Eccentric compression behaviour of rectangular concrete-filled steel tube columns with self-compacting lower expansion concrete

Abstract

The use of a self-compacting lower expansion concrete in a concrete-filled steel tube (CFST) structure not only promotes the quality of concrete pouring but also improves the bond behaviour between the steel and the concrete. In combination with the actual stress state of the columns in the engineering structure, it is necessary to study the eccentric compression behaviour of the column. In this study, experimental studies involving both uniaxial and biaxial bending tests of rectangular self-compacting lower expansion CFST columns were carried out. The variation laws of the load–displacement curves, the lateral deflection curves and the stress–strain curves during the loading phase were analysed. Furthermore, the failure modes and the mechanical properties of the specimens under eccentric compression loads were investigated. Subsequently, the numerical models of CFST columns with self-compacting lower expansion concrete were considered and established. In order to verify the rationality of the finite element modelling, the numerical calculation results were compared with test results. Then, a parametric analysis of the compression and the bending bearing capacities of each column was carried out by changing the eccentricity of the load, and the N–M curves or N-M_x-M_y surfaces describing the ultimate bearing capacity of the column were obtained. Finally, by the parametric finite element analysis of the rectangular CFST columns regarding to the bearing capacity under the same eccentricity, a conclusion was obtained: when the expansion agent content γ of a specimen increased from 0% to 10%, the bearing capacity of the columns increases significantly, but when continue increasing the expansive agent content, the expansion agent content has little effect on the compression–bending bearing capacity.

Keywords

self-compacting lower expansion concrete concrete-filled steel tube column N–M curve bearing capacity compression and bending

Introduction

Concrete-filled steel tube (CFST) columns show advantageous applications in construction field, especially for its high bearing capacity, good fire performance, fine seismic performance and enormous economic benefits, which have been widely used in high-rise and super high-rise building structures in recent years. The increasing applications of concrete-filled steel tube has aroused intense scholarly interest. Some scholars (An and Han, 2014; Muciaccia et al., 2001; Ouyang et al., 2017; Pi et al., 2019; Wang et al., 2018; Young and Ellobody, 2006; Yuan et al., 2019) have studied the influences of some factors, like slenderness ratio, eccentricity, concrete strength and steel tube thickness on the bearing capacity of CFST columns, by means of experimental research and numerical simulation and have found that the columns have the good bearing capacity. However, it has been pointed out that the pouring quality of ordinary concrete is difficult to control, and the shrinkage and the creep of ordinary concrete also cause voids and defects between the steel tube and the concrete, which has a great impact on the composite performances of CFST columns. Self-compacting low-expansion concrete can not only eliminate the need for vibration and improve the work efficiency, but also can compensate for the concrete shrinkage and effectively improve the bond between the steel tube and concrete, which will improve the bearing capacity of the specimens.

Many scholars have studied the mechanical properties of self-compacting micro-expansion concrete in steel tubes. Han and Yao (2004) adopted three kinds of concrete that was well compacted using poker vibrators, well compacted by hand and self-consolidating without any vibration to pour into hollow structural steel (HSS). Then, axial compressive tests were carried out. The results showed that the columns with self-compacting concrete (SCC) compacted without any vibration had a section capacity value comparable to that of the specimens with concrete compacted with a poker vibrator. Mahgub et al. (2017) presented an experimental study on the axial compressive behaviours of eight SCC-filled elliptical steel tube columns and two hollow section columns. The test results indicated that the composite columns possessed higher critical axial compressive capacities compared with their hollow section counterparts as a result of the composite interaction. Xu et al. (2016) conducted axial compression experiments on a steel tube filled with high-strength self-stressing self-compacting concrete and an ordinary CFST column and found that the initial self-stress, slenderness ratio and concrete strength could improve the axial compression bearing capacity to different degrees, with the slenderness ratio having the most significant influence. Liu et al. (2020) presented an experimental study of 54 self-stressing recycled aggregate concrete-filled steel tube (SSRCFST) columns under axial loading. The test results indicated that self-stress could enhance the ultimate capacity and rigidity of the columns by 6%–25%. Huang et al. (2020) carried out axial compressive tests on self-compacting micro-expansive CFST columns with a new type of expansive agent and found that the specimens with the expansive agent had good mechanical properties. Yu et al. (2020) presented an experimental investigation on the mechanical behaviour of self-stressing steel slag aggregate concrete-filled steel tubular (SSSACFST) short columns under axial compression. It was found that the expansion rate was beneficial to the bearing capacity of the specimens. The above researches show that the self-compacting micro-expansive CFST columns have good axial mechanical properties. But in the actual structure, members only subjected to axial compression are rare. And columns mainly sustain uniaxial eccentric loading and even biaxial eccentric loading sometimes. Therefore, it is of practical significance to study the calculation theory of rectangular concrete-filled steel tubular eccentric stress members. Xu et al. (2010, 2011) conducted a push-out test study on four micro-expansive concrete-filled steel tubes (MCFSTs) and three conventional concrete-filled steel tube (CFST) columns. It was found that both the mixture ratio of the expansion agent and the water–cement ratio had important influences on the constrained expansion of the concrete; the MCFST columns had higher bond strength than the conventional CFST columns. Chang et al. (2009) presented experimental and numerical investigations of pre-stressed concrete-filled circular steel tube by means of expansive and conventional CFST specimens under eccentric loading. The results indicated that the eccentrically loaded PCFT columns generally had higher load-carrying capacities than the CFT columns when the other parameters were kept the same. In conclusion, self-compacting micro-expansive CFST columns have been found to have a better bearing capacity. Thus, it is of theoretical and practical importance to carry out researches on the mechanical properties of self-compacting micro-expansive CFST columns under eccentric compression. However, there is few research on the influence degree content of the expansive agent, as well as the issue of eccentricity on the eccentric compression bearing capacity of CFST columns with self-compacting lower expansion. And the establishment method of the finite element model of CFST columns with self-compacting micro-expansion is also needed to be investigated. Therefore, eccentric compression tests of self-compacting micro-expansion concrete-filled rectangular steel tubular columns were carried out in this research. The influences of the main factors such as concrete strength, content of expansion agent, eccentricity and slenderness ratio on the compression–bending bearing capacity of the columns were investigated. Moreover, a numerical model of the self-compacting micro-expansion concrete-filled rectangular steel tubular columns was established, and the reliability of the model was verified. A parametric finite element analysis of the CFST columns under the same eccentricity was performed using different values for the length, D/B ratio, thickness and expansion agent content.

