International Journal of Mechanical Sciences 187 (2020) 105916 Contents lists available at ScienceDirect International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci Out-of-plane stability of concrete-filled steel tubular arches at elevated temperatures Yanni Bouras, Zora Vrcelj ∗ College of Engineering and Science, Victoria University, Melbourne, VIC, Australia a r t i c l e i n f o Keywords: CFST Creep Finite Element Fractional derivatives Lateral stability Thermal loading a b s t r a c t This paper investigates the flexural-torsional buckling behaviour of concrete-filled steel tubular circular arches under mechanical and thermal loading. A thermo-elastic pre-buckling analysis is first conducted by employing the principle of virtual work to derive the non-linear equations of equilibrium. The governing geometrical, equi- librium and constitutive material relations are numerically solved as a system of first-order differential equations with boundary conditions of pinned or fixed ends. The prebuckling analysis is then generalised to consider basic creep strain which is found to have a negligible impact on the prebuckling response under short-term heating. Subsequently, an elastic out-of-plane buckling analysis is performed using energy methods and the influence of thermal loading on buckling loads is examined. The results show that stability boundaries decrease with an in- crease in thermal loading, and that the rate of reduction is independent of the type of end-supports. Additionally, a Finite Element (FE) model is developed to analyse the inelastic lateral buckling strength of CFST arches under both uniform thermal and fire loading. The FE analysis is validated by comparison to the numerical method derived herein for the elastic buckling analysis. 1. Introduction The use of concrete-filled steel tubular (CFST) members in conven- tional structures provides many benefits relating to both mechanical be- haviour and constructibility. Advantages of the former include increased compressive strength, reduced shrinkage in the concrete core, concrete confinement and improved local buckling strength of the steel tube. Con- sequently, CFST sections have recently surged in popularity for use in arch bridges, with over 400 constructed worldwide [1]. However, the use of CFST arches is not limited to bridges as they can be utilised in buildings as large-span roof framing members [2] and in ground-support applications [3]. As arches experience primarily compression, they are prone to stability loss. In-plane buckling of arches may be in an anti- symmetric or symmetric form. Additionally, an arch may suddenly dis- place laterally and twist out of plane when subject to in-plane bending and/or compression in a flexural-torsional type buckling mode [4]. The problem of stability is paramount in CFST arches as the increased com- pressive strength gained with CFST sections may result in the use of slen- der structures. Geometrical non-linearities in shallow arches [5,6] con- volute the stability analysis and reduce load carrying capacity. Classic studies investigating elastic flexural-torsional buckling of arches include the work of Timoshenko and Gere [7], who developed closed form solutions for simply supported arches of rectangular cross- section under uniform compression and bending, and Vlasov [8] who ex- ∗ Corresponding author. E-mail address: zora.vrcelj@vu.edu.au (Z. Vrcelj). tended Timoshenko and Gere’s study to mono-symmetric cross sections. Since these works, many researchers have investigated elastic flexural- torsional buckling of arches [9–15]. As with in-plane stability analysis, out-of-plane buckling problems have been investigated using two meth- ods which include the static equilibrium and energy methods, adopted in [7,8] and [7,9–15] respectively. Critical reviews of these early studies were conducted by Papangelis and Trahair [11] and Kang and Yoo [14]. In these studies, classical buckling method was used to obtain the crit- ical load, thus the effects of in-plane pre-buckling deformations were ignored. In-plane pre-buckling deformations alter the curvature of an arch, which significantly influences the out-of-plane buckling resistance [16]. The effect of pre-buckling deformations on the elastic lateral- torsional buckling of simply supported arches subjected to uniform bending was studied in [9,10,16]. In these works, the in-plane pre- buckling deformations were found to increase the moments causing lateral instability. Furthermore, Pi et al. [16] discovered that incorpo- rating pre-buckling deformations in stability analyses allows torsional buckling to occur, in the case when lateral displacements are fully re- strained. As the lateral buckling behaviour of fixed arches differs from that of simply-supported arches, the pre-buckling effects on buckling of fixed arches cannot be assumed the same as for pinned arches [17]. Un- der uniform positive bending, the pre-buckling deformations reduce the moments causing lateral instability in fixed arches, contrasting the in- https://doi.org/10.1016/j.ijmecsci.2020.105916 Received 12 February 2020; Received in revised form 26 May 2020; Accepted 2 July 2020 Available online 4 July 2020 0020-7403/© 2020 Elsevier Ltd. All rights reserved.