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In this paper, the mechanical characteristics of concrete-filled stainless steel and steel tubular (CFSSAST) columns under axial and eccentric loads are analyzed by using the theory of structural stressing state. Firstly, the sum of generalized strain energy density (GSED) values of the short column at every load value (_{j}) is normalized as

The structure concrete-filled stainless steel and steel tubular (CFSSAST) column is a new combined structure developed on the basis of the traditional concrete filled double-skin steel tubular (CFDSST) columns. This kind of composite structure not only inherits the advantages of high bearing capacity, good toughness, good fire resistance, high bending rigidity, and light weight, but also has good corrosion resistance and durability due to the use of stainless steel. And it can be widely applied in structures such as cross-sea bridge structures and offshore platforms that require high resistance to corrosion.

As a kind of special concrete filled double-skin steel tubular, the mechanical properties of CFSSAST components are very similar to those of ordinary CFDSST columns. Therefore, the research on ordinary CFDSST columns could provide significant and valuable references. Tao conducted a series of experiments on concrete-filled double skin steel tubular stub columns (fourteen) and beam-columns (twelve), providing practical checking method for the bearing capacities of the composite columns [

In recent years, many scholars had conducted experimental research on concrete-filled stainless steel and steel tubular (CFSSAST) columns. For instances, Han et al. conducted a series of performance tests on CFSSAST columns and proposed a simplified model for predicting the strength of the column section [

Although these research results greatly promoted the application of CFSSAST columns in engineering projects, there are still some problems of CFSSAST columns to be resolved, summarized as follows: (1) Up to now, the failure load of CFSSAST columns is determined on the semiempirical and semitheoretical basis with considerable inaccuracy, and the failure mechanism of the columns is not involved. (2) At present, most of the researches tend to focus on the mechanical properties of CFSSAST columns under axial loads, while the researches of specimens under eccentric loads are inadequate.

In order to address these two issues, the authors deeply study the mechanical properties of CFSSAST columns under axial and eccentric loads, based on the theory of structural stressing states. The measured strain data of CFSSAST columns are modeled as generalized strain energy density (GSED) to describe the structural stressing state modes. Then M-K method is applied to GSED sum-load curve to distinguish the mutation feature of the curve and reveal the failure mechanism of CFSSAST columns in the process of loading, so as to update the definition of the existing column failure load.

The authors define the stressing state of a structure as the structural working behavior characterized by the distribution pattern of strain energy density values, displacements, strains, and stresses of measuring points [_{1}, _{2}, _{3} and _{1}, _{2}, _{3} are three principal stresses and strains, respectively; _{max} is the maximum of the strain energy values over the loading process. Thus, the

The Mann–Kendall (M-K) method is applied to distinguish the stressing state mutation of the structure through the _{m} at the ^{th} comparison. The mean value _{m}) and variance Var (_{m}) of _{m} are calculated by

Under the assumption that the {

Thus, the _{k} data, and the _{k} and NB_{k} curves can intersect at the mutation point of the

Wen et al. conducted experimental studies on the mechanical properties of the CFSSAST columns under axial and eccentric pressure [

Section diagram of CFSSAST column.

In the axial compression test, the hollow ratio

Size and strength of axial compression specimens.

Specimen number | _{0} × _{0} (mm × mm) | _{i} × | _{y0} (MPa) | _{yi} (MPa) | _{cu} (MPa) | ||
---|---|---|---|---|---|---|---|

Z-48-a | 114 × 2 | 48 × 1.6 | 342 | 0.44 | 278.7 | 235 | 48 |

Z-48-b | 114 × 2 | 48 × 1.6 | 342 | 0.44 | 278.7 | 235 | 48 |

Z-76-a | 114 × 2 | 76 × 1.6 | 342 | 0.69 | 278.7 | 235 | 48 |

Z-76-b | 114 × 2 | 76 × 1.6 | 342 | 0.69 | 278.7 | 235 | 48 |

Z-89-a | 114 × 2 | 89 × 1.6 | 342 | 0.81 | 278.7 | 235 | 48 |

Z-89-b | 114 × 2 | 89 × 1.6 | 342 | 0.81 | 278.7 | 235 | 48 |

Eighteen CFSSAST columns were made for the research of the eccentric compression test with the hollow ratio

Size and strength of eccentric compression specimens.

