Analytical behaviour of concrete-encased CFST box stub columns under axial compression

Concrete-encased CFST (concrete-filled steel tube) members have been widely used in high-rise buildings and bridge structures. In this paper, the axial performance of a typical concrete-encased CFST box member with inner CFST and outer reinforced concrete (RC) is investigated. A finite element analysis (FEA) model is established to analyze the compressive behavior of the composite member. The material nonlinearity and the interaction between concrete and steel tube are considered. A good agreement is achieved between the measured and predicted results in terms of the failure mode and the loaddeformation relation. The verified FEA model is then used to conduct the full range analysis on the load versus deformation relations. The loading distributions of different components inclouding concrete, steel tube and longitudinal bar during four stages are discussed. Typical failure modes, internal force distribution, stress development and the contact stress between concrete and steel tube are also presented. The parametric study on the compressive behavior is conducted to investigate the effects of various parameters, e.g. the strength of concrete and steel, longitudinal bar ratio and stirrup space on the sectional capacity and the ductility of the concrete-encased CSFT box member.


Introduction
Concrete-encased concrete-filled steel tube (CFST) is a steel-concrete composite member.Fig. 1(a) shows a schematic view of the cross section of this composite member, which consists of inner CFST component and outer reinforced concrete (RC) component.Compared to traditional steel columns and RC columns, the concrete-encased CFST columns have higher bearing capacity and better fire resistance due to the existence of outer concrete.Reinforced concrete (RC) box members have been widely used in bridges due to the large stiffness of bending and torsion [1].As shown in Fig. 1(b), RC box columns generally have inner and outer stirrup to meet the requirements of ductility.
As shown in Fig. 1(c), the concrete-encased CFST box members are developed in order to take the advantages of concrete-encased CFST columns and RC box columns, which have CFST component in the webs and corners of the RC box component.Fig. 1(d) shows a schematic view of an arch bridge with the concrete-encased CFST box arch ribs in Sichuan Province.The strength of core concrete is generally stronger than that of outer concrete.Some previous research has been done on concrete-encased CFST columns (e.g.[2][3][4]) and RC box columns (e.g.[1,5,6]).An et al. [7] have analyzed the performance of concrete-encased CFST box column which only has CFST in the corners of the cross section.This paper establishes a finite element analysis (FEA) model of concrete-encased CFST box stub column under axial compression.After verified by the test results, the model is used to analysis the complete load-deformation curves and interactions between steel and concrete.A parametric study is also carried out for the influence of ultimate load and ductility.

Finite element analysis (FEA) model
The ABAQUS/Standard module [8] is used to develop the FEA model of concrete-encased CFST box stub column under axial compression as shown in Fig. 2. The FEA model consists of steel tubes, concrete, longitudinal bars, stirrups and end plates.Considering the different confinement, the concrete can be divided as four regions: core concrete inside the steel tube, confined concrete in the corner, confined concrete in the web wall and unconfined concrete outside the stirrup.

Steel
Constitutive laws of steel tubes and bars are modeled through distinct non-linear material 2018, Universitat Politècnica de València models.A five-stage stress-strain model suggested by Han et al. [9] is applied for steel tube.A bi-linear model considering strain hardening effect adopted by Zhao et al. [10] is used for the uniaxial stress-strain curves of the rebar.The elastic modulus and Poisson's ratio of the steel are consistently defined as 206,000 N/mm2 and 0.3, respectively.

Concrete
The damage plasticity model is utilized for the concrete.The elastic modulus of concrete is ' 4730 c f as presented in ACI 38-11 [11], in which ' c f represents the compressive strength of concrete cylinder.The Poisson's ratio of concrete is taken as 0.2.As shown in Fig. 3, the concrete can be divided into four regions, namely core concrete inside the steel tube, confined concrete in the corner, confined concrete in the web wall and unconfined concrete outside the stirrup.Different stress-strain relations are applied depending on regions.For the core concrete in the tube, the model suggested by Han et al. [12] is adopted to represent the uniaxial stress-strain relation as shown in Fig. 4. A model of unconfined concrete provided by Attard and Setunge [13] is referred for the uniaxial stressstrain relation of unconfined concrete outside the stirrup.Fig. 4 also gives the stress-strain curves of the confined concrete in the corner and the web wall.Detailed description can be found in An et al. [7].The length B cx and B cy are illustrated in Fig. 3.
For concrete in tension, the work done by Spacone et al. [14] is referred for the stress-strain relation of concrete in tension.The cracking to Model Code 2010 [15].

Element type, mesh and boundary conditions and interface model
Eight-node-3-D solid element with reduced integration is utilized for the concrete components and end plates.The steel tubes are simulated by four-node conventional shell element.However, eight-node-3-D solid element is adopted for steel tubes with the sizes of 12×2mm and 20×2mm because similar results are achieved when using either the solid element or the shell element [16].The steel rebars are simulated by two-node truss elements.
Different mesh sizes are attempted to achieve the balance between accuracy and efficiency for calculation.The stiffness of end plates are assumed to be so large that the deformation can be neglected during the whole load stage.The load is simulated by applying displacement on one end plate along the column, while the displacement and rotation of the other end plate are restricted.
The rebar elements are embedded in the out concrete to restrict the degrees of freedom at the rebar node.In order to ensure the displacement and rotation of the interface remain consistent, "Tie" is utilized for the contact between steel tube and the end plate and the contact between concrete and the end plate.The contact between steel tube and concrete is simulated by the "Hard contact" model in the normal direction and the Mohr-Coulomb friction model in the tangential direction.Frictional coefficient of 0.6 suggested by Han and An [4] is used in this study.

