# Mechanical Properties of Steels for Cold-Formed Steel Structures at Elevated Temperatures

Authors: Zhen Nie; Yuanqi Li; Yehua Wang
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

It is highly important to clarify the high-temperature mechanical properties in the design of cold-formed steel (CFS) structures under fire conditions due to the unique deterioration feature in material properties under fire environment and associated reduction to the mechanical performance of members. This paper presents the mechanical properties of widely used steels for cold-formed steel structures at elevated temperatures. The coupons were extracted from original coils of proposed full annealed steels (S350 and S420, with nominal yielding strengths 280 MPa and 350 MPa) and proposed stress relieving annealed steels (G500, with nominal yielding strength 500 MPa) for CFS structures with thickness of 1.0 mm and 1.2 mm, and a total of nearly 50 tensile tests were carried out by steady-state test method for temperatures ranging from 20 to 700°C. Based on the tests, material properties including the yield strengths, ultimate strengths, the elasticity modulus, and the stress-strain curve were obtained. Meanwhile, the ductility of steels for CFS structures was discussed. Then, the temperature-dependent retention factors of yield strengths and elasticity modulus were compared to those provided by design codes and former researchers. Finally, a set of prediction equations of the mechanical properties for steels for CFS structures at elevated temperatures was proposed depending on existing tests data.


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## Body

## 1. Introduction

As the main components in light weight steel structural buildings worldwide, cold-formed thin-walled steel (CFS) members are manufactured from cold-rolled thin-walled steel sheets or strips, approximately from 0.3 mm to 3.0 mm thickness, with grades from 200 to 1000 [1–5]. The applicable steels for CFS structures are specified in codes [1–5] with different elongation and nominal yield strength. In these standards [1–5], elongation of 10% is a significant boundary for dividing the category of steel materials. In the meantime, 450 MPa is also a rough line for separating massive steels used for CFS structures [1–5]. Generally, the steel coils for manufacturing of CFS sections are made from both hot-rolled steel sheets and cold-rolled steel sheets [1–5], in which cold-rolled steel sheets may involve the annealing process. Also, for cold-forming process into cross section shapes, stress-hardening effect takes place leading to reduced ductility of the raw material. Hence, annealing [6] may be involved after the cold-forming process to improve the mechanical properties or to relief the residual stress. Steels with a specified minimum elongation of 10% or greater are full annealed steels, and the remaining part is the stress relieving annealed steels (the classification approach is proposed in this paper based on the manufacturing process of steels). For instance, G250 and G300 steels are widely used in North America, Australia, and Europe [1–4]; S280, with a nominal yielding strength of 280 MPa, and S350, with a nominal yielding strength of 350 MPa, steels, suggested by Chinses code [5], belong to the full annealed steels. On the other hand, G550 class steels, including G450, G500, and G550 steels [2, 5], are typical stress relieving annealed steels.At ambient temperatures, besides the yield strength, there is a significant difference on ductility between the full annealed and stress relieving annealed steels as mentioned above. These different characteristics of those two kinds of steels are determined by the variety in the manufacturing process especially heat treatment procedures [6].At elevated temperatures, the strain hardening in cold-rolled thin-walled steels is relieved with time; accordingly the strength reduction of this type of steel may be higher than that of hot-rolled steels. Meanwhile, these steels develop faster heating rates for having higher thermal conductivity ratio and thinner thickness than hot-rolled steels. However, current specifications [7–10] of steel structural fire designs on the mechanical properties at elevated temperatures were based on hot-rolled steels. Particularly, an integrated provision of high-temperature material models for the entire cold-formed thin-walled steel family has not been provided in current Chinese CFS design codes [5]. In recent years, there is already a considerable database established by global researches on material properties of flat steel sheets for CFS structures at elevated temperatures [11–19]. In general, tested specimens range from 0.50 mm to 2.50 mm thick, with yield strengths from 250 MPa to 550 MPa at ambient temperature. However, no systematic discussion on classification of steels for CFS structures has been conducted when exploring temperature-dependent mechanical properties. From the perspective of steel grades and the ductility at ambient temperature, tested steels in current researches can be divided into two groups: full annealed steels [11, 12, 14, 15, 17–19] (with nominal yielding strength under 450 MPa and elongation greater than 10%) and stress relieving annealed steels [12–16] (with nominal yielding strength over 450 MPa and elongation less than 10%).This paper presents a detailed experimental investigation of the material properties of two full annealed flat steel sheets (S350 and S420) and one stress relieving annealed flat steel sheet (G500) cut from original steel coils. Here, S350 is the most common grade in past tests [11, 17, 18]; however few data exist on S420 and G500 steels at elevated temperature. Then, by means of comparative study, discussion is conducted on the failure mode, ductility, constitutive relationships, and retention factors for both full annealed steels and stress relieving annealed steels. Meanwhile, after accumulating the existing test data so far, further comparison is made on the reduction trend of mechanical properties at elevated temperatures for two different group steels. Finally, a set of prediction equations of mechanical properties for the entire family of steels used in CFS structures at elevated temperatures is proposed.


## 2. Manufacturing Process of Steels for CFS Structures

Cold-rolled thin-walled steels are manufactured by cold working mild sheet steels on cold reducing roll to a thickness ranging from 0.3 mm to 3.0 mm. Cold reducing produces distinct deformations of the microcosmic grain texture and structure, which cause a strengthening in strength and hardness, a decrease inFu/Fy ratio, and a reduction in ductility. The effects of cold working are cumulative and harmful for steels that are used for structural members. Thus, it is necessary to change and recover the grain structure and to control the steel properties through subsequent heat treatment after cold rolling [6].The process of heat treatment is carried out first by heating the material and then cooling it in the brine, water, and oil. The purpose of heat treatment is to soften the metal, to change the grain size and structure, to modify the properties of the material, and to relieve the stress setup in the material after hot and cold working. The various heat treatment processes commonly employed in engineering practice include annealing, normalizing, quenching, and tempering. Specifically, annealing is the most commonly used heat treatment method in manufacturing of steels for CFS structures. Further, based on the heating temperatures, when annealing is carried out, there are several types annealing as follows [20, 21]:Full annealing - The steel is heated to above the critical temperatureAc3 (eutectoid point, 700°C–750°C for low carbon steel) for some time and then cooled in a specific rate. Here all the ferrite transforms into austenite. Full annealed steel is soft and ductile with no internal stress. Partial annealing - The steel is heated to a temperature below to the critical temperature Ac3, held at this temperature for some time, and then cooled slowly. The purpose is to relive stress and lower the hardness of the steel. Stress relieving annealing - The steel is heated to below the critical temperature Ac1 (pearlite transforms into austenite at this temperature point, 500°C–600°C for low carbon steel), held until the temperature is constant throughout its thickness, then cooled slowly. In this process, the steel is stress relieved; however recrystallization does not occur. Figure 1 illustrates the typical annealing process of steels.Figure 1
Annealing process.Table1 shows the chemical composition of tested metals, and Table 2 indicates the key temperatures during manufacturing procedures of tested steels, which are acquired from original manufacturer. It is easily find that the G500 steel experienced a significant lower annealing temperature than that of S350 and S420 steels. Thus, we can safely say that S350 and S420 steels are fully annealed, although the G500 steel is stress relieving annealed according to definitions of different annealing process. In other words, S350 and S420 steels are typical full annealed steels, and the G500 steel is the stress relieving annealed steels. Furthermore, after consulting CFS design standards provisions on materials, collecting current tested steels information, and exploring manufacturing process of steels, commonly used steels for CFS steel structures are divided into two categories: Full annealed steels—steels that experience full annealing process during manufacturing, with nominal yielding strength under 450 MPa and elongation greater than 10%. Stress relieving annealed steels—steels that experience stress relieving annealing process during manufacturing, with nominal yielding strength over 450 MPa and elongation less than 10%.Table 1
Chemical composition∗ of S350, S420, and G500 steels.
S350 (1.0 mm)C (%)Mn (%)Al (%)S (%)Nb (%)0.060.80.0450.020.015S420 (1.0 mm)C (%)Mn (%)Al (%)S (%)Nb (%)0.060.60.0450.0150.09G500 (1.2 mm)C (%)Mn (%)Al (%)S (%)B (%)0.040.220.0380.0150.002∗Percentage of element by mass.Table 2
Manufacturing key temperatures of S350, S420, and G500 steels.
Manufacturing key processHot rolling (°C)Final rolling (°C)Annealing (°C)S3501220Room temperature730S4201200Room temperature700G5001200870500Specifically, stress relieving annealed steels are basically equivalent to G550 series steels widely used in Australian and Chinese building industry. G550 series steels [2, 5], including three grades (G450, with thickness greater than or equal to 1.5 mm, G500 with thickness greater than 1.0 mm and less than 1.5 mm, and G550, with thickness less than or equal to 1.0 mm.), share similar features on mechanical properties at ambient temperatures [2, 5], and these features (high strength and low ductility) come from stress relieving annealing process [6] on production line.


