Flexural Behavior of Galvanized Iron Based Cold-Formed Steel Back-to-Back Built-Up Beams at Elevated Temperatures

Abstract

Cold-formed steel (CFS) sections have become popular in construction due to several advantages over structural steel. However, research on the performance of galvanized iron (GI)-based CFS under high temperatures, especially regarding its flexural behavior, has been limited. This study extensively investigates how GI-based CFS beams with varying spans behave under elevated temperatures and subsequent cooling using air and water. This study examines the impact of temperature loading and compares the effectiveness of air- and water-cooling methods. Experimental results are validated and analyzed alongside findings from finite element modeling (FEM) using ABAQUS (2019_09_13-23.19.31) and the Direct Strength Method (DSM). Additionally, this study conducts a parametric investigation to assess how beam span influences flexural capacity. Among beams heated to the same temperature, those cooled with water show slightly lower load capacities compared to those cooled with air. The highest load capacity observed is 64.3 kN for the reference specimen, while the lowest is 26.2 kN for the specimen heated for 90 min and cooled with water, a 59.27% difference between them. Stiffness decreases as heating duration increases, with the reference section exhibiting significantly higher stiffness compared to the section heated for 90 min and cooled with water, with a 92.76% difference in stiffness. As heating duration increases, ductility also increases. Various failure modes are observed based on different heating and cooling conditions across different beam spans. This study provides insights into how GI-based CFS beams perform under temperature stress and different cooling scenarios, contributing valuable data for structural design and safety considerations in construction.

1. Introduction

Cold-formed steel (CFS) is increasingly favored in construction due to its beneficial properties, such as high strength-to-weight ratio, ductility, and ease of customization. Unlike hot-rolled steel, CFS is produced without heat, making it a cost-effective alternative. However, CFS is vulnerable to fire damage. Understanding how it behaves in fire scenarios is crucial for effective risk management.

Research has extensively investigated the flexural behavior of CFS beams with hat-shaped profiles. It was found that initial imperfections significantly affect flexural behavior, highlighting their importance in determining section strength [1]. Further studies tested CFS tubular beams and conducted reliability analyses, showing that the mean moment capacity is unaffected by individual or combined variables, thus validating reliability analysis techniques.

The post-fire flexural behavior of CFS beams was also studied [2], indicating a decrease in load-carrying capacity with increased temperature exposure duration. This research enhances our understanding of how CFS beams perform after fire exposure. Recently, the authors of [3] investigated the flexural performance of thin-walled steel laminated bamboo truss beams, which showed that increasing the width and height of the beam and the number of self-drilling screws significantly improves the bending resistance of the composite truss beam. Recent studies [4] have also explored flexural performance in composite truss beams and CFS back-to-back built-up columns, revealing insights into improving load-bearing capacity through geometric modifications and screw spacing adjustments. Previous studies [5,6,7,8,9] on various CFS sections concluded that some of the techniques used for strengthening have the potential to improve the flexural strength of CFS beams.

Selvaraj and Madhavan [10] conducted both experimental and numerical studies on cold-formed steel (CFS) built-up sections with back-to-back sigma sections. Their research, which included validating different lengths and proposing new limits, highlights the need for comprehensive analysis and consideration of various configurations and lengths in evaluating structural performance under elevated temperatures. Landesmann and Camotim [11] examined the Direct Strength Method (DSM) for single-span-lipped channel beams under elevated temperatures. They found that the current DSM distortional strength curve was inadequate for predicting beam failure moments in such conditions. This insight underscores the importance of developing more accurate predictive models that are relevant to our study on the flexural behavior of GI-based CFS beams. Rodrigues et al. [12] explored the behavior of CFS GI beams under fire conditions. Their findings suggest that the choice between using CFS beams with and without web stiffeners depends on the section shape and internal forces during a fire. This aligns with our study’s exploration of different beam configurations and their impact on performance under elevated temperatures. Pannuzzo and Chan [13] investigated the flexural behavior of CFS square and rectangular sections with heat treatment through numerical methods and proposed new limits based on various codes. Their research, along with Zhu et al. [14], who assessed the flexural strength of CFS oval hollow section beams and confirmed the accuracy of DSM and continuous strength methods, supports the robustness of our methodology and its relevance in advancing design practices for CFS beams under high temperatures. Roy et al. [15] studied the collapse behavior of a single-story CFS building under severe fire conditions, developing a finite element model to predict the behavior of CFS cantilever wall systems in such scenarios.

