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Edited by: Zhao-Dong Xu, Southeast University, China

Reviewed by: Jianwei Zhang, Beijing University of Technology, China; Dejian Shen, Hohai University, China

This article was submitted to Structural Materials, a section of the journal Frontiers in Materials

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Concrete-filled steel tube (CFST) columns are increasingly used in composite construction. Under axial compression, the steel tube will sustain partial axial force and meanwhile provides the confinement to the infill concrete. The high axial strength capacity of CFST columns is largely related to the confinement provided by the steel tube. Extensive studies on CFST columns have been conducted. Nevertheless, how to quantify the efficiency of confinement effect in CFST columns using concrete with different strength grades is still missing. To address this issue, a series of compressive loading tests on CFST columns were conducted in present study. The variable parameters studied include concrete strength and diameter-to-thickness ratio of the steel tube. Six CFST stub columns in total were designed and tested under uniaxial compression. Axial strength, stress state in the steel tube, confined concrete strength and confining pressure acting on the infill concrete were carefully investigated. Test results show that the confinement factor (defined as the ratio of the nominal strength of empty steel tube to that of the unconfined concrete) is the most dominant factor influencing the confinement effect, and a larger confinement factor gives higher confinement effect. The low-strength concrete exhibits better performance of ductility and confinement compared with the high-strength concrete. The index of equivalent confining pressure was used to quantify the level of passive confinement provided by the steel tube in CFST columns. Based on the test results, a method to quickly quantify the confining pressure provided by the steel tube was proposed.

Concrete-filled steel tube (CFST) columns are increasingly used in the construction of highrise buildings which require high strength and large working space especially at lower stories. As compared to reinforced concrete columns, existence of the exterior steel tube not only bears a portion of axial load but also most importantly provides confinement to the infill concrete. With the confinement provided by the steel tube, axial strength of the infill concrete can be largely enhanced. Also, the restraining effect of the infill concrete can prevent or at least delay the local buckling of the steel tube. This interaction between the infill concrete and steel tube together contributes to the high strength and good ductility.

Within the domain of researches focusing on confined concrete, there were basically two categories according to the way how the confinement was applied, active confining and passive confining. In the study of actively confined concrete, the confining pressure was either initially increased to a target value and then kept constant or increased from zero to the target value and then kept constant (Imran and Pantazopoulou,

This paper aims to quantify the passive confinement effect in CFST columns. To address this, a series of CFST column specimens with infill concrete of different strength grades were designed and uniaxially compressed. Axial strength, stress state of steel tube and development and quantification of confinement effect were carefully investigated.

For CFST columns under axial compression, the axial load _{z}) and infill concrete (σ_{cc}), as shown in _{θ} of the steel tube is the source for the lateral confining pressure σ_{r} applied to the infill concrete. With the existence of σ_{r}, the concrete compressive strength is largely enhanced. In the actively confined concrete, the confined concrete strength, _{cc}, can be estimated by the following equation (Mander et al.,

Stress state:

where _{c} is the compressive strength of unconfined concrete; _{r} is the lateral confining pressure.

The value of the confinement coefficient

In CFST columns, the lateral confining pressure can be calculated according to the force equilibrium condition of the cross section. As it can be seen from _{r} and σ_{sθ} gives

where

Once the hoop stress in the steel tube is obtained, the confining pressure provided by the steel tube to the infill concrete can be estimated.

Rewriting Equation 2 gives

Compressive strength of the infill concrete can be obtained by subtracting the force undertook by the steel tube from the overall axial strength of the column as follows.

where _{cc} is the compressive stress of the infill concrete; _{s} and _{c} are the cross-sectional area of steel tube and concrete, respectively; and σ_{z} is the axial stress in the steel tube.

For the thin-walled steel tube, the von Mises yield criterion can be applied. Under both axial stress component σ_{z} and the hoop stress component σ_{θ}, the equivalent stress σ_{e} can be determined as follows.

