Keywords

1 Introduction

The composite columns, such as CFST(concrete filled steel tube) column and CFFT(concrete filled FRP tube), have been studied and widely applied in engineering. However, the composite column mentioned above seemly cannot satisfied the load bearing requirement, due to their respective shortcomings.

Recently, many studies focused on the new composite column with double wall, called DSTC (Double-skin tubular column). Two sectional forms are common: ISFTC (Inner steel FRP tubular column) and IFSTC (Inner FRP steel tubular column), as shown in Fig. 1.

Many researches focus on the ISFTC, the relative studies show that, comparing to hollow DSTC, the ISFTC present more axial bearing capacity but less ductility [1, 2]. The steel pipes between the concrete have already yielded, while the core concrete has almost no damage, which is related to the loading method [3]. The thinner the inter-layer, the better the coordinated working performance of the steel pipe concrete and FRP pipe. The research was subsequently verified by finite element analysis [4]. Many other scholars attempted to built IFSTC [5]. The specimen will not be damaged due to the brittle failure of the FRP pipe during the loading process, which is beneficial for improving the ductility of the component [6]. The ductility of this component is closely related to the inner FRP material, and the effect is better for materials with high fracture strain [7, 8].

Fig. 1.
figure 1

Section of DSTC

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The unified theory of computation for the bearing capacity of composite columns has not been formed in the current research to determine the optimal combination scheme. In this research, the finite element analysis was carried out to study the mechanical mechanism of composite column. The method to determine optimization scheme was proposed.

2 Database

Many literature focus on the compressive performance of two type composite column, ISFTC and IFSTC. The experimental database is composed of available data of some specimens in Table 1.

Table 1. Collection of specimens in literature
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3 Finite Element Analysis

3.1 Establishing of Finite Element Model

In the three-dimensional finite element models of two types of composite columns, the concrete are simulated using 8-node reduced integral solid element (C3D8R), while the steel pipe and FRP material are simulated using 4-node reduced integral membrane element (M3D4R). In the model, binding connections are used between FRP and concrete, and contact elements are used between steel pipes and concrete as shown in Fig. 2.

The ideal elasto-plastic model is used in the finite element simulation. The stress-strain of FRP is linear before fracture. The plastic damage model was used in simulation concrete, the tensile and compressed constitutive relationship using GB50010-2010 [9] model.

Fig. 2.
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Finite element model of specimen

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3.2 Validation of Model

The validation of finite element model was verified by test results in database. As seen in Fig. 3 and Fig. 4, the curves made by finite element analysis were all agree with the experimental results. It is obvious that the finite element model used in this study is effective.

The Influence of Concrete Strength Ratio of Inner and External Tube

As shown in Fig. 5a, fcin and fcex means the compressive strength of concrete in inner tube and external tube. It can be concluded that the larger difference of concrete strength, the higher bearing capacity of specimen. The axial compressive bearing capacity is improving the strength of inner tube.

Fig. 3.
figure 3

Load-displacement comparison

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Fig. 4.
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Load-lateral strain comparison

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The Influence of Constrain Ratio of Inner and External Tube

Figure 5b is the specimen with different constrain ratio, changed by inner tube, and Fig. 5c is the specimen with different constrain ratio, changed by external tube. In Fig. 5b, flin and flex means the constrain ratio of inner and external tube, respectively. It is obvious that with the constrain effect of inner tube and external tube increasing, the bearing capacity of specimen all increased. However, the extend of increment is different, the constrain effect increasing of external tube have more obvious effect.