Experimental study

Preparation of specimens

The main influencing factors investigated in the tests included the strength of concrete, expansion agent content and length of the specimen eccentricity, as shown in Table 1. Two kinds of concrete with different dosage of expansive agent were designed to analyse the influence of dosage of expansive agent on the mechanical properties of CFST columns. The concrete mix proportions are shown in Table 2. In Table 2, the C40 and C50 indicate the strength grade of concrete, while Ⅰ, Ⅱ and Ⅲ indicate the dosage of expansive agent 0%, 10% and 15%, respectively. The specimens were made of cold-formed steel tubes, with a 10 mm × 200 mm × 250 mm steel plate welded as the end plate at the lower end of the steel tube, into which the concrete was poured and compacted. Nine concrete cubes (100 mm × 100 mm × 100 mm) from each type of concrete were reserved for the compressive strength test according to GB/T 50081-2019 (2019). After 7 days, a 10 mm × 200 mm × 250 mm steel plate was welded across the upper end of the steel tube. The ultimate tensile strength ( f_u = 475 MPa) and yield strength ( f_y = 334 MPa) of the steel were determined based on the tensile test according to GB/T 228.1-2010 (2011). Concrete compression strength tests were carried out after the concrete test cubes had cured for 28 days. The strength results are included in Table 1 below.

Table 1.

Measured geometric properties of test specimens.

Specimen reference	D×B×t×L (mm)	Concrete grade	Concrete compression cube strength f_cu (MPa)	Steel yield strength f_y (MPa)	Dosage of expansion agent γ (%)	Loading eccentricity e (mm)	Experiment result N_e (kN)
PY1	200×150×6×1200	C40(Ⅰ)	45.5	334	0	e_x=60, e_y=0	1394
PY2	200×150×6×1200	C40(Ⅱ)	54.1	334	10	e_x=60, e_y=0	1354
PY3	200×150×6×1200	C40(Ⅲ)	51.4	334	15	e_x=60, e_y=0	1335
PY4	200×150×6×1500	C50(Ⅰ)	59.7	334	0	e_x=40, e_y=0	1623
PY5	200×150×6×1500	C50(Ⅱ)	54.6	334	10	e_x=40, e_y=0	1518
PY6	200×150×6×1500	C50(Ⅲ)	59.4	334	15	e_x=40, e_y=0	1622
PY7	200×150×6×1200	C40(Ⅰ)	45.5	334	0	e_x=40, e_y=40	1360
PY8	200×150×6×1500	C50(Ⅰ)	59.7	334	0	e_x=40, e_y=40	1287

Table 2.

Concrete mix proportions.

Mix ID	Cement (kg/m³)	Water (kg/m³)	Sand (kg/m³)	Gravel (kg/m³)	Fly ash (kg/m³)	Mineral powder (kg/m³)	Water reducing admixture (kg/m³)	Expansion agent (kg/m³)
C40(Ⅰ)	418	178	721	950	87	76	3.8	0
C40(Ⅱ)	418	178	721	950	87	76	3.8	58
C40(Ⅲ)	418	178	721	950	87	76	3.8	87
C50(Ⅰ)	502	181	616	916	122	93	5.0	0
C50(Ⅱ)	502	181	616	916	122	93	5.0	72
C50(Ⅲ)	502	181	616	916	122	93	5.0	108

Experimental setup

An eccentric compression test was carried out on a hydraulic test machine with a range of 500 t. As shown in Figure 1 (a), two knife edges were used at both ends for the specimens subjected to uniaxial eccentric loading, while two ball edges were used at both ends for the specimens subjected to biaxial eccentric loading. The design details of these knife edges and ball edges are shown in Figure 1 (b, c). Linear variable displacement transducers (LVDTs) were arranged at the centres of the four sides to measure the axial deformations of the specimens. An LVDT was positioned at each quarter-point along the specimen length to measure the lateral displacement. Longitudinal strain gauges and transverse strain gauges were also placed at each quarter-point of the height on each side of the specimen to record the steel tube strains during the testing. The strains were recorded using a DH3820 measurement system. In addition, the loading speed was set at 1 kN/s. The development of the load was recorded during the test, and the test was terminated when the load dropped to less than 85% of its maximum value.

Figure 1.

Loading equipment (a) Loading equipment and typical strain gauge setup; (b) Knife edges; (c) Ball edges.

Experimental results

Failure modes of specimens

The failure modes of all specimens are shown in Figure 2. It can be seen that most of the specimens failed by overall buckling accompanied by local buckling. For the specimens subjected to biaxial eccentric loading, such as PY7 and PY8, the phenomenon of local buckling occurred in the two adjacent compression sides. And for the specimens subjected to uniaxial eccentric loading, the phenomenon of local buckling occurred in the compression side. The phenomenon of local buckling mostly occurred at the end or quarter-points of the specimens subjected to uniaxial eccentric loading, while the phenomenon of local buckling mostly occurred at the middle of the specimens subjected to biaxial eccentric loading, as shown by the circles in Figure 2. However, it should be noted that the overall buckling was not obvious for some specimens such as PY1, where the local buckling near the top end was significant, resulting in a decrease in its bearing capacity.

Figure 2.

Typical failure modes of the specimens.