## 3. Experimental Study

### 3.1. Test Method

Two major methods [11–19] may be used to evaluate the mechanical behavior of construction materials under high-temperature environment [11–19]. The most common method currently used for investigating the mechanical properties of steels at elevated temperatures is the steady-state test in which the specimen is heated up to a target temperature and held for a period of time until the temperature is stable and uniform along the specimen, then gradually subjected to a tensile load through to fracture. Another well-known method is the transient-state test in which the specimen applied a static load and then is heated up slowly until failure criteria are met. Most researchers employ steady-state test technique since it is able to obtain stress-strain curves directly, avoids fluctuant temperature environment, eliminates the influence of thermal expansion, and generally saves resources. According to current papers, there is no final conclusion [11, 13, 16] yet on which method is more accurate for testing and predicting the mechanical properties of steels at elevated temperatures. Also, the main focus of this investigation is on the prediction of different types of steels for CFS structures material properties under high temperatures. Therefore, the steady-state test method was adopted in this test study.


### 3.2. Test Specimens

All coupons were cut by a wire cutting machine from original coils of S350 and S420 steels with nominal thickness of 1.0 mm, and G500 steels with nominal thickness of 1.2 mm. The dimension of the test specimens was determined by ISO standard [22], as presented in Figure 2. There were four small lugs at the edge of parallel part for fixing extensometer system and two holes for pinning extension tension rods. The metal thickness and gage width of the specimens were average of those values measured at three points within gauge lengths by using a micrometer before testing. The base metal thickness and real gage width were used in the calculations of the initial cross sectional area.Figure 2
Test specimens and dimensions.
(a)(b)


### 3.3. Test Devices and Procedure

The experiment setup is the EDC222 Doli testing system shown in Figure3, which is an integrated closed loop digital control thermal and mechanical testing system. The tensile testing machine is an electronic servo system with 100 kN capacity, which was calibrated before testing. A high-temperature stove with a maximum temperature of 1200°C was employed in the testing. Three pairs of thermocouples binding separately on upper rod, surface of specimen, and lower rod in a range of 150 mm provided signals for accurate feedback control of specimen temperatures, presented in Figure 4. In this way, a uniform temperature zone would be generated when the temperature of three thermal couples remained stable. The material for fixing thermocouples herein is the refractory heat insulation ceramic fiber cloth band, shown in Figure 5. A set of linear displacement gratings, including high-temperature resistance extension rods, with a range of 12.5 mm relative to 50 mm gauge was used to acquire the deformation of specimens between the gauge lengths. The extensometer system, detailed in Figure 6, created a 50 mm gauge, which was able to collect more displacement data from the gauge scope before the coupon failed, and was also calibrated before testing.Figure 3
Testing system (Doli control system).Figure 4
Details of the testing devices.Figure 5
Refractory heat insulation ceramic fiber cloth.Figure 6
High-temperature extensometer system.Tensile coupon tests were carried out by adopting the steady-state test method. First, the specimen was heated up to a preselected temperature at a rate of 20°C/min. Free thermal expansion was allowed when heating up by keeping tensile load zero. The temperature levels selected in this experiment were 20°C, 100°C, 200°C, 300°C, 400°C, 500°C, 600°C, and 700°C. The specimen was kept for 30∼40 min at this constant temperature until it reached the steady condition. Then the load was applied by controlling the displacement of the electronic tensile grip until failure while maintaining the set temperature degree. The displacement rate was set to 0.24 mm/min, which was, specifically in elastic stage, equivalent to a strain rate of 0.00007/s as the minimum rate specified by ISO standard [22]. Moreover, the sampling frequency was 10 Hz. Most of the specimens were repeated twice for double checking. Some additional experiments have been conducted for verification (500°C for G500 steel) and supplement (350°C and 700°C for S350 and S420 steels) at several temperature points. Summary of tested specimens is present in Table 3.Table 3
Number of tests performed in this study.
T (°C)20100200300350400500600700S350 (nominal thickness 1.00 mm)222212221S420 (nominal thickness 1.00 mm)222212221G500 (nominal thickness 1.20 mm)2222—232—Temperature control is the most critical part in a high-temperature material test undoubtedly. During tests procedure, real-time temperatures at three different points along the specimen were detected by thermocouples and recorded by data acquisition system. Figure7 gives a set of typical temperature curves from three thermal couples over time for a certain specimen at a certain temperature condition (take 500°C for example). At about 25 min, the coupon temperature reached preselected 500°C in the gross; however the temperature was quite uneven and unstable at that point. Until the 45 min, under the working of feedback control system, the heat conduction and thermal convection in the furnace were balanced dynamically. Consequently, three curves narrowed into a tiny range and the entire specimen was clearly and steadily at the target temperature. At that moment, the coupon was ready to be elongated.Figure 7
Typical temperature curves.


