Elsevier

Structural Safety

Volume 89, March 2021, 102051
Structural Safety

Reliability calibration for the design of multiple-chord CFST trusses by advanced analysis

https://doi.org/10.1016/j.strusafe.2020.102051Get rights and content

Highlights

  • Stochastic finite element analyses are presented on multiple-chord CFST trusses.

  • Reliability calibrations are conducted for multiple-chord CFST trusses.

  • Weighted system resistance factors with respect to target reliability are proposed.

Abstract

Concrete-filled steel tubular (CFST) truss with complex configurations are now widely used in practice, especially in large-scale bridge constructions. For such complex composite trusses, traditional structural analysis approaches are readily applied for the safety checks of individual members and connections, whilst inelastic analysis and reliability calibration are very limited. Recently, the development of advanced system-level analysis that takes into account various nonlinearities and uncertainties allows a rational reliability calibration for CFST trusses to assess their structural reliability. This paper aims to present reliability calibrations on three typical CFST trusses (two-chord, three-chord and four-chord) by advanced finite element models implemented with random uncertainties. The established finite element models are validated against experimental results. Afterwards, stochastic finite element analyses (FEA) are conducted taking into account the material and geometric nonlinearities, the random initial imperfections and the potential model errors. Using the obtained statistics of resistance, reliability calibration is then undertaken to calculate the reliability indexes of the three typical CFST trusses in respect of resistance factors under various load conditions, with the target reliability discussed in accordance with AASHTO and ANSI/AISC 360–16. The proposed novel computational approach and the reliability calibration contribute to both the practical design and the standard drafting for CFST trusses.

Introduction

Truss structures have been widely used in bridges, long-span roofs and floors. The structure effectively manages compression and tension through its complex configuration. The material use of trusses is more effective than that of frame structures, especially for large-span applications [1]. Concrete-filled steel tubular (CFST) trusses are proved to have high strength, good ductility, reduced cost and high construction efficiency. Compared to circular hollow section (CHS) trusses, the compression and flexural behaviour of such structures are greatly improved, resulting in an extensive utilization in large-span structures [2], [3], [4], [5], [6]. CFST trusses with two, three or four in-filled concrete chords (shown in Fig. 1), are widely used alone as bridge girders or as part of a supporting system in decking structures [7]. CFST trusses are composed of steel and concrete members with complex spatial configurations, nonlinear material properties, sophisticated connections and interactions, therefore, experiments on such structures are limited and costly compared to those on single material structural elements and individual CFST members. Therefore the advanced analysis of CFST trusses is one step closer to the structural system-level analysis of actual CFST truss bridges.

Liu et al. [8] tested and compared a couple of two-chord hollow steel truss with circular or rectangular chords and a couple of two-chord CFST truss with circular or rectangular chords, to explore and discuss their failure modes and structural behaviour. It was found that the geometry of chords had limited impact on the load-carrying capacity and the deformation of the truss, but the in-filled chord concrete improved the load-carrying capacity of the overall truss and the brace-chord connection regions. A total of twelve CFST trusses, hybrid CFST trusses and CHS trusses with three chords were examined and compared in [2], [9], [10]. Failure modes and load-transfer mechanism were illustrated for the three-chord trusses, and a simplified design method for the flexural behaviour of the CFST truss was proposed. CFST trusses with four chords were tested, with different brace types such as modified Warren, Pratt and Warren type were compared to explore their structural behaviours [11], [12].

The conventional design of a CFST truss is usually based on an overall load-transferring analysis of the trusses, followed by a detailed structural analysis of critical components, including capacity checks on individual members and connections. With the development of structural computational approaches and capacities, many recent editions of international design specifications, such as ANSI/AISC 360–16 [13], Eurocode 3:2005 [14] and AS/NZS 5100.6:2017 [15], permit the adoption of advanced analysis. It takes into account inelastic material behaviour, geometric nonlinearity and imperfections, providing more accurate predictions of the ultimate strength and resulting in a more efficient structure [16], [17]. Compared with those traditional design methods, all deformations which contribute to the displacements, the second-order effects, the imperfections, and the stiffness reductions are well captured by the advanced analysis [13]. Many studies have been carried out for the advanced analysis of steel structures [16], [17], [18], frame structures and space trusses [19], [20]. The benefits of more accurate predictions of the ultimate strength and the inelastic behaviour than traditional member-based design specifications are widely recognized.

