Effect of Protective Coatings on Post-Fire Performance and Behavior of Mild Steel-Based Cold-Formed Steel Back-to-Back Channel Columns with Bolted Connections

Abstract

This study investigates the buckling performance of built-up cold-formed steel (CFS) columns, with a focus on how different thermal exposures and cooling strategies influence their susceptibility to various failure mechanisms. Addressing the gap in the literature on the fire behavior of mild steel (MS)-based CFS columns, the research aims to provide new insights. Compression tests were conducted on MS-based CFS column specimens after they were exposed to fire, to assess their post-fire buckling strength. The columns were subjected to controlled fire conditions following standardized protocols and then allowed to cool to room temperature. The study examined axial load-bearing capacity and deformation characteristics under elevated temperatures. To improve fire resistance, protective coatings—gypsum, perlite, and vermiculite—were applied to certain specimens before testing, and their performance was compared to that of uncoated specimens. A comprehensive finite element analysis (FEA) was also performed to model the structural response under different thermal and cooling scenarios, providing a detailed comparison of the coating effectiveness, which was validated against experimental results. The findings revealed significant variations in axial strength and failure mechanisms based on the type of fire-resistant coating used, as well as the heating and cooling durations. Among the coated specimens, those treated with perlite showed the best performance. For example, the air-cooled perlite-coated column (MBC2AC) retained a load capacity of 277.9 kN after 60 min of heating, a reduction of only 6.0% compared to the unheated reference section (MBREF). This performance was superior to that of the gypsum-coated (MBC1AC) and vermiculite-coated (MBC3AC) specimens, which showed reductions of 3.6% and 7.9% more, respectively. These results highlight the potential of perlite coatings to enhance the fire resistance of CFS columns, offering valuable insights for structural fire design.

1. Introduction

Cold-formed steel (CFS) structures have become increasingly popular in modern construction due to their many advantages over traditional steel. These benefits include a lightweight design, high strength-to-weight ratio, ease of assembly, and quick installation. While CFS was initially favored for low-rise buildings, its use has expanded to mid-rise structures, mainly because of advancements in design and material technologies. CFS also supports sustainable construction practices due to its high recyclability. However, despite these advantages, there remain concerns about its performance in extreme conditions, particularly during fires. High temperatures can significantly reduce the load-bearing capacity, stiffness, and overall structural integrity of CFS components. Due to the high thermal conductivity of CFS, heat transfer is accelerated, and its large surface area-to-volume ratio makes it particularly vulnerable to rapid temperature increases. This can lead to severe deformation, buckling, or even premature failure of CFS components during or after a fire. Addressing these vulnerabilities is crucial to ensuring the safety and reliability of CFS structures in fire-prone environments.

Recent studies have examined the behavior of CFS under elevated temperatures. For example, Sabu Sam et al. [1] explored the buckling capacity of MS-based CFS columns under various heating scenarios, providing insights into failure mechanisms and fire-resistant column design. Ananthi et al. [2] investigated web-stiffened stainless steel channels under axial compression, identifying distortional–flexural buckling as the primary failure mode, emphasizing the need to account for interaction buckling in designs. Fang et al. [3] studied back-to-back CFS channels with web openings under high temperatures, highlighting DSM limitations in predicting axial strength and proposing refined design equations for perforated columns. Luo et al. [4] and He et al. [5] conducted numerical studies showing that DSM adjustments improve strength predictions for fire-exposed CFS columns with web holes and stiffeners. Ferreira Filho et al. [6] and Wang et al. [7] proposed DSM enhancements for fixed-end and box-section CFS columns, addressing fire-induced strength reductions.

Yin et al. [8] conducted fire tests on CFS square tubular columns with a new gypsum sheathing configuration, providing recommendations that improve fire resistance in CFS structures. These insights served as a benchmark for evaluating fire protection coatings in this research. Yang et al. [9] performed experiments, simulations, and parametric analyses on box-shaped CFS built-up columns, proposing a simplified design method for assessing load-bearing capacity under elevated temperatures. This study informed the thermal analysis in our research. Liu et al. [10] examined the impact of gypsum plasterboards on CFS wall fire performance, proposing a criterion for predicting fire-induced failure. These findings enhanced our understanding of how fire-resistant coatings affect CFS elements during fire exposure. Liu et al. [11] studied the effects of gypsum plasterboard joints on the fire performance of CFS walls, showing that studs near overlapped joints are more vulnerable to fire-induced failure. This research informed our evaluation of structural integrity in coated CFS columns.

Cerqueira et al. [12] studied post-buckling behavior and strength of CFS fixed-end singly symmetric columns, focusing on major-axis flexural–torsional buckling. They proposed a Direct Strength Method (DSM)-based approach for predicting failure loads, providing valuable insights that guided the analysis of CFS columns under fire exposure in this study. Li et al. [13] investigated the ultimate capacity of CFS built-up box-section columns, addressing assembly effects and instability mechanisms. Their design procedure for distortional buckling was crucial for understanding built-up CFS sections in this study, particularly under thermal exposure.

Hu et al. [14] examined buckling performance and design methods for lattice CFS columns, proposing a DSM-based approach to calculate axial compressive buckling capacity. Their methodology informed the assessment of axial buckling capacity in this study, especially under heating and cooling conditions. Shabhari et al. [15] analyzed local buckling of web-perforated CFS lipped channel columns, proposing design curve modifications to account for strength loss due to perforations. Their findings directly influenced the evaluation of web-perforated CFS columns in this study, particularly regarding load-carrying capacity and buckling behavior under thermal loading.

Despite these advances, significant knowledge gaps remain regarding the behavior of MS-based CFS sections, particularly in back-to-back configurations, under different thermal exposures. Most current studies focus on standard CFS sections, with limited investigation into the unique mechanical and thermal properties of MS-based variants. These back-to-back configurations, commonly used in structural applications due to their increased capacity and better load distribution, are not well-studied under high-temperature conditions. Additionally, there is a lack of detailed understanding of how various cooling methods, such as air cooling and water quenching, affect residual strength, deformation patterns, and susceptibility to different buckling modes. Cooling methods not only influence post-fire structural integrity but can also induce residual stresses and thermal gradients, complicating performance analysis. Furthermore, the effectiveness of fire-resistant coatings (such as gypsum, perlite, and vermiculite) has not been fully evaluated for MS-based CFS sections under realistic fire scenarios. These coatings are crucial for delaying thermal degradation and preserving structural capacity, but their comparative performance under varying fire durations and cooling conditions remains uncertain.

This study aims to fill these gaps by comprehensively evaluating the buckling strength and deformation behavior of MS-based CFS columns subjected to elevated temperatures and cooled using different methods. The research combines experimental investigations with numerical modeling to analyze and validate failure modes and assess the protective effects of fire-resistant coatings. The findings are expected to provide valuable insights into post-fire performance, improve understanding of the thermal effects on CFS structures, and contribute to refining design codes and safety standards. Additionally, the results will help inform best practices for selecting fire-resistant coatings and cooling methods to optimize structural resilience in fire-prone environments.

2. Experimental Data

2.1. Material

Cold-formed steel (CFS) back-to-back (BB) sections are typically created by fastening two single-channel sections together, forming a composite configuration that enhances structural efficiency. This approach is widely used in various construction applications, including purlins, struts, and light framing members, due to its simplicity and cost-effectiveness. In this study, the BB sections were assembled using self-tapping screws along the length, as shown in Figure 1. The precise dimensions of the sections are provided in Figure 2a, while Figure 2b presents a schematic of the BB configuration. The experimental specimens were fabricated using MS-based CFS of grade E350, with the following dimensions: height = 750 mm, flange width = 60 mm, lip depth = 20 mm, and thickness = 2 mm. A column length of 750 mm was selected to represent an intermediate slenderness ratio, capturing both local and global buckling behaviors relevant to CFS columns. For the tested BB channel sections, the radius of gyration was calculated based on geometric properties, yielding a slenderness ratio indicative of intermediate behavior. This length avoids premature failure from material yielding or global flexural buckling, enabling the study of distortional and local buckling under thermal and mechanical conditions.

The chosen length balances structural performance evaluation with furnace size limitations, ensuring relevance in assessing the combined effects of heating, cooling, and fire-resistant coatings on the columns.