## 3.1. Test Method

Two major methods [11–19] may be used to evaluate the mechanical behavior of construction materials under high-temperature environment [11–19]. The most common method currently used for investigating the mechanical properties of steels at elevated temperatures is the steady-state test in which the specimen is heated up to a target temperature and held for a period of time until the temperature is stable and uniform along the specimen, then gradually subjected to a tensile load through to fracture. Another well-known method is the transient-state test in which the specimen applied a static load and then is heated up slowly until failure criteria are met. Most researchers employ steady-state test technique since it is able to obtain stress-strain curves directly, avoids fluctuant temperature environment, eliminates the influence of thermal expansion, and generally saves resources. According to current papers, there is no final conclusion [11, 13, 16] yet on which method is more accurate for testing and predicting the mechanical properties of steels at elevated temperatures. Also, the main focus of this investigation is on the prediction of different types of steels for CFS structures material properties under high temperatures. Therefore, the steady-state test method was adopted in this test study.


## 3.2. Test Specimens

All coupons were cut by a wire cutting machine from original coils of S350 and S420 steels with nominal thickness of 1.0 mm, and G500 steels with nominal thickness of 1.2 mm. The dimension of the test specimens was determined by ISO standard [22], as presented in Figure 2. There were four small lugs at the edge of parallel part for fixing extensometer system and two holes for pinning extension tension rods. The metal thickness and gage width of the specimens were average of those values measured at three points within gauge lengths by using a micrometer before testing. The base metal thickness and real gage width were used in the calculations of the initial cross sectional area.Figure 2
Test specimens and dimensions.
(a)(b)


## 3.3. Test Devices and Procedure

The experiment setup is the EDC222 Doli testing system shown in Figure3, which is an integrated closed loop digital control thermal and mechanical testing system. The tensile testing machine is an electronic servo system with 100 kN capacity, which was calibrated before testing. A high-temperature stove with a maximum temperature of 1200°C was employed in the testing. Three pairs of thermocouples binding separately on upper rod, surface of specimen, and lower rod in a range of 150 mm provided signals for accurate feedback control of specimen temperatures, presented in Figure 4. In this way, a uniform temperature zone would be generated when the temperature of three thermal couples remained stable. The material for fixing thermocouples herein is the refractory heat insulation ceramic fiber cloth band, shown in Figure 5. A set of linear displacement gratings, including high-temperature resistance extension rods, with a range of 12.5 mm relative to 50 mm gauge was used to acquire the deformation of specimens between the gauge lengths. The extensometer system, detailed in Figure 6, created a 50 mm gauge, which was able to collect more displacement data from the gauge scope before the coupon failed, and was also calibrated before testing.Figure 3
Testing system (Doli control system).Figure 4
Details of the testing devices.Figure 5
Refractory heat insulation ceramic fiber cloth.Figure 6
High-temperature extensometer system.Tensile coupon tests were carried out by adopting the steady-state test method. First, the specimen was heated up to a preselected temperature at a rate of 20°C/min. Free thermal expansion was allowed when heating up by keeping tensile load zero. The temperature levels selected in this experiment were 20°C, 100°C, 200°C, 300°C, 400°C, 500°C, 600°C, and 700°C. The specimen was kept for 30∼40 min at this constant temperature until it reached the steady condition. Then the load was applied by controlling the displacement of the electronic tensile grip until failure while maintaining the set temperature degree. The displacement rate was set to 0.24 mm/min, which was, specifically in elastic stage, equivalent to a strain rate of 0.00007/s as the minimum rate specified by ISO standard [22]. Moreover, the sampling frequency was 10 Hz. Most of the specimens were repeated twice for double checking. Some additional experiments have been conducted for verification (500°C for G500 steel) and supplement (350°C and 700°C for S350 and S420 steels) at several temperature points. Summary of tested specimens is present in Table 3.Table 3
Number of tests performed in this study.
T (°C)20100200300350400500600700S350 (nominal thickness 1.00 mm)222212221S420 (nominal thickness 1.00 mm)222212221G500 (nominal thickness 1.20 mm)2222—232—Temperature control is the most critical part in a high-temperature material test undoubtedly. During tests procedure, real-time temperatures at three different points along the specimen were detected by thermocouples and recorded by data acquisition system. Figure7 gives a set of typical temperature curves from three thermal couples over time for a certain specimen at a certain temperature condition (take 500°C for example). At about 25 min, the coupon temperature reached preselected 500°C in the gross; however the temperature was quite uneven and unstable at that point. Until the 45 min, under the working of feedback control system, the heat conduction and thermal convection in the furnace were balanced dynamically. Consequently, three curves narrowed into a tiny range and the entire specimen was clearly and steadily at the target temperature. At that moment, the coupon was ready to be elongated.Figure 7
Typical temperature curves.


## 4. Test Results and Discussion

In this section, based on the purses of investigating the difference between two kinds of cold-rolled thin-walled steels on material properties at elevated temperatures, the results of tests are discussed in the way of comparison.


### 4.1. Failure Mode

Figures8–10 present the failure modes of three grades of tested coupons. All specimens fractured within the gauge length scope expectedly, which means the stress-strain curves recorded from data acquisition system were real stress-strain relationships within the gauge length. Meanwhile, the carburization layer coated the specimen for all tested grades when temperature reached 500°C, illustrated by the dark surface of those coupons in Figures 8–10. This carburization coating was incompact and could be scratched using thin sheet metal. Specifically, steel plates presented a blue brittle phenomenon like normal steels around 300°C, evidenced by the dark blue colored oxidation film on the fracture section of specimens, shown in Figure 11 for the fracture details.Figure 8
Failure modes for S350 steels.Figure 9
Failure modes for S420 steels.Figure 10
Failure modes for G500 steels.Figure 11
Blue brittle phenomenon for steel plates.For two full annealed steels, visually noticeable elongation and necking of the coupons occurred from ambient and continued to higher temperatures. For G500 steels, significant elongation and necking could not be observed until temperature exceeds 500°C. Considering the distinction on heat treatment temperatures between full annealed and stress relieving annealed steels, the G500 steel is more brittle at ambient temperature since the cold work forming effect is not eliminated during annealing. However, when temperature went up to 600°C, which was higher than the critical temperatureAc1 for low carbon steel, it was possible that the steel was partially annealed in the oven and lost part of the hardening influence. Afterwards, significant change on the failure mode of G500 at 600°C could partially support this assumption and we still need more data investigation to explore the relationship between temperatures and material properties for various steels used in CFS structures.Some of the failed specimens appear to be distorted after 500°C. During the tests at temperatures above 500°C, the specimens were stretched at a much higher displacement rate after the extensometer range was exceeded. In this case, the fracture of these specimens seems to be abnormal. It should be pointed that both ends of the tested specimens have been clamped tightly in the slot of extension loading rods by inserting shims at two sides of the coupon to avoid eccentric load.


