Cyclic Behavior of Square CFST Columns-Based Joint

. This paper investigates the cyclic behavior of six square concrete-ﬁ lled steel tube (CFST) columns that take the effect of width – thickness ratio ( D / t = 30, 40, and 60), slenderness ratio ( λ = 19.63 and 24.25), and axial force ratio ( n = 0.6, 0.4, and 0.2) into consideration. The failure modes, hysteretic behavior, energy dissipation capacities, stiffness degradation, and ductility of these specimens have been discussed and studied. The results revealed that a bigger D / t could reduce the energy dissipation capacities and bearing capacities of the columns. With increasing λ , the energy dissipation capacities and bearing capacities of columns reduced, and the stiffness deteriorated rapidly. The axial force ratio could enhance the bearing capacities but weaken their energy dissipation capacities and stiffness. Calculation formulae for ultimate moment strength of square CFST columns were exhibited to compare to the test results.

Researchers carried out experimental and numerical studies to investigate the bearing capacities of square CFST columns, they obtained great achievements.Ding et al. [4,5] performed axial compression tests for eight square CFST end columns.They found that high-steel strength improved the bearing capacity of columns.Lee et al. [6] found that highconcrete compression strength increased the bending capacity and stiffness of the square CFST columns.Evirgen et al. [7] executed axial compression experiments of square CFST stub columns under different width-thickness ratios (D/t, range: 50-100).They reported that the D/t was the key to affect the confining effect between steel tubes and infill concrete.And a smaller width-thickness ratio could intensify the columns bearing capability.Yang et al. [8] investigated axial compression tests on square CFST columns.They found that a smaller width-thickness ratio could delay postpeak strength degradation.Parameter analysis was also conducted by the finite element models with different finite element analysis software.
Ayough et al. [9] studied the axial compression behavior of CFST columns with ABAQUS.The results showed that high steel and concrete strength could significantly enhance the bearing capacities of CFST columns.Qasim [10] investigated CFST columns' axial compression performance by ANSYS.They found that the ultimate bearing capacity increased by 15.0% with decreasing D/t (range: 25-30).Qian and Jiang [11] developed a design approach for assessing axial bearing capacities of CFST composite columns.According to the unified strength theory, Yang et al. [8] proposed a formula to evaluate the bearing capacities of CFST columns with concrete strength from 70 to 150 MPa.Ke et al. [12] calculated and compared the bearing capacities of square CFST columns through unified strength and superposition theories.They found that calculation results by unified strength theory were more accurate.It indicated that material strength and width-thickness ratio were the main factors affecting the square CFST columns.
The cyclic behavior of CFST columns was also studied.Zhang and Gao [13] tested six square CFST columns under cyclic loading.The results showed that a smaller D/t could enhance the energy dissipation capacity, initial stiffness, and bearing capability of the CFST column.Silva et al. [14] carried out cyclic loading tests of square CFST columns, they found that the columns with smaller slenderness ratios had stronger energy dissipation capacity and bearing capability.Wang et al. [15] investigated the seismic performance on CFST columns connected to binding bars under the cyclic loadings and axial compression.They reported that a big axial force ratio could elevate the peak bearing capability and initial stiffness while weakening the energy dissipation capacity of the specimens.Chen et al. [16] tested six square CFST columns under cyclic loadings.They indicated that the high-axial force ratio increased the bearing capacity but accelerated the stiffness degradation.Parameter analysis were also conducted by the finite element analysis softwares.Zhou et al. [17] studied the seismic behavior of CFST columns by ABAQUS.The results revealed that the bearing capability of columns increased by 41%, and the ductility coefficient decreased by 30% with decreasing D/t (range: 58-100).Xu et al. [18] proposed the numerical model of square CFST columns with SeismoStruct.The parameter analysis showed that the specimen's ultimate bearing capacity improved and the ductility coefficient reduced with increasing steel strength.The cyclic behavior of square CFST columns with stiffeners was studied by Han et al. [19].They proposed an equation to calculate the flexural capacity of columns considering the influence of the stiffeners.Based on the superposition theory and limit equilibrium theory, Ke et al. [20] proposed the estimation approach to assess the compressing-bending capacity of square CFST composite columns.Additionally, different configurations of column-based joints were also reported.The seismic performance of the proposed CFST column base joints was investigated by Mou et al. [21].They found that axial force played a key role in improving the joints' flexural capacity.A special kind of exposed square CFST column base was presented by Qiao et al. [22].They investigated the seismic performance of the bases and presented a calculating method to predict the interaction curve of bending moment versus axial force at the ultimate state.
The paper investigates the seismic behavior of square CFST columns.Six CFST columns were examined by the axial constant and horizontal cyclic loadings tests to systematically analyze the effects of three parameters (λ, D/t, and n).The failure modes, hysteresis performance, energy dissipation capacities, stiffness degradation, and ductility of specimens were discussed and analyzed.A calculating approach for evaluating ultimate flexural strength of the square CFST column was also proposed.
where D and L are the width and height of columns; N is the axial force on the column top exerted through the oil jack; f y and A s are the yield stress and cross-section area of a square steel tube, respectively; f c and A c are compressive strengths and cross-section area of the infilled concrete, separately.Figure 1(a) shows the details of specimen No. 1 with height of 2,400 mm.The cross-sectional dimensions of a steel tube were 300 × 300 × 5 mm (length × width × thickness), while the steel plate fixed at the steel tube bottom was 700 × 500 × 20 mm (length × width × thickness) (Figure 1(b)).The RC foundation was 1,400 × 700 × 700 mm (length × width × thickness) (Figure 1(c)).