2.2. Geometrical Imperfections

To accurately assess the impact of geometric imperfections on the structural behavior of CFS sections, detailed measurements were taken for all test specimens. These imperfections, typically arising from manufacturing processes such as rolling, welding, and fastening, were systematically documented. Figure 3a depicts locations on the specimen where imperfection measurements were taken. Figure 3b illustrates the measurement points along the length of the specimens, with six key locations on both the flange and the web. The points are labeled “FP1” for the flange and “WP1” for the web at each position. Measurements were taken at 50 mm intervals along the specimen’s length to capture deviations from the intended geometry. To ensure accuracy, each specimen was placed on a perfectly level surface, with one end clamped to eliminate external movements during the measurement process. A digital dial gauge with a sensitivity of 0.01 mm was used to record the imperfections. This approach ensured that even minor deviations influencing the structural response under load were included in the analysis. The purpose of measuring initial imperfections provided a baseline for assessing distortional buckling and failure by analyzing geometric imperfections before thermal exposure incorporated into FE models to replicate realistic conditions, reflecting the imperfect geometry of practical CFS members, and allowed experimental data to be compared with FE model predictions, ensuring alignment with actual specimen behavior. Thermal expansion and contraction likely caused increased out-of-straightness, local buckling, or warping due to uneven thermal gradients. However, post-exposure measurements were not conducted due to experimental limitations. These changes can affect buckling resistance, and future studies should include post-heating measurements to assess thermal effects on geometry.

Pre-heating imperfections were incorporated into FE models as initial deflections based on measured values to accurately represent the physical specimens. While post-heating geometrical changes were not directly measured, the FE models accounted for thermal expansion, residual stresses, and material property changes by

• Using simulated temperature distributions.
• Applying temperature-dependent material properties (reduced yield strength and elasticity).
• Modifying boundary conditions for thermal expansion and cooling-induced gradients.

2.3. Coatings

To assess the thermal performance of CFS sections under fire exposure, three fire-resistant coatings—gypsum, perlite, and vermiculite [16,17]—were applied. To evaluate their fire-resistant properties, coatings were applied at a uniform thickness of 10–15 mm, selected for their thermal insulation and ability to reduce heat transfer to the steel substrate. Perlite-based, gypsum-based, and vermiculite-based coatings were tested due to their fire-resistance characteristics, which are vital for protecting cold-formed steel (CFS) structures from thermal degradation and preserving structural integrity under high temperatures. While the study focused on comparing these coatings’ performance, further research is needed to determine the optimal thickness.

Each coating was mixed with an epoxy hardener for adhesion and durability and applied uniformly at a thickness of 10–15 mm. The coatings were carefully applied to the CFS specimens using standard procedures, ensuring uniform coverage across all exposed surfaces. Six specimens of each type were exposed to fire for 60 min, followed by cooling with air or water.

2.3.1. Gypsum Coating

Gypsum is well-known for its fire-resistant properties and was selected for its ability to delay heat transfer. With a density ranging from 600 to 1400 kg/m³ and thermal conductivity between 0.17 and 0.25 W/m·K, gypsum offers effective thermal insulation. When heated, gypsum undergoes a dehydration process that releases water vapor, absorbing heat and slowing the heat penetration to the underlying material. Additionally, it forms a protective surface layer that shields the steel from direct flame exposure. Gypsum-coated specimens had a cream-colored appearance.

2.3.2. Perlite Coating

Perlite, a lightweight volcanic glass, was chosen for its excellent thermal insulation properties. In its expanded form, perlite has a density of 30 to 80 kg/m³ and thermal conductivity between 0.032 and 0.05 W/m·K. The porous structure of expanded perlite creates air pockets that act as thermal barriers. Its non-combustibility and high melting point further enhance its fireproofing capabilities. The perlite-coated specimens appeared light grey, and the material’s insulating properties helped form an effective barrier against heat.

2.3.3. Vermiculite Coating

Vermiculite, a hydrated mineral, is another highly effective fireproofing agent due to its ability to expand when heated, forming an intumescent layer. With a density ranging from 70 to 150 kg/m³ and thermal conductivity between 0.045 and 0.06 W/m·K, vermiculite provides robust thermal insulation. Upon exposure to heat, vermiculite swells, forming an insulating barrier that reduces heat transfer and protects the steel beneath. After application, vermiculite-coated specimens had a dark brown appearance.

2.3.4. Application and Preparation

The coating process followed standardized procedures to ensure uniform application and thickness. The specimens were prepared under controlled conditions, and Figure 4 shows the coated specimens after application.

Standard spraying or trowelling techniques were used based on material guidelines while maintaining uniform thickness for fair comparison. Care was taken to avoid uneven layers or thickness variations that could impact results. Thickness was measured at multiple points to ensure uniform protection across all specimens.

A uniform thickness of 10–15 mm was applied across all coatings to isolate the impact of the material type (perlite, gypsum, vermiculite) on fire protection performance. This approach ensures comparisons are based solely on material properties, not thickness variations, providing clear insights into their influence on post-fire strength and deformation. While the materials differed in thermal conductivity, the aim of this study was to compare their relative performance under identical conditions rather than optimize thickness for maximum protection.

Future studies will address variations in thickness requirements based on material type, fire rating duration, and specimen area, but for this study’s 60–90 min focus, a common thickness was used for consistency.

Coatings were applied uniformly using standard procedures:

• Gypsum: Trowelled to 10–15 mm thickness.
• Perlite: Sprayed for even coverage.
• Vermiculite: Sprayed and smoothed to a consistent thickness.

Specimens were inspected pre- and post-application to ensure proper adhesion and uniformity, avoiding gaps or uneven areas that could affect thermal resistance.

Selection of Coating Thickness:

• Industry Standards: The 10–15 mm thickness aligns with standard practices for fire-resistant coatings, balancing fire protection and practical application limits.
• Material Properties: Thickness was chosen to ensure consistent fire protection for perlite, gypsum, and vermiculite based on their thermal insulating properties.
• Experimental Insights: Preliminary tests and literature indicated this range optimizes protection while avoiding excessive weight or insufficient resistance.
• Practical Application: The range allows for uniform, feasible application, ensuring reliable performance and comparability across coating types.

The different appearances—cream for gypsum, light grey for perlite, and dark brown for vermiculite—allowed for easy identification during testing. These coatings played a crucial role in assessing the residual strength and deformation characteristics of the CFS sections after exposure to high temperatures and subsequent cooling.

2.4. Heating and Cooling

The test specimens were heated in an electric furnace to simulate real-world fire conditions (Figure 5). The furnace used electrical heating coils embedded within refractory masonry, positioned on both sides of the specimens to ensure even heat distribution. This setup allowed for controlled exposure to elevated temperatures, closely mimicking fire conditions. The specimens were heated according to the ISO 834 standard fire curve [18], which outlines typical temperature increases during a fire. Two heating durations were employed: 60 min and 90 min. After 60 min, the specimens reached 925 °C, and after 90 min, they reached 986 °C. These durations were selected to assess the effects of prolonged exposure to high temperatures and simulate different fire scenarios that CFS sections might experience in the field.

To simulate the effects of elevated temperatures on CFS columns, an electric furnace was used under controlled conditions following the ISO 834 standard fire curve [18]. While the ISO 834 curve [18] does not fully replicate real-world fire dynamics, it provides a globally accepted framework for consistent testing and comparison. Specimens were heated at approximately 5 °C/min using an electric furnace following the ISO fire curve, simulating realistic fire scenarios with a steady thermal load. Specimens were maintained at peak temperatures to study exposure effects, then cooled. Air cooling involved natural cooling to room temperature, while water cooling used spraying or pouring water.

2.4.1. Thermal Monitoring

Type K thermocouples were strategically placed on the heating coils and the surface of the specimens to accurately monitor the temperature. These thermocouples recorded temperature changes throughout the heating process, ensuring that the specimens were exposed to the correct temperatures during both heating durations [16]. Temperature varied within the columns due to furnace gradients, specimen placement, and material properties, influencing thermal degradation and behavior under fire.

2.4.2. Cooling Methods

After heating, the specimens were quickly removed from the furnace to prevent temperature fluctuations. Two cooling methods were applied to study their effect on the residual strength and performance of the CFS sections:

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Air Cooling: Specimens cooled naturally at room temperature via convective heat dissipation.

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Water Cooling: Specimens were sprayed with water for faster cooling, creating thermal gradients.

Cooling Rates:

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Air Cooling: approximate rate 3 °C/min.

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Water Cooling: approximate rate 10 °C/min, due to rapid heat absorption by water.

Even small temperature differences (e.g., 795 °C, 720 °C, and 705 °C) significantly affect steel’s mechanical properties, such as yield strength, tensile strength, and ductility, especially at high temperatures. Steel loses substantial strength above 400 °C and undergoes severe degradation around 800 °C, impacting post-fire performance. The thickness of fire protection coatings is critical for thermal insulation and temperature resistance. Thicker coatings slow the temperature rise, enhancing steel’s thermal protection. Without consistent coating thickness, temperature differences and performance variations may not be directly attributed to the coating itself, introducing potential error in conclusions.

While slight temperature variations can still yield insights, inconsistencies in coating thickness remain a key factor influencing fire resistance and structural performance. Specifically, it influences their load-bearing capacity after exposure to high temperatures and the effects of cooling methods (air versus water) and protective coatings (gypsum, perlite, and vermiculite) on structural performance. The study highlights how elevated temperatures and cooling techniques impact the strength, stability, and failure modes of CFS structures, rather than their intrinsic fire resistance.

