Out-of-plane creep buckling analysis on slender concrete-filled steel tubular arches
Introduction
The use of concrete-filled steel tubular (CFST) arches is gaining popularity for bridge applications because of the enhanced load carrying capacity and ease of construction provided by the composite solution. Current trend is to increase the span length of the arches and to remove the wind braces between adjacent arches for architectural purposes (Fig. 1). This is highlighted by the fact that, at present, among the 300 CFST arch bridges, 86 bridges have spans over 150 m and 26 bridges are supported by arches without wind braces [1]. For the majority of CFST arches that do not possess wind braces, the ratio between their arch length (S) and their radius of gyration about the vertical axis (ky) ranges between 150 and 300. The possible implications associated with this high out-of-plane slenderness need to be accurately evaluated from a structural viewpoint.
Extensive work has been performed to date in investigating the static behaviour of CFST arches, e.g. [[2], [3], [4], [5]], their seismic response, e.g. [[6], [7], [8]], their dynamic performance, e.g. [9], [10] and their long-term service deformations, e.g. [[11], [12], [13], [14]]. For long span CFST arches, the creep and shrinkage of the core concrete can increase the instantaneous arch deflections by about 20%–30% and produce increases in instantaneous steel tube stresses in the range of 30%–50% [[11], [12], [13], [14]]. These increased variations may trigger possible instability problems in slender CFST arches if not accurately accounted for. Ma et al. highlighted that creep effects might also considerably influence the dynamic behaviour of CFST arch bridges [15], [16], [17], [18].
Creep buckling problems associated with CFST members can be conveniently grouped into two main categories [19]. In the first group, the instability is induced by the increased deformations exhibited by the composite member under high sustained loads, typical of the situations with large dead-to-live load ratios, and, in these cases, the occurrence of the instability is usually expressed in terms of the critical time before buckling takes place. For this kind of problem, the material of the member may undergo nonlinear creep due to the high levels of sustained loading. The second creep buckling category is related to situations with small dead-to-live load ratios and the failure of the member occurs due to the application of an instantaneous overload, for example induced by a large live load. In this context, the creep law of the concrete is taken as linear, and creep and shrinkage tend to increase the displaced shape of the member as well as the stress level in steel tube prior to the application of the live load.
A number of researchers have numerically investigated the first kind of creep buckling problem and developed suitable theoretical models considering CFST circular arches with pinned and fixed ends to investigate their in-plane creep buckling due to sustained loading (e.g. [20], [21], [22], [23], [24]). No research has been published to date (to the knowledge of the authors) on CFST arch bridges to investigate how the possible increase in the time-dependent deformations influences the stability of CFST arches subjected to instantaneous overload. This situation is particularly critical for long-span CFST arch bridges for which the dominant load case consists of the out-of-plane instability under earthquake load combinations because of their low width to span ratio [25], [26].
In this context, the purpose of this paper is to numerically investigate how prebuckling deformations produced by creep and shrinkage influence the out-of-plane buckling of single parabolic CFST arches (Fig. 2). As the start of a serial investigation, circular cross-section is adopted in this investigation because this is the simplest cross-sectional shape and is the foundation to develop the whole designing theory for the out-of-plane stability of CFST arches with different cross-sectional shapes, e.g. rectangular shaped, dumbbell shaped, and lattice cross-sections. In this work, the arch ends are assumed to be fixed, which is representative of typical support arrangements of real CFST arch bridges. The loads applied to these arches are uniformly distributed along their span because this is one of the representative loading cases for arches and all the other kind of loads (e.g. the single concentrated force representing a heavy vehicle) are applied on the arches combining with the uniformly distributed loading in the real application. The sustained loading is applied with the value corresponding to the quasi-permanent loading combination (including the dead load and the quasi-permanent values of live loads, e.g. the lane traffic loads) in accordance with the Chinese code JTG D62-2004 [27]. In the following, the profile of the arch is expressed by the following parabolic equation:where l denotes the span length of the arch (m), h represents the rise of the arch, x and y depict the coordinates of the nodes defined with the Cartesian coordinates shown in Fig. 2.
