Structural performance of cold-formed lean duplex stainless steel beams at elevated temperatures

TL;DR: In this paper, the structural performance of cold-formed lean duplex stainless steel beams at elevated temperatures ranging from 24 to 900°C was investigated using a finite element model, and the numerical results were compared with the design values calculated by the existing design rules, including the American specification, Australian/New Zealand Standard, European Code, direct strength method and continuous strength method.

Abstract: The structural performance of cold-formed lean duplex stainless steel beams at elevated temperatures ranging from 24 to 900 °C was investigated in this study. A finite element model was developed. The numerical analysis covered the specimens of square and rectangular hollow sections. The material properties obtained from tensile coupon tests on lean duplex stainless steel at elevated temperatures were used in the finite element model. A total of 125 numerical flexural strengths were obtained from the finite element analysis. The numerical results were compared with the design values calculated by the existing design rules, including the American Specification, Australian/New Zealand Standard, European Code, direct strength method and continuous strength method. The suitability of these design rules for lean duplex stainless steel beams at elevated temperatures was assessed using reliability analysis. It was shown that the existing design rules are generally quite conservative in predicting the flexural strengths at elevated temperatures, except that the modified direct strength method provides accurate and reliable predictions. Therefore, it is recommended that the modified direct strength method be used for cold-formed lean duplex stainless steel beams at elevated temperatures.

Summary

1. Introduction

• Lean duplex stainless steel is characterized by a low nickel content of around 1.5%.
• The previous research on lean duplex stainless steel focused mainly on the material properties and design of structural members at room temperature.
• Some research has also been conducted for cold-formed lean duplex stainless steel beams [7, 8, 9, 10].
• The reduced mechanical properties at elevated temperatures were used in the FEM.
• A total number of 125 numerical flexural strengths were compared with the design values calculated from the existing design rules.

2. Finite Element Model

• The finite element model (FEM) for cold-formed lean duplex stainless steel flexural members was developed by Huang and Young [7] using the program ABAQUS version 6.11 [16].
• The FEM has been verified with the test results of four-point bending tests at room temperature.
• Similar to the FEM for beams at room temperature, the local imperfection of t/10 was incorporated into the FEM, where t is the thickness of the sections.
• The residual stresses in the sections were not included.

3. Parametric Study

• A total of 125 cold-formed lean duplex stainless steel flexural members at elevated temperatures, ranging from 24 – 900 ºC, were investigated in the parametric study.
• The finite element model (FEM) in the parametric study was identical to the FEM developed by Huang and Young [7], except that the mechanical properties obtained from the tensile coupon tests at elevated temperatures were used.
• Five different thicknesses were designed for each section, in order to cover a wide range of slenderness ratios, from stocky to slender sections.
• The numbers before the letter “L” defined the crosssectional dimensions (D×B×t), the number between the letter “L” and letter “T” was the specimen length in millimeters, and the number after the letter “T” was the specimen temperature in degrees Celsius.
• The dimension of the overall web depth (D) was larger than the overall flange width (B), thus the beam was subjected to major axis bending.

4. Design Rules & Comparison with Beam Strengths

• The existing and modified design rules for cold-formed lean duplex stainless steel flexural members at elevated temperatures were assessed by comparing the design values with the 125 FEA flexural strengths (MFEA,T), as summarized in Table 3.
• A target reliability index (0) of 2.5 for stainless steel structural members was used as the lower limit.
• For the purpose of direct comparison, a constant resistant factor (1) of 0.90 and a load combination of 1.2DL+1.6LL were used to calculate the reliability index (1) for the design rules; the values of the reliability index are also shown in Table 3.

4.2 American Specification and Australian/New Zealand Standard

• The design rules for calculating the moment capacity for flexural members in the ASCE [17] and AS/NZS [18] are same.
• Therefore, both approaches were assessed in this study.
• The design rules based on the inelastic reserve capacity were modified to provide more accurate and reliable predictions for the lean duplex stainless steel flexural members at room temperature by Huang and Young [7].
• The moment capacities (M#inelastic,T) calculated by the modified design rule were compared with the numerical moment capacities (MFEA,T) at elevated temperatures, as shown in Table 3 and Figure 6.

4.3 European Code

• The moment capacity (MEC3,T) at elevated temperatures was calculated by European Code Part 1.4 [20].
• Classification for the sections and calculation of effective widths are required in EC3.
• The comparison of the numerical moment capacity (MFEA,T) with the design values (MEC3,T) at elevated temperatures are shown in Table 3 and Figure 7.
• It is found that the design rules provided less conservative and less scattered predictions for the lean duplex stainless steel flexural members at elevated temperatures compared with those at room temperature [7].
• The classification limits and the effective width calculation in the European Code [19] were examined further in Huang and Young [7] using a large data pool of 180 lean duplex stainless steel flexural strengths at room temperature.

