Study on the mechanical behaviour of multicell T-shaped concrete-filled steel tubular short columns under axial and eccentric compression

Abstract

To investigate the mechanical performance of multicell T-shaped concrete-filled steel tubular (MCT-CFST) columns, five short columns composed of a rectangular cell and two U-shaped cells were tested under axial and eccentric compression loads. For the axial compression samples, the steel tube surface underwent wave buckling, and local buckling failure occurred along the X-axis direction of the section. For the eccentric compression samples, overall bending occurred first; then, local buckling deformation occurred on the surface of the steel tube. Furthermore, a finite element model (FEM) of MCT-CFST short columns was established in ABAQUS software. The FEMs were validated by the test results to further investigate the influence of the construction parameters on the axial and eccentric compression performance of the MCT-CFST short columns. Finally, the EC4, GB 50936 and JGJ 138 specifications were selected to predict the load-carrying capacity of the MCT-CFST short columns under eccentric loading. Compared with GB 50936, JGJ138 and EC4 yield good predictions according to the test and simulation results.

Keywords

multicell T-shaped columns axial compression performance eccentric compression performance finite element analysis design method

Introduction

Concrete-filled steel tubular (CFST) columns combine the favourable properties of steel and concrete. Owing to the confinement of the steel tube to infill concrete by the steel tube, CFST columns exhibit high bearing capacity, high stiffness and excellent ductility. Rectangular and square CFST columns are more widely used in apartment buildings than circular sections due to the easier connections between beams and CFST columns. To satisfy the structural requirements of load-carrying capacity and stiffness, rectangular and square CFST columns need larger cross-sectional areas and often protrude from the inside walls. This phenomenon severely reduces the indoor area and affects building aesthetics.

Specifically shaped (L-shaped, T-shaped and +-shaped) CFST columns have enhanced mechanical properties, are convenient to construct, and can hide in walls to avoid column protrusion in buildings. As special-shaped CFST columns, T-shaped CFST columns are typically used as edge columns, and their mechanical properties have been widely studied. Previous research has shown that the constraint effect of steel tubes on the core concrete in the negative angle part is weak for ordinary T-shaped CFST columns (Li and Lu, 2008; Lu et al., 2007; Wang and Lu, 2005; Zhao and Jing, 2011) (shown in Figure 1(a)). Therefore, researchers have proposed various construction techniques to enhance the constraint effect, which can be divided into two strategies: one involves setting stiffeners (Huang et al., 2018; Liu et al., 2018; Xu et al., 2018; Zheng et al., 2020; Zhu et al., 2020) and binding bars (Zuo et al., 2012a; Zuo et al., 2012b; Zuo et al., 2011a; Zuo et al., 2011b) inside the columns, and the other involves reducing the size of the units inside the columns, such as in lattice T-shaped CFST columns (Qiao, 2006), T-shaped CFST columns composed of rectangular steel tubes (Li et al., 2021) (shown in Figure 1(b)) and multicell T-shaped concrete-filled steel tubular (MCT-CFST) columns (Li et al., 2012) (shown in Figure 1(b)).

Figure 1.

T-shaped CFST columns with different configurations.

Lee et al. (2017) studied the effects of the steel tube width-to-thickness ratio, stiffeners, and steel strength on the compression bending performance of rectangular steel tube high-strength concrete samples. Stephen and Schneider (1998) focused on analysing the effects of several parameters on the mechanical properties of concrete-filled steel tubular samples, as well as the influence of the steel tube shape on the confinement of the internal concrete. Sakino et al. (2004), based on the mechanical experimental results of circular and square steel tube concrete samples, obtained a calculation method for axial compressive bearing capacity. Dundu (2012) studied the axial compressive mechanical properties of circular steel reinforced concrete columns by studying parameters such as length, diameter, and material strength.

Scholars in China have proposed different improvement measures for T-shaped CFSTs. Huang et al. (2018) carried out axial compression tests on T-shaped and L-shaped CFST columns with different ribbed shapes and reported that setting up stiffening ribs can effectively delay the local buckling of steel tubes outwards and improve the stability of steel tube walls.

Zuo investigated T-shaped, L-shaped and cross-sectional CFST columns with binding bars (Zuo, Cai and Liu, 2011; Zuo, Cai and Qian, 2011; Zuo et al., 2012, 2014). Their results showed that setting stiffeners and binding bars can effectively solve the problems existing in ordinary T-shaped CFST columns; however, the construction process is complicated, and the residual stress after internal welding has a greater impact on the bearing capacity of the column.

Du and Xu et al. (Du et al., 2008; Du et al., 2010; Xu et al., 2009) proposed the construction of T-shaped columns by directly welding rectangular steel tubes (shown in Figure 1(b)). The standard for dividing columns into long and short columns was examined, and the axial load-carrying capacity of the samples was calculated under eccentric compression.

