction factor, thickness correction factor, and material strength factor was proposed. The model demonstrated excellent predictive capability (mean = 1.00; COV = 0.036).

(5) Reliability calibration following AISI S100 resulted in a resistance factor of ϕ = 0.917, confirming the adequacy and safety of the proposed design formulation.

The findings provide clear quantitative guidance for the safe and efficient design of CF-HFCFS beams incorporating service openings, particularly in modular and lightweight composite floor systems. The proposed design method enables engineers to account for web opening effects without resorting to advanced numerical simulations.

Future research may extend this work to combined bending–shear interaction, non-circular openings, and experimental validation of large-scale members. Also, future study could explore the use of lightweight concrete, such as concrete made from recycled plastics, to reduce both costs and structural weight leading to more sustainable solutions.