Despite these advancements, comprehensive research gaps exist, particularly regarding the flexural response of galvanized iron (GI)-based CFS back-to-back sections under elevated temperatures. Additionally, there is a need to understand the impact of fire exposure on CFS built-up beams and analyze post-fire behavior using the Direct Strength Method (DSM). This study aims to investigate the flexural behavior of GI-based CFS beams under elevated temperatures and different cooling methods across various spans.

The anticipated outcomes aim to contribute valuable insights for design practices and facilitate a comparative analysis between experimental findings and numerical simulations. Recognizing the challenges of experimental investigations, this study underscores the importance of numerical simulations in gaining a comprehensive understanding of CFS beam behavior under fire conditions.

2. Materials and Methods

This study utilized back-to-back connected cold-formed steel (CFS) built-up channels made of grade 350 galvanized iron (GI) material, each with a length of 1.5 m. The dimensions of the channels used are illustrated in Figure 1. Additionally, this study includes an analytical and parametric investigation of beams with spans of 3 m, 4.5 m, and 6 m, as illustrated in Figure 2, Figure 3 and Figure 4. Figure 5 depicts a cross-sectional view of the built-up beam section. The sections were subjected to heating at specified temperatures and subsequently cooled using either air or water. An electric furnace, following the specifications outlined in [16], was used to heat the beams for durations of 60 and 90 min. For each temperature, the duration was pre-determined by ISO 834 guidelines; for example, exposing to 821 °C requires 30 min; 925 °C requires 60 min; 986 °C requires 90 min and 1029 °C requires 120 min. The back-to-back built-up sections were connected using 6 mm diameter self-tapping screws. Pinned and roller supports were installed at both ends to establish support conditions. The material properties of the sections used are detailed in

Table 1. Section property details.

Properties	Channel Section
Dimension (mm)	C200 × 60 × 20 × 20
Cross-sectional area (mm2)	684
Thickness (mm)	2
Radius of gyration rxx (mm)	77.34
Radius of gyration ryy (mm)	20.96
Moment of inertia in X-direction (mm4)	403.85 × 104
Moment of inertia in Y-direction (mm4)	29.72 × 104
Slenderness ratio	50.6
Length (m)	1.5
Elastic modulus (Gpa)	210
Yield strength (Mpa)	351

.

After the heating and cooling phases, the beams underwent testing on a Universal Testing Machine (UTM) under two-point loading conditions. Vertical stiffeners, 2 mm thick, were welded to the beams at both supports and two loading points, as shown in Figure 1. These stiffeners were incorporated to prevent twisting and lateral buckling during testing. Two-point loading was applied to simulate the flexural behavior of the beams. Specimen IDs and abbreviations are provided in

Table 2. Specimen ID and its definition.