2.5. Experimental Testing

The experimental program was designed to assess the performance of CFS compression members, specifically CFS sections of grade E350, under both ambient and elevated temperature conditions. The goal was to evaluate their load-carrying capacity and deformation behavior under different thermal exposures.

A total of 11 specimens were tested:

5 uncoated specimens: Exposed to 60 and 90 min of heating, followed by air or water cooling;

6 coated specimens: Coated with fire-resistant materials (gypsum, perlite, or vermiculite), exposed to 60 min of heating, and cooled using either air or water.

Testing was conducted using a computerized Universal Testing Machine (UTM) with a 1000 kN capacity, which applied concentric axial compressive loads at a rate of 10 kN/s to ensure consistency. A data acquisition system recorded the total displacement resulting from the applied compressive stress. Two deflectometers were placed on each specimen to monitor lateral displacement: One at the midpoint of the specimen and the other one near the support (Figure 6).

To ensure uniform load distribution throughout the column during testing, end plates were welded to both ends of the specimens. Importantly, the welding of these plates was carried out after the heating and cooling processes. This approach ensured that the heating and cooling cycles influenced only the column’s structural behavior, without introducing additional thermal effects or residual stresses from the welding process.

Impact of Welding End Plates:

• Welding Before Heating and Cooling:

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  Residual stresses from welding may interact with thermal expansion, causing distortions or warping.

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  Localized heating from welding could alter steel properties near the weld, reducing strength and buckling resistance in those areas.

• Welding After Heating and Cooling:

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  Welding after thermal exposure limits the impact on material properties, as thermal degradation has already occurred.

This approach minimizes additional thermal distortions, preserving the column’s overall integrity while introducing only localized mechanical stresses. Although the specimens were welded to the plates, the actual support conditions were modeled as pinned-end supports. This was achieved by placing the welded end plates over three rollers on each side, allowing rotation while preventing lateral displacement. This setup accurately replicated pinned-end boundary conditions, ensuring consistency with real-world structural applications.

These instruments provided real-time data on both lateral and vertical deformations, which were critical for analyzing the maximum load the specimens could withstand and the corresponding displacements at different stages of the test. The collected data also provided valuable insights into the failure modes and residual strength of the CFS sections after fire exposure. Each specimen was assigned a unique ID (detailed in

Table 1. Specimen IDs.

Specimen ID	Abbreviation
MBREF, MB60AC, MB90AC	C sections unheated and heated for 60 and 90 min and cooled by air. (2 specimens)
MB60WC, MB90WC	C sections heated for 60 and 90 min and cooled by water. (2 specimens)
MBC1AC, MBC1WC	C section coated with gypsum and epoxy hardener, heated for 60 min and cooled by air and water. (2 specimens, coated using trowel)
MBC2AC, MBC2WC	C section coated with perlite and epoxy hardener, heated for 60 min and cooled by air and water. (2 specimens, coated through spraying)
MBC3AC, MBC3WC	C section coated with vermiculite and epoxy hardener, heated for 60 min and cooled by air and water. (2 specimens, coated through spraying)

), which helped track the specific conditions and results associated with each test.

3. Results and Discussions

3.1. Changes on Surface After Heating

3.1.1. Before the Heating Process

All the specimens exhibited a mat brown color across their surfaces, as illustrated in Figure 1. However, upon exposure to high temperatures for 60 min and 90 min, significant changes in the color and surface condition of the specimens were observed. For the uncoated specimens, the surface color transformed to dark brown after being heated, indicating the beginning of material degradation due to the elevated temperatures. In the case of the coated specimens, the following observations were made:

3.1.2. Gypsum-Coated Specimens

These sections developed a black color after the heating process, accompanied by the presence of black dust on the surface. Additionally, light grey patches appeared scattered across the coated areas. This suggests that the gypsum coating underwent some degradation, but it managed to provide a certain level of protection against the heat exposure.

3.1.3. Perlite-Coated Specimens

The color of these specimens shifted to black, with distinct yellow and white hints visible. The coating appeared to have broken down, turning into dust in certain areas. In some places, the perlite coating had peeled off, which indicates that the heat exposure was more aggressive in this case, leading to the degradation and partial loss of the protective layer.

3.1.4. Vermiculite-Coated Specimens

After heating, the vermiculite-coated sections showed a dark grey color. Some areas still retained the residual coating, but there were black patches scattered across the surface, suggesting that while the vermiculite coating was able to withstand some heat exposure, parts of it were still affected by the high temperatures.

The color changes and surface conditions of the specimens after heating served as indicators of the thermal degradation and the protective effectiveness of the various fire-resistant coatings. These observations, as depicted in Figure 7, highlight the differences in performance between the coatings and provide insight into how each material interacts with high-temperature conditions.

3.2. Temperature Measurement

Temperature variation across different points on the CFS specimens was carefully monitored to assess their thermal behavior during both heating and cooling phases. The specimens were subjected to heating according to the ISO fire curve [18], and temperature measurements were recorded at three key locations: the furnace control temperature (coil), the surface of the specimen, and just beneath the surface, which was accessed through shallow drilling. This approach was used to evaluate the effectiveness of the fire-resistant coatings. The detailed temperature readings are shown in Figure 8, where coat.1, coat.2, and coat.3 represent specimens coated with gypsum, perlite, and vermiculite, respectively.

For the uncoated specimens, it was observed that the surface temperatures were consistently lower than the coil temperature, with the temperature difference increasing over time. This suggests that the heat was not immediately transferred through the specimen. The temperature below the surface followed a similar trend, exhibiting a gradual reduction compared to the surface temperature. This indicates a delay in heat transfer from the outer layer to the core, which could influence the structural performance under prolonged heating.

The gypsum coating provided moderate thermal resistance, reducing the surface temperature to 795 °C after 60 min, compared to 810 °C for the uncoated B60AC specimen. The temperature just beneath the surface was significantly lower at 720 °C, indicating gypsum’s ability to slow down heat penetration and thus enhance fire resistance. The perlite coating demonstrated superior thermal insulation properties. The surface temperature of the perlite-coated specimen was reduced to 775 °C, and the temperature beneath the surface showed a further decrease. This indicates that perlite was particularly effective in delaying heat transfer, highlighting its strong insulating properties. The vermiculite coating also performed well in terms of thermal protection, with a surface temperature of 805 °C and an internal temperature of 660 °C. Although its performance was not as high as that of perlite, vermiculite still provided substantial protection, reducing heat penetration into the core.

Each specimen was inspected pre- and post-application to ensure proper adhesion and uniform coverage. Coated columns reached temperatures of 720 °C, 775 °C, and 805 °C after 60 min, close to that of the uncoated column (810 °C). Although these coatings did not prevent temperatures from exceeding the critical steel range (550–600 °C), they delayed heat transfer, providing vital time for evacuation and mitigating structural degradation.

After 60 min of heating, surface and depth temperatures varied due to differences in material composition and thermal resistance, not thickness inconsistencies. Each material’s thermal response differed based on conductivity, specific heat, and emissivity, causing minor temperature variations at different depths. However, since all coatings were applied within the same thickness range under controlled conditions, conclusions regarding perlite, gypsum, and vermiculite remain valid.

Perlite-coated columns performed best, retaining 7.9% of their strength compared to gypsum (3.6%) and vermiculite (6.7%). While these values appear small, they significantly outperformed uncoated specimens, which lost nearly all load capacity. The coatings’ primary role was to delay temperature rise and improve post-fire load-bearing capacity rather than act as complete thermal barriers. Perlite demonstrated superior performance in maintaining residual strength, offering the best fire resistance among the tested coatings.

The analysis of temperature variation across the different measurement points revealed the effectiveness of the fire-resistant coatings in reducing heat penetration into the CFS sections. Among the tested coatings, perlite proved to be the most effective thermal insulator, followed by vermiculite and gypsum.

The findings highlight the importance of coating thickness. While this study used 12 mm, a thickness of at least 30 mm may be required for a one-hour fire rating. Future discussions will emphasize these small but meaningful differences in fire protection performance.

These results underscore the critical role of selecting the right fire-resistant coatings to improve the fire resistance of CFS structures, particularly in environments prone to high temperatures. Such coatings can prevent or delay structural failure due to prolonged fire exposure.

Table 2. Temperature measured at different locations of the coated specimens.

Coating	Temperature at Coil (°C)	Temperature at Surface (°C)	Temperature at a Depth (°C)
1	821	795	620
2	821	775	550
3	821	805	660

shows the internal temperature of perlite coated specimens measured at various locations.

3.3. Sections After Testing

Upon applying the mechanical load to the CFS columns, significant buckling was observed, especially in the upper middle sections and near the supports of the specimens, as illustrated in Figure 9. This buckling phenomenon became more pronounced in specimens exposed to longer heating durations, with local buckling also occurring around the edges nearer to the welded plates. These plates experienced localized stress concentrations under axial loading, particularly due to elevated temperatures.

The failure pattern remained consistent across all specimens, with major buckling concentrated in the upper middle sections and near the supports.