Bearing capacity analysis

As shown in Table 1, under the condition of the same concrete strength, the influence of the different eccentric load conditions on the ultimate bearing capacity can be found by the comparison of specimens PY1 and PY7 and the comparison of specimen PY4 and PY8. When the self-compacting micro-expansion CFST columns were subjected to biaxial eccentric loading, the ultimate bearing capacity was lower than that of the self-compacting micro-expansion CFST columns subjected to uniaxial eccentric loading. And by comparing specimen PY2 and PY5, it can be found that the ultimate bearing capacity of the self-compacting micro-expansion CFST columns decreased as the eccentricity increased. The curves that present the change of the ultimate bearing capacity of the specimens subjected to uniaxial eccentric loading with the dosage of expansion agent are plotted, as shown in Figure 3. By comparing specimen PY1 and PY3, it can be found that the ultimate bearing capacity of the specimens slightly decreased as the dosage of expansion agent increased. However, by comparing specimen PY4 and PY6, the ultimate bearing capacity of the specimens increased first and then decreased, the change of the ultimate bearing capacity was in accordance with that of the concrete strength. Overall, the dosage of expansion agent had a relatively small effect on the ultimate bearing capacity of the self-compacting micro-expansion CFST columns. And it is mainly because, to a certain extent, the addition of expansion agent in concrete has a negative effect on the concrete strength (Lin et al., 2015), especially when the dosage of expansion agent increases from 10% to 15%, which affects the mechanical properties of the columns. But under the condition of the same concrete strength and only changing the dosage of expansion agent, the ultimate bearing capacity of the self-compacting micro-expansion CFST columns was increased, the further analysis is provided in parametric analysis of bearing capacities of rectangular CFST columns.

Figure 3.

Influence of the dosage of expansion agent on the ultimate bearing capacity.

Load–displacement curves

The recorded load–displacement curves for the four sides of each of the specimens are plotted in Figure 4. For specimens PY1–PY6, which were subjected to compression and uniaxial bending, the average vertical displacement measured on both sides was taken as the vertical displacement of the lateral side of the specimen.

Figure 4.

Load–displacement curves of all specimens (a) PY1; (b) PY2; (c) PY3; (d) PY4; (e) PY5; (f) PY6; (g) PY7; (h) PY8.

It can be seen that the trends of the load–displacement curves are similar to those for the uniaxial eccentric specimens. This is because the eccentricities of the specimens were not significantly different under the biaxial and uniaxial eccentric loading conditions (the eccentricity values are listed in Table 1), and the lateral deflection continuously increased away from the loading point. When the lateral deflection reached a critical value, the specimens experienced overall bending failure. The load–displacement curves of all specimens under eccentric compression could be roughly divided into three phases: a linear growth phase, nonlinear growth phase and load decreasing phase. The slope of the curve gradually decreased with an increase in the load and then entered the phase of nonlinear growth, which was characterised by a gradual increase in the displacement growth rate. When the load increased to the peak, the growth rate of the displacement of the compression side was greater than that of the tensile side.

Because of the overall bending deformations of the specimens under eccentric loads, the axial compressive deformations on the tensile side in a few specimens (PY4 and PY5) dropped after the load reached the peak value.

In addition, it can be seen that the CFST columns had better ductility. When the load exceeded the peak value, the displacement increased rapidly and the load decreased slowly, and the columns could maintain a good bearing capacity after the peak loads (85% of N_u.). The overall trend of the load–displacement curve for the lateral side was similar to that for the compression side, and the vertical displacement of the lateral side was always smaller than the vertical displacement of the compression side during the loading process.

Lateral deflection along height of specimen

As shown in Figure 1, three lateral LVDTs were arranged in the height direction to measure the lateral deflection of the tensile side of the specimen. Based on the test loading sequence, Figure 5 shows a lateral deflection distribution diagram of the four typical load rising sections of 0.6 N_u, 0.8 N_u, 0.9 N_u and N_u, and meanwhile the load falling section of 0.858 N_u. It can be seen that the development speed of the lateral displacement at the middle height of the columns was rapid, and the lateral displacement decreased from the middle to both ends. As the load increased, the lateral displacement at both ends gradually increased, and the curve formed an approximately sinusoidal distribution. For biaxial eccentric specimens (PY7 and PY8), the trend of the lateral displacement development at the two tension sides was similar to that of the uniaxial eccentricity specimens (PY1–PY6). In addition, for the area in tension, the lateral deformation (Ux) in the narrow face direction was smaller than the lateral deformation (Uy) in the wide face direction.

Figure 5.

Distribution of displacements along the height of specimens (a) PY1; (b) PY2; (c) PY3; (d) PY4; (e) PY5; (f) PY6; (g) PY7(the wide face); (h) PY7(the narrow face); (i) PY8(the wide face); (j) PY8(the narrow face).

Diagrams of load–strain relationships

The vertical and transverse strain data for the compression side, tension side and two lateral sides measured at the 1/4L, 1/2L and 3/4L heights of the specimens were extracted, and the load–strain curves of PY1–PY8 were shown in Figure 6, respectively.

Figure 6.

Load–strain curves (a) PY1; (b) PY2; (c) PY3; (d) PY4; (e) PY5; (f) PY6; (g) PY7; (h) PY8.

As shown in the figures, as the load increased, the strain increase rate in the middle height of the columns was faster than those at the other two points, which was similar to the development of the deflection along the column height discussed in the previous section. It can be seen that the fastest development of strain in the middle height of the column generally occurred during the period of decrease in the load resistance after the peak value. The strain at the middle height of the column increased rapidly, but the load decreased slightly, indicating that it had good ductility after the failure and still maintained a high bearing capacity. In addition, from the development process of the strain curves in the figure, it can be seen that the strains on both the compressed and tensile sides were stable as a result of the concrete infill. This indicated that the concrete-filled steel tubular column composite members were relatively stable when resisting compressive loads.