Based on domestic and international research on T-shaped CFST columns, the above configurations were used. Tu et al. (Liu et al., 2011; Sui et al., 2019; Tu et al. 2012a; Tu et al. 2012b; Zhang et al., 2015) proposed multicell T-shaped concrete-filled steel tubular (MCT-CFST) columns by dividing the cells in the cross section, which can effectively reduce the effect of welding residual stress while reducing the width-to-thickness ratio of each steel plate and avoiding waste caused by overlapping the steel plates. Experimental studies on the axial compression of short columns, axial compression of medium-length columns, and eccentric compression of long columns were carried out, which indicated that the separation of cells can effectively enhance the constraint effect and make full use of the material properties. Zheng et al. (Zheng, Liang and Liang, 2022; Zheng, Liang and Ma, 2022; Zheng and Lai, 2020; Zheng and Zeng, 2021) carried out tests on multicell special-shaped CFST columns. Their results showed that this configuration can effectively reduce the width-to-thickness ratio of the sample and delay the occurrence of local buckling of the steel tube. Cheng et al. (2022) designed 11 improved multicell T-shaped CFST columns and investigated the effects of the height-to-width ratio of the web, eccentricity direction and eccentricity direction on the mechanical performance of the columns. Zhang et al. (2023) investigated the effects of the slenderness ratio, steel tube thickness, concrete strength and steel grade on N‒M correlation curves through eccentric tests and finite element parameter analysis. Xiao et al. (2020) reported through tests that when the height of a column is constant, as the hoop coefficient and steel ratio increase and the slenderness ratio decreases, the ultimate capacity of the sample increases.

To further investigate the mechanical performance of multicell T-shaped CFST (MCT-CFST) columns, in this work, five MCT-CFST short columns composed of a rectangular cell and two U-shaped cells (shown in Figure 2) were tested under axial and eccentric compression loads. Then, solid models of the test samples were established in ABAQUS software and validated by test results to conduct a parametric analysis. Finally, the EC4, GB 50936, and JGJ 138 specifications were selected to predict the eccentric load-carrying capacity of the MCT-CFST short columns and were compared with the test results.

Figure 2.

Cross section of the MCT-CFST short columns.

Test design

Test samples

Five MCT-CFST columns were designed to conduct axial and eccentric compression tests, as shown in Figure 2 and Table 1. To better describe and analyse the results, the cross section is divided into two parts: a web limb and a flange limb (Liu et al., 2011) (the protruding parts on both sides of the T-shaped section are called flanges, and the middle part is called the web), b_f and h_f represent the extended width and height of the flange limb of the column section, respectively, and b_w and h_w represent the width and height of the web limb of the column section, respectively. t is the steel tube thickness. l is the clear height of the steel tube.

Table 1.

Design size and parameters of the samples.

Sample number	D × B × b_w × h_w × b_f × h_f (mm)	l (mm)	t (mm)	e₀ (mm)	Eccentric direction
TA				0	—
TE1				10	X+
TE2	225 × 150 × 75 × 75 × 75 × 75	600	8	20	X+
TE3				10	Y+
TE4				20	Y+

The multicell steel tube of the sample was welded to steel plates, after which self-compacting concrete was poured inside the steel tube, after which a concrete vibrator was used to compact the concrete. The two ends of the column were welded with 70-mm-thick end plates to ensure the uniformity of the force of the sample during the loading process and the accuracy of the loading. To facilitate a description of the test phenomenon and failure modes of the MCT-CFST short columns, each face of the T-shaped steel tube was numbered, and the numbering is shown in Figure 2. The samples were fabricated at a 1/2 scale.

Material properties

The strength of the steel tube material is Q355 (Q355 means that the yielding strength is 355 MPa), and the strength of the concrete is C40 (C40 means that the cubic compression strength is 40 MPa). Based on the tensile test results, the yield strength (f_y), ultimate strength (f_u), modulus (E_s) and elongation percentage (δ) are 406 MPa, 489 MPa, 206 GPa, and 23.6%, respectively. Three concrete cubes with dimensions of 150 × 150 × 150 mm and three concrete prisms with dimensions of 150 × 150 × 300 mm were tested under compression. The measured properties of the concrete material are cubic compression strength (f_cu) = 48.6 MPa and prism compressive strength (f_c) = 37.5 MPa. The elastic modulus (E_c) of the concrete is calculated via Eq. (1) and is 34.31 GPa.

E_{c} = \frac{10^{5}}{2.2 + \frac{34.7}{f_{c u}}}

(1)

Loading and measurement scheme

The test setup for the MCT-CFST short columns is shown in Figure 3. The linear variable displacement transducer (LVDT) arrangement is shown in Figure 3. Two LVDTs were placed diagonally along the lower endplates of the axial and eccentric compression samples to measure the vertical displacement. Three LVDTs were placed at the quarter points and at the mid-height to measure the lateral deflection of the eccentric compression samples. Longitudinal and transverse strain gauges were arranged in the middle of each tube surface of the samples, and the strain arrangement is shown in Figure 2. The odd numbers in the diagram are the transverse strain gauge numbers, and the even numbers are the longitudinal strain gauge numbers.

Figure 3.

Test setup for the MCT-CFST short columns (units: mm).