In terms of utilizing the advanced analysis to CFST trusses to fulfil a more accurate design approach and a satisfactory level of safety, the ultimate strength of the structural shall equal or exceed the required structural loads, which is given by,ϕsRniγiQni

where ϕs and γi denote the resistance factor and the load factor corresponding to different design specifications. Rn and Qni are the nominal resistance and the structural loads, with the latter being considered as random variables in this study. The above load and resistance factor design (LRFD) format is then converted into solving the probability of possible exceedance of the limit state of the structure. The probability of failure (Pf) is estimated through the First-Order Reliability Method (FORM) [18], [21], [22], and the obtained Pf is then converted to a reliability index (β) as follows,β=Φ-11-Pf

where Φ−1 is the inverse of the cumulative distribution function of a standard normal distribution.

System reliability assessments have been conducted for many types of structures. For steel structures, the system reliabilities for different planar frames were examined, which include partial or full uncertainties in steel properties, geometric imperfections, different levels of live-to-dead load ratios (Ln/Dn) [17], [23]. For steel bridges, the reliability of steel members in tension and compression were evaluated in Norton et al. [24]. The reliability and redundancy of highway bridges were investigated, and system factors for different bridge configurations were developed in Ghosn and Moses [25]. The reliability of steel bridge systems to resist progressive collapse and relevant system resistance reduction factors were further proposed in Miao and Ghosn [26]. Reliability analysis and design code provisions of concrete-filled steel columns with different configurations and material properties were evaluated in Beck et al. [21] and An et al. [27]. Chen et al. [10] developed a framework for reliability assessment of CFST truss with three chords by using stochastic finite element analyses (FEA). Then, a further study was carried out to investigate and compare mainstream design specifications in terms of sufficient and uniform reliability criteria for such structures [28]. The framework of CFST trusses with three chords in previous research set a foundation for the reliability analysis of CFST truss structures in this paper.

In this study, the above-mentioned reliability framework for obtaining the reliabilities of CFST trusses is further developed on comprising two-chord, three-chord and four-chord CFST trusses. Therefore, a more comprehensive investigation of CFST trusses as the bridge supporting system is carried out. The reliability calibration method and results, including the probabilistic models of random uncertainties, i.e., material properties, geometric configuration, initial steel imperfection, initial concrete imperfection, model error and Ln/Dn, are discussed. The resistance factor (ϕs) suitable for the design of CFST trusses through advanced analysis is hereby derivated. The comprehensive method and results of reliability calibration on CFST trusses contribute to both the practical design and the drafting of specific structural standard for the composite trusses.

Section snippets

Reliability calibration method

With the advanced analysis of CFST trusses, the overall behaviour can be analyzed and the structural safety can be evaluated directly, reducing the needs for separate safety checks on individual members. Reliability calibration of CFST trusses will also be conducted. By considering the statistics of various uncertainties which have impacts on the ultimate strength, advanced analysis can provide more accurate predictions of the ultimate strength while maintaining acceptable reliability of CFST

Advanced numerical models with random uncertainties

The three typical types of CFST trusses selected in this study to represent a typical supporting system of bridges are shown in Fig. 3. The geometric information of the CFST truss prototypes are summarized in Table 1. The configuration of the two-chord CFST truss sample, i.e., C2-two chord specimen, is shown in Fig. 3(a), which can be installed quickly due to simple but effective configuration. T8-three chord and W2-four chord specimens which show in Fig. 3(b) and Fig. 3(c) refer to CFST

Statistics of the ultimate strength

The current design methods for CFST truss are mainly based on analysis at the component or the connection levels, whilst the inelastic behaviour of the whole truss has not been revealed previously. The above advanced analysis method allows the CFST truss to be treated as a whole with stochastic uncertainties taken into account. The stochastic models are consistent with the facts that structures have potential uncertainties during construction. The statistics of the ultimate strength on

Conclusion

The reliability calibration for the design of typical concrete-filled steel tubular (CFST) trusses (two-chord, three-chord and four-chord) by advanced analysis is presented in this paper. The proposed stochastic finite element analysis (FEA) method and the relevant reliability calibration contribute to the practical design and standard drafting for such composite trusses. Conclusions are presented as follows,

  • (1)

    FEA models are developed under flexural loading and validated with experimental data

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The current research is part of the Project 51678341 supported by the National Natural Science Foundation of China (NSFC). The financial support is highly appreciated.

References (45)

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