A comparison of the strain development on the tension side with that on the compression side for all specimens showed that the position of maximum longitudinal strain in the steel tube on the compression side was the first location to fail, which should be taken into account in the design. The development of tensile strains was generally limited, and the longitudinal strains were much larger than the transverse strains. As shown in Figure.6(a)–(c), a comparison of the strain development processes on the tensile side of the steel tube under different eccentricities showed that at larger eccentricities (PY1–PY3), the longitudinal strains on the opposite sides had the opposite signs, while the transverse strains were compression ones. However, for the columns with smaller eccentricities, the longitudinal strains were compression and the transverse strains were tensile at the initial stage of loading. With an increase in the load, longitudinal tensile strains and transverse compressive strains could develop, and the stress conditions of the members should be fully analysed during their design. Therefore, during eccentric compression, specimens may be subjected to compression or tension, and their stress conditions should be fully considered in the design. For the biaxial bending test specimens, the trends of the changes in the load–strain development were similar due to their similar load eccentricities. With increasing load, the longitudinal strain on the side of the column cross-section far from the loading point changed from the initial compressive strain to a tensile strain, as shown in tension side 2 of both PY7 and PY8 in Figure 6 (h).

Numerical analysis

Finite element model

Finite element model for CFST column without expansion agent

An elastic–plastic model was selected for the stress–strain relationship of the steel (equation (1)), as shown in Figure 7. It should be noted that the steel’s yield strength and ultimate tensile strength were determined according to the material test results, and Young’s modulus of the steel was 2.06 × 10⁵ MPa. To consider the beneficial confinement provided by the steel tube, the equivalent stress–strain relationship model proposed in the literature (Han and Tao, 2001) was adopted for determining the uniaxial stress–strain curve of the core concrete, as shown in equation (2), combined with the material test results for the concrete

σ_{s} = \begin{matrix} {\begin{cases} E_{s} ε_{s} \\ f_{y} + α E_{s} (ε_{s} - ε_{y}) \end{cases} & \begin{array}{l} (ε_{s} \leq ε_{y}) \\ (ε_{s} > ε_{y}) \end{array} \end{matrix}

(1)

σ_{c} = {\begin{cases} σ_{0} [A \frac{ε_{c}}{ε_{0}} - B {(\frac{ε_{c}}{ε_{0}})}^{2}] (ε_{c} \leq ε_{0}) \\ σ_{0} (\frac{ε_{c}}{ε_{0}}) \frac{1}{β {(\frac{ε_{c}}{ε_{0}} - 1)}^{η} + \frac{ε_{c}}{ε_{0}}} (ε_{c} > ε_{0}) \end{cases}

(2)

here

σ_{0} = f_{ck} [1.194 + {(\frac{13}{f_{ck}})}^{0.45} (- 0.01961 ξ^{2} + 0.1447 ξ)]

ε_{0} = ε_{cc} + [1330 + 760 (\frac{f_{ck} - 20}{20})] ξ^{0.2} (μ ε)

A = 20 - k; B = 1.0 - k; k = 0.1 ξ^{0.745}

ε_{cc} = 1300 + 14.93 f_{ck} (μ ε); η = 1.60 + 1.5 \frac{ε_{0}}{ε_{c}}

β = {\begin{cases} \frac{0.75}{1 + \sqrt{ξ}} f_{ck}^{0.1} (ξ \leq 3.0) \\ \frac{0.75}{(1 + \sqrt{ξ}) {(ξ - 2)}^{2}} f_{ck}^{0.1} (ξ > 3.0) \end{cases}

Figure 7.

Ideal elastic–plastic model for steel.

Eight-node 3D solid elements with reduced integration (C3D8R) were selected for the element types of the steel tube and core concrete. The surface-to-surface contact was set to simulate the interaction between the two parts. Specifically, the steel tube was set as the master surface, and the concrete was set as the slave surface. Hard contact was selected to simulate the normal behaviour of the interface. The tangent behaviour of the interface was simulated using the Coulomb friction model, with a value of 0.6 used for the friction coefficient (Baltay and Gjelsvik, 1990). The finite sliding method was selected as the tracking method to determine the contact state.

The line load and point load were used to simulate the uniaxial eccentricity and biaxial eccentricity loading modes, respectively. Two steel plates were included in the finite element model, bound to the top and bottom surfaces of the specimen. For the uniaxial eccentricity specimens, the reference points of each specimen were set according to the eccentricity and coupled to the loading line. For the biaxial eccentric specimens, the reference point could directly be used as the loading point, and the change in the eccentricity of the model was realised by changing the coordinates of the reference points. In addition, the boundary conditions of the rectangular CFST column model were consistent with the tests. For the uniaxial eccentricity specimens, the boundary conditions were $U_{1} = U_{2} = U_{3} = U R_{2} = U R_{3} = 0$ at the lower reference points of the specimen and $U_{1} = U_{2} = U R_{2} = U R_{3} = 0$ at the upper reference points of the specimen. For the biaxial eccentric specimens, the boundary conditions were $U_{1} = U_{2} = U_{3} = U R_{3} = 0$ at the lower reference points of the specimen and $U_{1} = U_{2} = U R_{3} = 0$ at the upper reference points of the specimen. To ensure a better convergence of the results (Tao et al., 2013), the load was applied using the displacement control method. The amount of displacement $U_{3}$ was set at the upper reference points.