For the axial compression test, a laser was used for geometric alignment, preloaded in the elastic range and physically aligned by longitudinal strain gauge values. For the eccentric compression test, the hinge supports were fixed on the top and bottom bearing pads of the testing machine to achieve a constrained state of hinged support at both ends. The finite element software ABAQUS was used to simulate the predicted axial load-carrying capacity (N_uFE) of the samples before loading. Preloading with 0.1 N_uFE was carried out before formal loading to eliminate the gap between the loading device and the samples, and whether the strain gauge worked normally was checked. For formal loading, the hierarchical loading system of load control was adopted. Before the load reached 0.5 N_uFE, the load in each stage was 0.1 N_uFE, and the load was held for 2 minutes after the loading was completed. When the load exceeded 0.5 N_uFE, the load in each stage was 0.05 N_uFE, and the holding time was 2 minutes; when the bearing capacity of the sample decreased to 85% of the measured peak load or when the sample deformation was too large to continue loading, loading was stopped. During the whole loading process, no cracking damage occurred in the welds between the steel tubes. After testing, the steel tube was cut open to observe the damage to the concrete at the buckling position. The concrete at the corner was essentially intact.

Test results and analysis

Test phenomenon

For the axial compression samples, when the applied load increased to 0.75N_u, the longitudinal strains in the TA steel tube were greater than the yielding strain, which indicated that the steel tube yielded. Slight buckling was observed in the middle of surfaces B2 and D1. Local buckling occurred in the 240∼270 mm section of surface A2 from the bottom of the sample. When the load was close to the axial load-carrying capacity of the sample, the deformation increased sharply, and different degrees of wave buckling occurred on all surfaces of the steel tube. The buckling waves in the lower and middle parts of the sample developed rapidly along the X-axis direction. The failure mode of the axial compression sample was local buckling failure of the steel tube along the X-axis direction. The test results revealed that the synergistic force of the steel tube and the concrete on the surface effectively restrained the deformation of the concrete, and the ductility of the sample significantly improved.

For the eccentric compression samples, before the load reached 0.7N_u, the mid-span deflection was low. With continued loading, the strain in the compression zone of the steel tube gradually increased, and the mid-span deflection increased. The whole sample exhibited slight bending. When the load reached N_u, the sample bent rapidly in the eccentric direction, and the load started to decrease. Local buckling occurred in the mid-span of the steel tube in the compression zone of the sample. The eccentric compression samples all exhibited the failure mode of bending first and then buckling. With increasing eccentricity, the bending deformation of the samples gradually increases. After the test, the steel tube surfaces of TE2 and TE4 were partially cut open. The concrete of the buckling surface in the compression zone was essentially crushed, the weld between the steel tubes did not crack, and there was no slip between the steel tube and the core concrete.

Load‒displacement relationship

The load–vertical displacement curves of the axial and eccentric compression samples are shown in Figure 4(a), and the load–mid-height deflection curve of the eccentric compression samples is shown in Figure 4(b). In the same eccentric direction, with increasing eccentricity, the initial stiffness and axial load-carrying capacity of the samples decrease. At the same eccentricity, the initial stiffness and axial load-carrying capacity of the eccentric samples loaded along the X-axis are greater. Figure 4(b) shows that the eccentric compression samples exhibit strong ductility because the large bending deformation and lateral deflection of the eccentric compression samples develop rapidly. The mid-height deflection of some samples is negative at the initial stage of loading. Each sample is affected by the horizontal component force to negative bending. As the loading continues, because the sample experiences large bending deformation, the horizontal deflection changes from negative to positive.

Figure 4.

Load‒displacement curves.

In addition, Δ_y represents the yield displacement of the sample, Δ_u represents the vertical displacement corresponding to the peak load, and Δ_0.85 represents the vertical displacement corresponding to the load falling to 85% of the peak load. K_i represents the initial stiffness of the sample, and DI represents the ductility coefficient of the sample. For the axial compression samples, DI = Δ_u/Δ_y, and for the eccentric compression samples, DI = Δ_0.85/Δ_y. Because the load‒displacement curve of the TA has no descending section, the average axial strain corresponding to the axial load-carrying capacity obtained at the end of the test is 5.28%, which is not realistic for an axial compression sample. Wang et al. (2017) defined the axial load-carrying capacity N_u of an axial compression column without a clear descending section as the load corresponding to an axial average strain of 1%. For sample TA, Nu is 3816.92 kN.

Table 2 and Figure 5(a) show that in the same eccentric direction, as the eccentricity increases, the initial stiffness and axial load-carrying capacity of the sample decrease. Compared with those of TA, the axial load-carrying capacities of TE1, TE2, TE3 and TE4 are 16.64%, 22.17%, 25.18% and 43.26% lower, respectively. The analysis revealed that eccentricity is an important factor affecting the bearing capacity of a sample. In the same eccentric direction, the N_u of the sample with a larger eccentricity is lower; however, the DI will be improved.

Table 2.

Analysis and calculation of the test data.

Sample number	N_u (kN)	Δ_y (mm)	Δ_u (mm)	Δ_0.85 (mm)	K_i (kN/mm)	DI
TA	3816.92	4.96	21.49	—	2456.75	4.33
TE1	3181.70	3.15	18.49	22.73	2194.28	7.22
TE2	2970.70	3.67	30.46	30.46	1697.54	8.30
TE3	2855.70	2.84	13.10	32.97	1427.85	11.61
TE4	2165.70	2.42	14.54	35.43	1332.31	14.64

Figure 5.

