Numerical study on I-section steel-reinforced concrete-filled steel tubes (SRCFST) under bending
Introduction
Concrete-filled steel tubes (CFSTs) have been widely used in buildings and bridges. Many researchers have investigated the structural performance of CFSTs in recent years [1]. With the wide application of CFSTs, higher requirements are put forward for the load-bearing capacity of CFST components. There are many methods for improving the load-bearing capacity of CFST members, e.g. using high-strength concrete or high-strength steel, increasing the area of the steel tubes or concrete, and using internal stiffeners. However, for large-scale structural members, it is uneconomical and unreasonable to increase the material strength and size of the structural components, because using high-strength concrete and steel usually increases the brittleness of the components, and increasing the area of the steel tubes may cause economic and fabrication problems [1]. Therefore, internal stiffening components such as shaped steel (I-section steel or crossed I-section steel), rebar, and lattice steel angles are usually embedded into the CFSTs to improve their structural behaviour without using expensive materials or increasing the cross-sectional area of the components [2], [3], [4], [5], [6], [7]. CFST members with internal stiffening parts are called steel-reinforced CFSTs (SRCFST), and several commonly used configurations of the cross section of SRCFST members are shown in Fig. 1 [8].
Studies on CFST members with inner stiffening parts mostly focused on their compressive behaviour, and the section types of Fig. 1(a)–(d) have been investigated. For example, Qi et al. [2] performed an experimental study on the axial compressive behaviour of CFST specimens with the section type illustrated in Fig. 1(a), and test results indicated that SRCFST stub columns exhibited a higher axial load capacity than steel-reinforced concrete columns with the same steel ratio. Wang et al. [3] conducted a series of tests on the axial compressive properties of specimens with the section type of Fig. 1(b), and the results indicated that the inner stiffening parts enhanced the strength, ductility, and energy absorption of the CFSTs. Cai et al. [4] performed a numerical investigation of the axial compressive behaviour of specimens with the section type of Fig. 1(b), and the results indicated that the composite effect between the CFSTs and the inner stiffening parts significantly affected the axial compressive behaviour. Liu et al. [5] investigated the axial compressive behaviour of specimens with the section type of Fig. 1(c) and found that the height-to-diameter ratio of the steel tubes hardly affected the failure mode and axial load strength of SRCFST stub columns. Xu et al. [6], [7] performed experimental and parametric analyses of the axial compressive behaviour of specimens with the section type of Fig. 1(d). The results indicated that the lattice steel angles could significantly enhance the strength of the CFSTs and were helpful for resisting the diagonal cracking of the core concrete. The previous studies on the axial compressive behaviour of SRCFST members (i.e. CFST members with shaped steel, rebar, and lattice steel angles infilled) have proven that embedded shaped steel, rebar, or lattice steel angles can improve the load-bearing capacity and stiffness of the members under axial compression. Additionally, the use of inner stiffeners can delay the evolution of shear diagonal cracks in the core concrete.