Verification
Four concrete-encased CFST box stub columns tested by the authors are adopted to verify the FEA model above.Table 1 summarizes the geometric dimensions of all specimens.Fig. 5 shows the comparison of predicted and measured load (N) versus longitudinal strain () relations.The mean value

2018, Universitat Politècnica de València
Typical failure modes from finite element simulations are compared with those from tests and the comparisons are presented in Fig. 6.It can be found that the outer concrete is crushed and bulged outward in the middle of the specimen.Bending deflection is observed in the inner CFST component, while the core concrete maintains intact due to the confinement of steel tube.

Analysis of complete load-deformation curves
A typical concrete-encased CFST box stub column with the section shown as Fig. 2(a) is designed to investigate the axial behavior.The sectional width B, height H and length L are 120 mm, 160 mm and 900 mm, respectively.The width B h , and the height H h of hollow section are 24 mm and 76 mm, respectively.The diameter and the wall thickness of the steel tube D are 12 mm and 2.1 mm, respectively.The material properties are as follows: f cu,core =101 N/mm 2 , f cu,out =59 N/mm 2 , f ys =527 N/mm 2 , f yl =383 N/mm 2 , longitudinal bar ratio  l =1.1%, diameter and space of stirrup are 4 mm and 50 mm, respectively.The thickness of concrete cover is 5 mm.

Interactions between steel and concrete
The out concrete is confined by stirrup in the composite column.Fig. 8  The confinements to steel tubes are provided by both core concrete and encased concrete.Fig. 9 (a) shows the interaction stresses between steel tubes and core concrete (p 1 ) while Fig. 9 (b) shows the interaction stresses between steel tubes and out concrete (p 2 ).When  is less than 1600 , p 1 remains zero because the Poisson's ratio of steel tube is larger than that of core concrete in elastic stage and the lateral expansion of steel tube is larger than that of core concrete.
When  is larger than 1600 , p 1 appears for the reason that the expansion of core concrete is larger than that of steel tube after concrete come into plastic stage.The longitudinal stress of core concrete is higher than that of unconfined concrete at Point C due to the existence of p 1 .
When  is smaller than 1600 , p 2 appears because the lateral expansion of steel tube is larger than that of out concrete.However p 2 is zero when  is larger than 1600  because the lateral expansion of encased concrete is larger than that of steel tube.When  reaches 4000 ,

Parametric analysis
The influence on the axial load (N) versus the longitudinal strain () relation of various parameters is analyzed.The parameters are as follows: out concrete strength f cu,out =40-60 N/mm 2 , longitudinal bar ratio  l =0.5%-1.5%,yield stress of longitudinal bar f yl =235-400N/mm 2 , space of stirrup s=50-100mm, core concrete strength f cu,core =60-100N/mm 2 and yield stress of steel tube f ys =235-420N/mm 2 .Fig. 10 gives the effect of different parameters on N - relations.
(1) Out concrete strength (f cu,out ): As shown in Fig. 10(a), the peak load N u increases as f cu,out increases, but the ductility decreases due to the confinement provided by the stirrup.
(2) Longitudinal bar ratio ( l ): It can be seen that N u increases slightly as  l increases in Fig. 10(b).The effect of  l on ductility is not

Conclusions
Based on the study in this paper, the following conclusions can be drawn: (1) A FEA model of concrete-encased CFST box stub column under axial compression is established.Considering the difference of confinement, the concrete regions are divided as core concrete within the steel tube, confined concrete in the corner, confined concrete in the web wall and unconfined concrete outside the stirrup.A good agreement is achieved between the predicted and measured results.
(2) The axial load (N) versus longitudinal strain () relation can be divided as four stages.The unconfined concrete outside the stirrup, confined concrete in the web wall and confined concrete in the corner reaches their ultimate loads while the axial load N reaches N u .
(3) The influence of different parameters on the peak load and ductility of the concreteencased CFST box stub column is discussed.

Fig. 1 .
Fig. 1.A schematic view of typical cross section.
Concrete-encased CFST box column.(a) Concrete-encased CFST column.A typical arch bridge with concrete-encased CFST box arch ribs in Sichuan Province.Concrete-encased CFST box arch ribs (a) Cross section.y =d z =0 r x =r y =r z =0 End plate Axial load, d x =d y =0 (b) Schematic view.

Fig. 3 .
Fig. 3.A schematic view of concrete regions in the concrete-encased CFST box section.
concrete in the web wall B cx B cy unconfined concrete outside the stirrup confined concrete in the corner core concrete inside the tube confined concrete in the web wall c c0 εc0 O εcand the standard deviation of N uc /N ue (where N uc and N ue are the calculated and measured ultimate loads, respectively) are 0.948 and 0.035, respectively.It can be seen that a good agreement is achieved between the predicted and experimental results.

Fig. 7 Fig. 7 .
Fig. 7 gives the calculated axial load (N) versus axial strain () relation of the concreteencased CFST box column.The N- response of different components including core concrete of CFST, confined concrete, unconfined concrete, steel tube and longitudinal bar are also shown in the Fig. 7. Four characteristic points are marked in the curve.At point A, the longitudinal bars begin yielding; at point B, the unconfined concrete reaches the ultimate strength; at point C, the column reaches the ultimate load (N u ); at point D, the load fails to 85% of N u .