The numerical model is developed using ABAQUS [28] based on which a parametric study is performed to investigate the occurrence of out-of-plane creep buckling of CFST arches due to the application of the instantaneous overload. The creep and shrinkage of the core concrete are modelled using the Eurocode 2 [29] implemented using the integral-type creep law, while the material nonlinearities and the possible confinement effects for the core concrete under high stress level are modelled with constitutive equations proposed by Han [30]. These constitutive models are implemented within the ABAQUS numerical model using the user-defined UMAT subroutine. The analysis method is benchmarked against available experimental data from an out-of-plane buckling experiment of a CFST arch. Relying on the results of parametric study, a design equation is then derived based on regression techniques for possible use in routine design to enable engineers to predict the out-of-plane stability resistance of CFST arches accounting for time effects.
Section snippets
Finite element formulation
The finite element model is developed with ABAQUS [28], assuming that plane sections remain plane and that no slip or separation occurs between the steel tube and the concrete core in both long-term and buckling analyses. The concrete core and the steel tubes are modelled separately using Timoshenko beam elements (using element B31 in ABAQUS) and are specified using same discretisations in the finite element model. The full shear interaction is enforced by using the same group of nodes for the
Validation of the model
Out-of-plane buckling experiments on the 1:10 scaled CFST arch conducted by Chen et al. [43] have been adopted to evaluate the capability of the finite element model to predict the buckling behaviour of CFST arches. The scaled parabolic arch model has a span length of 7.5 m. The rise-to-span ratio is 1/5. The hollow steel tube with circular cross-section has an outer diameter of 121 mm and a thickness of 4.5 mm. Key parameters in the model formulations describing the material properties of both
Parametric studies
The proposed parametric study considered 1776 arch cases selected to covers all key parameters commonly specified in real CFST arch bridge applications that do not make use of wind braces. In particular, the rise-to-span ratios (h/l) considered for the CFST arches varied between 1/2 and 1/10 while the ratios between the arch length (S) and the radius of gyration about the vertical axis (ky) ranged between 150 and 300. The ratios of steel area over concrete area for the composite cross-section
Design approach
Since there are no available design equations from the codes to calculate the out-of-plane resistance of CFST arches, this section presents a design approach for estimating the instantaneous out-of-plane stability of CFST parabolic arches subjected to distributed loading first, and then a reduction factor is introduced into the proposed design approach to consider the influence of the prebuckling deformation induced by time effects.
Conclusions
In this paper, a finite element model has been built with ABAQUS to make it possible to account for the influence of the prebuckling deformation induced by creep and shrinkage of concrete on the stability of CFST members with circular cross-sections. In this model, the creep and shrinkage of the concrete core has been modelled with EC2 and the corresponding long-term response under varying stress state has been calculated using the step-by-step (SBS) method. The material nonlinearity and the
Acknowledgements
The research reported in the paper was supported by the National Natural Science Foundation of China (No. 51208147), the Heilongjiang Postdoctoral Financial Assistance (No. LBH-Z121070), the General Financial Grant from the China Postdoctoral Science Foundation (No. 2013M531048), the National Science and Technology Pillar Program during the twelfth Five-year Plan Period (2011BAJ09B02-03) and the contribution of the second author by the Australian Research Council's Future Fellowship funding
References (46)
- et al.
In-plane strength of concrete-filled steel tubular circular arches
J. Constr. Steel Res.
(2012) - et al.
Static analysis of cable-stayed bridge with CFT arch ribs
J. Constr. Steel Res.
(2009) - et al.
Study on steel box girder bridges partly stiffened by CFT arch ribs
J. Constr. Steel Res.
(2012) - et al.
Nonlinear seismic properties of the Second Saikai Bridge: a concrete filled tubular (CFT) arch bridge
Eng. Struct.
(2006) - et al.
Stochastic seismic analysis of a concrete-filled steel tubular (CFST) arch bridge under tridirectional multiple excitations
Eng. Struct.
(2013) - et al.
Seismic performance and collapse prevention of concrete-filled thin-walled steel tubular arches
Thin-Walled Struct.
(2014) - et al.
Dynamic analysis of a large span specially shaped hybrid girder bridge with concrete-filled steel tube arches
Eng. Struct.
(2016) - et al.
Creep influence on structural dynamic reliability
Eng. Struct.
(2015) - et al.
Long-term non-linear behaviour and buckling of shallow concrete-filled steel tubular arches
Int. J. Non Linear Mech.