Finite element model for CFST column with expansion agent

The finite element model of a CFST column without an expansion agent was established using to the steps explained above. However, unlike ordinary concrete, expansion concrete can produce constraining stresses due to the constraint imposed by the steel tube. Therefore, it was also necessary to consider the effect of the concrete expansion stress on the performance of the specimens. Referring to the literature (Lu et al., 2007), it is assumed that the ordinary concrete expands uniformly when the temperature rises $Δ T$ , under the confinement of the steel tube, the stress caused by temperature rise is equal to the self-stress of the self-compacting low-expansion concrete under the restraint of the steel tube. The elastic recovery strain, caused by the released expansion energy with rising temperature, shall be equal to the elastic recovery strain which is generated by expansion of the expansive concrete under the confinement of the steel tube. Considering the linear volume effect between the specimen and the standard length of the free expansion rate test block, the elastic recovery strain $\bar{ε_{r}}$ can be equivalent to the free expansion rate $ε_{0}$ through a linear volume coefficient $λ$ , which means the equation is $\bar{ε_{r}} = λ ε_{0}$ . Therefore, the equivalent temperature $Δ T$ can be expressed by the equation (3) (Lu et al., 2007)

Δ T = λ \frac{ε_{0}}{α_{c}}

(3)

Here, thermal expansion coefficient $α_{c}$ is equal to 1 × 10^-5/°C according to GB 50010-2010 (2015), $λ$ is the linear volume coefficient, λ = d/l, d is the side length of the core concrete and l is the standard length of the free expansion rate test mould.

Thus, by coupling the ordinary concrete and the rising temperature in the finite element model, the constrained stress of the steel tube can be calculated using equations (4) and (5), and the self-stress of the concrete, generated by expansion concrete can be calculated using equations (6) and (7). According to the literature (Hu and Ding, 2007), the free expansion rate of the concrete, $ε_{0}$ , can be calculated by equation (8)

σ_{x} = \frac{E_{s}}{1 - μ^{2}} (ε_{x}^{'} + μ ε_{zx}^{'})

(4)

σ_{y} = \frac{E_{s}}{1 - μ^{2}} (ε_{y}^{'} + μ ε_{zy}^{'})

(5)

Here, $ε_{x}^{'}$ and $ε_{y}^{'}$ are the equivalent lateral strains on the narrow and wide faces of the CFST columns, respectively. $ε_{zx}^{'}$ and $ε_{zy}^{'}$ are the equivalent axial strains on the narrow and wide faces of the CFST columns, respectively. E_s is the elastic modulus of the steel tube, and μ is the Poisson’s ratio of the steel.

q_{x} = \frac{2 t}{D - 2 t} \cdot σ_{x}

(6)

q_{y} = \frac{2 t}{B - 2 t} \cdot σ_{y}

(7)

Here, D and B are the measured depth and width of the CFST columns, respectively, and

t

is the measured wall thickness of the steel hollow section.

ε_{0} = \frac{q}{E_{c} (1 - \frac{K E_{c}}{K E_{c} + E_{s}})} + ε_{A}

(8)

Here,

ε_{0}

is the concrete free expansion rate and

ε_{A}

is the modified value of the concrete expansion rate.

The free expansion rate of the concrete was not measured in the eccentric compression tests for PY1–PY8, but the free expansion rate is a key factor when calculating the equivalent temperature. Therefore, three self-compacting lower expansion small CFST specimens were made with the same amount of expansion agent as the test specimen. The effect of the concrete self-stress on the strain distribution of the steel tube was determined by studying the free expansion rate of the concrete in small tubular specimens with a 100 × 100 × 4 mm cross-section and 500 mm length. In order to measure the strain distribution in the steel hollow section, a series of strain gauges was affixed to the steel tubes, as shown in Figure 8. After the concrete was poured, the steel strains were continuously measured for 28 days. The development of the steel strains in the specimens over time is shown in Figure 9. Based on the measured data, equations 9, and 10 can be used to calculate the equivalent lateral strains of CFST columns with other section sizes.

ε_{x}^{'} = ε_{x} \cdot \frac{K_{x} E_{c} + E_{s}}{K_{x}^{'} E_{c} + E_{s}}, ε_{zx}^{'} = ε_{zx} \cdot \frac{K_{x} E_{c} + E_{s}}{K_{x}^{'} E_{c} + E_{s}}, K_{x} = D / t, K_{x}^{'} = D^{'} / t^{'}

(9)

ε_{y}^{'} = ε_{y} \cdot \frac{K_{y} E_{c} + E_{s}}{K_{y}^{'} E_{c} + E_{s}}, ε_{zy}^{'} = ε_{zy} \cdot \frac{K_{y} E_{c} + E_{s}}{K_{y}^{'} E_{c} + E_{s}}, K_{y} = B / t, K_{y}^{'} = B^{'} / t^{'}

(10)

Here,

ε_{x}

and

ε_{y}

are the lateral strains measured on the narrow and wide faces of the small CFST columns, respectively.

ε_{zx}

and

ε_{zy}

are the axial strains measured on the narrow and wide faces of the small CFST columns, respectively. E_c is the elastic modulus of the concrete,

D^{'}

is the depth of the equivalent CFST column,

B^{'}

is the width of the equivalent CFST column and

t^{'}

is the thickness of the equivalent steel tube.

Figure 8.

Arrangement of strain gauges.

Figure 9.

Strain–time diagrams of steel tube for specimens with different dosages of expansion agent.

Thus, temperatures $Δ T_{1}$ and $Δ T_{2}$ on the wide and narrow sides of the steel tube, respectively, were obtained using equation (3). According to the linear relationship of the dimensions and referring to equation (11), the equivalent temperature, $Δ T$ , of the entire CFST column was calculated. Here, $Δ T$ can be taken to be 33.4 °C when the amount of expansion agent is 10%, and as 39.9°C when the amount of expansion agent is 15%.

Δ T = \frac{D^{'} Δ T_{1} + B^{'} Δ T_{2}}{(D^{'} + B^{'})}

(11)

Analysis of finite element results

The failure modes from the FEM analyses are shown for all the specimens in Figure 10. As shown in Figure 10, the failure modes obtained by the finite element simulations were consistent with the experimental failure modes. And the bending deformations of the specimens were more symmetrical as a result of the uniform material properties used in the numerical simulations.

Figure 10.