In this study, elastic-perfectly plastic model is assumed for the tube steel. By comparing the equivalent stress σ_{e} with the yield stress, the steel tube can be identified to being yielding or not. The stress state of the steel tube can be calculated using the strain increment method (Hu et al.,

where σ_{z} and σ_{θ} are the axial stress and hoop stress, respectively; ε_{z} and ε_{θ} are the axial strain and hoop strain, respectively; _{s} is the elastic modulus; ϑ is Poisson's ratio of the steel tube; and

For the elastic-plastic range, the stress increments are calculated from strain increments by the following equation:

where _{x} and _{θ} are the deviatoric strain and stress, respectively.

After obtaining the axial and hoop stresses of the steel tube based upon the measured axial and hoop strains at each loading step and the above equations, the confined concrete strength can be estimated according to Equation 4.

All specimens were designed to have a same length-to-diameter ratio of 3 to ensure stub column behavior. ^{2}, respectively; Specimens in Group 2 used two grades of concrete, with cylinder compressive strengths of 32.0 and 64.0 N/mm^{2}, respectively. All steel tubes were cold-formed carbon steel and seam welded by machine welding. To get the basic mechanical property of the steel material, three coupons were randomly cut from the steel tube and were tested according to standard procedures (Davis,

Summary of test specimens.

_{c}^{2}) |
_{s}^{2}) |
_{0} (kN) |
||||||
---|---|---|---|---|---|---|---|---|

1 | 165.2 | 3.7 | 44.6 | 29.5 | 366.0 | 1.19 | 1,264 | 1.13 |

2 | 165.2 | 3.7 | 44.6 | 43.5 | 366.0 | 0.81 | 1,538 | 1.09 |

3 | 165.2 | 3.7 | 44.6 | 58.0 | 366.0 | 0.61 | 1,821 | 1.15 |

4 | 165.2 | 3.7 | 44.6 | 81.6 | 366.0 | 0.43 | 2,283 | 1.10 |

5 | 230.0 | 2.3 | 100.0 | 32.0 | 360.8 | 0.46 | 1,870 | 1.06 |

6 | 230.0 | 2.3 | 100.0 | 64.0 | 360.8 | 0.23 | 3,147 | 1.04 |

All specimens were subjected to monotonic axial compression exerted by a universal testing machine with a maximum capacity of 5,000 kN. At two end surfaces of the CFST column, two steel plates with a thickness of 50 mm were used to ensure even axial compression. Monotonic axial loading with displacement control was applied. For displacement control, axial shortening, the relative displacement between the top and bottom steel plates, was recorded and used as the actual compressive deformation. Two linear variable differential transducers (LVDTs) with a stroke of 50 mm was installed in parallel with the longitudinal axis of specimens to measure the axial shortening, as shown in

Test setup:

All specimens were centrally compressed. The compression loading was stopped when either the maximum axial shortening reached 5% of column length or axial strength dropped sharply.

All loadings went smooth without brittle deformation observed. ^{2} respectively, exhibited clear sign of concrete crushing at the mid-height, which indicated the brittle characteristic of the high-strength concrete.

Failure modes:

In order to compare the results, the nominal axial strength of CFT columns is defined as _{0} = _{s}_{s} + _{c}_{c}, where _{s} is steel tube yield strength; _{s} is the sectional area of steel tube; _{c} is concrete cylinder compressive strength; and _{c} is the sectional area of concrete.

_{0}, and the abscissa of axial shortening is the ratio of axial displacement measured by LVDTs to the height of columns. The most obvious difference in the load-deformation curves is the post-peak behavior. Only Specimen 1 demonstrated hardening behavior while the rest specimens showed more or less softening. Specimen 6 showed the sharpest decrease of strength beyond the peak strength and its deformability was the worst with the maximum axial displacement of only about 1% of the column length. Its axial strength dropped to less than half of the peak strength almost right after reaching the peak strength. Such a sudden decrease of axial strength needs to be avoided in view of collapse resistance capacity of the building. For specimens in both Group 1 and Group 2, low-strength concrete demonstrated less post-peak strength decrease than high-strength concrete. The width-to-thickness ratio of specimens in Group 2 is much larger than that of specimens in Group 1. While there is no clear difference in the shape of axial load-deformation curve, which means the width-to-thickness of the steel tube is not the controlling parameter for the post-peak behavior. As listed in the last column of

Axial load-deformation curves: _{c} = 29.5, λ = 1.19; _{c} = 43.5, λ = 0.81; _{c} = 58.0, λ = 0.61; _{c} = 81.6, λ = 0.43; _{c} = 32.0, λ = 0.46; _{c} = 64.0, λ = 0.23.