In specimens that were heated for 90 min, the buckling was particularly severe in the middle sections, which further emphasized the detrimental effects of prolonged exposure to high temperatures. This observation indicates that longer heating durations significantly affect the structural stability of CFS columns. Specimens that underwent water cooling exhibited slightly higher deformation compared to those cooled by air, suggesting that the cooling process also played a role in the structural changes. The cooling method seems to influence the residual strength and performance of the CFS sections, with water cooling causing somewhat more deformation. The physical changes observed in both coated and uncoated specimens were similar, with buckling occurring on the web parts and flanges, as well as local buckling in samples subjected to longer heating durations. This suggests that both the thermal exposure and the cooling methods affect the buckling behavior similarly, regardless of the presence of fire-resistant coatings.

The study demonstrates that the structural performance of CFS columns is significantly influenced by thermal exposure and the cooling methods applied. These thermal processes cause substantial alterations in the material properties, including the yield strength (YS) and elastic modulus (E).

As steel columns are exposed to high temperatures, their yield strength, ultimate strength, and stiffness degrade significantly due to thermal effects. This occurs as a result of the following:

• Recrystallization: Elevated temperatures reduce dislocation density, lowering steel’s strength and stiffness.
• Thermal Expansion: Expansion creates internal stresses that weaken the material’s load-carrying capacity.

Phase Changes: Above 500 °C, microstructural changes reduce yield strength and ductility, increasing susceptibility to plastic deformation.

The E, which is a measure of the material’s stiffness, also decreases with rising temperatures, although the reduction in elastic modulus is typically less severe than the drop in YS. However, this reduction still plays a critical role in the overall performance of the material during and after thermal exposure, influencing the buckling behavior and the residual load-carrying capacity of the CFS columns.

The cooling process also plays a significant role in the post-fire behavior of steel columns, particularly when rapid cooling methods like air or water cooling are employed. During the cooling phase, the following occurs:

• Thermal Contraction: Uneven cooling creates thermal gradients, leading to internal residual stresses.
• Brittleness and Fracture: Rapid cooling induces brittleness, causing cracks or micro-cracks that weaken the steel.

Distortion and Warping: Uneven contraction distorts the steel, affecting geometry and reducing load-carrying capacity.

The degradation during heating and thermal contraction during cooling are interconnected. Heating weakens the steel (reducing strength, stiffness, and ductility), making it more vulnerable to rapid cooling effects, such as

• Enhanced Residual Stresses: Cooling intensifies residual stresses from heating, increasing structural failure risks.
• Compromised Integrity: Combined weakening and residual stresses lead to cracks, distortions, and reduced post-fire strength.

The cooling method (air or water) further impacts internal stresses and post-fire strength, with heating-induced degradation and cooling-induced stresses jointly reducing structural capacity.

Test results demonstrated that water-cooled specimens exhibited slightly greater deformation than air-cooled specimens, highlighting the impact of cooling methods on post-fire residual strength. This suggests that rapid cooling may intensify residual stresses, leading to greater structural changes. While failure patterns remained consistent, columns exposed to longer heating durations experienced more severe buckling, particularly in the middle sections, emphasizing the adverse effects of prolonged high-temperature exposure.

The heating process causes significant microstructural changes in steel, such as recrystallization and grain coarsening, reducing dislocations, yield strength, and modulus of elasticity. These effects were incorporated into the FE models through

Experimental Measurement:

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Steel coupons were subjected to the same heating and cooling protocols as the columns.

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Tensile tests evaluated temperature-dependent yield strength, ultimate strength, and modulus of elasticity, capturing mechanical degradation.

Material Data Integration:

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Experimentally obtained temperature-dependent properties were input into the FE models, defining reductions in yield strength, modulus of elasticity, and stress–strain behavior.

Model Validation:

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FE predictions were validated against experimental load-carrying capacity and failure modes, showing close agreement and confirming the accuracy of microstructural effects.

Post-Fire Behavior Simulation:

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Residual material properties after cooling, including reductions in strength and modulus of elasticity, were used to simulate post-fire behavior.

By incorporating these measured changes, the FE models accurately reflected real-world CFS column performance under thermal exposure.

3.4. Load Deformation

Figure 10 represents the load–deformation curves, which illustrate the relationship between the applied loads (in kN) and the resulting deformations (in mm) for both coated and uncoated CFS sections subjected to varying heating and cooling treatments. These curves provide insights into the structural behavior of the specimens, highlighting how different heating durations and subsequent cooling methods affect the load-carrying capacity and deformation characteristics. As the heating duration increases, a clear decrease in the load-bearing capacity of the sections is observed, consistent with the findings from [1]. This reduction is attributed to the thermal degradation of material properties, particularly the yield strength and elastic modulus. Additionally, specimens that were cooled by water showed a further decrease in load-carrying capacity compared to those cooled by air, under the same heating conditions. This trend aligns with previous research by [19], which observed that rapid cooling methods, like water quenching, lead to thermal contraction and further material stress, diminishing the overall performance of the specimens. Among the coated specimens, those with perlite coatings displayed the best fire resistance performance. Specifically, the perlite-coated section (MBC2AC), which underwent 60 min of heating and was cooled by air, achieved a load-bearing capacity of 277.9 kN, representing a 6.0% reduction compared to the unheated reference section (MBREF). This performance outstripped the gypsum-coated (MBC1AC) and vermiculite-coated (MBC3AC) specimens by 3.6% and 7.9%, respectively. When subjected to water cooling, the perlite-coated section (MBC2WC) demonstrated a 1.2% reduction in load-bearing capacity compared to its air-cooled counterpart (MBC2AC), yet it still outperformed the gypsum-coated (MBC1WC) and vermiculite-coated (MBC3WC) sections by 4.7% and 10.1%, respectively. These results underscore perlite’s superior thermal insulation properties. In contrast, the gypsum-coated section (MBC1AC) showed a 9.2% reduction in load capacity compared to MBREF, while the vermiculite-coated section (MBC3AC) had a 12.9% reduction. After water cooling, MBC1WC and MBC3WC exhibited 11.2% and 15.6% lower ultimate loads compared to the reference section, respectively. For the uncoated sections, the air-cooled specimens (MB60AC and MB90AC) demonstrated significant reductions in ultimate load, with decreases of 18.0% and 31.5%, respectively, when compared to MBREF. When subjected to water cooling, MB60WC and MB90WC showed additional reductions of 4.9% and 5.8%, respectively, compared to their air-cooled counterparts. This further emphasizes the negative impact of water quenching on the structural capacity of CFS columns. The results highlight the effectiveness of fire-resistant coatings in mitigating performance losses caused by thermal exposure.

Cooling Method Effects on Load–Deflection Behavior:

Although the load–deflection curves for air and water cooling are similar after 60 and 90 min of heating, minor but notable differences exist, impacting post-fire performance.

Thermal Gradients and Residual Stresses:

• Water cooling induces rapid temperature drops, creating steeper thermal gradients and higher residual stresses, particularly at the steel’s surface.
• Air cooling, with its slower temperature drop, results in milder thermal gradients and lower residual stresses.

Load-Carrying Capacity:

Air-cooled specimens exhibit slightly higher load-carrying capacity, particularly after 90 min of heating, due to reduced thermal damage from gradual cooling.

While the differences are subtle, they highlight the influence of cooling methods on post-fire strength and deformation, underscoring their importance in minimizing thermal damage.

Water cooling significantly reduces load-carrying capacity compared to air cooling, especially for uncoated specimens. This highlights the negative effects of rapid cooling, which increases residual stresses and thermal contraction.

Supporting Evidence:

Load Reduction in Uncoated Specimens:

MB60AC (Air Cooled, 60 min): 18.0% reduction from MBREF

MB60WC (Water Cooled, 60 min): Further 4.9% reduction vs. MB60AC

MB90AC (Air Cooled, 90 min): 31.5% reduction from MBREF

MB90WC (Water Cooled, 90 min): Further 5.8% reduction vs. MB90AC

The additional reduction in water-cooled specimens indicates that rapid cooling induces higher thermal stresses, weakening the material more than gradual cooling.

Comparison of Fire-Resistant Coatings Under Cooling Conditions:

Perlite-coated:

MBC2AC (Air Cooled, 60 min): 6.0% reduction from MBREF

MBC2WC (Water Cooled, 60 min): Further 1.2% reduction vs. MBC2AC

Gypsum-coated:

MBC1AC (Air Cooled): 9.2% reduction from MBREF

MBC1WC (Water Cooled): 11.2% reduction from MBREF

Vermiculite-coated:

MBC3AC (Air Cooled): 12.9% reduction from MBREF

MBC3WC (Water Cooled): 15.6% reduction from MBREF

Water cooling negatively impacts all specimens, but perlite-coated sections retain the most strength, demonstrating superior fire resistance.