N_u values of the test samples.

Strain analysis

The load–longitudinal strain curves and strain distribution diagrams of typical samples are shown in Figures 6 and 7. The strain is positive in tension and negative in compression. x and y represent the horizontal and vertical coordinates of the column section, respectively, in Figure 8. In the initial stage of loading, the sample was in the elastic stage, and the longitudinal strain in the steel tube was essentially linear with increasing load. The longitudinal strain gauge gradually yielded under continuous loading, and the sample entered the elastic–plastic stage. The load–longitudinal strain curve continued to rise, but the slope decreased. For the eccentric compression samples, the strain was fully developed because of the increase in the deflection at the mid-height of the column. In the later period, due to the local buckling of the steel tube, some of the strain is converted from the compression trend to the tension trend. As shown in Figure 6(d), for eccentric compression samples, the strain in the compression zone is always greater than the strain in the tension zone. The compressive zone of the samples yields before the tensile zone, and the failure of the eccentric compression samples starts from the compression zone, which begins to withdraw from work. In the same eccentric direction, the larger the eccentricity is, the greater the strain development in the compression zone of the samples.

Figure 6.

Load–longitudinal strain curves.

Figure 7.

Strain distribution diagrams of typical samples.

Figure 8.

Typical failure characteristics of the samples.

Owing to the column section form and the effect of the eccentric load, there is a certain deviation between the neutral axis and the centroid axis of the section. The distance between the neutral axis and the centroid axis of TE2 is approximately 56 mm, and the distance between the neutral axis and the centroid axis of TE4 is approximately 50 mm. The strain distribution of the samples is approximately linear before reaching the ultimate load, which conforms to the plane section assumption. When approaching or reaching the ultimate load, the strain distribution of the section is not uniform, and the strain in the tension zone still conforms to the plane section assumption. The strain distribution does not conform to the plane section assumption due to the large mid-height deformation in the compression zone. For samples with the same eccentricity, the second-order effect caused by the increase in eccentricity causes the neutral axis to move in the direction of the centroid axis.

Finite element analysis

Finite element method

Finite element models of MCT-CFST short columns were established with ABAQUS software, and the mechanical properties of the MCT-CFST columns under axial and eccentric loading were studied. The plastic damage model was adopted for the constitutive relation of the core concrete. For the MCT-CFST columns, the confinement factor in each cell can be determined independently according to the measurements of each rectangular CFST (GB50936-2014, 2014). The constitutive relation of the concrete and the value of each parameter were established using the model proposed by Zhang et al. (2015) based on the Mander model. The constitutive relation of steel was determined with the secondary plastic flow model proposed by Han (2016).

The FE models were established according to actual tests. Eight-node solid elements with reduced integration and three translational degrees of freedom per node (C3D8R) were chosen for all the parts. The surface-to-surface contact was selected as the interaction between the steel tube and the concrete surface. The ‘hard contact’ function was used to simulate the normal behaviour of the steel tube and the core concrete, whereas the penalty function was used to simulate the tangential behaviour. The friction coefficient was selected as 0.6. The ‘tie’ constraint was adopted to simulate welds. The interactions between the steel tube and the endplates and the foot ribs were simulated by this constraint. For the axial compression model, the reference points (RPs) were coupled at the centroid position of the upper and lower endplates, which were named RP1 and RP2, respectively. The displacements of RP1 along the X and Y axes and rotation around the Z axis were restricted, whereas the displacements of RP2 along the X, Y and Z axes and rotation around the Z axis were restricted. For the eccentric compression models, RP1 and RP2 were coupled at the hinge action points of the upper and lower endplates. For the models with an eccentric X-axis direction, the displacement of RP1 along the Z-axis and rotation around the Y-axis and the displacement of RP2 rotation around the Y-axis were released. For the models with an eccentric Y-axis direction, the displacement of RP1 along the Z-axis and rotation around the X-axis and the displacement of RP2 rotation around the X-axis were released. A vertical load was imposed on RP1 of the upper endplate (Figure 9).

Figure 9.

Finite element models of MCT-CFST short columns.

Finite element model validation

A comparison of the FEA results with the test results of typical samples is shown in Figure 10. A comparison of the failure modes reveals that the simulated failure modes are in good agreement with the test results. The axial compression samples exhibited local bucking along the X-axis, and the eccentric compression samples exhibited bending in the eccentric direction. The two curves are in good agreement. In the initial elastic stage of loading, the stiffness of the FEA is slightly greater than that of the test. The main reason is that the deformation of the upper endplate and its fixed screw during the loading process and the gap between the cutter hinge plate and the cutter hinge port cannot be completely ruled out, while the boundary conditions of the test cannot reach the ideal state. The axial load-carrying capacity of the FEA samples during testing is similar to that shown in Table 3. The average N_TEST/N_FEM was 1.002, and the standard deviation was 0.027. When the load exceeds the peak load, it is difficult for the FEA curve to be consistent with the test curve because of the many accidental factors in the loading process. However, the overall decreasing trend is basically the same. Therefore, this FEA method can better reflect the compression performance of MCT-CFST short columns.