### 4.2. Ductility

In this part, percentage elongation after fracture [22], as shown in equation (1), calculated from original gauge length and final gauge length after fracture, is used to indicate the ductility of specimens. The final gauge length for fractured and cooled down specimens was measured by piecing the segments of specimens tightly at the fracture. Table 4 presents the average percentage elongation after fracture at different temperatures for specimens and its curves are shown in Figure 12.(1)AT=lu,t−l0l0×100.Table 4
Average percentage elongation after fracture (cooled down).
T (°C)Percentage elongation after fracture (%)S350S420G5002032.0229.992.7610022.7120.826.0620022.4023.923.9430040.2541.4112.0140043.1845.6710.3450049.0754.1710.6860063.8066.9768.3870064.0056.80Figure 12
Average percentage elongation after fracture at different temperatures.It is interesting to find that S350 and S420 steels, when the temperature increased from 20°C to 200°C, lose their ductility obviously. Some researchers [11, 12] noted a similar behavior for full annealed steels. This material behavior may be attributed to chemical transformations taking place in the steel base. After 300°C, since chemical reactions were taken over by temperature effects as the dominate factor, the ductility grows continually as expected. At the same time, S350 and S420 steels presented a very close trend on ductility development with temperature rising.Stress relieving annealed steels showed lower ductility than that of full annealed steels at ambient temperature due to the different heat treatments in manufacturing process as mentioned before. Under 200°C, the ductility of G500 steels maintained low values, even close to room temperature value. Then there was a higher platform of ductility in the range of 300°C∼500°C, though it was still lower than that of full annealed steel at the same temperatures. Up to 600°C, the effect of strain hardening and heat treatment has been eliminated, so that both full annealed and stress relieving annealed steels showed the same level of ductility. Since the flashover temperature of fire is over 600°C, the lack of ductility cannot be considered as a characteristic for stress relieving annealed steels at fire conditions.


### 4.3. Constitutive Relationship

Since the measurement range of the displacement grating is 12.5 mm, the stress-strain curves are given within the strain of 0.2, as shown in Figures13–15. All stress-strain curves of tested specimens (shown in Figure 3) are summarized together for S350, S420, and G500 steels, respectively. For each of the temperature conditions (marked in the same black circles), curves of repeated tests accord well with each other, indicating the stability of tested materials, test devices, and test operations.Figure 13
Stress-strain curves of S350 steels at different temperatures.Figure 14
Stress-strain curves of S420 steels at different temperatures.Figure 15
Stress-strain curves of G500 steels at different temperatures.As shown in Figures13 and 14, the stress-strain curves of S350 and S420 steels present a similar variation trend: (1) For temperatures below 200°C, an obvious yield plateau occurs when the load reaches the ultimate strength and disappears after temperatures beyond 200°C. (2) From 20∼300°C, the strain-hardening ranges at different temperatures pinch into a small zone, which illustrates that only yield strength experiences degradation at those temperature cases but ultimate strength dose not. (3) At temperatures beyond 200°C, the stress-strain curves were of the gradual yielding type, and both yield strength and ultimate strength deteriorate with temperature rising. The yield plateaus with multiple yield points are the result of interrupted motion of the Luders band along the specimen. The movement of dislocations near the band front becomes locked when temperature reaches 300°C, and thus yield plateaus disappeared over these temperatures [23].Unlike the full annealed steels, the G500 steel gave gradual yielding type stress-strain curves at both ambient and elevated temperatures, referring to Figure15. Then, it appears that the yield strengths do not decrease much up to 200°C. Furthermore, the stress-strain curves have a similar shape and ultimate deformation at temperatures from 300°C to 500°C. When temperature reaches 600°C, the ultimate strain increases significantly. Meanwhile, the load decreases very slowly after the ultimate strength at this condition, and the corresponding failure mode changes to ductile fracture with clear necking.


### 4.4. Retention Factors

Primarily, Table5 shows the tensile test results of all three steels at ambient temperature, which are fundamental parameters for calculating high-temperature material properties. Besides the apparent higher strength of G500 steels, the elastic modulus of this high strength steel is also higher than that of full annealed steels at room temperature.Table 5
Mechanical properties of cold-rolled thin-walled steels at ambient temperature.
Steel gradeE20 (GPa)Fy,20 (MPa)Fu,20 (MPa)S350 (1.0 mm)211.9411.3472.2S420 (1.0 mm)212.9434.6488.1G500 (1.2 mm)218.5686.8689.8Retention factors for the elastic modulus, yield strength, and ultimate strength were computed as the ratios of material properties at high temperatures to their values at ambient conditions, which is 20°C in this paper. The elastic modulus was calculated by fitting the initial portion of the stress-strain curves via using the least squares method, following ISO standard [22]. For the curves with smooth and long yield plateau, the yield strength was taken as the average value of stresses in the plateau. Then for the gradual yielding cases, the yield strength was determined by the 0.2% proof stress method, which uses the intersection point of the stress-strain curve and the proportional line offset by 0.2% strain. Results are shown in Table 6.Table 6
Retention factors for the elastic modulus, yield strength, and ultimate strength.
T (°C)S350,t = 0.96 mmS420,t = 0.96 mmG500,t = 1.16 mmET/E20Fy,T/Fy,20Fu,T/Fu,20ET/E20Fy,T/Fy,20Fu,T/Fu,20ET/E20Fy,T/Fy,20Fu,T/Fu,20201.0001.0001.0001.0001.0001.0001.0001.0001.0001000.9380.8700.9490.9410.9370.9661.0260.9590.9712000.9670.7871.0520.9670.6771.0040.9760.9771.0573001.0760.5931.0541.0560.5731.0410.9130.8360.9143500.9380.4880.8450.8210.5240.857———4000.8910.4670.6800.7850.4670.6890.6100.6650.7075000.6020.3210.3810.5780.3190.3840.4660.3570.3966000.2870.1760.1810.3140.1820.1920.2530.0650.0947000.1590.0700.0680.1670.0700.074———Figures16 and 17 provide the retention factors for full annealed and stress relieving annealed steels obtained through steady-state tests from this study and current steel structural fire design codes.Figure 16
Comparison of the retention factors of elastic modulus according to test results with the current design codes.Figure 17
Comparison of the retention factors of yield strength according to test results with the current design codes.By comparing tests data in this paper for cold-rolled thin-walled steels with current design codes, retention factors from existing steel design codes are generally unsafe, especially for yield strength prediction. As for elastic modulus, retentions factors predicted by Eurocode 3 [9] and AISC 360 [7] agree well with the present full annealed steels tests data before 500°C, but somewhat are unsafe beyond 500°C. These two curves are also suitable for G500 steels, although being a little conservative around 300°C and slightly unsafe beyond 400°C. In addition, the elastic modulus retention factors curve provided by AS 4100 [8] are unsafe beyond 400°C for both full annealed and stress relieving annealed steels. Yield strength retentions factors from hot-rolled steel experimental data provisioned by AISC and Eurocode 3 were the most unsafe, whereas AS 4100 and BS5950-8 [10] are less unsafe relatively. This confirms that, by directly using retention factors developed for hot-rolled steel to calculate yield strength, they are not suitable for cold-rolled thin-walled steels.Therefore, the provisioned curves in current codes cannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study.In order to investigate the relationship on high-temperature material properties between the steels for CFS structures with different manufacturing process, this paper collected the existing test data of cold-rolled thin-walled steels at elevated temperatures in the recent 20 years, as presented in Table7. Specifically, based on previous discussion, S420 steel shares a very similar trend on failure mode, ductility, constitutive relationship, and retention factors with S350 steel (typical full annealed steels), even though its nominal yield strength is close to G450 steel (stress relieving annealed steels). Thus, in Table 7, the level of ductility (elongation) is the reliable and significant classification standard for commonly used steels for CFS structures, which is mainly due to the different annealing process during manufacturing.Table 7
Compilations of basic information for current test data.
YearResearchersGradeThickness (mm)Elongation∗ (%)Full annealed steels1999Qutinen [11]S3502.00>202003Lee et al. [12]G3000.40No information0.60No information1.00No information2009Ranawaka and Mahendran [14]G2500.60>300.80>300.95>302011Kankanamge and Mahendran [15]G2501.55>301.95>302013Ye and Chen [17]Q3451.50>302015Batista Abreu [18]S2301.44>20S3451.15>201.55>202.58>202016Craveiro et al. [19]S2802.50>20This researchS3501.0032.02S4201.0029.99Stress relieving annealed steels2003Lee et al. [12]G5001.20No informationG5500.42No information0.60No information0.95No information2007Chen and Young [13]G4501.9011.3G5501.009.82009Ranawaka and Mahendran [14]G5500.60<30.80<30.95<32011Kankanamge and Mahendran [15]G4501.50<101.90<102012Chen and Ye [16]G5501.00<10This researchG5001.202.76∗The elongation here represents the percentage elongation after fracture of specimens at ambient temperatures. However, most researches have not given the elongation data directly; stress-strain curves are major clues to estimate the ductility of steels.Figures18 and 19 illustrate the retention factors for full annealed and stress relieving annealed steels in this test study and other publications available in the literature.Figure 18
Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with available research results.Figure 19
Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available research results.Those two scatter diagrams show a significant dispersion in the existing data on the retention factors of elastic modulus and yield strength, which can be mainly attributed to the measuring method, strain rate, heating rate, material type, and the criteria used to determine the parameters. Consequently, most of the provisioned equations based on past investigations are not suitable for predicting the degradation properties of cold-rolled thin-walled steels due to significant scatters existence.Despite the discrete of those scatters, there are still basic regulations to follow when scatters have been divided into two groups: full annealed and stress relieving annealed steels. As shown in Figure18, there is a consistent trend for retention factors of elastic modulus for both full annealed steels and stress relieving annealed steels. Therefore, the influence from different manufacturing process on elastic modulus of steels for CFS structures is less obvious. In the yield strength case contrarily, as Figure 19, red scatters and black scatters went to two different shapes obviously, though they agree well generally with the distribution of themselves. Under 300°C, the yield strength of full annealed steels reduces much faster than stress relieving annealed steels when temperatures rise. From 300°C to 600°C, the yield strength for stress relieving annealed steels drops drastically with temperatures elevating, although those for full annealed steels fall smoothly at this stage. After 600°C, the descending slope of stress relieving annealed steels becomes gentler than full annealed steels again. In this case, steels with different manufacturing process behave totally different for reduction rules on yield strength at elevated temperatures.In conclusion, it is meaningful to produce statistical conclusion and raise general equations for predicting the reduction of material properties on steels used for CFS structures at elevated temperatures.