Comparison of simulated failure modes (a)PY1; (b) PY2; (c) PY3; (d) PY4; (e) PY5; (f) PY6; (j) PY7; (k) PY8.

Verification of the finite element model

The reaction forces at the reference points in the finite element model were extracted to obtain the finite element simulation results for the specimen bearing capacity, as shown in Figure 11. A comparison of the simulation results and test results showed good agreement. Thus, the model had good accuracy and provided a good basis for subsequent parametric studies on the behaviour of eccentrically loaded CFST columns.

Figure 11.

Comparison of bearing capacities.

The load–displacement curve of each test specimen was obtained by extracting vertical reaction force FR3 at the loading point of the finite element model and the displacement at the centre point of the top surface of the specimen. Taking test specimens PY2 and PY8 as examples, the simulation and experimental curves are compared in Figure 12. It can be found that the simulation results shown in the curve are similar to the experimental results, but the simulation curve is more ideal. The rising section of the simulation curve has a large stiffness, and the displacement at the peak is generally smaller than the experimental value. Because of safety considerations, the test was stopped when the load dropped to 85% of the peak value. Thus, the numerical curve is suitable for reflecting the degradation of the bearing resistance in the descending part of the response diagram.

Figure 12.

Comparison of simulation and experimental load–displacement curves (a) PY2; (b) PY8.

Specimen PY2 subjected to uniaxial eccentric loading and specimen PY8 subjected to biaxial eccentric loading are taken as examples to plot load–mid-span lateral displacement curves. For specimen PY8, the side with relatively big lateral displacement at mid-span (tension side 2, as shown in Figure 1) are taken in the examples, and the comparison of the test results and the numerical simulation results is shown in Figure 13. It can be found that the numerical simulation curves of both the specimens subjected to uniaxial eccentric loading and the specimens subjected to biaxial eccentric loading are basically consistent with the test curves.

Figure 13.

Comparison of simulation and experimental load–mid-span lateral displacement curves (a) PY2; (b) PY8.

According to the comparisons of the ultimate bearing capacity, load–displacement curves and load–mid-span lateral displacement curves of each specimen between the test results and the finite element prediction results, the finite element modelling method adopted in this paper is reasonable and effective.

N–M diagrams

A previous study found that the finite element model used in tests was very accurate when estimating the bearing capacity of CFST columns under eccentric compression. Therefore, on the basis of the model, ultimate internal force values n (Y coordinate) and m (X coordinate) under different eccentricities were obtained by changing the eccentricity of the specimens and are plotted in Figure 14. The figure also shows the N–M diagrams based on both the test and specifications BS EN 1994-1-1:2004 and CECS 159:2004. As can be seen from Figure 14, the N–M diagrams obtained by specification BS EN 1994-1-1:2004 are in good agreement with the N–M diagrams obtained by the finite element models, especially when the specimens under the condition of small eccentricity. From the N–M diagrams based on specification CECS 159: 2004, it can be seen that the predicted results are smaller than that of specifications BS EN 1994-1-1:2004 and the finite element models.

Figure 14.

N–M curves for PY1–PY6 (a) PY1; (b) PY2; (c) PY3; (d) PY4; (e) PY5; (f) PY6.

Based on the existing models, five eccentric angles of eccentricity, θ = 0° ( $e_{x} = 0$ ), 26.565° ( $e_{x} = 2 e_{y}$ ), 45° ( $e_{x} = e_{y}$ ), 63.5° ( $e_{x} = 0.5 \cdot e_{y}$ ) and 90° ( $e_{y} = 0$ ), were selected to calculate the internal forces of biaxial eccentric specimens with different eccentricities. The MATLAB software was used to plot and merge the simulation results. Based on the collation of the current data, the N-M_x-M_y surfaces of specimens PY7–PY8 are shown in Figure 15. When the eccentricity was smaller, N_u. decreased with an increase in M_u, and when the eccentricity was larger, N_u. increased with an increase in M_u. For a specimen with a given value of eccentricity, when the loading point was closer to the wide side of the cross-section, the value of N_u. was larger, but the effect was limited. According to the simulation results, it was found that the inflexion points of the N–M diagrams with different eccentricities formed a trajectory on the fitted curved surface. The trajectories were approximately parallel to the M_x-M_y plane, indicating that the inflexion points were substantially at the same level. Comparing the N–M curves obtained by the whole test loading procedure with the merged curved surfaces, it was found that the finite element prediction results were close to the experimental values, and the experimental values were slightly larger than the predicted values; thus, the prediction was safe and reasonable.

Figure 15.

N-M_x-M_y curve of PY7–PY8 (a) PY7; (b) PY8.

The bearing capacities of specimens PY1–PY8 were predicted by using the relevant calculation formulas in specifications BS EN 1994-1-1:2004 and CECS 159:2004, and the predicted results of specifications BS EN 1994-1-1:2004 and CECS 159:2004 and the finite element models were compared with the experimental values. The analysis results are shown in Table 3. In Table 3, N_e is experimental bearing capacity of specimen; N_p is predicted bearing capacity of specimen;

N_{pi} / N_{ei}

is ratio of N_p to N_e for each specimen; _i is serial number of specimens, from 1 to 8;

θ

is mean value of

N_{pi} / N_{ei}

;

D

is variance value of

N_{pi} / N_{ei}

;

τ

is coefficient of variation of

N_{pi} / N_{ei}

and

n

is the number of specimens.

Table 3.

Comparisons of predicted results with experimental results.