Specimen ID	Definition of Section Type
	Experimental models (C profile)
EREF	Reference beam section, which is not exposed to heat.
E60: A-C	Beam section heated for 60 min cooled by air.
E60: W-C	Beam section heated for 60 min cooled by water.
E90: A-C	Beam section heated for 90 min cooled by air.
E90: W-C	Beam section heated for 90 min cooled by water.
	FEM and Parametric models
C3 REF	Reference beam section, which is 3 m long.
C3: 60A-C	Beam section with 3 m long heated for 60 min cooled by air.
C3: 60 W-C	Beam section with 3 m long heated for 60 min cooled by water.
C3: 90 A-C	Beam section with 3 m long heated for 90 min cooled by air.
C3: 90 W-C	Beam section with 3 m long heated for 90 min cooled by water.
C4.5: REF	Reference beam section, 4.5 m long.
C4.5: 60 A-C	Beam section with 4.5 m lonming heated for 60 min cooled by air.
C4.5: 60 W-C	Beam section with 4.5 m long heated for 60 min cooled by water.
C4.5: 90 A-C	Beam section with 4.5 m long heated for 90 min cooled by air.
C4.5: 90 W-C	Beam section was 4.5 m long and heated for 90 min cooled by water.
C6: REF	Reference beam section, 6 m long.
C6: 60 A-C	Beam section with 6 m long heated for 60 min cooled by air.
C6: 60 W-C	Beam section with 6 m long heated for 60 min cooled by water.
C6: 90 A-C	Beam section with 6 m long heated for 90 min cooled by air.
C6: 90 W-C	Beam section with 6 m long heated for 90 min cooled by water.

.

Deflectometers were placed beneath the bottom flange of the section at both loading points and at the midpoint of the beam. Linearly variable differential transducers (LVDTs) were attached to the side of the web of the beam to measure deflections. The experimental setup is shown in Figure 6.

3. Results

3.1. Physical Changes after Heating

Prior to the heating process, the beam sections exhibited a uniformly light glossy gray color, as depicted in Figure 6. Following the heating procedure, visible flaking appeared on the surface, as illustrated in Figure 7. After 60 min of heating, the observed color was dark blue. Additionally, a noticeable presence of brown dust was observed on the surface of all specimens.

3.2. Physical Changes after Loading

After testing, the specimens exhibited distortional buckling and local buckling for all durations of heating. Particularly, local buckling was evident on the stiffeners situated beneath the loading points, as shown in Figure 8, Figure 9 and Figure 10. After 90 min of heating, the color pattern is changed to a greenish-olive shade, as depicted in Figure 10. Distortional buckling occurred in the middle region of the beams, indicating compression failure at the top flange. The addition of stiffeners on bearings and the restrained supports effectively prevented lateral-torsional buckling.

3.3. Load Deflection Response:

Figure 11 depicts load–deflection graphs for beam sections tested in the experiment. The graphs show that as temperature increases, load capacity decreases. Beams cooled with water generally exhibit lower loads compared to those cooled with air. The maximum load observed was 64.3 kN for the reference specimen, while the minimum was 26.2 kN for the 90 min heated specimen cooled with water, a difference of 59.27%. Significant load decreases were noted, especially for the 60 min heated section cooled with water, showing a 24.53% lower load compared to air-cooled sections. Factors beyond heating and cooling, like material degradation due to prolonged exposure to high temperatures, affect load capacity.

3.4. Stiffness

Stiffness values, derived from the load–deflection curves (Figure 12), decrease as the heating duration increases. The reference section exhibits the highest stiffness, while the 90 min heated section cooled with water shows the lowest stiffness, with a difference of 92.76%. A notable stiffness drop is observed for the 90 min heated sections. A 34.8% difference in stiffness is noted between the 60 min and 90 min heated sections cooled with air.

For a linear elastic system, stiffness:

k is given by:

$$k={\displaystyle \frac{F}{\delta }}$$

(1)

where:

• F is the applied load.
• δ is the resulting displacement.

3.5. Ductility Factor

Figure 13 presents the ductility factors for all beam specimens. The ductility factor is a measure of the extent to which a material can undergo plastic deformation before failure. It is a ratio of the ultimate displacement to the yield displacement. The ductility factor increases with heating duration. The reference section has the lowest ductility factor, while the 90 min heated section cooled with water has the highest, with a 64.7% difference. Prolonged heating leads to significant changes in material properties, including reductions in yield strength, ultimate strength, and elastic modulus. These changes can enhance ductility by allowing the material to deform more before failure. Conversely, rapid cooling with water can alter material properties by reducing residual stresses, which may also increase ductility. This process can help mitigate the effects of prolonged heating and improve the material’s performance under stress. The ductility ratio is found using Equation (2),

$$\mu ={\displaystyle \frac{{\delta }_u}{{\delta }_y}}$$

(2)

where:

• ${\delta }_u$—the ultimate displacement (at failure).
• ${\delta }_y$—the yield displacement.