## 4.1. Failure Mode

Figures8–10 present the failure modes of three grades of tested coupons. All specimens fractured within the gauge length scope expectedly, which means the stress-strain curves recorded from data acquisition system were real stress-strain relationships within the gauge length. Meanwhile, the carburization layer coated the specimen for all tested grades when temperature reached 500°C, illustrated by the dark surface of those coupons in Figures 8–10. This carburization coating was incompact and could be scratched using thin sheet metal. Specifically, steel plates presented a blue brittle phenomenon like normal steels around 300°C, evidenced by the dark blue colored oxidation film on the fracture section of specimens, shown in Figure 11 for the fracture details.Figure 8
Failure modes for S350 steels.Figure 9
Failure modes for S420 steels.Figure 10
Failure modes for G500 steels.Figure 11
Blue brittle phenomenon for steel plates.For two full annealed steels, visually noticeable elongation and necking of the coupons occurred from ambient and continued to higher temperatures. For G500 steels, significant elongation and necking could not be observed until temperature exceeds 500°C. Considering the distinction on heat treatment temperatures between full annealed and stress relieving annealed steels, the G500 steel is more brittle at ambient temperature since the cold work forming effect is not eliminated during annealing. However, when temperature went up to 600°C, which was higher than the critical temperatureAc1 for low carbon steel, it was possible that the steel was partially annealed in the oven and lost part of the hardening influence. Afterwards, significant change on the failure mode of G500 at 600°C could partially support this assumption and we still need more data investigation to explore the relationship between temperatures and material properties for various steels used in CFS structures.Some of the failed specimens appear to be distorted after 500°C. During the tests at temperatures above 500°C, the specimens were stretched at a much higher displacement rate after the extensometer range was exceeded. In this case, the fracture of these specimens seems to be abnormal. It should be pointed that both ends of the tested specimens have been clamped tightly in the slot of extension loading rods by inserting shims at two sides of the coupon to avoid eccentric load.


## 4.2. Ductility

In this part, percentage elongation after fracture [22], as shown in equation (1), calculated from original gauge length and final gauge length after fracture, is used to indicate the ductility of specimens. The final gauge length for fractured and cooled down specimens was measured by piecing the segments of specimens tightly at the fracture. Table 4 presents the average percentage elongation after fracture at different temperatures for specimens and its curves are shown in Figure 12.(1)AT=lu,t−l0l0×100.Table 4
Average percentage elongation after fracture (cooled down).
T (°C)Percentage elongation after fracture (%)S350S420G5002032.0229.992.7610022.7120.826.0620022.4023.923.9430040.2541.4112.0140043.1845.6710.3450049.0754.1710.6860063.8066.9768.3870064.0056.80Figure 12
Average percentage elongation after fracture at different temperatures.It is interesting to find that S350 and S420 steels, when the temperature increased from 20°C to 200°C, lose their ductility obviously. Some researchers [11, 12] noted a similar behavior for full annealed steels. This material behavior may be attributed to chemical transformations taking place in the steel base. After 300°C, since chemical reactions were taken over by temperature effects as the dominate factor, the ductility grows continually as expected. At the same time, S350 and S420 steels presented a very close trend on ductility development with temperature rising.Stress relieving annealed steels showed lower ductility than that of full annealed steels at ambient temperature due to the different heat treatments in manufacturing process as mentioned before. Under 200°C, the ductility of G500 steels maintained low values, even close to room temperature value. Then there was a higher platform of ductility in the range of 300°C∼500°C, though it was still lower than that of full annealed steel at the same temperatures. Up to 600°C, the effect of strain hardening and heat treatment has been eliminated, so that both full annealed and stress relieving annealed steels showed the same level of ductility. Since the flashover temperature of fire is over 600°C, the lack of ductility cannot be considered as a characteristic for stress relieving annealed steels at fire conditions.