(2011) - et al.
Time-dependent in-plane behaviour and buckling of concrete-filled steel tubular arches
Eng. Struct.
(2011)
Investigation into long-term behaviour and stability of concrete-filled steel tubular arches
J. Constr. Steel Res.
Finite element models for nonlinear analysis of steel–concrete composite beams with partial interaction in combined bending and shear
Finite Elem. Anal. Des.
Time-dependent behaviour of expansive concrete-filled steel tubular columns
J. Constr. Steel Res.
Application of concrete filled steel tubular arch bridges in China, tubular structures XIV—proc.
In-plane strength and design of fixed concrete-filled steel tubular parabolic arches
J. Bridg. Eng.
Dynamic analysis of a cable-stayed concrete-filled steel tube arch bridge under vehicle loading
J. Bridg. Eng.
Creep analysis of concrete filled steel tube arch bridges
Struct. Eng. Mech.
Time-dependent behaviour of concrete-filled steel tubular arch bridge
J. Bridg. Eng.
Time-dependent analysis of long-span, concrete-filled steel tubular arch bridges
J. Bridg. Eng.
Long-term analyses of concrete-filled steel tubular arches accounting for interval uncertainty, CMES
Comput. Model. Eng. Sci.
Creep effects on dynamic behaviour of concrete filled steel tube arch bridge
Struct. Eng. Mech.
Creep effects on the reliability of a concrete-filled steel tube arch bridge
J. Bridg. Eng.
Influence of creep on dynamic behavior of concrete filled steel tube arch bridges
Steel Compos. Struct.
Cited by (22)
Comparison and design of stiffened rectangular concrete-filled steel tubular members
2023, Journal of Constructional Steel ResearchTime-dependent non-linear buckling of 3D CFST arch structures with hybrid random interval uncertainties
2023, Engineering StructuresExperimental investigation of in-plane ultimate bearing capacity of parabolic high strength concrete-filled-steel-tubular arch
2023, Thin-Walled StructuresCitation Excerpt :Liu et al. [19,20] carried out an experimental investigation on 6 fixed CFST arches under mid-span or quarter-point loadings with different rise-to-span ratios. Geng et al. [21] studied the effect of pre-buckling deformation on the out-of-plane stability of CFST arches, and obtained a design model for out-of-plane creep buckling resistance. Huang [22] conducted tests on the ultimate load-carrying capacity of 4 CFST arches with different initial stress levels and, explored the influence of initial stress on the ultimate load-carrying capacity of CFST arches.
Seismic stability analysis of the large-span concrete-filled steel tube arch bridge considering the long-term effects
2022, Engineering StructuresCitation Excerpt :Previous research validated that the creep and shrinkage of concrete will lead to stress redistribution within CFST sections [28,29]. The buckling behaviour and bearing capacity of CFST arches are found to be affected by such long-term effects [30–33], and corresponding analytical models considering such long-term effect are developed as well [34–36]. Besides, the creep of the confined concrete no longer follows the linear assumption when CFSTs are at a high-stress level, and the nonlinear creep behaviour will redistributed the stress within the section and change the sectional stiffness [37,38].
Experimental and numerical study on slender concrete-filled steel tubular arches subjected to tilting loads
2022, Thin-Walled StructuresCitation Excerpt :The flexible suspenders were simulated by truss element T3D2. According to the recommendations of [10,65,66], the concrete core and steel tube elements have shared nodes to simulate the perfect bond assumption and the material properties of the concrete core and the steel tube were assigned separately. Based on the mesh sensitivity analyses, the mesh number of the concrete and the steel was selected as 60 along the arch span length.
Out-of-plane stability of concrete-filled steel tubular arches at elevated temperatures
2020, International Journal of Mechanical SciencesCitation Excerpt :Jiang and Lu [51] studied the reliability and sensitivity of the out-of-plane buckling loads of CFST arches while considering creep effects using a time-integrated approach and the finite element reliability method. Geng et al. [52] investigated the out-of-plane creep buckling behaviour of CFST arches caused by instantaneous overload. The significance of prebuckling time effects on the ultimate capacity of fixed-ended parabolic arches under uniformly distributed radial loading were analysed using FE analysis, and it was found that time effects may reduce buckling loads up to 18%.