Fig. 5.
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Analysis of effect factors

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4 Optimization Calculation of Cross Section of Composite Columns

For confined concrete materials, the octahedron double shear mechanical model is represented by cohesion \(c\) and internal friction angle \(\varphi \). According to the molar strength theory, the double shear strength can be expressed as [10]:

$$ f_{cc} = f_c + k\sigma_{rc} $$
(1)

wherein, \(f_c = \frac{2c\cos \varphi }{{1 - \sin \varphi }},k = \frac{1 + \sin \varphi }{{1 - \sin \varphi }},\sigma_{rc}\) is the lateral pressure. The bearing capacity of IFSTC composite columns can be calculated by the following equation:

$$ \begin{array}{*{20}c} {N = (f_c + k\frac{2t_1 \sigma_f }{{d_1 }})(d_1^2 - d_2^2 )\frac{\pi }{4} + \sigma_s \pi t_2 d_2 } \\ { + [f_c + k(\frac{2t_1 \sigma_f }{{d_1 }} + \frac{2t_2 \sigma_s }{{d_2 }})]\frac{\pi }{4}(d_2 - 2t_2 )^2 } \\ \end{array} $$
(2)

It can be seen that the essence of the strength improvement of IFSTC and ISFTC is all the result of the inner and outer double layer constraint effect. However, for IFSTC composite columns, there is no significant damage in the core FRP tube, and the ultimate state of the inner and outer tubes is different. Therefore, it is necessary to reduce the inner tube sub items when calculate the bearing capacity. As shown in equation:

$$ \begin{array}{*{20}c} {N_u = (f_{cex} + k\frac{{2t_{ex} \sigma_{ex} }}{{d_{ex} }})(d_{ex}^2 - d_{in}^2 )\frac{\pi }{4} + \sigma_s \pi t_s d_s } \\ { + \alpha [f_{cin} + k(\frac{{2t_{ex} \sigma_{ex} }}{{d_{ex} }} + \frac{{2t_{in} \sigma_{in} }}{{d_{in} }})]\frac{\pi }{4}(d_{in} - 2t_{in} )^2 } \\ \end{array} $$
(3)

In the formula, \(-ex\) represents the outer pipe, \(-in\) represents the inner pipe, and \(-s\) represents the steel pipe parameters, \(\alpha \) Is the reduction coefficient, \(k\) is the constraint coefficient, taken as 2.26. Based on the numerical analysis, for IFSTC composite columns with steel pipes as the inner tube, \(\alpha \) Taking 1.0, for ISFTC composite columns, \(\alpha \) Take 1.9. The collected specimens were used for verification calculations, and the comparison between the calculation results and the experimental results is shown in Fig. 6. As shown in the figure, the calculated results are in good agreement with the experimental results. The bearing capacity of the columns can be calculated using Eq. (3), and the optimal diameter selection for the inner tube can be calculated using Eq. (4):

Fig. 6.
figure 6

Comparing of calculated and experimental results

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Order

$$ \frac{dN_u }{{dd_{in} }} = 0 $$
(4)

The optimal arrangement of the inner diameter \({d}_{in}\) and outer diameter \({d}_{ex}\) of the combined column satisfies the following equation:

$$ d_{in}^3 - pd_{in}^2 - q = 0 $$
(5)
$$ p = \frac{{16f_{cin} t_{in} d_{ex} + 32kt_{ex} \sigma_{ex} t_{in} - 8kt_{in} \sigma_{in} d_{ex} - \sigma_s \pi^2 t_s d_{ex} }}{{8f_{cin} d_{ex} + 16kt_{ex} \sigma_{ex} - 8f_{cex} d_{ex} - 16kt_{ex} \sigma_{ex} }} $$
(6)
$$ q = \frac{{4kt_{in}^3 \sigma_{in} d_{ex} }}{{f_{cin} d_{ex} + 2kt_{ex} \sigma_{ex} - f_{cex} d_{ex} - 2kt_{ex} \sigma_{ex} }} $$
(7)
figure a

Configure the inner pipe diameter according to din to obtain the maximum axial compression bearing capacity of the combined column.

5 Conclusion

  1. (1)

    The axial compressive bearing capacity of DSTC is improving mainly with the concrete strength of inner tube.

  2. (2)

    The constrain effect increasing of external tube have more obvious effect.

  3. (3)

    The bearing of composite column can be understood as the effect of internal and external double-layer constraints. The optimal combination method for the cross-section of the composite composite column is proposed, and formulas (4)–(9) can provide reference for the engineering design of the composite column.