## 4.3. Constitutive Relationship

Since the measurement range of the displacement grating is 12.5 mm, the stress-strain curves are given within the strain of 0.2, as shown in Figures13–15. All stress-strain curves of tested specimens (shown in Figure 3) are summarized together for S350, S420, and G500 steels, respectively. For each of the temperature conditions (marked in the same black circles), curves of repeated tests accord well with each other, indicating the stability of tested materials, test devices, and test operations.Figure 13
Stress-strain curves of S350 steels at different temperatures.Figure 14
Stress-strain curves of S420 steels at different temperatures.Figure 15
Stress-strain curves of G500 steels at different temperatures.As shown in Figures13 and 14, the stress-strain curves of S350 and S420 steels present a similar variation trend: (1) For temperatures below 200°C, an obvious yield plateau occurs when the load reaches the ultimate strength and disappears after temperatures beyond 200°C. (2) From 20∼300°C, the strain-hardening ranges at different temperatures pinch into a small zone, which illustrates that only yield strength experiences degradation at those temperature cases but ultimate strength dose not. (3) At temperatures beyond 200°C, the stress-strain curves were of the gradual yielding type, and both yield strength and ultimate strength deteriorate with temperature rising. The yield plateaus with multiple yield points are the result of interrupted motion of the Luders band along the specimen. The movement of dislocations near the band front becomes locked when temperature reaches 300°C, and thus yield plateaus disappeared over these temperatures [23].Unlike the full annealed steels, the G500 steel gave gradual yielding type stress-strain curves at both ambient and elevated temperatures, referring to Figure15. Then, it appears that the yield strengths do not decrease much up to 200°C. Furthermore, the stress-strain curves have a similar shape and ultimate deformation at temperatures from 300°C to 500°C. When temperature reaches 600°C, the ultimate strain increases significantly. Meanwhile, the load decreases very slowly after the ultimate strength at this condition, and the corresponding failure mode changes to ductile fracture with clear necking.


## 4.4. Retention Factors

Primarily, Table5 shows the tensile test results of all three steels at ambient temperature, which are fundamental parameters for calculating high-temperature material properties. Besides the apparent higher strength of G500 steels, the elastic modulus of this high strength steel is also higher than that of full annealed steels at room temperature.Table 5
Mechanical properties of cold-rolled thin-walled steels at ambient temperature.
Steel gradeE20 (GPa)Fy,20 (MPa)Fu,20 (MPa)S350 (1.0 mm)211.9411.3472.2S420 (1.0 mm)212.9434.6488.1G500 (1.2 mm)218.5686.8689.8Retention factors for the elastic modulus, yield strength, and ultimate strength were computed as the ratios of material properties at high temperatures to their values at ambient conditions, which is 20°C in this paper. The elastic modulus was calculated by fitting the initial portion of the stress-strain curves via using the least squares method, following ISO standard [22]. For the curves with smooth and long yield plateau, the yield strength was taken as the average value of stresses in the plateau. Then for the gradual yielding cases, the yield strength was determined by the 0.2% proof stress method, which uses the intersection point of the stress-strain curve and the proportional line offset by 0.2% strain. Results are shown in Table 6.Table 6
Retention factors for the elastic modulus, yield strength, and ultimate strength.
T (°C)S350,t = 0.96 mmS420,t = 0.96 mmG500,t = 1.16 mmET/E20Fy,T/Fy,20Fu,T/Fu,20ET/E20Fy,T/Fy,20Fu,T/Fu,20ET/E20Fy,T/Fy,20Fu,T/Fu,20201.0001.0001.0001.0001.0001.0001.0001.0001.0001000.9380.8700.9490.9410.9370.9661.0260.9590.9712000.9670.7871.0520.9670.6771.0040.9760.9771.0573001.0760.5931.0541.0560.5731.0410.9130.8360.9143500.9380.4880.8450.8210.5240.857———4000.8910.4670.6800.7850.4670.6890.6100.6650.7075000.6020.3210.3810.5780.3190.3840.4660.3570.3966000.2870.1760.1810.3140.1820.1920.2530.0650.0947000.1590.0700.0680.1670.0700.074———Figures16 and 17 provide the retention factors for full annealed and stress relieving annealed steels obtained through steady-state tests from this study and current steel structural fire design codes.Figure 16
Comparison of the retention factors of elastic modulus according to test results with the current design codes.Figure 17
Comparison of the retention factors of yield strength according to test results with the current design codes.By comparing tests data in this paper for cold-rolled thin-walled steels with current design codes, retention factors from existing steel design codes are generally unsafe, especially for yield strength prediction. As for elastic modulus, retentions factors predicted by Eurocode 3 [9] and AISC 360 [7] agree well with the present full annealed steels tests data before 500°C, but somewhat are unsafe beyond 500°C. These two curves are also suitable for G500 steels, although being a little conservative around 300°C and slightly unsafe beyond 400°C. In addition, the elastic modulus retention factors curve provided by AS 4100 [8] are unsafe beyond 400°C for both full annealed and stress relieving annealed steels. Yield strength retentions factors from hot-rolled steel experimental data provisioned by AISC and Eurocode 3 were the most unsafe, whereas AS 4100 and BS5950-8 [10] are less unsafe relatively. This confirms that, by directly using retention factors developed for hot-rolled steel to calculate yield strength, they are not suitable for cold-rolled thin-walled steels.Therefore, the provisioned curves in current codes cannot be used to calculate the retention factors for cold-rolled thin-walled steels considered in this study.In order to investigate the relationship on high-temperature material properties between the steels for CFS structures with different manufacturing process, this paper collected the existing test data of cold-rolled thin-walled steels at elevated temperatures in the recent 20 years, as presented in Table7. Specifically, based on previous discussion, S420 steel shares a very similar trend on failure mode, ductility, constitutive relationship, and retention factors with S350 steel (typical full annealed steels), even though its nominal yield strength is close to G450 steel (stress relieving annealed steels). Thus, in Table 7, the level of ductility (elongation) is the reliable and significant classification standard for commonly used steels for CFS structures, which is mainly due to the different annealing process during manufacturing.Table 7
Compilations of basic information for current test data.
YearResearchersGradeThickness (mm)Elongation∗ (%)Full annealed steels1999Qutinen [11]S3502.00>202003Lee et al. [12]G3000.40No information0.60No information1.00No information2009Ranawaka and Mahendran [14]G2500.60>300.80>300.95>302011Kankanamge and Mahendran [15]G2501.55>301.95>302013Ye and Chen [17]Q3451.50>302015Batista Abreu [18]S2301.44>20S3451.15>201.55>202.58>202016Craveiro et al. [19]S2802.50>20This researchS3501.0032.02S4201.0029.99Stress relieving annealed steels2003Lee et al. [12]G5001.20No informationG5500.42No information0.60No information0.95No information2007Chen and Young [13]G4501.9011.3G5501.009.82009Ranawaka and Mahendran [14]G5500.60<30.80<30.95<32011Kankanamge and Mahendran [15]G4501.50<101.90<102012Chen and Ye [16]G5501.00<10This researchG5001.202.76∗The elongation here represents the percentage elongation after fracture of specimens at ambient temperatures. However, most researches have not given the elongation data directly; stress-strain curves are major clues to estimate the ductility of steels.Figures18 and 19 illustrate the retention factors for full annealed and stress relieving annealed steels in this test study and other publications available in the literature.Figure 18
Comparison of the retention factors of elastic modulus for cold-rolled thin-walled steels according to test results with available research results.Figure 19
Comparison of the retention factors of yield strength for cold-rolled thin-walled steels according to test results with available research results.Those two scatter diagrams show a significant dispersion in the existing data on the retention factors of elastic modulus and yield strength, which can be mainly attributed to the measuring method, strain rate, heating rate, material type, and the criteria used to determine the parameters. Consequently, most of the provisioned equations based on past investigations are not suitable for predicting the degradation properties of cold-rolled thin-walled steels due to significant scatters existence.Despite the discrete of those scatters, there are still basic regulations to follow when scatters have been divided into two groups: full annealed and stress relieving annealed steels. As shown in Figure18, there is a consistent trend for retention factors of elastic modulus for both full annealed steels and stress relieving annealed steels. Therefore, the influence from different manufacturing process on elastic modulus of steels for CFS structures is less obvious. In the yield strength case contrarily, as Figure 19, red scatters and black scatters went to two different shapes obviously, though they agree well generally with the distribution of themselves. Under 300°C, the yield strength of full annealed steels reduces much faster than stress relieving annealed steels when temperatures rise. From 300°C to 600°C, the yield strength for stress relieving annealed steels drops drastically with temperatures elevating, although those for full annealed steels fall smoothly at this stage. After 600°C, the descending slope of stress relieving annealed steels becomes gentler than full annealed steels again. In this case, steels with different manufacturing process behave totally different for reduction rules on yield strength at elevated temperatures.In conclusion, it is meaningful to produce statistical conclusion and raise general equations for predicting the reduction of material properties on steels used for CFS structures at elevated temperatures.


