Flexural-Torsional Buckling Resistance Design of Circular Arches with Elastic End Restraints Chao Dou 1 and Yong-Lin Pi 2 Abstract: This paper presents the flexural-torsional buckling resistance and design of steel circular arches subjected to uniform compression with elastic end bending restraints by using finite element (FE) numerical analyses. Firstly, effects of geometric and mechanical parameters such as initial imperfections, section types, material properties, slenderness, rise-to-span ratios, and end restraints on flexural-torsional buck- ling resistances of arches are investigated and are found to be eliminated to a large extent by introducing the normalized slenderness. Then, on the basis of extensive numerical results, a design method is proposed to predict the flexural-torsional buckling resistances of circular arches in uniform compression with elastic end restraints by the column curves according to the normalized slenderness and a specific section type, namely curve ‘a’ for hollow sections, curve ‘b’ for welded box sections, and curve ‘c’ for welded I-sections. Next, the flexural stiffness of an arch is studied, taking the destabilizing effect of the axial force into account to calculate the end restraining provided by adjacent arch segments to the adverse segment in a laterally-braced arch in uniform compression to obtain the flexural-torsional buckling resistance using the normalized slenderness and the column curve analytically. The result shows a good agreement with that gained from finite element numerical analyses, and proves it very conservative when the adverse segment is assumed to be hinged without any end restraining. DOI: 10.1061/(ASCE)ST.1943-541X.0001373. © 2015 American Society of Civil Engineers. Author keywords: Steel arch; Flexural-torsional; Buckling resistance; Elastic restraint; Normalized slenderness; Column curve; Braced arch; Metal and composite structures. Introduction Due to the curved profile which brings high-efficient in-plane load- carrying capacity, circular arches have been widely adopted in spatial and bridge structures. However, steel arches are prone to out-of-plane buckling that controls its strength design rather than in-plane flexural buckling. Before investigations into the ultimate resistance design of arches under general loading by a combination of axial compression and bending actions, inelastic flexural-tor- sional buckling of arches in uniform compression needs be studied (Timoshenko and Gere 1961; Ziemian 2010; Dou and Guo 2013). Under the action of uniformly distributed radial load, circular arches are in the ideal status of uniform compression without in-plane bending moment. Several investigations have been carried out primarily looking into flexural-torsional inelastic buckling and design of circular arches in uniform compression. Sakimoto and Kamatsu (1983) introduced three coefficients to reflect the effects of the arch end restraint, loading direction, and lateral restraint on arch ribs, respectively, and proposed a design formula for flexural- torsional buckling resistances of arches by using an effective length procedure and the straight column curves, but the rise-to-span ratios were limited in a narrow range of 0.1–0.2. Pi and Trahair (1998) and Pi and Bradford (2005) explored the flexural-torsional buckling strength and proposed design equations for pinned and fixed cir- cular arches by using a self-developed finite element (FE) curved beam program. Dou and Guo (2012) and Spoorenberg et al. (2012) adopted a commercial finite element package for elasto-plastic sta- bility analyses to establish design approaches for steel circular arches, in which the arches were modeled and analyzed with straight beam elements (BEAM188) or shell elements (SHELL181), respec- tively. La Poutré et al. (2013) carried out a systematic investigation of 15 test models into flexural-torsional stability and strength of roller bent I-section steel arches, which were subjected to a single force exerted to the arch crown with a subtended angle varying from 90 to 180°. Despite the previous-described studies, they were all carried out for arches with ideal end boundary conditions (namely hinged arches, pinned arches, or fixed arches) in which the degree of free- dom (dof) at the arch ends was either fully restrained or fully free. In fact, as indicated by the experimental study conducted by Dou et al. (2015), although for fixed arches all the dofs at the arch ends can be fabricated rigidly restrained which was close to the assumption in an ideal model, for pinned arches in practical use the arch ends can be treated as in-plane free to rotate, but with re- spect to the out-of-plane bending, they are actually semi-rigidly re- strained rather than fully restrained [Fig. 1(a)]. Therefore in practical engineering design, much attention needs to be paid to the cases of arches with elastic end bending restraints. Moreover as shown in Fig. 1(b), in discretely laterally braced arches the arch segment with a larger length between two lateral bracings is prone to flexural-torsional buckling in ahead of the other segments. In this circumstance, adjacent arch segments provide restraint to the ends of the so-called adverse segment and the latter can be treated to be elastically end restrained. Thus, it is also a problem how to predict the flexural-torsional buckling load of the adverse arch segment by taking the restraining effects into account. 1 Associate Professor, School of Civil Engineering, Beijing Jiaotong Univ., Beijing 100044, P. R. China; and Beijing’ s Key Laboratory of Struc- tural Wind Engineering and Urban Wind Environment, Beijing 100044, China (corresponding author). E-mail: [email protected] 2 Professor, School of Civil and Environmental Engineering, Univ. of New South Wales, Sydney, NSW 2052, Australia. E-mail: y.pi@unsw .edu.au Note. This manuscript was submitted on November 12, 2014; approved on June 10, 2015; published online on July 17, 2015. Discussion period open until December 17, 2015; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural En- gineering, © ASCE, ISSN 0733-9445/04015104(10)/$25.00. © ASCE 04015104-1 J. Struct. Eng. J. Struct. Eng. Downloaded from ascelibrary.org by Beijing Jiaotong University on 09/08/15. Copyright ASCE. For personal use only; all rights reserved.
Flexural-Torsional Buckling Resistance Design of Circular Arches with Elastic End Restraints
May 20, 2023
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