This study provides direct evidence of cooling methods’ impact on post-fire performance, beyond literature-based discussions. The data clearly show a trend: water cooling consistently reduces load capacity more than air cooling, across different coatings and heating durations. These findings emphasize the need to consider cooling methods when designing fire-resistant CFS structures, making this a crucial conclusion for both research and practical applications.

Among the coatings, perlite proved to be the most effective at maintaining load-carrying capacity after heating, showcasing its excellent thermal insulation properties. On the other hand, gypsum and vermiculite coatings, while still beneficial, demonstrated relatively poorer performance in comparison to perlite. The cooling method played a crucial role in determining the material behavior of the CFS sections. Water cooling, which involves rapid thermal contraction, was shown to negatively affect the material properties, leading to reduced load-bearing capacity. This was particularly evident in the uncoated specimens, where water cooling caused more significant deformation and performance degradation compared to air cooling.

Perlite’s superior performance can be attributed to its unique material properties. As a volcanic glass, perlite undergoes significant expansion when heated due to the trapped water inside, forming a lightweight, porous structure that acts as an excellent thermal insulator. This high porosity significantly reduces heat transfer to the CFS section, enhancing fire resistance. In contrast, gypsum releases water vapor when heated, which aids in cooling but lacks the thermal insulation effectiveness of perlite. Vermiculite, while providing some degree of fire resistance, is less effective than both perlite and gypsum, as it forms a less expansive structure and provides comparatively lower thermal insulation. In conclusion, the findings emphasize the importance of selecting appropriate fire-resistant coatings and cooling methods to enhance the performance of CFS structures under elevated temperature conditions. Coatings like perlite provide substantial benefits, while the cooling method plays a key role in minimizing thermal-induced damage.

3.5. Lateral Deformation

Figure 11 illustrates the lateral deformations observed across all sections that were measured after loading, highlighting the effects of heating duration and cooling methods. The load-bearing resistance decreases as the heating duration increases, resulting in greater lateral deformations. The uncoated specimens demonstrated a substantial rise in deformation with prolonged heating. The coated specimens, in contrast, showed a much better ability to control lateral deformation under thermal exposure.

The perlite-coated section (MBC2AC) tested after 60 min of heating and cooled by air exhibited a lateral deformation of 1.89 mm, which was only 21.5% higher than the unheated reference section (MBREF). This was 17.8% lower than the gypsum-coated section (MBC1AC) and 27.3% lower than the vermiculite-coated section (MBC3AC). When cooled by water, the perlite-coated section (MBC2WC) showed a 5.8% increase in lateral deformation compared to MBC2AC, but remained 20.0% lower than the gypsum-coated section (MBC1WC) and 23.7% lower than the vermiculite-coated section (MBC3WC).

In comparison, the gypsum-coated section (MBC1AC) had a lateral deformation 47.4% higher than MBREF, while the vermiculite-coated section (MBC3AC) demonstrated an increase of 66.7% compared to MBREF. After water cooling, the gypsum-coated section (MBC1WC) showed an increase of 60.3%, and the vermiculite-coated section (MBC3WC) exhibited a 67.9% increase compared to MBREF. This suggests that, although water cooling tends to lead to greater deformations, the extent of increase may vary based on the specific heating duration and coating type applied. For the uncoated sections, MB60AC and MB90AC exhibited lateral deformations 79.5% and 111.5% higher than the unheated reference section (MBREF), respectively. When cooled by water, MB60WC showed a 10.7% increase in lateral deformation compared to MB60AC, while MB90WC displayed a 6.1% increase in deformation compared to MB90AC.

Both air and water cooling increased lateral deformations compared to the unheated reference, with greater effects in coated sections. Water cooling caused more deformation than air cooling, varying by coating type and heating duration. Water cooling caused greater deformations than air cooling, but the performance varied by coating type, with perlite-coated sections showing the best results. Perlite-coated columns demonstrated superior resilience and better post-fire performance compared to gypsum or vermiculite coatings, especially under prolonged heating and cooling conditions.

3.6. Axial Stiffness

Axial stiffness refers to the ability of a structural element to resist deformation when subjected to an axial force, such as compression or tension along its length. This parameter is crucial in understanding the structural integrity of materials under loading conditions. Axial stiffness, defined as the resistance to axial deformation under load, calculated as the ratio of axial force to displacement. For fire-tested CFS columns, stiffness was determined using a monotonic axial load procedure, with displacement measured at the ultimate load.

As observed in Figure 12, the axial stiffness of CFS sections declines with increased heating duration. The most significant reduction in axial stiffness was observed in B90WC, the specimen heated for 90 min and water-cooled, indicating that prolonged exposure to high temperatures followed by rapid cooling greatly diminishes stiffness. In contrast, the highest axial stiffness was recorded in the unheated specimen (BREF), demonstrating the adverse impact of thermal exposure on the material’s stiffness properties.

Among the heated specimens, those cooled by water consistently showed lower axial stiffness compared to air-cooled ones, highlighting the detrimental effects of water cooling on structural performance [20]. However, the coated specimens performed better in maintaining axial stiffness compared to their uncoated counterparts, particularly under 60 and 90 min of heating. The coatings likely helped mitigate some of the degradation in material properties caused by thermal exposure, leading to improved stiffness retention in coated sections. This is particularly evident with BC2 (perlite), which exhibited higher stiffness among the coated specimens across both cooling methods.

The perlite-coated section (MBC2AC) demonstrated a stiffness of 76.16 kN/mm, which was 5.8% lower than the unheated reference section (MBREF) but still outperformed the gypsum-coated (MBC1AC) and vermiculite-coated (MBC3AC) specimens by 11.1% and 22.8%, respectively. After water cooling, the perlite-coated section (MBC2WC) showed a 5.0% reduction in stiffness compared to MBC2AC, while maintaining superior performance compared to the gypsum-coated (MBC1WC) and vermiculite-coated (MBC3WC) specimens by 3.8% and 20.2%, respectively.

The gypsum-coated section (MBC1AC) exhibited a stiffness 15.2% lower than MBREF, while MBC1WC showed an increase in stiffness by 1.7% compared to MBC1AC, suggesting that the water-cooled specimen performed better than the air-cooled one in this case. This improvement could be attributed to the thermal properties of gypsum, which, in combination with water cooling, might lead to more uniform cooling, thus preserving stiffness better. The vermiculite-coated sections (MBC3AC and MBC3WC), however, displayed stiffness values 23.3% and 25.5% lower than MBREF, respectively, indicating that vermiculite performed the weakest among the coatings, likely due to its lower structural strength under thermal loading.

For uncoated sections, MB60AC and MB90AC had stiffness values 27.1% and 60.2% lower than MBREF, respectively, showing significant degradation after longer heating durations. The water-cooled specimens, MB60WC and MB90WC, displayed an even more pronounced stiffness reduction of 10.7% and 9.0% compared to their air-cooled counterparts (MB60AC and MB90AC). This trend suggests that water cooling leads to more abrupt thermal shock, likely causing greater microstructural damage and stiffness reduction.

In summary, water-cooled sections tend to exhibit slightly lower stiffness than their air-cooled counterparts. While cooling methods influence stiffness, they are not the sole factor. Air cooling caused moderate reductions, while perlite-coated specimens consistently outperformed gypsum and vermiculite-coated sections, even under air cooling. This highlights the significant role of coating materials in mitigating stiffness loss.

The improved stiffness retention in perlite-coated sections (MBC2AC) suggests that coating type plays a crucial role, challenging the conclusion that cooling methods alone determine stiffness retention.

The key parameters affecting axial stiffness in differently cooled columns are as follows:

• Heating Duration: Longer exposure leads to greater material degradation, significantly reducing axial stiffness.
• Cooling Method: Water cooling leads to a more pronounced reduction due to thermal shock and microstructural changes.
• Coating Type: Perlite performed best in retaining stiffness, while vermiculite exhibited the weakest performance.

These findings confirm that cooling methods influence stiffness but are not the sole determinant—coating type plays a major role in stiffness retention. The lower stiffness values in water-cooled specimens can be attributed to higher thermal contraction stresses, which result in microstructural changes that reduce the material’s elastic properties. The weakest performance was observed in the vermiculite-coated sections, likely due to vermiculite’s inability to provide as much structural resistance during thermal cycles.

Study Objective and Key Findings:

The study aimed to assess the load-bearing capacity, deformation behavior, and failure modes of CFS columns exposed to high temperatures, focusing on the effectiveness of fire protection coatings (gypsum, perlite, and vermiculite) in improving post-fire performance. The findings provide insights for designing resilient fire-resistant CFS structures.

Key Results:

➢

Figure 11: Highlights lateral deformation under axial compression for varying heating durations and cooling methods (air vs. water), offering design insights for predicting deformation under fire.

➢

Figure 12: Shows axial stiffness behavior, essential for understanding structural stability and load-bearing capacity after fire exposure.

Fire Protection Coatings:

Coatings such as paint and gypsum, though widely used for CFS structures, primarily delay temperature rise but cannot prevent significant material degradation at high temperatures. The dramatic reduction in load-bearing capacity after fire exposure, even with coatings, underscores the need for improved fire protection measures.