## 5. Prediction Equations

### 5.1. Retention Factors Prediction for Elastic Modulus

Due to the weak dependence of manufacturing procedure of steels for CFS structures on the elastic modulus reduction development, a single equation is provided here for calculating retention factors of elastic modulus by fitting the scatters (polynomial regression) in the entire database (compiled in Table6).(2)ETE20=4.826E−16T5+1.224E−12T4−5.808E−10T3−1.742E−06T2−2.070E−04T+1.004,20°C≤T≤800°C.Figure20 shows the fitting curve of the retention factors for elastic modulus with original scatters, and Figure 21 gives the comparison of the proposed equation curves with code curves for predicting elastic modulus. Recommended retention factors for the elastic modulus extracted from fitting equation at temperatures of hundreds are provided in Table 8.Figure 20
Fitting curve of the retention factors for elastic modulus.Figure 21
Comparison of the proposed equation curves with code curves for predicting elastic modulus.Table 8
Recommendation retention factors for the elastic modulus.
T (°C)20100200300400500600700800ET/E201.0000.9660.8910.7810.6420.4840.3240.1820.086


### 5.2. Retention Factors Prediction for Yield Strength

Considering the separation of full annealed and stress relieving annealed steels on retention factors for yield strength, two sets of equations were promoted here through polynomial and exponential regressions for predicting retention factors of yield strength correspondingly, as equation (3) for full annealed steels and equation (4) for stress relieving annealed steels. Figures 22 and 23 show the fitting curves of the retention factors for yield strength of full annealed steels and stress relieving annealed steels separately. Meanwhile, Figure 24 gives the comparison of the proposed equation curves with code curves for predicting yield strength. Recommended retention factors for the yield strength extracted from fitting equation at temperatures of hundreds are provided in Table 9. In general, as revealed by Figures 21 and 24, equations provided by current standards [1–6] are unsafe for predicting elastic modulus and yield strength.(3)Fy,TFY,20=−2.272E−14T5+4.931E−11T4−3.418E−08T3+7.512E−06T2−1.230E−03T+1.023,20°C≤T≤800°C,(4)Fy,TFy,20=2.855E−14T5−9.820E−12T4−1.991E−08T3+8.483E−06T2−1.030E−03T−1.018,20°C≤T≤600°C,Fy,TFy,20=9.467E+07T−3.222,600°C≤T≤800°C.Figure 22
Fitting curve of the retention factors for yield strength of full annealed steels.Figure 23
Fitting curve of the retention factors for yield strength of stress relieving annealed steels.Figure 24
Comparison of the proposed equation curves with code curves for predicting yield strength.Table 9
Recommendation retention factors for the yield strength.
T (°C)20100200300400500600700800Full annealed steelsFy,T/Fy,201.0000.9460.8760.7510.5750.3850.2290.1380.095Stress relieving annealed steelsFy,T/Fy,201.0000.980.9860.9250.7310.4150.1040.0650.042


### 5.3. Constitutive Relationship Models

In order to carry out advanced FEA simulation and fire safety design, complete constitutive models are required. Generally, temperature-dependent constitutive relationship models are based on the Ramberg–Osgood three-parameter (elastic modulus, yield strength, and temperature) gradual yielding model [24]. As for equation (5), εT, σT, ET and Fy,T are the strain, stress, elastic modulus, and yield strength at T (°C), respectively; and KT and ηT are parameters obtained from regression analysis.In Ramberg–Osgood model,KT is strength coefficient and ηT is hardening parameter. In past researches, some researchers [13–15] use temperature-dependent KT and ηT simultaneously, some researchers [12] use fixed ηT and the rest of researchers [16–18] use constant KT. Considering that the yield strength was obtained through the 0.2% offset method, stress-strain data was fitted to equation (5) (exponential regression) with the Ramberg–Osgood strength parameter KT set to 0.002. Therefore, the strain computed at the 0.2% offset stress corresponds with the yield strain. Furthermore, the temperature-dependent Ramberg–Osgood hardening parameters ηT were fitted to equation (6) (polynomial regression) for the entire temperature range.(5)εT=σTET+σTFy,TηT,(6)ηT=aT2+bT+c.For S350 and S420 steels, since there is an obvious yield plateau for stress-strain curves up to 200°C, it was reasonable to apply elastic-perfectly plastic model under 200°C. Meanwhile, due to the lacking of strengthening stage for G500 steel up to 100°C, elastic-perfectly plastic model was adopted also for G500 steel under 100°C. Consequently, Ramberg–Osgood model regression fitting started from 300°C for S350 and S420 steels, and from 200°C for G500 steel. The resulting Ramberg–Osgood hardening parameters are shown in Table10, constants for Ramberg–Osgood hardening parameters are shown in Table 11, and stress-strain fitting curves are compared with test results in Figure 25. Based on Figure 25, there is a very good agreement between the predicted stress-strain curves from equations (5) and (6) and test results. Therefore, these equations are recommended for the determination of the stress-strain curves of S350 (1.0 mm), S420 (1.0 mm), and G500 (1.2 mm) steels at elevated temperatures.Table 10
Ramberg–Osgood hardening parameters from regression fitting, withKT = 0.002.
T (°C)ηT for S350 steelsηT for S420 steelsηT for G500 steels200——0.9803000.9460.9800.9864000.8760.9860.9255000.7510.9250.7316000.5750.7310.0427000.0950.042—Table 11
Constants for Ramberg–Osgood hardening parameters.
Steel gradesT (°C)a (×10−4) (1/°C2)b (×10−1) (1/°C)cS350[300, 500]2.646−1.69633.231(500, 700]4.577−3.61680.909S420[300, 500]2.111−1.28725.946(500, 700]−6.3608.264−239.832G500[200, 400]10.400−5.779110.897(400, 600]6.639−8.364274.440Figure 25
Stress-strain test curves (solid lines) and fitting curves (dashed lines). (a) S350 steels. (b) S420 steels. (c) G500 steels.
(a)(b)(c)


