Elastic buckling and second-order behaviour of pitched-roof steel frames Abstract Department of Civil Engineering and Architecture, ICIST/IST, Technical of Lisbon Abstract The aims of this work are two-fold: (i) to present the results of a study concerning the elastic in-plane stability and second-order behaviour of unbraced single-bay pitched-roof steel frames and (ii) to propose, validate and illustrate the application of an efficient methodology to design this type of commonly used frame. After (i) characterizing the relevant frame buckling modes and P–Δsecond-order effects, and (ii) addressing the exact and approximate calculation of the associated bifurcation loads and secondary bending moments, the paper deals with the incorporation of these concepts in the definition of an efficient design procedure. In particular, it is clearly shown that, due to the rafter slope, the geometrically nonlinear behaviours of orthogonal beam-and-column and pitched-roof frames are qualitatively different. Finally, the proposed concepts and methodologies are illustrated through the presentation and discussion of numerical results involving fixed and pinned-base frames.52595

Keywords: Pitched-roof frames; Buckling behaviour; Second-order behaviour; Amplification method; Design approach; Eurocode 52595

1. Introduction

   Due to their high structural efficiency, single-bay pitchedroof steel frames of the type shown in Fig. 1(a) are widely used in the construction industry, namely in large-span industrial buildings or sport pavilions (e.g. [9]). Indeed, the considerable stiffness increase induced by the rafter slope makes it possible for frames built with rather slender columns and (mostly) rafters to withstand quite large loads. However, unlike in orthogonal beam-and-column frames, the pitched-roof configuration leads to the development of significant rafter compressive forces (of the same order of magnitude as the column ones), a feature that (i) may have a major impact on the frame structural response but (ii) is often neglected by a large number of designers . In the last few years, the authors have devoted an extensive amount of research work to investigate and clarify several issues concerning the geometrically nonlinear global behaviour of plane pitched-roof frames.

   In general, the elastic in-plane buckling behaviour of single-bay unbraced pitched-roof frames is conditioned by two bifurcation loads, associated with antisymmetrical and symmetrical buckling modes, both involving lateral displacements at the column tops. The fact that these two bifurcation loads are often very close (mostly in fixed-base frames) may has far-reaching implications in the design and safety checking procedures applicable to such frames, which are not explicitly addressed by the current steel codes, namely by the existing and upcoming versions of Eurocode 3 (EC3): EC3-ENV [4] and EC3-EN [5]. In the context of the particular design approach followed by EC3, specific provisions and/or guidelines are necessary regarding the (i) classification of the frame with respect to the need to consider second-order effects of the P– type and (ii) the definition of an appropriate indirect method to incorporate those effects into the design values of the frame internal forces and moments. Very recently, Lim et al. [13] also proposed simple rules for the plastic design of portal frames, according to EC3-EN, which take into account the inplane stability effects. In their work, pitched-roof frames are pided into two categories, namely Category A, which includes mono-pitch, single-bay and multi-bay regular frames, and Category B, comprising all the remaining pitched-roof frames— distinct design rules are proposed for the two categories.

   The aims of this paper are two-fold: (i) to present an in-depth overview of the results obtained in previous investigations and concerning the elastic in-plane buckling and second-order behaviours of laterally unrestrained (unbraced) symmetrical single-bay pitched-roof steel frames,1 and also (ii) to propose,validate and illustrate the application of an efficient elastic design and safety checking approach developed for this type of commonly used plane frames. One begins by characterizing the relevant buckling modes and addressing the exact and approximate determination of the associated bifurcation loads. Then, the paper focuses on the evaluation of the P–Δsecondorder effects and it is shown that, due to the rafter slope, several concepts applicable to orthogonal beam-and-column frames cease to be valid: indeed, as far as the design of unbraced pitched-roof frames is concerned, it is no longer correct to base both (i) the decision to take into account P–Δeffects and (ii) the indirect evaluation of such effects solely on the value of the frame elastic (sway-mode) critical bifurcation load, as prescribed by virtually all the current steel design codes (namely EC3-ENV and EC3-EN). In order to overcome this limitation, one proposes and validates here novel classification and indirect amplification methods, which have been specifically devised for pitched-roof frames and take into account the above buckling and second-order results. Next, in order to illustrate the application of the proposed methods and, at the same time, to provide a better grasp of the concepts involved, numerical results concerning fixed and pinned-base frames, are presented and discussed. Finally, one lists the most relevant conclusions drawn from the research work reported in this paper. 斜屋顶钢框架结构的弹性屈曲英文文献和中文翻译:http://www.youerw.com/fanyi/lunwen_56544.html