Stability criteria for roller-bent circular-hollow-section steel arches

Highlights

• Investigating the stability of roller-bent circular-hollow-section steel arches.

• Nonlinear finite element modeling accounting for residual stresses & imperfections.

• Development of design buckling curves for CHS arches.

• Proposing stability criteria according to structural steel design standards.

Abstract

The structural stability of steel arches comprising Circular-Hollow-Sections (CHS) is examined in the present study. Appropriate finite element models are developed, accounting for geometry and material nonlinearities, as well as, incorporating residual stresses and geometric imperfections of roller-bent arches. A verification study is first performed to evaluate the accuracy of the proposed finite element modeling, followed by sensitivity analyses aiming at estimating the effects of residual stresses and geometric imperfections on the structural response. Findings reveal that the magnitude of geometric imperfections and the distribution of residual stresses significantly affect the arch's buckling resistance. An extensive parametric study is carried out to assess the spatial stability of arches comprising a wide range of non-dimensional slenderness, commonly encountered in the civil engineering practice. Based on the results of parametric analyses, suitable parameters are determined for the in-plane and out-of-plane buckling. Finally, stability criteria are proposed via regression analyses, which are used to define relevant buckling curves according to structural steel design standards.

Introduction

Steel arches are encountered in many structural and infrastructure engineering applications, such as atriums, bridges, buildings, etc. Apart from constituting an attractive solution due to their aesthetic appeal, arches can cover significant spans without intermediate supports, as loads are carried largely in compression rather than bending. The analysis and design of arches is widely associated with structural stability. The arch stability can be characterized by snap-through, in-plane, or out-of-plane buckling, as shown in Fig. 1. Snap-through buckling is usually the prevailing instability mechanism in cases of shallow arches, which are restrained against out-of-plane displacements. In this case, the arch stiffness gradually reduces due to the induced axial shortening, resulting in a limit point where transition from compressive to tensile action occurs suddenly. In-plane buckling is predominant in cases of non-shallow arches, which are adequately braced against out-of-plane displacements. In this context, either symmetric or antisymmetric mode shapes can be developed. Out-of-plane buckling occurs in cases of arches exhibiting significant free-standing portions. This type of instability comprises a combination of flexural and lateral-torsional buckling, and therefore is also denoted as flexural-torsional buckling.

The structural behavior of arches with emphasis on stability is presented in several literature sources. An overview of the research studies prior to 1970 is given in the “Handbook of Structural Stability” [1]. In the “Stability of Metal Structures, a World View” [2], a comparison is presented between standard provisions for the spatial stability of arches. The arch elastic and inelastic stability are discussed in a book chapter of the “Structural Stability Design, Steel and Composite Structures” [3]. A summation of experimental studies on arches is presented in the “Buckling Experiments” by Singer et al. [4]. In the “Design of curved steel” by King and Brown [5], a comprehensive methodology is proposed for the practical design of curved members including several worked examples. The spatial stability of arches, pertinent design criteria and several bracing recommendations, are thoroughly discussed in a book chapter of the “Guide to Stability Design Criteria for Metal Structures” [6]. In the “Curved Member Design” by Dowswell [7], a contemporary guide is presented including practical information related to fabrication, detailing and design issues of curved steel members.

The roller-bending process is the most common method for producing circular arches in the steel constructional industry. It is a cold-forming process, where the workpiece is passed iteratively through three rollers. In each subsequent pass, the bending rolls are manipulated in an appropriate manner causing local plastification of steel, until the desired curvature is reached. Residual stresses are induced to steel profiles after roller-bending due to the plastic deformations caused by three-point bending. A theoretical distribution of the residual stresses emanating from the inelastic bending of beams is given by Timoshenko [8], as function of the steel's yield stress f_y and the ratio α between the plastic and elastic section modulus. By aggregating the bending stresses due to inelastic M_pl and elastic ‘spring-back’ M_sb moments, the self-equilibrated locked-in distribution is obtained, shown in Fig. 2. This theoretical distribution, exhibiting an anti-symmetrical layout about the neutral axis, makes no differentiation with regard to the cross-sectional shape. Based on the classical beam theory, the theoretical distribution is generally valid for the inelastic bending of beams incorporating small shear stresses relative to the bending stresses.

