Cross-sectional bending strength of steel Elliptical-Hollow-Sections (EHSs) based on Equivalent-Resistance-Capacity-Method (ERCM)

Highlights

• Improved expression for the equiv. CHS diameter of the EHS under bending.

• New cross-section slenderness limits for CHS and EHS members under bending.

• Transformed expression in the form of RRD based traditional shell buckling capacity curve.

• Resistance capacity curves for CHS and EHS cross-sections under normal and cyclic bending.

Abstract

An expression for cross-sectional bending capacity prediction curve is proposed in this study based on the Direct-Strength-Method (DSM) approach using a comprehensive data from the literature on structural carbon steel Circular-Hollow-Sections (CHSs). Later, according to the Equivalent-Resistance-Capacity-Method (ERCM), improved empirical expressions for the equivalent CHS diameter of Elliptical-Hollow-Section (EHS) are derived using the proposed CHS bending capacity prediction curve and the data of EHSs from the literature. A unified set of cross-section slenderness limits for assessing the CHS and EHS members under bending is proposed. Also, the proposed expression for the bending resistance curve based on DSM is transformed into the generalized form of the traditional cylindrical shell buckling capacity curve as a practical solution in harmony with the newly introduced Reference-Resistance-Design (RRD) guidelines. Finally, the behaviour of EHS cantilever members under cyclic bending is assessed in terms of cyclic moment resistance and rotation capacities based on the authors' previous study.

Introduction

Circular, elliptical and flat-oval (see e.g., Ref. [1] in Fig. 1) hollow sections are known to exhibit relatively higher impact load endurance owing to their streamlined surface finishing with a lesser degree of local-imperfections (see e.g., Ref. [2,3]). Elliptical-Hollow-Section (EHS) members under torsion and compression loads are structurally more efficient because of their larger ratio of the radius of gyration, r_gy to cross-sectional area, A (see e.g., Ref. [3,4]). EHS can deliver higher flexural rigidity than a Circular-Hollow-Section (CHS) of equal wall-thickness, t and cross-sectional steel area, A due to the disposition of weaker and stronger principal axis directions while preserving a smooth curved shape [5,6]. Consequently, as a structural member, EHS could be a more productive alternative for Rectangular-Hollow-Section (RHS) and CHS with more methodical usage of steel in a variety of major structural configurations [7]. EHSs have earned marketability as Architecturally-Exposed-Structural-Steel (AESS) supporting elements, especially in Canada, Hong-Kong, Western Europe and western half of Southern Europe [5,6]. Pronouncing implementations (see e.g., Ref. [5,8,9] in Fig. 2) of EHS include electricity transmission line pylons, beams, columns, struts, bracing members, arches, etc. [10,11].

The induction of EHS into the category of cylindrical Hollow-Structural-Sections (HSSs) around the beginning of the 21^st century with the offering of additional scope for architectural essence drawn the attention of architects and engineers. Since then, there is a steady upsurge in the demand for conducting finite element (FE) simulation and experimental programs (see e.g., Refs. [7,[10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]) to establish various aspects like design strength curves and cross-section classification criteria for EHS members, so as to accredit the inclusion of design guidelines for EHSs in various design specifications (e.g., Refs. [[27], [28], [29], [30], [31], [32]]). Despite the implementation of EHSs in a wide range of infrastructure projects and those numerous studies (see e.g., Ref. [7,[10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]), there isn't a globally recognized design specification to date with the guidelines like cross-section capacity curves and cross-section classification for EHSs as per the authors' literature survey.

Gardner and associates [14,20,21,[33], [34], [35]] have put forward equations for the equivalent CHS diameter of EHS in terms of the radius of curvature at the point of initiation of local buckling, with an aim to implement the existing CHS cross-section classification criteria to EHSs also. But, Zhao and Packer [19], Haque et al. [17] and Chen and Young [18] reported significant conservatism involved in utilizing those equations for the equivalent CHS diameter of EHS formulated by Gardner and associates [14,20,21,[33], [34], [35]]. In a recent study by Fang et al. [36], it is found that the EHSs which are categorized as Class 4 based on the equivalent CHS diameter expressions proposed by Gardner and associates [14,20,21,[33], [34], [35]], offered significant cyclic energy dissipation capacities under combined cyclic bending and axial compressive loads. Previous studies [16,20,21] also indicated varying cross-sectional strength curves with respect to cross-sectional aspect ratio of EHSs based on those equivalent CHS diameter equations proposed by Gardner and associates [14,20,21,[33], [34], [35]] and consequently implying different slenderness limits for different aspect ratios in addition to the conservatism expressed by Zhao and Packer [19], Haque et al. [17] and Chen and Young [18].

Of late, significant inconsistencies (discussed in the further Section 2.3 and Table 3) among the cross-sectional compact and yield section slenderness limits for CHSs under bending specified in various international design standards [[27], [28], [29], [30], [31], [32]] are reported in the literature (see Ref. [[37], [38], [39], [40]]). Hence, firstly, it is decided to establish the moment resistance capacity curve and the cross-section slenderness limits for CHSs which can be used uniformly across all the design standards [[27], [28], [29], [30], [31], [32]], by using a comprehensive data of results from the literature (see Ref. [37,38,[41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57]]). But, the main motive of this study is to analyse the efficiency of the cross-section slenderness parameter expressions for EHSs under bending, which are suggested by Chan and Gardner [21] and improve them with a rational approach based on the existing data of carbon steel CHSs and EHSs under bending from the literature (see Refs. [18,21,58]). In interest of promoting reliable application of the CHS cross-section classification criteria also to the EHSs, it is intended to acquire empirical expressions for the equivalent CHS diameter of the EHS under bending based on the Equivalent-Resistance-Capacity-Method (ERCM) which involves fitting the data of EHS bending analysis results from the literature [18,21,58] by preserving consistency with the CHS bending capacity curve. The authors already used the concept of ERCM and determined the equivalent CHS diameter expression for the EHSs under axial compression in their previous study [59]. ERCM is utilized herein to estimate the diameter of a CHS which offers an equal cross-sectional resistance capacity of that of the EHS made with the same wall thickness, t and material. Lastly, it is also intended to estimate the performance of EHS cantilever members under cyclic bending by using the results of an earlier FE simulation study [11] carried out by the authors.