3.6. Ductility Index

Figure 14 shows ductility index values for all sections. The ductility index is a measure of ductility, often used to compare the ductile behavior of different materials or structural systems. It is the ratio of energy absorbed in plastic deformation to the energy absorbed in elastic deformation.

The ductility index generally decreases with higher temperatures. The reference specimen has the highest index, while the 90 min heated section cooled with water has the lowest, with a 5.35% difference. Water-cooled sections generally exhibit lower indices compared to air-cooled sections. A higher index indicates greater plastic deformation capacity, which is desirable for designs focusing on lateral load resistance. The ductility index is calculated using Equation (3),

$$\mathrm{Ductility} \mathrm{index} ={\displaystyle \frac{\mathrm{Area} \mathrm{under} \mathrm{plastic} \mathrm{portion} \mathrm{of} \mathrm{load}-\mathrm{displacement} \mathrm{curve}}{\mathrm{Area} \mathrm{under} \mathrm{elastic} \mathrm{portion} \mathrm{of} \mathrm{load}-\mathrm{displacement} \mathrm{curve}}}$$

(3)

4. Finite Element Analysis

4.1. Modeling

Finite element modeling (FEM) of beam sections was conducted using ABAQUS software (2019_09_13-23.19.31 ) [17]. This approach ensured the validation of numerical analysis by closely mimicking real-world conditions observed in experiments. The simulations replicated dimensions, support conditions, and loading similar to the experimental setup for accuracy and consistency in computational analysis.

4.2. Material Properties

Material properties for GI-based CFS beam sections were derived from temperature-dependent coupon test results [18]. An engineering stress–strain curve was initially generated and converted to a real stress–strain curve to accurately depict material behavior under varying loading conditions, especially at elevated temperatures.

4.3. Element Type and Meshing

S4R elements were used to model all components of GI-based CFS beam sections, known for accurately representing these beam types [19,20]. A mesh size of 5 × 5 mm was adopted based on prior research [21] to balance computation time and result accuracy (see Figure 15). Tie constraints were implemented to replicate the presence and interactions of self-tapping screws within the beams, ensuring accurate simulation of their behavior.

4.4. Loading and Boundary Conditions

Loading and boundary conditions were precisely defined with reference points at loading and support centers. Node sets were established to specify degrees of freedom during the meshing process. Linear bifurcation analysis and nonlinear analysis using the Modified Riks method were employed to capture structural instability, large deformations, and post-buckling responses effectively. Eigenvalue analysis addressed geometric imperfections in FE models, enhancing accuracy in representing structural behavior.

4.5. Comparison of FEA Results with Experimental Observations

Comparison between FEA and experimental results (Figure 16) showed a high level of agreement. Minor discrepancies between predictions and observations were negligible, affirming the reliability and precision of FE models in simulating GI-based CFS beam section behaviors under varying thermal and cooling conditions.

4.6. Failure Modes and Load Comparison

Distortional buckling was identified as the primary failure mode, with occasional local buckling under loading points on stiffeners. Failure modes observed in FEM models closely mirrored experimental observations (Figure 17, Figure 18 and Figure 19). Load–deflection curves from FEM analysis (Figure 20, Figure 21 and Figure 22) showed reduced load-carrying capacity with increased heating duration, consistent with experimental findings. Figure 23 illustrates load comparisons between experiments and FEM analysis, highlighting significant reductions in load capacity with increasing span lengths and heating durations.