Steel Properties.
The steel tubes' mechanical properties were obtained from the coupon tests on standard specimens (Figure 2), according to the Standard GB/T 228.1-2010 [23].The stress-strain relationship of the steel part is exhibited in Figure 3(a).Table 2 shows the steel properties, such as E s (Young's modulus), f y (yield stress), and f t (tensile stress).The same concrete was used for the columns and foundations.Six concrete cubic specimens were tested in the reference to Standard GB/T 50081-2019 [24].Figure 3(b) shows the stress-strain relationship of the concrete.Its corresponding axial compressive strength ( f c ) equaled 23.3 MPa. 4 exhibits the test apparatus of square CFST columns.The RC foundation was fixed by pressure beams and anchor rods.An oil jack connected with a girder imposed the constant axial loading through sliding support.A 500 kN actuator applied the horizontal cyclic loadings to the column end.The horizontal cyclic loading was conducted by the combined force-displacement controlling program [25] (Figure 5).P y and △ y are the yield load and yield displacement.The column end pushed south was identified as the negative direction, and the other column end pulled north as the positive direction.The testing process was load control initially and the load was applied with the amplitude of 1/3 P y , 2/3 P y , and P y step by step.Each loading level was cycled once.When the column yielded, the lateral load would be changed to a displacementcontrolled program with an increment of △ y .Each loading level    Advances in Civil Engineering was cycled twice.The loading process would be stopped until the lateral loadings reduced to 85% of the maximum loading.

Test Apparatus. Figure
2.4.Measurements.The strain of steel tubes was recorded by strain gauges (Figure 6).Three strain rosettes were pasted on the column in the east direction (S e ), 20, 150, and 300 mm far away from the RC surface, respectively.A strain rosette was stuck on the column in the west direction (S w ), 150 mm far away from the RC surface.Six strain gauges were stuck on the column in the north (S n ) and south (S s ) directions, respectively.The displacement and load information could be measured through the transducer in the actuator and checked by the transducer set at the column end (Figure 6(b)).

Result Analysis
3.1.Experimental Phenomenon.The failure modes of the six square CFST column specimens were similar (Figure 7).The failure of the six columns showed a compression-flexure failure mode.Table 3 lists the failure phenomenons in the tested process.The tested columns had no obvious change in the initial loading stage.After the yield point, the slight local buckling appeared on the north and south bottom of the steel tube successively.It was due to the compression and expansion of the infilled concrete during loading.As the lateral load increased, the local buckling became gradually severe.
In addition, the local buckling also appeared on the east and west bottom of the steel tube.The lateral support devices in the test were not set, some specimens were stopped loading due to serious eccentric compression.The phenomenon of steel tube buckling in Specimen No. 5 occurred later than the other specimens.A higher axial compression ratio could alleviate the buckling of the steel tube.The weld cracking occurred at the steel tube corners of specimens No. 4 and No.5 (Figure 7(h) and 7(j)).

Hysteretic Performance.
The relationships between the loading (P) and displacement (△) were illustrated in Figure 8.
The maximum loading force (P max ) of all specimens appeared in the second loading level of the displacementcontrol program and was represented by the solid points in the figure.
As the width-thickness ratio (D/t) decreased, the P max of Specimen No. 6 and No. 2 were increased by 31.8% and 60.0%, separately.In comparison to Specimen No. 1, the P max of No. 6 was 32.5% higher than that of Specimen No. 3 due to the decrease in slenderness ratio (λ).Compared to Specimen No. 4, the P max of Specimen No. 6 and No. 5 was increased by 9.9% and 12.1%, respectively.A larger axial compression ratio (n) showed a significant function in improving P max of the square CFST columns.

Skeleton Curve and Main Performance
Points.The skeleton diagrams of tested specimens with various parameters (D/t, λ, and n) are performed (Figure 9(a-c)), and the slope factor method (Figure 10) [21] was employed to determine the plastic and yield points.Table 4 lists the main performance points of the six specimens.As the width-thickness ratio decreased, the P y and P p of Specimen No. 1, No. 6, and No. 2 increased gradually.Compared with Specimen No. 3 and No. 6, a small slenderness ratio could improve the P y and P p of the square CFST columns.In Specimen No. 4-No.6, the n has a limited impact on the P y and P p of the columns.