As introduced in the section of instrumentation, both the axial and hoop strains in the steel tube were measured by electrical strain gauges. The recorded strain readings were given in

Recorded strain data: _{c} = 29.5, λ = 1.19; _{c} = 43.5, λ = 0.81; _{c} = 58.0, λ = 0.61; _{c} = 81.6, λ = 0.43; _{c} = 32.0, λ = 0.46; _{c} = 64.0, λ = 0.23.

Substituting the recorded strain data into Equations 6 and 7 gives the axial stress σ_{z} and hoop stress σ_{θ} of the steel tube, as shown in

Calculated stress data: _{c} = 29.5, λ = 1.19; _{c} = 43.5, λ = 0.81; _{c} = 58.0, λ = 0.61; _{c} = 81.6, λ = 0.43; _{c} = 32.0, λ = 0.46; _{c} = 64.0, λ = 0.23.

The improved compressive strength of CFST columns is ascribed to the confinement provided by the steel tube to the infill concrete. The confinement effect is usually quantified by the confinement factor λ, expressed by _{s} and _{c} are the cross-sectional area of steel tube and concrete; and _{s} and _{c} are the strength of steel and concrete, respectively.

As described in a previous session, the maximum normalized axial strength (

It is also can be seen from

After obtaining the axial stress and hoop stress in the steel tube, the confining pressure applied by the exterior steel tube to the infill concrete can be calculated according to Equation 3; the confined concrete strength can be calculated according to Equation 4.

Relationship between confined concrete strength and confining pressure.

For actively confined concrete with constant confining pressure, the relationship between the compressive strength and confining pressure can be given by the following equation (Zhao et al.,

To quantify the level of confinement effect in passively confined CFST columns, Equation 13 can be adopted as an equivalent method. The level of confinement effect in CFST columns can be estimated by the equivalent confining pressure which gives the same confined concrete strength in the actively confined concrete. Equation 13 was also plotted in _{req}. From a regression analysis, the equivalent confining pressure in CFST columns can be roughly estimated as follows.

Equivalent confining pressure.

The mean and coefficient of variance of the ratio of estimation according to Equation (14) to tested values are 1.0209 and 0.3255, respectively.

To this end, knowing the confinement factor of a CFST column, the level of confinement effect can be quickly estimated.

This study worked on the confinement effect in CFST columns and a method to quantify the equivalent confining pressure applied to the infill concrete by the steel tube was developed. The major findings are summarized as follows:

The confinement factor was verified as the key parameter for the axial load carrying capacity. Basically, a larger confinement factor gave smaller post-peak axial strength decrease and larger ductility. With the similar confinement factor, the low-strength concrete exhibited less strength decrease.

The confinement factor was directly related to the level of confining pressure provided by the steel tube to the infill concrete. The strength grade of infill concrete also influenced the confining pressure and CFST columns using low-strength infill concrete showed greater confining pressure.

The stress state of the steel tube and the confined concrete strength were analyzed. To quantify the confinement level in CFST columns, the concept of confining pressure in actively confined concrete was adopted and an index of equivalent confining pressure was proposed. An equation capable of quickly estimating the passive confining pressure in CFST columns was proposed.

All datasets generated for this study are included in the manuscript and/or the supplementary files.

LH supervised the research and wrote the first draft manuscript. SL analyzed test data. HJ reviewed and revised the manuscript, and approved the submitted version. All the authors participated in discussion of the research.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.