Specimens	N_e (kN)	CECS 159:2004		BS EN 1994-1-1:2004		Finite element model
		N_p (kN)	N_p/N_e	N_p (kN)	N_p/N_e	N_p (kN)	N_p/N_e
PY1	1394	1119	0.80	1239	0.89	1263	0.86
PY2	1354	1166	0.86	1331	0.98	1336	0.94
PY3	1335	1152	0.86	1303	0.98	1320	0.94
PY4	1623	1398	0.86	1643	1.01	1551	0.96
PY5	1518	1363	0.90	1579	1.04	1525	1.00
PY6	1622	1396	0.86	1643	1.01	1579	0.97
PY7	1360	971	0.71	1177	0.87	1359	0.86
PY8	1287	1027	0.80	1198	0.93	1357	0.93
$θ= \frac{\sum_{i = 1}^{n} \frac{N_{p i}}{N_{e i}}}{n}$		0.832		0.964		0.931
$D= \frac{Σ_{i = 1}^{n} {(\frac{N_{p i}}{N_{e i}} − θ)}^{2}}{n}$		0.003		0.003		0.002
$τ= \frac{\sqrt{D}}{θ}$		0.066		0.061		0.051

The analysis results in Table 3 indicate that specifications BS EN 1994-1-1:2004 and CECS 159: 2004 and the finite element models have relatively high prediction accuracy in predicting the bearing capacities of the specimens under eccentric loading. For specimens PY1–PY8, the predicted results of specification CECS 159: 2004 are smaller than the experiment results; the difference of the predicted results of specification BS EN 1994-1-1:2004 with the experimental results and the difference of the predicted results of the finite element models with the experimental results are both relatively small, the consistencies of the predicted results of both specification BS EN 1994-1-1:2004 and the finite element models with the experiment results are relatively high.

Parametric analysis of bearing capacities of rectangular CFST columns

In order to study the influence of the expansion agent content on the compression–bending capacity of self-compacting micro-expansion rectangular CFST columns, 225 specimens with different parameters were designed. These combinations of parameters (D/B ratios, cross-sectional sizes, expansion agent content γ, wall thicknesses and lengths of steel tubes) are listed in Table 4. The finite element analyses of the CFST columns under unidirectional eccentric compression with the same eccentricity condition (e_x=60, e_y=0) were carried out. The material properties of the concrete and steel tube were adopted based on the test data of specimens PY2 and PY3. The compressive strength of concrete with an expansion agent content of 10% was 54.1 MPa, and the compressive strength of concrete with an expansion agent content of 15% was 51.4 MPa. Under the same conditions, a control group with the expansion agent of 0% was set up for each type of self-compacting micro-expansion CFST column with the same concrete strength.

Table 4.

Specimens parameters.

Parameters	Values of parameters
D×B (mm)	180×140/186×140/190×140/200×140/210×140
D/B ratios	1.28/1.33/1.35/1.43/1.5
Thicknesses of steel tube t (mm)	4/5/6/7/8
Expansion agent content γ	0%/10%/15%
Length L (mm)	1200/1500/1800

The establishment of the finite element model was explained in finite element model, and it yielded the equivalent temperature, ΔT. With expansion agent γ = 10%, ΔT = 17–53 °C, and with γ = 15%, ΔT = 22–64 °C. The finite element simulation provided failure modes for the specimens that were close to those found in the experiments and those of simulated specimens PY1–PY8, as shown in Figure 16.

Figure 16.

Simulated failure modes (a) L = 1200; (b) L = 1500; (c) L = 1800.

The maximum bearing capacity calculated by the numerical analysis was extracted, and the bearing capacity increase coefficient β was calculated according to equation (12)

β = \frac{N}{N_{0}}

(12)

where N indicates the compression–bending capacity of the column with the expansion agent and N₀ is the capacity without it.

As shown in Figure 17, the specimens were classified according to length, and a comparison of the bearing capacity increase coefficient β curves showed that when the D/B ratio and thickness changed, the influence of the amount of expansion agent γ on the compression–bending capacity of the CFST columns with self-compacting micro-expansion concrete followed a certain law. For specimens with different cross-sectional dimensions, the degree of influence and change tendency for the compression–bending capacity of CFST columns with the same expansion agent content γ were basically the same. The bearing capacity of a specimen with the same D/B ratio and expansion agent content γ was significantly increased by an increase in the thickness. In addition, it was found that different expansion agent contents had different effects on the compression–bending capacity of the rectangular CFST columns. When the expansion agent content γ of a specimen increased from 0% to 10%, the compression–bending capacity improved by 1.03%–4.21%. When the dosage of expansion agent γ of a specimen increased from 0% to 15%, the compression–bending capacity improved by 1.79%–5.10%. For the specimens with same size, when the expansion agent content of the specimens increased from 10% to 15%, the compression–bending capacity improved by 0.4%–0.7%. Therefore, when the expansion agent content γ of a specimen increased from 0% to 10%, the bearing capacity of the columns increases significantly. However, the strength of concrete decreases with the increase of expansive agent content, when continue increasing the expansive agent content, the expansion agent content has little effect on the compression–bending bearing capacity.

Figure 17.

β change curves with t and D/B (a) L = 1200 mm; (b) L = 1500 mm; (c) L = 1800 mm.

Conclusions

This paper presented the results of tests on eight rectangular self-compacting lower expansion CFST columns, along with an analysis of the mechanical behaviours of the specimens under uniaxial and biaxial compression–bending loads. A numerical model of the columns with the expansion agent was developed by adding the temperature field, and the model was verified by comparison with the test results. Then, the N–M curves of the CFST columns under the compression–bending load were obtained through parametric numerical analyses of the model. The prediction accuracies of the existing codes for calculating the bearing capacity of the columns were compared, and the following conclusions were drawn.

(1) The failure mode, load–displacement curves, lateral deflection distribution curves and load–strain curves were obtained through compression–bending tests. Compared to the failure modes of the specimens, the overall deformation shape of the column was sinusoidal, which was seen more clearly in specimens with larger slenderness ratios. The maximum deflection was located near the middle height of the column.