Figure 10.

Comparisons of the FEA results with the test results for all the samples.

Table 3.

Axial load-carrying capacity comparison of the finite element analysis (FEA) and test results.

Sample number	N_TEST/kN	N_FEM/kN	N_TEST/N_FEM
TA	3816.92	3926.44	0.97
TE1	3181.70	3119.01	1.02
TE2	2970.70	2987.06	0.99
TE3	2855.70	2908.64	0.98
TE4	2165.70	2068.10	1.05
Average value			1.002
Standard deviation			0.027

Parametric analyses

Axial compression performance

The strength enhancement index (SEI) was used to evaluate the constraint effect of the steel tube on the core concrete. The effects of different parameters on the axial load-carrying capacity N_a, initial stiffness K_i and SEI of the MCT-CFST columns were studied. The calculation formula for the SEI is as follows:

S E I = N_{a} / (f_{y} A_{s} + f_{c} A_{c})

(2)

A_s and A_c represent the steel area and the concrete area, respectively. f_y and f_c represent the measured values of the steel and concrete material properties, respectively. These data are consistent with the data in Section: Material properties.

The main parameters are the height-to-width ratio h_w/b_w of the web, the section size of the column D × B × b_w × h_w × b_f × h_f, the thickness of the steel tube wall t and the slenderness ratio λ. The calculation of λ refers to the calculation method proposed by Han (2016), and the calculation formula is shown in Formula. 4. The number and simulation results are shown in Table 4. The four sets of data after the sample number represent h_w/b_w of the web, t, λ and the column section size D × B.

λ = 2 \sqrt{3} l_{0} / B

(3)

Table 4.

Number and simulation results of the axial compression samples.

Sample number	b_w × h_w × b_f × h_f/mm	h_w/t	N_a/kN	K_i/(kN/mm)	SEI
A1.0-8-14-225 × 150	75 × 75 × 75 × 75	9.38	3926.44	3504.56	1.187
A1.5-8-14-225 × 187.5	75 × 112.5 × 75 × 75	14.06	4255.47	2730.26	1.171
A2.0-8-14-225 × 225	75 × 150 × 75 × 75	18.75	4506.04	2474.39	1.137
A2.5-8-14-225 × 262.5	75 × 187.5 × 75 × 75	23.44	4834.78	2686.46	1.128
A1.0-8-14-450 × 300	150 × 150 × 150 × 150	18.75	10061.77	8492.73	1.185
A1.0-8-14-600 × 400	200 × 200 × 200 × 200	25	14579.98	12886.53	1.131
A1.0-2-14-225 × 150	75 × 75 × 75 × 75	37.5	1640.3	1495.26	1.097
A1.0-4-14-225 × 150	75 × 75 × 75 × 75	18.75	2385.43	2123.18	1.124
A1.0-6-14-225 × 150	75 × 75 × 75 × 75	12.5	3154.32	2727.52	1.156
A1.0-10-14-225 × 150	75 × 75 × 75 × 75	7.5	4667.35	3865.45	1.207
A1.0-8-28-225 × 150	75 × 75 × 75 × 75	9.38	3733.28	1575.75	1.128
A1.0-8-42-225 × 150	75 × 75 × 75 × 75	9.38	3477.87	1056.05	1.051
A1.0-8-55-225 × 150	75 × 75 × 75 × 75	9.38	3260.11	769.6	0.985

l₀ represents the effective length of the column, and B represents the side size of the column section.

The load–vertical displacement curves and SEI analysis of the axial compression samples are shown in Figures 11 and 12. For the height-to-width ratio of the web, the overall trend of the load‒vertical displacement curves of each sample is consistent, and the initial stiffness difference of each sample in the elastic stage is small. In the elastic‒plastic stage, as the height-to-width ratio of the web increases, the stiffness decreases rapidly, and the peak load of the samples increases continuously. Compared with those of the samples with a height-to-width ratio of 1, the axial load-carrying capacities of the samples with height-to-width ratios of 1.5, 2 and 2.5 increased by 8.38%, 14.76% and 23.13%, respectively, and the SEIs decreased by 1.35%, 4.21% and 4.97%, respectively. The increase in the height-to-width ratio of the web causes the width‒thickness ratio of the web to increase, the effective confinement area of the steel tube to the internal concrete to decrease, and the strengthening ability of the “hooping effect” of the component on height-to-width ratio is thus reduced. The SEI density of the samples decreases continuously. As the column section size increases, the axial load-carrying capacity of the samples increases continuously. Compared with those of A1.0-8-14-225 × 150, the SEIs of A1.0-8-14-450 × 300 and A1.0-8-14-600 × 400 decreased by 0.17% and 4.72%, respectively. The reason is similar to the effect of increasing the height-to-width ratio of the web. An increase in the column section size decreases the effective confinement area of the steel tube to the internal concrete, reduces the effective constraint area of the steel pipe on the internal concrete, and reduces the strength improvement coefficient of the samples. The SEI density decreases continuously. As the thickness of the steel tube wall increases, the initial stiffness and peak load of each sample increase continuously. Compared with those of the samples with a steel tube wall thickness of 2 mm, the stiffnesses of the samples with t = 4, 6, 8 and 10 mm increased by 29.36%, 56.68%, 99.65% and 124.15%, respectively; the axial load-carrying capacities increased by 45.43%, 92.3%, 139.37% and 185.54%, respectively; and the SEIs increased by 2.42%, 5.42%, 8.19% and 10.07%, respectively. This is because a decrease in the width–thickness ratio of the steel plate and an increase in the steel ratio increase the effective confinement area of the steel tube to the internal concrete, and the SEI of the samples thus increases. With increasing slenderness ratio, the initial stiffness of each sample in the elastic stage gradually decreases. In the elastic‒plastic stage, the stiffness of the sample decreases faster, and the axial load-carrying capacity decreases continuously. Compared with those of the samples with a slenderness ratio of 14, the stiffnesses of the samples with slenderness ratios of 28, 42, and 55 decreased by 51.75%, 68.25% and 76.13%, respectively; the axial load-carrying capacities decreased by 14.26%, 22.16% and 31.6%, respectively; and the SEIs decreased by 4.97%, 11.46% and 17.02%, respectively. When the slenderness ratio exceeds 42, the curve trend becomes steeper after reaching the peak load because the initial defect causes the sample to no longer experience axial compression with increasing sample height. This causes the failure mode of the sample to change from strength failure of the short column to instability failure of the long column.