4.7. Relationship between Yield Strength and Moment Capacity

Figure 24 depicts a relationship between yield strength and moment capacity derived from experimental loads across different heating and cooling durations. A noticeable trend indicated that as yield strength decreased, moment capacity also decreased. This reduction depended on the heating duration and cooling method, emphasizing the critical role of yield strength in resisting bending moments and structural integrity under thermal stress.

5. Current Design Rules of DSM

In this study, the Direct Strength Method (DSM) was used to evaluate the design moment capacities of the CFS beams. The required section properties for this analysis were taken from the experiments. Additionally, buckling analysis was conducted using the software CUFSM (V5.04) [22], employing equations outlined in the AISI guidelines [8].

Table 3. Comparing moments obtained from experiment, FEM, and DSM.

SL. No.	Specimen ID	Experimental Load kN	Experimental Moment (kNm)	FEM Load (kN)	FEM Moment (kNm)	DSM Moment (kNm)	MEXP/ MFEM	MEXP/ MDSM	MFEM/ MDSM
1	EREF	64.30	15.72	71.26	16.12	15.66	0.98	1.00	1.03
2	E60: A-C	48.40	12.95	50.21	13.24	14.31	0.98	0.90	0.93
3	E60: W-C	36.53	9.42	40.29	10.52	14.03	0.90	0.67	0.75
4	E90: A-C	29.10	7.43	37.95	7.94	11.32	0.94	0.66	0.70
5	E90: W-C	26.20	6.21	28.94	6.82	10.73	0.91	0.58	0.64
	Mean						0.94	0.76	0.81
	COV						0.05	0.10	0.10

displays the moments obtained from experiments, FEA, and DSM. Mean values and coefficients of variation are computed and presented. Notably, moments calculated using FEA exceed those obtained through other methods. Conversely, moments determined via the DSM show the lowest values among all approaches [23].

Figure 25 illustrates the signature curve derived through CUFSM [22] for reference beam sections. These curves provide valuable insights into the thermal stress-induced behavior of the beam sections, enhancing our understanding of their performance. The signature curve represents the relationship between the axial strength and slenderness of a structural member. It helps in characterizing the buckling behavior of cold-formed steel members under different loading conditions, such as axial compression, bending, and shear. The curve aids in identifying the critical buckling load for members, which is essential for assessing their stability. By plotting the load versus slenderness, one can determine the point at which the member will buckle. As the slenderness ratio increases, the strength of the member typically decreases.

6. Conclusions

This study comprehensively examined the flexural behavior of GI-based CFS back-to-back built-up channel beams subjected to elevated temperatures and cooled using either air or water. Experimental analysis under two-point loading was conducted to investigate their flexural behavior, with validation through the finite element method (FEM). Parametric studies were performed on beams of varying lengths (3 m, 4.5 m, and 6 m), and manual computations of moments using the Direct Strength Method (DSM) enabled comparative analysis of outcomes. The key conclusions from this research are listed below:

• Distortional buckling and local buckling were observed across all heating durations, particularly evident at stiffeners beneath loading points.
• Beams cooled with water after heating exhibited slightly lower loads compared to those cooled with air at the same temperature. The maximum load of 64.3 kN was observed for the reference specimen, while the minimum load of 26.2 kN occurred for the specimen heated for 90 min and water-cooled, representing a 59.27% difference.
• Stiffness decreased with longer heating durations, with the reference section showing the highest stiffness and the 90 min heating and water-cooled section displaying the lowest, differing by 92.76%.
• Ductility increased with longer heating durations, with the reference section having the lowest ductility factor and the 90 min heating and water-cooled section the highest.
• Increasing the span length drastically reduced load-carrying capacity. For unheated sections, the difference in load capacity between 1.5 m and 6 m spans was 116.4%. Even after heating for 60 min and water-cooling, the difference remained significant at 117.7%.

This research provides valuable insights into the behavior of GI-based CFS beams under fire conditions, highlighting the effects of cooling methods, heating duration, and span length on their mechanical properties. These findings contribute to enhancing the design and performance assessment of CFS structures subjected to fire hazards.