## 5.1. Retention Factors Prediction for Elastic Modulus

Due to the weak dependence of manufacturing procedure of steels for CFS structures on the elastic modulus reduction development, a single equation is provided here for calculating retention factors of elastic modulus by fitting the scatters (polynomial regression) in the entire database (compiled in Table6).(2)ETE20=4.826E−16T5+1.224E−12T4−5.808E−10T3−1.742E−06T2−2.070E−04T+1.004,20°C≤T≤800°C.Figure20 shows the fitting curve of the retention factors for elastic modulus with original scatters, and Figure 21 gives the comparison of the proposed equation curves with code curves for predicting elastic modulus. Recommended retention factors for the elastic modulus extracted from fitting equation at temperatures of hundreds are provided in Table 8.Figure 20
Fitting curve of the retention factors for elastic modulus.Figure 21
Comparison of the proposed equation curves with code curves for predicting elastic modulus.Table 8
Recommendation retention factors for the elastic modulus.
T (°C)20100200300400500600700800ET/E201.0000.9660.8910.7810.6420.4840.3240.1820.086


## 5.2. Retention Factors Prediction for Yield Strength

Considering the separation of full annealed and stress relieving annealed steels on retention factors for yield strength, two sets of equations were promoted here through polynomial and exponential regressions for predicting retention factors of yield strength correspondingly, as equation (3) for full annealed steels and equation (4) for stress relieving annealed steels. Figures 22 and 23 show the fitting curves of the retention factors for yield strength of full annealed steels and stress relieving annealed steels separately. Meanwhile, Figure 24 gives the comparison of the proposed equation curves with code curves for predicting yield strength. Recommended retention factors for the yield strength extracted from fitting equation at temperatures of hundreds are provided in Table 9. In general, as revealed by Figures 21 and 24, equations provided by current standards [1–6] are unsafe for predicting elastic modulus and yield strength.(3)Fy,TFY,20=−2.272E−14T5+4.931E−11T4−3.418E−08T3+7.512E−06T2−1.230E−03T+1.023,20°C≤T≤800°C,(4)Fy,TFy,20=2.855E−14T5−9.820E−12T4−1.991E−08T3+8.483E−06T2−1.030E−03T−1.018,20°C≤T≤600°C,Fy,TFy,20=9.467E+07T−3.222,600°C≤T≤800°C.Figure 22
Fitting curve of the retention factors for yield strength of full annealed steels.Figure 23
Fitting curve of the retention factors for yield strength of stress relieving annealed steels.Figure 24
Comparison of the proposed equation curves with code curves for predicting yield strength.Table 9
Recommendation retention factors for the yield strength.
T (°C)20100200300400500600700800Full annealed steelsFy,T/Fy,201.0000.9460.8760.7510.5750.3850.2290.1380.095Stress relieving annealed steelsFy,T/Fy,201.0000.980.9860.9250.7310.4150.1040.0650.042


## 5.3. Constitutive Relationship Models

In order to carry out advanced FEA simulation and fire safety design, complete constitutive models are required. Generally, temperature-dependent constitutive relationship models are based on the Ramberg–Osgood three-parameter (elastic modulus, yield strength, and temperature) gradual yielding model [24]. As for equation (5), εT, σT, ET and Fy,T are the strain, stress, elastic modulus, and yield strength at T (°C), respectively; and KT and ηT are parameters obtained from regression analysis.In Ramberg–Osgood model,KT is strength coefficient and ηT is hardening parameter. In past researches, some researchers [13–15] use temperature-dependent KT and ηT simultaneously, some researchers [12] use fixed ηT and the rest of researchers [16–18] use constant KT. Considering that the yield strength was obtained through the 0.2% offset method, stress-strain data was fitted to equation (5) (exponential regression) with the Ramberg–Osgood strength parameter KT set to 0.002. Therefore, the strain computed at the 0.2% offset stress corresponds with the yield strain. Furthermore, the temperature-dependent Ramberg–Osgood hardening parameters ηT were fitted to equation (6) (polynomial regression) for the entire temperature range.(5)εT=σTET+σTFy,TηT,(6)ηT=aT2+bT+c.For S350 and S420 steels, since there is an obvious yield plateau for stress-strain curves up to 200°C, it was reasonable to apply elastic-perfectly plastic model under 200°C. Meanwhile, due to the lacking of strengthening stage for G500 steel up to 100°C, elastic-perfectly plastic model was adopted also for G500 steel under 100°C. Consequently, Ramberg–Osgood model regression fitting started from 300°C for S350 and S420 steels, and from 200°C for G500 steel. The resulting Ramberg–Osgood hardening parameters are shown in Table10, constants for Ramberg–Osgood hardening parameters are shown in Table 11, and stress-strain fitting curves are compared with test results in Figure 25. Based on Figure 25, there is a very good agreement between the predicted stress-strain curves from equations (5) and (6) and test results. Therefore, these equations are recommended for the determination of the stress-strain curves of S350 (1.0 mm), S420 (1.0 mm), and G500 (1.2 mm) steels at elevated temperatures.Table 10
Ramberg–Osgood hardening parameters from regression fitting, withKT = 0.002.
T (°C)ηT for S350 steelsηT for S420 steelsηT for G500 steels200——0.9803000.9460.9800.9864000.8760.9860.9255000.7510.9250.7316000.5750.7310.0427000.0950.042—Table 11
Constants for Ramberg–Osgood hardening parameters.
Steel gradesT (°C)a (×10−4) (1/°C2)b (×10−1) (1/°C)cS350[300, 500]2.646−1.69633.231(500, 700]4.577−3.61680.909S420[300, 500]2.111−1.28725.946(500, 700]−6.3608.264−239.832G500[200, 400]10.400−5.779110.897(400, 600]6.639−8.364274.440Figure 25
Stress-strain test curves (solid lines) and fitting curves (dashed lines). (a) S350 steels. (b) S420 steels. (c) G500 steels.
(a)(b)(c)


## 6. Conclusions

This paper has reported a detailed experimental study of the mechanical properties of steels for CFS structures at elevated temperatures. Different manufacturing processes and their influence on the properties of steels for CFS structures were discussed. The experimental study included tensile coupon tests conducted on S350, S420, and G500 steels via steady-state test methods, and a careful discussion of the test results was provided. The failure mode, ductility, stress-strain relationship, and material reductions were elaborated in a comparison way. Then based on the testing and literature data, retention factors for elastic modulus and yield strength were established for the two types of steels used in CFS structures as functions of temperature. At last, constitutive relationship models were proposed based on tests data for S350, S420, and G500 steels separately.



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