(2) When developing the numerical model for the rectangular self-compacting lower expansion CFST columns, the equivalent expansion of the concrete was simulated by applying a temperature field to the column cross-section. The validity of the numerical simulation was verified by comparing it with the test results. The N–M curve for each column was obtained based on a parametric analysis of the eccentricities. Compared with the experimental results and simplified N–M calculation curves calculated using the existing specifications (BS EN 1994-1-1:2004, CECS 159:2004), the values predicted by the model had better accuracy.

(3) By setting various values for the length, D/B ratio, thickness and expansion agent content, parametric finite element analyses of CFST columns with self-compacting micro-expansion concrete were performed under the same eccentricity. It was found that when the expansion agent content γ of a specimen increased from 0% to 10%, the bearing capacity of the columns increases significantly, but when continue increasing the expansive agent content, the expansion agent content has little effect on the compression–bending bearing capacity. The influence of the expansion agent content on the compression–bending capacity has great theoretical significance for engineering application.

Footnotes

Acknowledgements

Thanks to the teachers and students of the structural laboratory of Beijing university of architecture and civil engineering for their kind help for our tests.

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

This paper is funded by the Natural Science Foundation of Beijing (8202011), National Natural Scientific Fund (51408026), Beijing University of Civil Engineering and Architecture Pyramid Talents Cultivation Project (JDYC20160205) and National Key R&D Plan (2017YFC0703806).

ORCID iD

XiuShu Qu

Appendix

References

Y-F

Han

L-H

(2014) Behaviour of concrete-encased CFST columns under combined compression and bending. Journal of Constructional Steel Research 101: 314–330.

Baltay

Gjelsvik

(1990) Coefficient of friction for steel on concrete at high normal stress. Journal of Materials in Civil Engineering 2(1): 46–49.

BS EN 1994-1-1 (2004) Eurocode 4: Design of Composite Steel and Concrete Structures-Part 1-1 General Rules and Rules for Buildings. European Committee for Standardization

Chang

Huang

C-K

Chen

Y-J

(2009) Mechanical performance of eccentrically loaded pre-stressing concrete filled circular steel tube columns by means of expansive cement. Engineering Structures 31(11): 2588–2597.

CECS 159 (2004) Technical Specification for Structures with Concrete-filled Rectangular Steel Tube Member. China: China Planning Press.

GB/T 50081-2019 (2019) Standard for Test Method of Concrete Physical and Mechanical Properties. China: China Architecture & Building Press.

GB/T 228.1-2010 (2011) Metallic materials -Tensile testing -Part l : Method of test at room temperature. China: Standards Press of China.

GB 50010-2010 (2015) Code for Design of Concrete Structures. China: China Architecture & Building Press.

Ding

(2007) Concrete-filled Steel Tube. 1rd. Beijing: China Communications Press.

10.

Han

Tao

(2001) Study on behavior of concrete filled square steel tubes under axial load. China Civil Engineering Journal 34(2): 17–25.

11.

Han

L-H

Yao

G-H

(2004) Experimental behaviour of thin-walled hollow structural steel (HSS) columns filled with self-consolidating concrete (SCC). Thin-Walled Structures 42(9): 1357–1377.

12.

Huang

Fan

Shen

, et al. (2020) Experimental and numerical study on the compressive behavior of micro-expansive ultra-high-performance concrete-filled steel tube columns. Construction and Building Materials 254: 119150.

13.

Lin

Huo

(2015) Research on the application of expansive agent in C60 self-compacting concrete. Key Engineering Materials 629-630: 425–431.

14.

Liu

, et al. (2020) Behavior of steel tube columns filled with steel-fiber-reinforced self-stressing recycled aggregate concrete under axial compression. Thin-Walled Structures 149: 106521.

15.

Sun

(2007) Nonlinear equivalent simulation of mechanical properties of expansive concrete-filled steel tube columns. Advances in Structural Engineering 10(3): 273–281.

16.

Muciaccia

Giussani

Rosati

, et al. (2001) Response of self-compacting concrete filled tubes under eccentric compression. Journal Of Constructional Steel Research 67(5): 904–916.

17.

Mahgub

Ashour

Lam

, et al. (2017) Tests of self-compacting concrete filled elliptical steel tube columns. Thin-Walled Structures 110: 27–34.

18.

Ouyang

Kwan

AKH

, et al. (2017) Finite element analysis of concrete-filled steel tube (CFST) columns with circular sections under eccentric load. Engineering Structures 148: 387–398.

19.

Chen

, et al. (2019) Study on circular CFST stub columns wit double inner square steel tubes. Thin-Walled Structures 140: 195–208.

20.

Tao

Wang

(2013) Strength of concrete filled steel box columns incorporating local buckling. Journal of Materials in Civil Engineering 25(9): 1306–1316.

21.

Wang

Shen

Wang

, et al. (2018) Experimental and analytical studies on CFRP strengthened circular thin-walled CFST stub columns under eccentric compression. Thin-Walled Structures 127: 102–119.

22.

Zhou

, et al. (2016) Experimental research on axial compression performance of medium-and-long steel tubular columns filled with high-strength self-stressing self-compacting concrete. China Civil Engineering Journal 49(11): 26–34.

23.

Chen

Yuan

(2010) Push-out test on bond property of micro-expansive concrete-filled steel tube columns. Advanced Materials Research 163-167: 610–614.

24.

Chen

Yuan

(2011) Confined expansion and bond property of micro-expansive concrete-filled steel tube columns. The Open Civil Engineering Journal 5: 173–178.

25.

Young

Ellobody

(2006) Experimental investigation of concrete-filled cold-formed high strength stainless steel tube columns. Journal of Constructional Steel Research 62(5): 484–492.

26.

Yuan

Huang

Chen

(2019) Effect of stiffeners on the eccentric compression behaviour of square concrete-filled steel tubular columns. Thin-Walled Structures 135: 196–209.

27.

Cao

Fang

, et al. (2020) Mechanical behavior of self-stressing steel slag aggregate concrete filled steel tubular short columns with different loading modes. Structures 26: 947–957.