Cold-formed high strength steel SHS and RHS beams at elevated temperatures
Introduction
High strength steel (HSS) hollow sections are being increasingly applied in structural applications owing to their superior strength-to-weight ratios, which result in material savings and easier handling in construction. With the advances in steel production technologies, HSS hollow sections that had nominal yield strength of 1300 MPa are available in the market [1,2]. In recent years, extensive research work, both experimentally and numerically, has been conducted to study the behaviour of HSS hollow section structural members subjected to various loading conditions at ambient temperature [[3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]]. On the other hand, steel structures may expose to fire hazards, during which the capacities of the members would reduce significantly at elevated temperatures. The behaviour of HSS materials (defined in this paper as those with nominal yield strengths no less than 690 MPa) at elevated temperatures have attracted much research attention after the September 11 attacks [[20], [21], [22], [23], [24], [25]]. However, the investigations on HSS hollow section structural members at elevated temperatures are rather limited.
Chen and Young [26] studied the behaviour of HSS fabricated box section (also I-section) stub and slender columns at elevated temperatures up to 900 °C using finite element (FE) analyses. The investigated HSS sections had nominal yield strength of 690 MPa. The obtained elevated temperature column strengths were compared with nominal resistances as per the ANSI/AISC 360 [27], EN 1993-1-2 [28] and AS 4100 [29] provisions for members in compression by substituting the elevated temperature material properties. Direct strength method (DSM) was also used by Chen and Young [26] to assess the HSS hollow section column strengths at elevated temperatures. In general, it was concluded by Chen and Young [26] that the ANSI/AISC 360 [27], EN 1993-1-2 [28] and DSM conservatively predicted the HSS column strengths at elevated temperatures, while the AS 4100 [29] predictions were generally unconservative for the HSS box section slender columns at elevated temperatures. More recently, a numerical study on flexural behaviour of HSS square and rectangular hollow section (SHS and RHS) columns at elevated temperatures was performed by Winful et al. [30]; the studied HSS SHS/RHS had two steel grades: S690QL and S700MC. The columns were isothermally simulated by incorporating measured stress-strain curves up to 800 °C. It was found that the EN 1993-1-2 [28] generally predicted the buckling resistances of the S700MC columns safely, while a lower buckling curve may be needed for S690QL compression members at elevated temperatures [30]. To date, the structural responses of cold-formed HSS SHS/RHS beams at elevated temperatures remain unexplored, which is the focus of this paper.
In this study, stress-strain relationships for cold-formed HSS at elevated temperatures are proposed. The proposed stress-strain relationships were verified with the measured material stress-strain curves that previously reported by the authors in Ref. [25]. A numerical investigation was performed to study the behaviour of cold-formed HSS SHS/RHS in-plane beams at elevated temperatures up to 1000 °C by incorporating the proposed stress-strain relationships. A FE model was built and verified with the available test results of cold-formed HSS SHS/RHS beams [9,31]; upon verification, a total of 252 numerical simulations were performed. The numerical results were applied to appraise the suitability of existing cross-section slenderness limits to the cold-formed HSS SHS/RHS at elevated temperatures. The applicability of flexural design provisions in the EN 1993-1-2 [28], ANSI/AISC 360 [32] and AISI S100 [33] specifications to the investigated HSS tubular beams at elevated temperatures was also assessed. A modified design rule is proposed based upon the AISI S100 [33] DSM. Furthermore, reliability analyses were carried out to assess the reliability levels of the codified and modified design rules.
Section snippets
Cold-formed high strength steel stress-strain relationships at various temperatures
Accurate representations of elevated temperature stress-strain relationships are essential for the numerical modelling of steel members in fire. At both ambient and elevated temperatures, the stress-strain relationships of cold-formed high strength steels exhibited gradually yielding (i.e. without distinct yield plateau) [25]. This is similar to the rounded stress-strain response of stainless steels, the stress-strain behaviour of which has been analytically represented by constitutive
General
A numerical investigation was undertaken to study the behaviour of cold-formed HSS tubular beams at elevated temperatures. The finite element (FE) package ABAQUS [41] was employed for the investigation. A FE model was first developed and then verified by results of cold-formed HSS tubular beam tests conducted by the authors [31] and Ma et al. [9] at ambient temperature. Upon verification, a numerical parametric study was carried out based upon the verified FE model to explore the structural
General
In this section, the suitability of the existing slenderness limits to the cold-formed HSS SHS/RHS at elevated temperatures was firstly appraised. Secondly, the MFEA,T at elevated temperatures were compared with current codified provisions to assess their applicability to cold-formed HSS tubular sections at elevated temperatures. Note that the comparisons were performed by setting resistance factors/partial factors as unity, namely, the MFEA,T were compared with nominal flexural resistances.
Slenderness limits at elevated temperatures
Modified direct strength method and comparison with flexural strengths
In this study, the DSM was modified in order to provide a more accurate design rule for cold-formed HSS SHS/RHS beams at elevated temperatures. The modified DSM curve, underpinned by 216 elevated temperature data, as illustrated by Eq. (8), is plotted in Fig. 11 together with the original DSM curve as per the AISI S100 [33].in which, the MDSM#,T is the nominal moment resistance calculated from the
Reliability analysis
In this study, reliability analyses were undertaken to examine the reliability levels of the existing codified provisions and the modified DSM; the calculations performed herein conformed to the principles that detailed in the AISI S100 Commentary [57]. The target reliability index applied herein was 2.5, which is in accordance with the AISI S100 [33]. The reliability calculations are illustrated in Eq. (9).in which, β0 is the reliability index; ϕ0 is the
Conclusions
A constitutive model is presented in this paper to predict the stress-strain curves of cold-formed high strength steels (HSS) at elevated temperatures. It has been demonstrated that stress-strain relationships generated based upon the proposed model can accurately represent the full range stress-strain curves obtained from material coupon tests up to 1000 °C, and therefore, are recommended to be used for numerical investigation of cold-formed HSS members at elevated temperatures. A numerical
Acknowledgement
The research work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. 17209614).
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Formerly, Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China.