The residual stresses of roller-bent arches have been investigated by means of experimental and numerical methods [[9], [10], [11], [12], [13]]. Pertinent residual stress models for roller-bent arches of wide-flange-sections and rectangular-hollow-sections have been proposed by Spoorenberg et al. [11] and Chiew et al. [12], respectively. Following an extensive parametric study, a residual stress model for roller-bent arches of Circular-Hollow-Sections (CHS) has been proposed by Thanasoulas and Gantes [13]. The locked-in stress distributions in all cases (Fig. 3) are found to differ significantly from Timoshenko's theoretical distribution. Differences have been interpreted by considering that the classical beam theory is not appropriate for bending beams that are deep and short in length, like the beam segment within the three-point-bending length, where shear stresses become large relative to the bending stresses and thus cannot be neglected. The roller-bent flanged or hollow sections exhibit effects of plates or shells [14], such as stress concentrations at the web-to-flange junctions or transverse bending, which result in non-uniform bending stress distributions over the cross-sectional width. Therefore, the main assumptions of beam theory do not hold in the case of roller-bending, and thus the theoretical distribution cannot be accurately applied.

Residual stresses and geometric imperfections significantly affect the inelastic stability of steel members under axial compressive loads as in the case of arches. The effects of geometric imperfections and residual stresses on the stability of arches have been reported in early studies conducted by Komatsu and Sakimoto [15] and Sakimoto et al. [16]. In these studies, arches of welded wide-flange and box sections were examined, revealing that the presence of geometric imperfections and residual stresses can cause a significant reduction on buckling resistance. The in-plane stability of steel arches was studied by Pi and Trahair [17] and Pi and Bradford [18], while the out-of-plane stability was studied by Pi and Trahair [19] and Pi and Bradford [20]. In these studies, appropriate axial force - bending moment interaction design formulas were proposed for circular arches of I-sections. La Poutré et al. [21] carried out an experimental study on the out-of-plane stability of roller-bent arches comprising wide-flange-sections, while pertinent finite element simulations were carried out by Spoorenberg et al. [22]. Experimental tests and numerical analyses on roller-bent arches of rectangular-hollow-section were performed by Thanasoulas et al. [23], highlighting the presence of the Bauschinger effect on arches' inelastic response due to roller-bending.

Analysis and design methods of steel arches are based on the evaluation of their structural adequacy, considering the nonlinear effects due to material yielding and elastic/inelastic buckling. Several design methods for evaluating the structural adequacy of steel arches are based on normative provisions developed for straight members. Such methods are very popular in the structural steel design practice due to their simplicity, as second-order analyses are usually not required. A state-of-the-art design procedure is described in the “Curved Member Design” [7], in which design equations of the “Specification for Structural Steel Buildings” [24] are employed. A similar design methodology is proposed by King and Brown [5], based on the requirements of BS 5950–1 [25] with appropriate modifications to account for the effects of arcs curvature. Relevant design formulas are also given in the “Guide to Stability Design Criteria for Metal Structures” [6], which were originally developed by Pi and Trahair [17] and Pi and Bradford [18] for the in-plane strength, as well as, by Pi and Trahair [19] and Pi and Bradford [20] for the out-of-plane strength. The implementation of such design methods is mainly dependent on the existence of appropriate buckling curves accounting for reliable residual stress distributions and representative geometric imperfection magnitudes. Pertinent buckling curves have been proposed for the out-of-plane buckling of roller-bent arches comprising wide-flange-sections by Spoorenberg et al. [22].

In the present study, the in-plane and out-of-plane stability of roller-bent CHS arches is investigated by means of finite element analyses accounting for geometry and material nonlinearities. The effects of geometric imperfections and residual stresses are included in the developed numerical models, incorporating reliable residual distributions and geometric tolerances of roller-bent arches. A verification study is first performed to evaluate the accuracy of the proposed finite element modeling, followed by sensitivity analyses aiming at estimating the separate and combined effects of residual stresses and geometric imperfections on the arch structural response. An extensive parametric study is performed to assess the spatial stability of steel arches exhibiting various geometric dimensions. Several arches that are not prone to snap-through buckling are examined, comprising a wide range of arch non-dimensional slenderness, commonly encountered in the civil engineering practice. A systematic methodology is employed to determine buckling parameters for the spatial stability of steel arches using the column-curve formulation. Based on the results of parametric analyses, appropriate design formulas are proposed via regression equations which are used to define relevant buckling curves according to structural steel design standards.