Advantages of Coatings:

➢

Provide thermal insulation to steel surfaces.

➢

Lightweight, cost-effective, and easy to apply.

Coatings alone cannot ensure full fire resistance, especially under extreme conditions. Exploring lightweight mineral-based fire retardants and passive fire protection systems could enhance resilience. Extending these methods to hot-rolled sections through targeted experiments is recommended.

3.7. Reduction Factor

Reduction Factor (RF) is a key parameter used to evaluate the relative strength of heated specimens compared to their unheated (reference) counterparts. It is defined as the ratio of the ultimate strength of a specimen subjected to thermal exposure to the strength of an unheated reference specimen. This factor is critical for understanding how structural elements perform under high temperatures, helping engineers incorporate appropriate safety margins and account for uncertainties in structural designs.

As shown in

Table 3. Reduction factors.

Specimen ID	Reduction Factors
MBREF	1.00
MB60AC	0.94
MB60WC	0.93
MB90AC	0.78
MB90WC	0.75
MBC1AC	0.94
MBC1WC	0.93
MBC2AC	0.97
MBC2WC	0.96
MBC3AC	0.86
MBC3WC	0.84

, the RF values vary significantly across different specimens based on their heating duration, cooling methods, and coating materials. The general trend indicates that the RF decreases as heating duration increases, reflecting the detrimental effects of prolonged heat exposure on the structural strength of the specimens. The specimens subjected to 90 min of heating show the lowest RF values, indicating a substantial loss in strength due to elevated temperatures.

For water-cooled specimens, the reduction factor is lower compared to air-cooled ones, reaffirming that rapid cooling has a more pronounced negative impact on structural performance. Among the coated specimens, BC2 (perlite) demonstrates a higher reduction factor, implying that the perlite coating is more effective in preserving the structural strength after heating compared to other coatings like BC1 (gypsum) and BC3 (vermiculite). In particular, the RF for perlite-coated specimens remained consistently higher across both air and water cooling, highlighting its superior fire-resistant properties.

Overall, the RF values indicate that both the heating duration and the cooling method significantly influence the strength of CFS sections, with coatings providing an added layer of protection against strength degradation.

4. Numerical Modeling

4.1. General

To validate the experimental observations and gain deeper insights into the structural behavior of CFS columns, Finite Element (FE) models were developed using ABAQUS software [21]. A static nonlinear analysis replicated experimental conditions to capture buckling behavior. Axial loading was applied under displacement control, with one end fixed and the other displaced gradually. The modeling process began with the creation of an accurate geometric representation of the CFS columns. Two channel sections were modeled to represent BB arrangements identical to those of sections tested experimentally. The CFS profile was represented using shell elements with dimensions of 200 × 60 × 20 mm, accurately reflecting the channel’s cross-section. The material properties, such as YS, E, and Poisson’s ratio, were assigned to the model elements, and the thickness of the CFS section was applied according to the experimental parameters. This ensured the model closely matched the physical characteristics of the specimens used in the tests. After the geometric configuration was established, the model was assembled with careful attention to detail, ensuring that the alignment and positioning adhered to the defined reference origin. This step ensured the consistency and accuracy of the model’s representation in comparison to the experimental setup. Boundary conditions and loading steps were defined with precision, considering the time intervals and load increments used in the actual experiments. Pinned boundary conditions replicated the experimental setup. Refined mesh ensured accurate results, capturing critical behaviors like buckling and deformation. The BB sections were aligned with a 1–2 mm gap, incorporating surface-to-surface contact with a small friction coefficient to replicate self-tapping screw interactions. The mesh size was refined to ensure the model’s results would accurately reflect the experimental findings, with enough elements to capture the behavior of the CFS columns under loading.

Once the model setup was complete, the axial loading was applied to the columns in the ABAQUS software [21] to replicate the actual experimental loading procedure. The results from the FE simulations provided a detailed evaluation of the CFS column behavior, allowing for the assessment of critical parameters such as buckling, deformation patterns, and stress distribution under different loading and boundary conditions. This comprehensive modeling approach helped to cross-check the experimental results and provided a robust platform for understanding the performance of CFS columns under various fire and mechanical loading conditions.

The numerical modeling of CFS columns began with the creation of BB channels modeled in a two-dimensional (2D) format, ensuring a simplified and computationally efficient initial representation. These 2D models were subsequently converted into three-dimensional (3D) models, allowing for a more detailed and realistic simulation of the complex behaviors observed in the experimental study. The transition to 3D modeling was crucial in capturing the intricate interactions between the structural elements and accurately simulating the buckling patterns, deformation modes, and failure mechanisms under axial compression. The 2D analysis identified critical buckling modes via eigenvalue analysis. Three-dimensional (3D) analysis captured nonlinear behavior, including post-buckling and deformation interactions. The dimensions of the CFS channels used in the numerical models closely followed the specifications from the experimental tests. This ensured consistency between the numerical models and the physical specimens, enabling the validation of results across both platforms.

4.2. Material Properties

The material properties used in the FE analysis were derived from temperature-dependent coupon tests conducted in accordance with the methodology outlined by [17]. This study was conducted on samples of grade and thickness similar to those used in this study under analogous heating and cooling conditions. These tests provided critical data on the mechanical behavior of CFS at various temperatures, forming the foundation for accurately simulating the material’s response under thermal and mechanical loads. Stress stain graphs obtained from this coupon test are provided in Figure 13.

• Material Properties:

  ➢

  Yield Stress: 351 MPa at ambient temperature, decreasing with temperature.

  ➢

  Ultimate Strength: 450 MPa at ambient, reducing similarly to yield stress.

  ➢

  Elastic Modulus (E): 200 GPa at ambient temperature.

  ➢

  Thermal Conductivity (k): 55 W/m·K at ambient, decreasing at higher temperatures.

  ➢

  Specific Heat Capacity (C): 500 J/kg·K at ambient, increasing with temperature.

  ➢

  Plasticity: Modeled using a bilinear isotropic hardening approach.

These tests were crucial for determining the thermal effects on the material’s mechanical behavior, providing a foundation for simulating the temperature-dependent material properties in the FE models. The coupon tests involved subjecting steel specimens to various heating and cooling cycles, similarly to the conditions used in this study, with both air-cooled and water-cooled specimens being tested to capture a range of thermal histories. The essential material properties were obtained at varying temperature intervals from ambient conditions to required high temperatures. Thermal degradation curves for yield stress, elastic modulus, and ultimate tensile strength were derived from tests and implemented in the FE models to reflect observed thermal histories.

The temperature-dependent material properties were integrated into the FE models as input parameters, allowing for a realistic simulation of the thermal and mechanical response of the CFS columns. These properties were used to simulate the heating and cooling conditions applied to the specimens during testing. In particular, the effect of the fire-resistant coatings was modeled by adjusting the material property values and considering the insulating properties of materials such as gypsum, perlite, and vermiculite. The material properties used for FEM analysis taken from coupon testing are given below in

Table 4. Material properties used for FE analysis.

Duration of Heating	Yield Strength Air Cooled (MPa)	Yield Strength Water Cooled (MPa)	Ultimate Strength Air Cooled (MPa)	Ultimate Strength Water Cooled (MPa)	Elastic Modulus Air Cooled (GPa)	Elastic Modulus Water Cooled (GPa)
Reference	351	351	450	450	212	212
30 min	335.21	317.18	426.64	401.25	156	152
60 min	254.54	233.73	386.28	362.96	147	143
90 min	182.65	166.43	256	197.89	101	93

for your kind reference.

By using these temperature-dependent material properties, the FE models were able to more accurately reflect the thermal degradation and mechanical performance of the CFS columns under elevated temperatures. This approach ensured that the numerical predictions closely matched the experimental results, offering valuable insights into how the CFS columns would perform under fire scenarios and how fire-resistant coatings influence their behavior. The incorporation of these material characteristics into the model enabled a more comprehensive understanding of the structural integrity of CFS columns subjected to extreme thermal conditions.

The heating process indeed induces significant changes in the steel’s microstructure, including recrystallization and grain coarsening, which reduce dislocations and ultimately decrease the yield strength and modulus of elasticity. These changes were measured and included in the FE models through the following steps:

Experimental Measurement:

➢

Steel coupons were subjected to the same heating and cooling protocols as the columns.

➢

Tensile tests evaluated temperature-dependent yield strength, ultimate strength, and modulus of elasticity, capturing mechanical degradation.

Material Data Integration:

➢

Experimentally obtained temperature-dependent properties were input into the FE models, defining reductions in yield strength, modulus of elasticity, and stress–strain behavior.

Model Validation:

➢

FE predictions were validated against experimental load-carrying capacity and failure modes, showing close agreement and confirming the accuracy of microstructural effects.

Post-Fire Behavior Simulation:

➢

Residual material properties after cooling, including reductions in strength and modulus of elasticity, were used to simulate post-fire behavior.