Figure 11.

Load–vertical displacement curves of the axial compression samples.

Figure 12.

SEIs of the axial compression samples.

Eccentric compression performance

Parametric analysis of the MCT-CFST columns was carried out to explore the influence of the eccentricity ratio, height-to-width ratio of the web, eccentric direction and slenderness ratio on the mechanical properties, such as the axial load-carrying capacity, stiffness and ductility. The eccentricity ratio is calculated as e₀/D (Xiao, 2020)27]. The sample numbers and simulation results of the eccentric compression samples are shown in Table 5. The four data points after the sample number represent the height-to-width ratio of the web, eccentricity ratio, slenderness ratio and eccentricity direction. The thickness of the steel tube wall of all the samples is 8 mm, and the flange extension width and flange height are 75 mm.

Table 5.

The number and simulation results of eccentric compression samples.

Sample number	D × B × b_w × h_w/mm	e ₀	N_a/kN	K_i/(kN/mm)	DI
B1.0-0.067-14-X	225 × 150 × 75 × 75	10	3119.01	3160.72	—
B1.0-0.133-14-X	225 × 150 × 75 × 75	20	2987.07	2468.26	—
B1.0-0.267-14-X	225 × 150 × 75 × 75	40	2349.74	2343.67	—
B1.0-0.400-14-X	225 × 150 × 75 × 75	60	1907.03	1722.54	—
B1.0-0.067-14-Y+	225 × 150 × 75 × 75	10	2908.64	3102.5	14.45
B1.0-0.133-14-Y+	225 × 150 × 75 × 75	20	2068.08	2468.26	24.06
B1.0-0.267-14-Y+	225 × 150 × 75 × 75	40	1577.17	1532.58	26.19
B1.0-0.400-14-Y+	225 × 150 × 75 × 75	60	1299.35	1001.37	28.5
B1.5-0.267-14-Y+	225 × 150 × 75 × 75	50.06	1880.27	1798.86	16.24
B2.0-0.267-14-Y+	225 × 150 × 75 × 75	60.08	2051.54	2067.31	19.12
B2.5-0.267-14-Y+	225 × 150 × 75 × 75	70.09	2226.57	2229.15	17.02
B1.5-0.267-14-Y-	225 × 187.5 × 75 × 75	50.06	2348.86	1857.41	13.71
B2.0-0.267-14-Y-	225 × 225 × 75 × 75	60.08	2652.58	2059.13	17.41
B2.5-0.267-14-Y-	225 × 262.5 × 75 × 75	70.09	2919.54	2304.31	20.43
B1.0-0.067-14-Y-	225 × 150 × 75 × 75	10	3271	3012.5	13.52
B1.0-0.267-14-Y-	225 × 150 × 75 × 75	40	2049.21	1684.14	7.33
B1.0-0.133-28-X	225 × 150 × 75 × 75	20	2598.8	1406.25	6.63
B1.0-0.133-42-X	225 × 150 × 75 × 75	20	2359.38	925.37	3.91
B1.0-0.133-55-X	225 × 150 × 75 × 75	20	2073.33	695.82	2.99
B1.0-0.133-28-Y+	225 × 150 × 75 × 75	20	2002.69	1273.37	5.33
B1.0-0.133-42-Y+	225 × 150 × 75 × 75	20	1741	816.79	3.69
B1.0-0.133-55-Y+	225 × 150 × 75 × 75	20	1497.2	615.94	3.3