4.4 Direct Strength Method

• Flexural strength for local buckling (Mnl) is calculated by Eqs F3.2.1-1 and 3.2.1-2 in AISI [21] when the inelastic bending reserve is not considered.
• The nominal flexural strengths, calculated by the AISI [21] with and without considering the inelastic bending reserve, were represented by MDSM and M^DSM, respectively.
• The direct strength method (DSM) in AISI [21] was shown to provide conservative predictions for lean duplex stainless steel flexural members at room temperature and elevated temperatures, as shown in Huang and Young [7] and Table 3.

4.5 Continuous Strength Method

• The continuous strength method (CSM) proposed by Saliba and Gardner [9] was assessed for flexural members at elevated temperatures.
• The calculation procedure of CSM was the same as those described in Huang and Young [7].
• Therefore, the flexural strengths of 98 specimens that meet the requirement of the CSM are compared with the design values (MCSM,T) calculated by the continuous strength method, as shown in Table 3.
• The reliability index (0) was 2.35, which was considered not reliable at its current resistance factor (0) of 0.91 and the load combination.

5. Conclusions

• The study reported here investigated the structural performance of lean duplex stainless steel flexural members at elevated temperatures.
• The design rules in ASCE [17] and AS/NZS [18] were found to provide quite conservative predictions for the cold-formed lean duplex stainless steel flexural members at elevated temperatures.
• Huang and Young [7] found that the modified design rules provide more accurate and less scattered predictions for the moment capacities at elevated temperatures.
• The EC3 [19] and the EC3 suggested by Gardner and Theofanous [20] provide less conservative predictions for the flexural members at elevated temperatures than the predictions for members at room temperature.
• The direct strength method in the AISI [21] provides quite conservative predictions for flexural members at elevated temperatures.

Figures

Table 2: Parametric study results at elevated temperatures

Table 3: Comparison of numerical results with design moment capacities at elevated temperatures

Figure 6: Comparison of numerical results with design strengths by ASCE and AS/NZS at elevated temperatures

Figure 7: Comparison of numerical results with design strengths by EC3 at elevated temperatures

Table 1: Material properties of the specimens at high temperatures [12]

Figure 8: Comparison of numerical results with design strengths by DSM at elevated temperatures

Figure 1: Finite element model of specimen 50×100×2L900T700 in parametric study

Figure 3: Moment-curvature curves obtained from FEA for specimen 300×100×7L2100 at elevated temperatures

Figure 2: Moment-curvature curves obtained from FEA for specimen 300×100×10L2100 at elevated temperatures

Figure 4: Moment-curvature curves obtained from FEA for specimen 100×300×15L1500 at elevated temperatures

Figure 5: Moment-curvature curves obtained from FEA for specimen 100×300×4L1500 at elevated temperatures

Full text

Edinburgh Research Explorer
Structural Performance of Cold-formed Lean Duplex Stainless
Steel Beams at Elevated Temperatures
Citation for published version:
Huang, Y & Young, B 2018, 'Structural Performance of Cold-formed Lean Duplex Stainless Steel Beams at
Elevated Temperatures', Thin-Walled Structures, vol. 129, pp. 20-27.
https://doi.org/10.1016/j.tws.2018.03.031
Digital Object Identifier (DOI):
10.1016/j.tws.2018.03.031
Link:
Link to publication record in Edinburgh Research Explorer
Document Version:
Peer reviewed version
Published In:
Thin-Walled Structures
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Download date: 10. Aug. 2022

1
Structural Performance of Cold-formed Lean Duplex Stainless
Steel Beams at Elevated Temperatures
Yuner Huang
1
* and Ben Young
2
1
Institute for Infrastructure and Environment, School of Engineering, University of Edinburgh, UK
2
Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China
ABSTRACT: The structural performance of cold-formed lean duplex stainless steel beams at
elevated temperatures ranging from 24  900 ºC was investigated in this study. A finite element
model was developed. The numerical analysis covered the specimens of square and rectangular
hollow sections. The material properties obtained from tensile coupon tests on lean duplex
stainless steel at elevated temperatures were used in the finite element model. A total of 125
numerical flexural strengths were obtained from the finite element analysis. The numerical
results were compared with the design values calculated by the existing design rules, including
the American Specification, Australian/New Zealand Standard, European Code, direct strength
method and continuous strength method. The suitability of these design rules for lean duplex
stainless steel beams at elevated temperatures was assessed using reliability analysis. It was
shown that the existing design rules are generally quite conservative in predicting the flexural
strengths at elevated temperatures, except that the modified direct strength method provides
accurate and reliable predictions. Therefore, it is recommended that the modified direct
strength method be used for cold-formed lean duplex stainless steel beams at elevated
temperatures.
Keywords: Beam; cold-formed; elevated temperatures; lean duplex; stainless steel; structural
design.
Corresponding author. Tel.: +44 (0) 131 650 5736; Fax: +44 (0) 131 650 6554.
E-mail address: Yuner.Huang@ed.ac.uk