4.3. Element Type and Meshing

In ABAQUS software [21], a variety of shell elements are available for structural modeling, each suited for different purposes depending on the complexity and behavior of the structure being analyzed. For the modeling of BB built-up channel sections in CFS columns, the S4R shell element was chosen due to its optimal performance for this type of structure [22,23]. The S4R element is a fully integrated, 4-node shell element, which provides a good balance between accuracy and computational efficiency. It is particularly well-suited for modeling built-up CFS sections, where plate elements need to capture both bending and membrane forces accurately. Previous studies [24,25] have demonstrated the effectiveness of S4R elements in capturing the nonlinear behavior and buckling effects of CFS beams and columns under thermal loading.

When it comes to mesh size, it is critical to strike a balance between accuracy and computational cost. A finer mesh typically improves accuracy but also increases the time and resources required for the simulation. To optimize both aspects, a mesh size of 5 mm by 5 mm was chosen for the length and width of the channel sections after conducting a sensitivity analysis. This mesh size was found to offer sufficient resolution for capturing key structural behaviors such as buckling, local deformations, and stress concentrations while maintaining computational efficiency [26].

Modeling of Connections:

In the FE models, bolt connections were simplified using tie constraints for computational efficiency and ease. While this ensures effective load transfer, it does not fully capture the localized flexibility or slip of bolted connections.

Limitations of Tie Constraints:

➢

Tie constraints assume rigid coupling, potentially overestimating stiffness and underestimating local deformations near connections.

➢

Future studies could model bolts as discrete fasteners or use connector elements with appropriate stiffness properties for better accuracy.

FEM versus Experimental Results:

➢

FEM load–deflection curves closely matched experimental results, validating the global response.

➢

However, tie constraints lack the detail to capture localized effects like bolt-bearing or connection slip.

Justification of Current Approach:

This study focused on global buckling behavior and load-carrying capacity, where tie constraints provided sufficient accuracy. Future work will refine connection modeling to better predict localized phenomena.

These constraints ensured that the structural behavior of the bolted connections and the interaction between the channel sections were accurately represented in the model. The tie constraint technique is essential for modeling contact interactions where elements are joined together but do not penetrate each other, ensuring that the interaction forces and deformations are realistic. In the FE model, tie constraints simulated the connections between BB channel sections, replicating the bolted behavior observed experimentally. The constraints were applied along the overlapping flanges to enforce a rigid connection, ensuring no relative displacement or rotation. The tie constraint in ABAQUS software [21] connected the master surface (one flange) to the slave surface (overlapping flange), enforcing a no-penetration and no-slippage condition. This ensured uniform load transfer and accurate representation of bolted joints. The overlapping regions along the flanges were carefully identified, and sensitivity analysis verified that the modeled connections matched the behavior of experimental bolted connections. This approach allowed the FE model to simulate load transfer, stress distribution, and interaction forces effectively. Tie constraints were computationally efficient and aligned with experimental conditions, enabling realistic simulation of global buckling modes, local deformations, and failure mechanisms under axial compression and thermal loading. The constraints enhanced the model’s reliability, providing valuable insights into the performance of built-up CFS columns.

By utilizing this method, the model effectively simulated the built-up structure’s response under both axial load and thermal exposure. The chosen element type and mesh refinement, in conjunction with accurate material properties and boundary conditions, provide a robust framework for simulating the behavior of CFS columns under fire exposure and structural loading.

The core objective of the numerical modeling was to replicate the experimental setup as closely as possible. This involved applying similar boundary conditions and loading scenarios, specifically focusing on axial compression and the loading rates employed during the experimental testing. In the model, concentric axial loads were applied to the CFS columns, and the resulting displacements and stresses were monitored throughout the simulation. The model’s performance was then evaluated by comparing the axial compression capacity obtained from the numerical simulations with the experimental data. This allowed for a direct assessment of the model’s accuracy in predicting the load–deformation behavior, especially under varying conditions of heating and cooling. The numerical results provided additional insights into the buckling modes, stress distribution, and local failure mechanisms, which helped explain the observed experimental outcomes. By successfully replicating the experimental conditions and validating the numerical approach, the model served as an effective tool for predicting the behavior of CFS columns in real-world applications, especially in scenarios involving fire exposure and thermal loading. Figure 14a depicts the meshed FE model used for analysis, and 14b depicts the FE model with boundary conditions. Pinned supports replicated experimental setups. End plates ensured uniform load distribution, with tie and coupling constraints preventing eccentricity.

4.4. Validation

The FE model aimed to replicate experimental conditions to analyze failure mechanisms (local, distortional, global buckling). It was also used for parametric studies on thermal exposure, imperfections, and coating effects. The validation of the FE model was conducted by comparing the ultimate loads and failure modes with experimental outcomes, demonstrating a strong correlation between the two approaches. The FE simulations accurately replicated the load-bearing capacities of the CFS columns under various heating and cooling scenarios. Both the experimental and numerical results consistently exhibited similar failure mechanisms, as illustrated in Figure 15 and Figure 16. At ambient conditions, the columns primarily failed due to web buckling, a characteristic mode of failure for slender, thin-walled sections like CFS columns under axial compression. This behavior was mirrored in the FEM results, confirming the model’s ability to capture the intrinsic structural response. For specimens subjected to elevated temperatures and cooled either by air or water, the failure mode largely remained web buckling, indicating that the primary structural behavior of the sections persisted despite thermal exposure. However, local buckling of the flanges became more prominent as the heating duration increased, particularly in sections subjected to prolonged exposure. The pronounced buckling in the upper halves of the BB sections was observed in both experimental and numerical studies. This can be attributed to stress concentration in these regions due to the distribution of axial loads and the inherent geometry of the sections. While the lower halves also experienced deformations, these were comparatively less severe, reflecting the stress gradient along the height of the section. A key observation was the influence of heating and cooling methods on the failure modes. Prolonged heating led to material softening, causing additional local deformations, especially in the flange regions. Specimens cooled by water exhibited slightly more severe buckling compared to those cooled by air, consistent with the observed microstructural changes and residual stresses induced by rapid cooling. The FEM model effectively integrated temperature-dependent material properties and thermal effects, enabling a precise simulation of the structural response under various conditions. It accurately predicted both the failure modes and the load capacities, capturing the impacts of elevated temperatures and different cooling methods on the structural behavior.

• Material Property Variations:

  ➢

  FE models approximate material properties and may not capture localized variations observed in tests.

  ➢

  Differences in temperature-dependent properties like yield strength, modulus, and ductility, especially after thermal degradation, can cause deviations.

• Modeling Assumptions:

  ➢

  Simplified boundary conditions, loading rates, and stiffness assumptions in FE models may not match experimental setups.

  ➢

  Effects like localized buckling, material nonlinearities, or residual stresses from cooling are often approximated, impacting post-peak accuracy.

• Geometrical Imperfections and Residual Stresses:

  ➢

  Real-world imperfections and residual stresses, difficult to replicate in FE models, influence post-peak behavior.

  ➢

  Cooling methods introduce varying residual stresses, causing complex experimental behavior not fully captured by the FE model.

• Post-Peak Behavior and Nonlinear Effects:

  ➢

  The nonlinear behavior of materials post-peak, including softening and plastic deformation, may not be fully calibrated in FE models.

Test setups may allow additional factors like slippage, microstructural changes, or further plastic deformation, leading to greater post-peak deformations than predicted by simulations.

The close agreement between experimental and FEM results underscores the reliability of the numerical approach. The model serves as a robust tool for analyzing the performance of CFS sections under fire conditions, providing insights into their buckling behavior, load capacity, and failure mechanisms. This validation strengthens the model’s applicability for future studies involving thermal effects on structural systems. Discrepancies in failure modes arose primarily due to limitations in modeling imperfections and residual stresses after heating and cooling. Improving the FE models by incorporating measured residual stresses and more detailed imperfection data could enhance alignment with experimental failure modes. The models also assumed uniform imperfection profiles for post-heated specimens, which may have contributed to minor discrepancies in failure mode predictions. Coatings were not modeled as structural contributors to buckling but rather as thermal protection. Their influence was limited to delaying the onset of temperature-induced strength degradation.

Table 5. Comparison of ultimate loads obtained through experiment and FEM analysis.

Sl No	Specimen ID	Temperature (°C)	PExp (kN)	PFEM (kN)	PExp/PFEM
1	MBREF	25	295.64	302.75	0.98
2	MB60AC	821	242.32	250.38	0.97
3	MB60WC	821	235.89	248.94	0.95
4	MB90AC	925	202.41	207.56	0.98
5	MB90WC	925	190.64	196.37	0.97
6	MBC1AC	821	268.3	276.3	0.97
7	MBC1WC	821	262.4	265.68	0.99
8	MBC2AC	821	277.9	282.36	0.98
9	MBC2WC	821	274.7	279.45	0.98
10	MBC3AC	821	257.53	261.74	0.98
11	MBC3WC	821	249.41	255.82	0.97
Mean					0.97
Coefficient of variation					0.98

depicts a comparison of ultimate loads obtained through experiment and FEM analysis.