Stiffness Degradation.
Stiffness degradation coefficient (K j ) can be calculated by Equation (3) as follows: where P i,j is the peak loading force on the i-th hysteretic loop at the j-th phase; △ i,j is the displacement corresponding to P i,j ,; N c is the amount of cycles.Figure 11 demonstrates the stiffness degradation in six specimens.When △ was smaller than 15 mm, the stiffness of each specimen had almost no degradation.The stiffness of Advances in Civil Engineering specimens decreased rapidly during the △ = 15-50 mm, and degraded slowly after △ = 50 mm.In attention, the stiffness of each specimen was different during the initial phase under two opposite directions.With increased load, the stiffness of each specimen under two loading directions degraded to the same level.Table 5 lists the stiffness of specimens at the key performance points, the ratio of the stiffness between peak and    8

Advances in Civil Engineering
Advances in Civil Engineering yield point (K m /K y ), and the ratio of the stiffness between plastic and yield point (K p /K y ).The K p /K y ranged from 0.68 to 0.91.The K m /K y ranged from 0.37 to 0.85.

Ductility and Energy Dissipation Capacity.
Energy dissipation (E) in each cycle and accumulated energy dissipation (E a ) of each square CFST column are both exhibited in Figure 12.
When △ was less than 20 mm, six specimens were in the elastic deformation phase.After △ = 20 mm, the energy dissipation increased gradually.With the width-thickness ratio decreased, the energy dissipation capacities in columns No. 1, No. 6, and No. 2 improved gradually.Compared with Specimen No. 3 and No. 6, a small slenderness ratio could improve the energy dissipation capacities.Among No. 4-No.6, the cumulative energy dissipation of No. 5 was the lowest, and No. 4 dissipated the most energy.It indicates that reducing the axial compression ratio could improve the energy consumption capacities.
The equivalent viscous damping coefficient (ξ eq ) is assessed by Equation (4). Figure 13(a) shows the calculation diagram.
where S ABCD represents the cycle area on the hysteresis curves; S OBF and S ODE represent the area of triangles OBF and ODE, separately.With the displacement increasing, the coefficient ξ eq generally increased (Figure 13(b)).The ξ eq corresponding to the plastic point (ξ eq,p ), yield point (ξ eq,y ), and ultimate point (ξ eq,u ) are exhibited in Table 6.Coefficients ξ eq,y , ξ eq,p , and ξ eq,u were in a range of 0.078-0.131,0.084-0.159,and 0.321-0.384,respectively.
where △ y and △ μ represent the yield and ultimate displacement, separately.The ultimate moment strength of square CFST columns was assessed according to the limit equilibrium theory.The section of CFST columns is composed of the concrete portion and steel tube.The full section yield criterion was adopted.While, the tensile contribution of concrete was ignored.The ultimate bending strength is defined in Figure 14.
where A si ʹ and f yi ʹ represent the area and yield strength of the i-th compressed steel plate, separately; A si and f yi represent the area and yield strength of the j-th tensile steel plate, separately; r i and r j represent spacing between the i-th compressed steel plate and the j-th tensile steel plate to the centroid axis, respectively; x n the height of the concrete compression area.

Results
Comparison.The N-M interaction curves of six columns are exhibited in Figure 15.Table 8 compares their maximum moments obtained by calculation (M max,C ) and test (M max,T ).The ratio of the maximum moment between the test and calculation (M max,T /M max,C ) ranged from 0.93 to 1.11.The average of M max,T /M max,C was 1.03 and the variation coefficient was 0.057.The results indicated that the proposed calculating method could accurately evaluate the bearing capacities of square CFST columns.

Conclusion
The paper studies the effects of width-thickness ratio (D/t), axial compression ratio (n), and slenderness ratio (λ) on the cyclic behavior of the square CFST columns under the cyclic loading.The bending capacity was evaluated by the proposed calculation method.The primary conclusions are summarized as follows: (1) A bigger D/t would weaken the energy dissipation capacities and bearing capacities of the CFST columns but has little effect on ductility.( 2) With an increased λ, the energy dissipation capacities and bearing capacities of CFST columns decreased, and the stiffness of the columns deteriorated rapidly.(3) As the n increasing, the bearing capacities of CFST columns could be intensified but the energy dissipation capacities and the stiffness would be weakened.(4) The ultimate moment strength of the square CFST columns was assessed according to the limit equilibrium theory.M max,T /M max,C ranged from 0.93 to 1.11.The average of M max,T /M max,C was 1.03, and the coefficient of variation was 0.057.The proposed calculation method could accurately predict the bearing capacities of CFST columns.

FIGURE 11 :
FIGURE 11: Curves of the stiffness degradation of K j −△.

FIGURE 14 :
FIGURE 14: Stress distribution of the CFST column.

TABLE 1 :
Main information of specimens.

TABLE 2 :
Material properties of steel parts.

TABLE 4 :
Main performance points.Note: K e is initial stiffness, P y is yield loading force, P p is plastic loading force, P max is maximum loading force, △ y is yield displacement, △ p is plastic displacement, and △ max is displacement of P max .

TABLE 5 :
K y , K p , K m , K p /K y , and K m /K y .

TABLE 8 :
Comparison between the tested and calculated results.