The load‒vertical displacement curves of the samples subjected to MCT-CFST eccentric compression are shown in Figure 13. Owing to the large deformation displacement of some samples, observing the overall trend of the curve is not easy. Therefore, all the curves before 25 mm are analysed. With increasing eccentricity ratio, the initial stiffness of the samples decreases, and the decreasing trend of the samples with larger eccentricity ratios is gentler, indicating better ductility. This is because of the second-order effect and the decreasing compression zone height. At the same eccentricity ratio, the initial stiffness and axial load-carrying capacity of the samples loaded eccentrically along the X-axis are greater than those of those loaded eccentrically along the Y+ axis. Because the moment of inertia of the section of the X-axis is relatively large, its stiffness is also relatively high. With increasing height-to-width ratio, the initial stiffness and axial load-carrying capacity of the samples loaded along the Y+ and Y-axes increase. The ductility of the samples loaded along the Y+ axis tends to decrease, whereas the ductility of the samples loaded along the Y-axis gradually increases. The reason is that as the height-to-width ratio of the web increases, the width‒thickness ratio of the steel plate increases, resulting in a weakening of the constraint effect of the steel tube in the compression zone on the internal concrete. For the samples loaded along the Y-axis, the compression zone is in the flange limb area, the increase in the width-to-thickness ratio has little effect on the constraint effect of the steel tube, and the compression zone area clearly increases with the increase in the height-to-width ratio of the web compared with that of the samples loaded along the Y+ axis. For the eccentric direction, in the elastic stage of loading, because the moment of inertia of the section of the X-axis is relatively large, the initial stiffness loaded along the X-axis is greater than that loaded along the Y-axis. In the elastic‒plastic stage, owing to the difference in bending stiffness, the axial load-carrying capacity of the samples along the X, Y and Y+ axes tends to decrease, whereas the area of the compression zone at the flange is larger than that of the web, which makes the stiffness and bearing capacity of the samples loaded along the Y-axis greater than those loaded along the Y+ axis. With increasing eccentricity ratio, this difference becomes increasingly significant because the asymmetric stress conditions of the cross section become more prominent. With increasing slenderness ratio, the stiffness decreases. In the elastic‒plastic stage, the axial load-carrying capacity and ductility tend to decrease. This is due to the increase in the slenderness ratio, and the second-order effect of the sample causes the height of the section compression zone to gradually decrease. At the same slenderness ratio, the stiffness and bearing capacity of the samples loaded eccentrically along the X-axis are greater than those loaded eccentrically along the Y+ axis because the X-axis has a larger cross-sectional moment of inertia.

Figure 13.

Load–vertical displacement curves of eccentric compression samples.

Design of MCT-CFST columns under eccentric loading

At present, the technical codes for CFST columns are focused on circular, square and rectangular CFST columns. Studies on the compression performance of MCT-CFST short columns are rare. In this work, the eccentric compression bearing capacity of the MCT-CFST short columns was calculated according to relevant domestic and foreign codes (Eurocode 4, 2004; GB50936-2014, 2014; JGJ-138-2016, 2016). The calculated results were compared with the test and simulation values to verify the applicability of the current codes for determining the eccentric loading bearing capacity of MCT-CFST columns.

According to relevant research at home and abroad, the current codes for CFST columns are generally based on superposition theory, unified theory or the limit equilibrium calculation method. The corresponding codes are the European Code (EC4), the Technical Specification for Concrete-filled Steel Tubular Structures (GB50936-2014, 2014) and the Code for the Design of Composite Structures (JGJ138-2016, 2016).

Referring to the calculation method of Tu et al. (Zhang et al., 2015; Sui et al., 2019) for the compression bearing capacity of T-shaped CFST columns, the bearing capacity of each cell of the CFST column is calculated separately. After superposition, the bearing capacity of the additional steel plate is subtracted from the eccentric compression bearing capacity of the T-shaped CFST columns. The MCT-CFST short column is divided into three independent rectangular cells, and the distance from the centroid point of each cell to the compression position is taken as the eccentricity of the cell. The calculation of the eccentric compression bearing capacity of each rectangular cell still refers to the calculation method of the bearing capacity of the compression–bending members in the three codes. The sum of the eccentric compression bearing capacity of each cell is taken as the final eccentric compression bearing capacity of the MCT-CFST columns. A comparison of the theoretical calculation values and test and simulation values of the eccentric compression bearing capacity of the MCT-CFST columns is shown in Table 6.

Table 6.

Comparison of the theoretical calculation values and test and simulation values of the eccentric compression bearing capacity of the MCT-CFST Columns.