In recent years, the flexural behaviours of CFSTs and concrete-filled double steel skin tubes (CFDSTs) have been investigated by Han et al. [9], [10], [11] and Tao et al. [12], and the corresponding design equations for CFSTs and CFDSTs were proposed according to the unified strength theory. Lu et al. [13] and Moon et al. [14] investigated the flexural performance of CFSTs via finite-element (FE) analysis. The composite action between the steel tube and the concrete and the confinement effect were analysed. Roeder et al. [15] investigated the flexural strength and stiffness of circular CFSTs and proposed a new stiffness expression based on the collected experimental data. Denavit et al. [16] studied the elastic flexural rigidity of CFST columns through a broad parametric study and presented practical design recommendations for the elastic flexural rigidity. The flexural behaviours of SRCFSTs have been investigated by several researchers; for example, Shi et al. [17] investigated the mechanical performance of SRCFST beams with the sections of Fig. 1(a) and (b) that were subjected to four-point bending loads and proposed a simplified formula for predicting the flexural strength. Their results indicated that the specimens underwent flexural failure instead of local buckling and that the steel tube carried most of the bending moment. Wang et al. [18] investigated the flexural performance of square-tubed SRCFST beams with shear studs welded on the flange of I-section steel. The test results indicated that the shear studs were not effective for enhancing the flexural stiffness, and a simplified design equation for the flexural strength of square-tubed SRCFST beams was derived. Moon et al. [19] used the plastic-stress distribution method proposed by AISC (2010) to determine the flexural strength of SRCFST beams with the section of Fig. 1(c), and the results indicated that the AISC (2010) provision can provide a reasonable prediction of the flexural capacity. As indicated by the previous research results, the existing design equations for the flexural strength of SRCFSTs are mainly based on the superposition of the flexural strength of CFSTs and the flexural strength of the inner steel section corresponding to design provisions. Thus, the present paper proposes a new design formula for the flexural strength of SRCFSTs that considers the structural steel index and the enhancement effect of the inner steel section, according to a comprehensive parametric analysis. First, the flexural behaviour of SRCFST members with internal I-section steel, as shown in Fig. 1(a), was numerically investigated using an FE model validated by the experimental results of Liu et al. [20], Zha et al. [21], and Shi et al. [17]. Second, a parametric analysis was performed using the validated FE model to investigate the effects of parameters such as the area of the I-section steel, yield strength of the outer steel tubes and I-section steel, concrete strength, and thickness of the outer steel tubes on the moment vs. midspan deflection curves and the flexural strength. Finally, design equations for determining the flexural strength of the SRCFST members with internal I-section steel were derived, and predictions based on the design equations were compared with the simulation results.
Section snippets
Experimental data from literature
The experimental flexural behaviours of SRCFST members with internal I-section steel (shown in Fig. 1(a)) were investigated by Liu et al. [20], Zha et al. [21], and Shi et al. [17]. Liu et al. [20] performed three-point bending tests on such specimens, where the I-section steel was placed along the strong and weak axes. Zha et al. [21] performed four-point bending tests, where the I-section steel was placed along the strong axis. Shi et al. [17] performed four-point bending tests, where the
Moment–deflection relationship
The flexural behaviours of SRCFST members with internal I-section steel subjected to four-point bending were analysed for better understanding its structural performance. The typical specimen G-3 (dimensions and material strengths of G-3 are presented in Table 1) and the corresponding CFST specimen (pure CFST specimen without I-section steel; dimensions and material strengths were consistent with specimen G-3) were analysed.
Fig. 9 presents the typical moment vs. midspan deflection curves for
Parametric analysis
The effects of important parameters, including the area of the I-section steel (Asi), yield strength of the outer steel tubes (fyo), yield strength of the I-section steel (fyi), concrete strength (fc'), and the thickness of the outer steel tubes (to), on the moment vs. midspan deflection curves and the flexural strength were analysed and are discussed in this section.
The specimens used for the parametric analysis were labelled according to their types. For example, “SRCFST-I16” indicates an
Discussion of parametric-analysis results
According to the foregoing parametric-analysis results, the dominant parameters affecting the flexural strength of the specimens include the thickness of the outer steel tubes, the yield strength of the outer steel tubes, and the area of the I-section steel. Hence, design equations for the flexural strength of SRCFST specimens should consider these parameters.
The thickness and yield strength of the outer steel tubes reflect the geometric and material characteristics of the outer steel tubes.
Conclusions
The flexural behaviour of SRCFST specimens with internal I-section steel was investigated, and the following conclusions are drawn.
- (1)
Comprehensive FE modelling of SRCFST specimens was performed to replicate experimental results. The FE models were validated through comparisons with test results from the perspectives of the moment vs. midspan deflection curves, moment vs. curvature curves, moment vs. ultimate tensile strain curves, and flexural strength. The comparisons revealed that the flexural
CRediT authorship contribution statement
Jun Wang: Conceptualization, Methodology, Software, Validation, Writing - original draft, Writing - review & editing. Xianfeng Cheng: Data curation, Software. Libo Yan: Methodology, Visualization. Chao Wu: Supervision, Writing - original draft, Writing - review & editing, Resources, Project administration, Funding acquisition.
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.
Acknowledgement
This work was supported by the National Natural Science Foundation of China [grant numbers 51908016, 51978025, and 51911530208].
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