The most critical factors affecting the deviations between FE results and experimental outcomes are geometrical imperfections and residual stresses.

Real-world imperfections and residual stresses are inherently present in CFS sections due to the manufacturing and forming process. These imperfections significantly influence the buckling behavior but are challenging to capture precisely in FE models. While FE models typically use idealized or uniform imperfection profiles, actual specimens exhibit varying imperfections that affect localized buckling patterns.

The cooling method (air or water) introduces different levels of residual stresses due to thermal gradients and contraction effects. Rapid water cooling induces higher residual stresses, which can lead to more severe distortional buckling, but FE models may not fully capture these residual stress distributions. This can explain why experimental specimens, especially water-cooled ones, exhibited more severe buckling compared to the predictions of the FE model.

Experimental specimens may exhibit additional softening, stress redistribution, and nonlinear post-peak deformations due to imperfections and residual stresses. The FE model approximates these effects but cannot fully replicate the unpredictability of real-world residual stress patterns. The discrepancies in failure modes between experimental and FE results were primarily due to limitations in modeling imperfections and residual stresses. The study acknowledged that improving FE models by incorporating measured residual stresses and more detailed imperfection data could enhance alignment with experimental failure modes.

Thus, while other factors like material property variations and modeling assumptions contribute to deviations, geometrical imperfections and residual stresses remain the most critical due to their direct influence on buckling behavior and post-peak response.

5. Buckling Stress

Figure 17 presents the variation in buckling stress for BB connected sections exposed to different heating durations and coatings, subsequently cooled to ambient temperature through either air or water. The behavior of these sections under axial compression is heavily influenced by both the duration of thermal exposure and the resulting degradation in material strength. Buckling stress, the critical stress causing instability due to compression, depends on material properties, geometry, boundary, and loading conditions. In this study, it was calculated analytically using equations (Equation (1)) incorporating temperature-dependent material properties.

$${\sigma }_{cr}={\displaystyle \frac{{\pi }^{2}EI}{[{\frac{KL}{r}]}^2}}$$

(1)

where

• ${\sigma }_{cr} is buckling stress$
• $E is Young’s modulus (temperature - dependent, derived from coupon tests)$
• $K is Effective length factor (based on boundary conditions)$
• $L is Effective length of the column$
• $r is Radius of gyration of the cross - section$

Euler’s buckling equation was used as a first-order approximation to estimate buckling stress, incorporating temperature-dependent material properties. Since Young’s modulus and yield strength degrade at high temperatures, this approach helped assess buckling trends. However, its limitations in capturing inelastic buckling behavior are recognized.

While FE models in this study accounted for material nonlinearities, the analytical comparison was based on elastic buckling theory. The stress contours (Figure 16) confirm that after 60 min of heating, yielding occurs before buckling, indicating inelastic buckling dominance. This suggests that inelastic buckling criteria, such as the Johnson–Ostenfeld method or the tangent modulus approach, would provide a more accurate failure prediction at high temperatures. Implementing plastic reduction factors or temperature-adjusted buckling curves could further improve predictive accuracy.

Material properties such as E were adjusted to reflect the degradation due to elevated temperatures and cooling. These values were derived from coupon tests conducted at various temperatures. The reduction in E with temperature significantly influenced the calculated buckling stresses.

For heating durations of up to 60 min, the failure is predominantly governed by material yielding, as the yield strength remains the primary factor determining the load-carrying capacity. However, beyond 60 min of exposure, buckling becomes the dominant failure mode.

This conclusion is based on experimental and numerical observations rather than a direct comparison of yield strength and elastic buckling stress. Key factors supporting this transition include

Material Degradation: As temperature rises, both yield strength and elastic modulus decrease, reducing structural stiffness and increasing buckling susceptibility.

Geometric Instabilities: Prolonged heating amplifies initial imperfections and residual stresses, promoting inelastic buckling over yielding.

Observed Deformations: Stress contours (Figure 16) show significant lateral displacements and buckling-dominated failure patterns, especially for specimens heated for 90 min and water-cooled.

Reconciling Yield Strength and Buckling Stress

The fact that yield strength is lower than the calculated elastic buckling stress does not imply yielding governs failure because Euler’s equation assumes purely elastic behavior, while inelastic buckling can occur at lower stresses due to plasticity. Plastic deformations accumulate at high temperatures, reducing actual buckling resistance. Rapid water cooling introduces residual stresses, further lowering the effective buckling capacity and shifting failure from yielding to buckling.

This transition highlights the critical influence of prolonged heating on structural stability, as buckling represents a premature failure mechanism compared to yielding. Such a shift is particularly significant in fire scenarios, where sustained high temperatures can alter the structural response, necessitating a thorough understanding of this behavioral transition. At elevated temperatures, the buckling response of CFS columns deviates substantially from their behavior under ambient conditions. The principal reason for this shift lies in the thermal degradation of material properties, especially the yield stress. Elevated temperatures reduce the modulus of elasticity and yield strength, leading to a significant decrease in the buckling capacity of the sections.

Additionally, cooling methods influence the residual stress distribution and microstructural changes in the material [27]. Water-cooled specimens, subjected to rapid quenching, tend to experience a more pronounced reduction in buckling capacity compared to air-cooled ones. This behavior can be attributed to the higher thermal gradients and contraction stresses induced by rapid cooling, which exacerbate the weakening of the material. Overall, the findings underscore the importance of evaluating buckling capacity in the context of elevated temperature exposure. Prolonged heating and rapid cooling are critical factors that accelerate the onset of buckling and reduce the structural capacity of CFS columns. These insights are essential for designing fire-resistant CFS sections and improving their performance under thermal loading conditions.

6. Relationship Between Yield and Buckling Stress

Figure 18 illustrates the relationship between yield stress and buckling stress for CFS columns subjected to different heating durations and cooling methods. The results reveal a linear correlation, with R² values approaching 1, indicating a strong proportionality between these two parameters across all sections under both air and water cooling scenarios. Even though the steel used in the columns was of the same nominal grade, production tolerances and batch-to-batch variations led to slight differences in the material’s actual mechanical properties. This linear trend underscores that variations in yield strength directly influence buckling stress, maintaining a consistent relationship up to the failure point. The findings highlight that the reduction in buckling capacity is predominantly governed by the material’s yield strength. As heating duration increases, the yield strength decreases due to thermal degradation, resulting in a corresponding decline in buckling stress. This proportional behavior persists regardless of the cooling method, although water-cooled sections exhibit slightly lower buckling capacities than air-cooled ones due to the additional stresses induced by rapid cooling. The thermal exposure during the heating phase led to variations in microstructure, which affected the YS of the material. For instance, the prolonged exposure to high temperatures during heating caused grain coarsening, phase transformations, and the precipitation of carbides, all of which affected the material’s YS. Different cooling methods also influenced the material’s properties by introducing residual stresses and potentially altering the thermal gradients across the column.

Recognizing this yield–buckling relationship is crucial for developing reliable predictive models for structural performance under elevated temperatures. It enables the formulation of design equations and performance criteria that account for the effects of heating and cooling on material properties. Furthermore, understanding this proportional relationship provides valuable insights into the failure mechanisms of CFS columns, aiding in the design of fire-resistant structures that can withstand thermal challenges effectively.

7. Conclusions

This study examines the axial compressive response of mild steel (MS) cold-formed steel (CFS) columns, with a particular focus on the structural integrity of back-to-back (BB) connections using self-tapping screws. The research used Grade E350 steel and involved an experimental program with 11 pin-ended column specimens. The test setup included an unheated reference specimen, six specimens coated with gypsum, perlite, or vermiculite for thermal insulation, and four uncoated specimens subjected to gradual temperature exposures followed by different cooling methods—air or water—to investigate the resulting material behavior.

• Uncoated specimens turned dark brown after heating, indicating material degradation due to high temperatures.
• Buckling behavior intensified with longer heating durations, with local buckling near welded areas and significant buckling in the upper middle sections and near supports.
• Uncoated specimens MB60AC and MB90AC showed stiffness reductions of 27.1% and 60.2% compared to MBREF, while water-cooled specimens (MB60WC and MB90WC) exhibited additional reductions of 10.7% and 9.0% compared to their air-cooled counterparts.
• Perlite-coated specimens demonstrated the best fire resistance, with MBC2AC retaining 277.9 kN load capacity, only 6.0% lower than MBREF.
• Perlite coatings provided superior thermal insulation, outperforming gypsum and vermiculite coatings, though the latter still showed benefits.
• Experimental and numerical results showed consistent failure mechanisms.
• The FEM model accurately simulated structural responses, predicting failure modes, load capacities, and the effects of elevated temperatures and cooling methods.

These findings emphasize the potential of perlite coatings to enhance the fire resistance of CFS columns, offering valuable insights into structural fire design