Sample number	N_a/kN	N_J/kN	N_G/kN	N_E/kN	θ	N_J/N_a	N_G/N_a	N_E/N_a
TE1	3181.70	2713.07	1469.18	2818.33	4.58	0.853	0.462	0.886
TE2	2970.70	2350.88	1262.9	2396.15	4.58	0.791	0.425	0.807
TE3	2855.70	2650.82	1311.15	2713.07	4.58	0.928	0.459	0.950
TE4	2165.70	2224.11	1111.68	2275.04	4.58	1.027	0.513	1.050
B1.0-0.067-14-X	3119.01	2713.07	1469.18	2818.33	4.58	0.870	0.471	0.904
B1.0-0.133-14-X	2987.07	2350.88	1262.9	2396.15	4.58	0.787	0.423	0.802
B1.0-0.267-14-X	2349.74	1715.90	987.46	1777.02	4.58	0.730	0.420	0.756
B1.0-0.400-14-X	1907.03	1398.98	811.22	1444.26	4.58	0.734	0.425	0.757
B1.0-0.067-14-Y+	2908.64	2650.82	1311.15	2713.07	4.58	0.911	0.451	0.933
B1.0-0.133-14-Y+	2068.08	2224.11	1111.68	2275.04	4.58	1.075	0.538	1.100
B1.0-0.267-14-Y+	1577.17	1758.91	852.92	1788.34	4.58	1.115	0.541	1.134
B1.0-0.400-14-Y+	1299.35	1423.88	692.18	1464.63	4.58	1.096	0.533	1.127
B1.5-0.267-14-Y+	1880.27	1794.96	1129.83	1777.59	4.38	0.955	0.601	0.945
B2.0-0.267-14-Y+	2051.54	1930.39	1255.5	1879.46	4.22	0.941	0.612	0.916
B2.5-0.267-14-Y+	2226.57	2032.26	1369.41	1981.32	4.09	0.913	0.615	0.890
B1.5-0.267-14-Y-	2348.86	1471.99	1110.84	1404.50	4.38	0.627	0.473	0.598
B2.0-0.267-14-Y-	2652.58	1557.30	1245.47	1506.37	4.22	0.587	0.470	0.568
B2.5-0.267-14-Y-	2919.54	1642.61	1397.81	1522.92	4.09	0.563	0.479	0.522
B1.0-0.067-14-Y-	3271.00	2608.94	1332.39	2690.44	4.58	0.798	0.407	0.823
B1.0-0.267-14-Y-	2049.21	1423.88	986.1	1444.26	4.58	0.695	0.481	0.705
				Average value		0.850	0.490	0.859
				Standard deviation		0.160	0.063	0.172

Table 6 shows that the predicted average theoretical bearing capacity of each code is less than the test and simulation values. Compared with those of the JGJ138 code, the theoretical calculation values of the EC4 code for the eccentric compression bearing capacity of the MCT-CFST columns are more consistent with the test and simulation values, but the calculation results of both are safe. The differences between the theoretical values of the GB50936 code and the test and simulation values are large. This is because the constraint effect coefficient θ of all the samples is between 4.09 and 4.58, which is greater than 3.12. As the θ of the samples approaches 3.12, the theoretical calculations of the GB50936 code are in better agreement.

The theoretical N‒M curves and a comparison of the theoretical calculation values and test and simulation values are shown in Figures 14 and 15, respectively. Table 6 shows that when the samples are loaded along the X-axis, the average N_J/N_a is 0.794, and the average N_E/N_a is 0.819. When the samples are loaded along the Y+ axis, the average N_J/N_a is 0.996, and the average N_E/N_a is 1.005. When the samples are loaded along the Y-axis, the average N_J/N_a is 0.654, and the average N_E/N_a is 0.643. These findings show that when the samples are loaded along the Y+ axis, the EC4 code and the JGJ138 code can accurately predict the eccentric compression bearing capacity. When the samples are loaded along the X-axis and Y-axis, the theoretical calculation values of the EC4 code and the JGJ138 code are relatively conservative. Combined with the comparison between the calculated values of the code and the test and simulation values of the eccentric compression samples in Figure 15, the calculated values of the JGJ code and EC4 code are in good agreement with the test and simulation values, but both are generally conservative. However, the GB50936 code cannot accurately predict the eccentric compression bearing capacity of the MCT-CFST columns because of the high constraint effect of the samples.

Figure 14.

N‒M curves.

Figure 15.

Comparison between the calculated values of the code and test and simulation values of the eccentric compression test samples.

Conclusions

This work focused on the mechanical behaviours of multicell T-shaped concrete-filled steel tubular short columns subjected to axial and eccentric loads. Based on the experimental, numerical and theoretical studies, the following conclusions can be drawn.

(1) The failure mode of the axial compression sample was local buckling failure of the steel tube along the X-axis direction. The eccentric compression samples all exhibited bending first and then buckling.

(2) At the same eccentricity, the initial stiffness and load-bearing capacity of the eccentric samples loaded along the X-axis are greater. In the same eccentric direction, with increasing eccentricity, the initial stiffness and load bearing capacity decrease, and the ductility improves.

(3) The parametric analysis results indicate that as the height-to-width ratio and section size of the web increase, the axial load-carrying capacity increases, the SEI decreases, and the stiffness and axial load-carrying capacity are negatively correlated with the slenderness ratio. All the parameters are positively correlated with the steel tube wall thickness. The samples subjected to eccentric loading along different axes have different initial stiffnesses and load-carrying capacities; as the eccentricity increases, both of these values decrease. However, a decrease in the height of the compression zone results in better ductility for samples with higher eccentricity.

(4) The predicted load-carrying capacity of each specification is conservative. For the Y-axis loaded samples, the EC4 code and JGJ 138 can accurately predict the eccentric compression load-carrying capacity. For the X-axis- and Y-axis-loaded samples, the theoretical calculation values of the EC4 code and the JGJ 138 code are relatively conservative. However, GB50936 cannot accurately predict the eccentric load-carrying capacity because of the high constraint effect.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Fundamental Research Funds for the Central Universities of China (No. PA2024GDSK0084).

ORCID iDs

Anying Chen

Hanqin Wang

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