2
1. Introduction
A relatively new type of cold-formed lean duplex stainless steel is becoming an attractive
choice as a construction material. Lean duplex stainless steel is characterized by a low nickel
content of around 1.5%. Thus, lean duplex stainless steel has economic advantages over the
other types of stainless steel. In addition, it is regarded as a high strength material with the
nominal yield strength (0.2% proof stress) of 450 MPa [1]. However, there has been limited
research on the structural performance and design of lean duplex stainless steel members,
especially at elevated temperatures. Therefore, research on the lean duplex stainless steel
material and structural members is required.
Lean duplex stainless steel is a relative new construction material. The previous research on
lean duplex stainless steel focused mainly on the material properties and design of structural
members at room temperature. Huang and Young [2], as well as Theofanous and Gardner [3],
conducted tensile coupon tests and stub column tests to investigate the mechanical and section
properties of cold-formed lean duplex stainless steel rectangular and square hollow sections.
Experimental and numerical investigations were carried out on cold-formed lean duplex
stainless steel columns [3, 4, 5, 6], and the test and numerical data were compared with the
predicted column strengths calculated by the existing design rules. It was shown that the
existing design rules, including design rules in the European Code, explicit approach in the
Australian/New Zealand Standard and the direct strength method, are quite conservative for
the lean duplex stainless steel. The implicit approach for column design in the American
Specification and Australian/New Zealand Standard provides accurate predictions, but the
iterative calculation procedure is tedious. Therefore, modified design rules have been proposed
for better prediction of lean duplex stainless steel structural strengths. Some research has also
been conducted for cold-formed lean duplex stainless steel beams [7, 8, 9, 10]. This research
indicated that the existing European Code and direct strength method are quite conservative
for lean duplex stainless steel flexural members, while the continuous strength method provides
a better prediction. The European Code and direct strength method were found to be suitable
for the shear design of lean duplex stainless steel rectangular hollow beams. The existing design
rules in the European Code and the Australian/New Zealand Standard are generally quite
conservative for lean duplex stainless steel beam-column members [11, 12]. The mechanical
properties of cold-formed lean duplex stainless steel at elevated temperatures have been

3
investigated in previous research [13, 14]. Huang and Young [13] conducted tensile coupon
tests on lean duplex stainless steel in both steady and transient states. The existing design rules
for predicting the reduced material properties at elevated temperatures were assessed for lean
duplex stainless steel. A modified design rule was proposed for lean duplex stainless steel
material properties at elevated temperatures. Gardner et al. [14] summarized the results of tests
on material properties of various stainless steel alloys at elevated temperatures, including the
lean duplex stainless steel material reported by Outokumpu [15]. Reduction factors of strength
and stiffness for lean duplex stainless steel were proposed according to the available data.
A search of the literature revealed a lack of research on cold-formed lean duplex stainless steel
beams at elevated temperatures. Therefore, the objective of this study was to investigate the
structural performance of cold-formed lean duplex stainless steel beams at elevated
temperatures, ranging from 24  900 ºC, using finite element analysis. The reduced mechanical
properties at elevated temperatures were used in the FEM. A total number of 125 numerical
flexural strengths were compared with the design values calculated from the existing design
rules. The applicability of the existing design rules for the lean duplex stainless steel beams
was assessed using reliability analysis. According to the comparison, recommendations for
designing cold-formed lean duplex stainless steel flexural members at elevated temperatures are
proposed based on this study.
2. Finite Element Model
The finite element model (FEM) for cold-formed lean duplex stainless steel flexural members
was developed by Huang and Young [7] using the program ABAQUS version 6.11 [16]. The
FEM has been verified with the test results of four-point bending tests at room temperature.
The moment-curvature curves and the failure modes predicted by the FEM have been found to
agree well with the test results. In this study, the FEM developed by Huang and Young [7] was
used for the finite element analysis of flexural members at elevated temperatures, except that
the materials properties at room temperature were replaced by the reduced material properties
obtained from tensile coupon tests at elevated temperatures [13]. The mechanical properties of
section 50×50×1.5 obtained from the tensile coupon tests at 24 ºC, 300 ºC, 500 ºC, 700 ºC and
900 ºC using the steady-state test method were used in the FEM. ABAQUS allows for a multi-
linear stress-strain curve to be used. Similar to the Huang and Young FEM [7], the first part of

