Reliability calibration for the design of multiple-chord CFST trusses by advanced analysis
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,
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,
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)
- et al.
Flexural behaviour of concrete filled steel tubular (CFST) chord to hollow tubular brace truss: experiments
J Constr Steel Res
(2015) - et al.
Square hollow section (SHS) T-joints with concrete-filled chords subjected to in-plane fatigue loading in the brace
Thin-Walled Structures
(2010) - et al.
Advanced design for trusses of steel and concrete-filled tubular sections
Eng Struct
(2011) - et al.
Experimental and analytical study on fatigue behavior of composite truss joints
J Constr Steel Res
(2013) - et al.
Developments and advanced applications of concrete-filled steel tubular (CFST) structures: Members
J Constr Steel Res
(2014) - et al.
Experimental research on RHS and CHS truss with concrete filled chord
Journal of Building Structures
(2010) - et al.
Analytical behaviour of CFST chord to CHS brace truss under flexural loading
J Constr Steel Res
(2017) - et al.
Steel design by advanced analysis: material modeling and strain limits
Engineering
(2019) - et al.
System reliabilities in steel structural frame design by inelastic analysis
Eng Struct
(2014) - et al.
Advanced inelastic analysis of frame structures
J Constr Steel Res
(2000)
Out-of-plane advanced analysis of steel structures
Eng Struct
Reliability-based evaluation of design code provisions for circular concrete-filled steel columns
Eng Struct
Reliability analysis and design optimization of nonlinear structures
Reliab Eng Syst Saf
System-based design of planar steel frames, I: Reliability framework
J Constr Steel Res
Reliability evaluation of axially loaded steel members design criteria in AASHTO LRFD bridge design code
Reliab Eng Syst Saf
Reliability-based progressive collapse analysis of highway bridges
Struct Saf
Behaviour and design calculations on very slender thin-walled CFST columns
Thin-Walled Structures
Reliability-based evaluation for concrete-filled steel tubular (CFST) truss under flexural loading
J Constr Steel Res
Flexural behaviour of curved concrete filled steel tubular trusses
J Constr Steel Res
Experimental study on column buckling of 420 MPa high strength steel welded circular tubes
J Constr Steel Res
Behaviour of CFST stub columns with initial concrete imperfection: Analysis and calculations
Thin-Walled Structures
LRFD: implementing structural reliability in professional practice
Eng Struct
Cited by (9)
Flexural performance of steel fiber reinforced concrete filled stainless steel tubular trusses
2023, Composite StructuresCitation Excerpt :Although CFST truss has the advantage of light weight and high bearing capacity, its performance in engineering application is still necessary to be improved. On one hand, the CFST trusses are often used in large bridge structures or marine engineering [12,13]. In this relatively humid environment, steel tubular components are prone to corrosion and thus reduce the overall mechanical performance of the truss.
Axial loading mechanism analyses and evaluation methods of CCFT short columns with gap defects
2022, StructuresCitation Excerpt :The influence of the gap defect ratio on the load bearing capacity, rigidity and stability of CFT members has been qualitatively clarified. Chen et al. [7,19,20] presented a list of advanced numerical analyses on the flexural response of CFT trusses considering the impact of random steel and concrete imperfections, and the ultimate flexural resistance of the CFT trusses with random defects was properly evaluated on the basis of the reliability analysis method. Moreover, Wang et al. [21] further utilized the fiber reinforced polymer (FRP) to treat and strengthen the axial-compressed CCFT short columns offering gap defects.
System reliability-based design of steel-concrete composite frames with CFST columns and composite beams
2022, Journal of Constructional Steel ResearchCitation Excerpt :When it comes to system design of the steel-concrete composite frames in this study, these uncertainties are explicitly considered and the proposed resistance factors of investigated frames are in the range above, which is obviously reasonable. It has been found in some studies that the values of Ln/Dn ratios are in the range from 0.5 to 5 [16,30]. Therefore, many values of Ln/Dn ratios in the range mentioned above including 0.5, 1.0, 2.0, 3.0, 5.0 are considered to investigate their influence on the reliability index and the system resistance factor of frames subjected to only gravity load.