4
the curve represents the elastic part up to the proportional limit stress with the measured
 ratio taken as 0.3. In the plastic analysis, the static stress-strain
curve obtained from tensile coupon tests was converted to true stress and logarithmic true
plastic strain curve, as described by Huang and Young [7]. The material properties adopted in
the FEM, including the modulus of elasticity, yield strength, and ultimate strength at high
temperatures ranging from 24  900 C, are summarized in Table 1. Similar to the FEM for
beams at room temperature, the local imperfection of t/10 was incorporated into the FEM,
where t is the thickness of the sections. The residual stresses in the sections were not included.
3. Parametric Study
A total of 125 cold-formed lean duplex stainless steel flexural members at elevated
temperatures, ranging from 24  900 ºC, were investigated in the parametric study. The finite
element model (FEM) in the parametric study was identical to the FEM developed by Huang
and Young [7], except that the mechanical properties obtained from the tensile coupon tests at
elevated temperatures were used. The parametric study included square hollow sections (SHS)
and rectangular hollow sections (RHS), which had one SHS of 300×300 (overall depth ×
overall width) as well as four RHS of 100×50, 50×100, 300×100 and 100×300. Five different
thicknesses were designed for each section, in order to cover a wide range of slenderness ratios,
from stocky to slender sections. The length of moment span between the two loading points
was equal to the length of shear spans between the loading points to the supports for the flexural
members. The lengths were designed carefully so that the section flexural capacity could be
reached without shear failure. The specimens with the same cross-sectional dimensions and
specimen lengths were investigated under five different temperatures in the finite element
analysis, including 24 ºC, 300 ºC, 500 ºC, 700 ºC and 900 ºC. The RHS specimens were
subjected to both major and minor axes bending. The specimens in the parametric study were
labelled such that the cross-section dimension, specimen length and the specimen temperature
could be identifid the cross-
sectional dimensions (D×B×t          was the
specimen length in millimeters        was the specimen
temperature in degrees Celsius. For example, the label 100×50×5L900T300 defined the
flexural member with cross-section (D×B×t) of 100×50×5 in millimeters, and the specimen
length of 900 mm as well as the specimen temperature of 300 ºC. The dimension of the overall

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Structural performance of cold-formed lean duplex stainless steel beams at elevated temperatures" ?

The structural performance of cold-formed lean duplex stainless steel beams at elevated temperatures ranging from 24 – 900 oC was investigated in this study. It was shown that the existing design rules are generally quite conservative in predicting the flexural strengths at elevated temperatures, except that the modified direct strength method provides accurate and reliable predictions. 

Q2. What is the reliability index of the design rules?

In calculating the reliability index, Eq. K2.1.1-4 in the North American cold-formed steel Specification AISI S100 [21] was used to calculate the correction factor, in order to account for the influence of the number of data. 

Q3. What is the recommended resistance factor for a member with stiffened compression flanges?

The resistance factors (0) of 0.90 for members with stiffened compression flanges subjected to bending is recommended by ASCE [17], AS/NZS [18], and AISI Standard [21] for the direct strength method (DSM), while the resistance factors of 0.91 are used by the EC3 [19] and modified EC3 by Gardner and Theofanous [20] as well as the continuous strength method (CSM) [9]. 

Q4. What is the length of moment span between the two loading points?

The length of moment span between the two loading points was equal to the length of shear spans between the loading points to the supports for the flexural members. 

Q5. What is the flexural strength for local buckling?

when the inelastic reserve local buckling strength is considered, Eq. F3.2.3-1 in AISI [21] is used for sections with first yield in compression. 

Q6. What are the design rules for lean duplex stainless steel rectangular hollow beams?

The European Code and direct strength method were found to be suitable for the shear design of lean duplex stainless steel rectangular hollow beams. 

Q7. What are the nominal flexural strengths of lean duplex stainless steel?

In this study, the nominal flexural strengths, calculated by the AISI [21] with and without considering the inelastic bending reserve, were represented by MDSM and M^DSM, respectively. 

Q8. What temperature was used to determine the cross-sectional dimensions of the specimen?

The specimens with the same cross-sectional dimensions and specimen lengths were investigated under five different temperatures in the finite element analysis, including 24 ºC, 300 ºC, 500 ºC, 700 ºC and 900 ºC.