Specimen number | _{0} × _{0} (mm × mm) | _{i} × _{i} (mm × mm) | _{y0} (MPa) | _{yi} (MPa) | _{cu} (MPa) | |
---|---|---|---|---|---|---|

P800-50-4-a | 114 × 2 | 50 × 1.2 | 800 | 278.7 | 235 | 58 |

P800-50-4-b | 114 × 2 | 50 × 1.2 | 800 | 278.7 | 235 | 58 |

P800-76-14-a | 114 × 2 | 76 × 1.6 | 800 | 278.7 | 235 | 58 |

P800-76-14-b | 114 × 2 | 76 × 1.6 | 800 | 278.7 | 235 | 58 |

P800-89-45-a | 114 × 2 | 89 × 1.6 | 800 | 278.7 | 235 | 58 |

P800-89-45-b | 114 × 2 | 89 × 1.6 | 800 | 278.7 | 235 | 58 |

P1300-50-4-a | 114 × 2 | 50 × 1.2 | 1300 | 278.7 | 235 | 58 |

P1300-50-4-b | 114 × 2 | 50 × 1.2 | 1300 | 278.7 | 235 | 58 |

P1300-76-14-a | 114 × 2 | 76 × 1.6 | 1300 | 278.7 | 235 | 58 |

P1300-76-14-b | 114 × 2 | 76 × 1.6 | 1300 | 278.7 | 235 | 58 |

P1300-89-45-a | 114 × 2 | 89 × 1.6 | 1300 | 278.7 | 235 | 58 |

P1300-89-45-b | 114 × 2 | 89 × 1.6 | 1300 | 278.7 | 235 | 58 |

P1800-50-4-a | 114 × 2 | 50 × 1.2 | 1800 | 278.7 | 235 | 58 |

P1800-50-4-b | 114 × 2 | 50 × 1.2 | 1800 | 278.7 | 235 | 58 |

P1800-76-14-a | 114 × 2 | 76 × 1.6 | 1800 | 278.7 | 235 | 58 |

P1800-76-14-b | 114 × 2 | 76 × 1.6 | 1800 | 278.7 | 235 | 58 |

P1800-89-45-a | 114 × 2 | 89 × 1.6 | 1800 | 278.7 | 235 | 58 |

P1800-89-45-b | 114 × 2 | 89 × 1.6 | 1800 | 278.7 | 235 | 58 |

500tYAW-5000 pressure tester is used for axial compression and eccentric compression test, as shown in Figure

The loading device of (a) CFSSAST column under axial compression and (b) CFSSAST column under eccentric compression.

Figure

FEA model of short column (a) under axial compression and (b) under eccentric compression.

The concrete adopted Guo tensile concrete constitutive relationship model [

For the Z-48-b short column exampled here, the sum of GSED at each load (_{j}) can be normalized as

To verify the general applicability of the failure load to all test short columns, the mutation of

In order to verify the accuracy of the simulated data, the ultimate loads and failure loads of the experimental columns and the models are compared, as shown in Table

Comparison of experimental data and simulated data.

Specimen number | Failure load of experiment (kN) | Simulated ultimate load (kN) | Error (%) | Failure load of experiment (kN) | Simulated failure load (kN) | Error (%) |
---|---|---|---|---|---|---|

Z-48-a | 698 | 670 | 4.0 | 613 | 610 | −0.6 |

Z-48-b | 660 | 670 | 1.5 | 609 | 610 | 0.1 |

Z-48-a | 618 | 567 | 8.3 | 535 | 521 | −2.8 |

Z-76-b | 578 | 567 | 1.9 | 540 | 521 | −3.6 |

Z-89-a | 493 | 494 | 0.2 | 462 | 459 | −0.7 |

Z-89-b | 520 | 494 | 5.0 | 468 | 459 | −2.0 |

It can be seen from Figure

(a)

The model Z-76 is taken as an example to analyze the stress change of the CFSSAST column during the loading process. The stress contour maps corresponding to the four characteristic loads are selected for analysis, and the sequence is: (1) point A: elastoplastic critical load; (2) point B: failure load; (3) point C: ultimate load; (4) point D: unloading load, as shown in Figure

Figure

The longitudinal stress contour maps of the stainless steel tube. (a) Point A. (b) Point B. (c) Point C. (d) Point D.

Figure

The longitudinal stress contour maps of the core concrete. (a) Point A. (b) Point B. (c) Point C. (d) Point D.

As shown in Figure

The longitudinal stress contour maps of the carbon steel tube. (a) Point A. (b) Point B. (c) Point C. (d) Point D.

In this paper, _{16} (4^{5}) orthogonal table is selected for parameter analysis, where 16 represents the number of models to be established; 4 means setting 4 levels for each parameter; 5 means that there are five parameters. The specific parameter settings of all 16 short column models are shown in Table _{u}) and the range of failure load (_{f}) are shown in Table _{u} is the ultimate load of short column and _{f} is the failure load of short column.

Model parameter level settings.

Specimen number | _{i} (mm) | _{0} (mm) | _{cu} (MPa) | _{yo} (MPa) | _{yi} (MPa) | _{u} (kN) | _{f} (kN) |
---|---|---|---|---|---|---|---|

1 | 40 | 1.2 | 40 | 275 | 235 | 514 | 481 |

2 | 40 | 1.6 | 50 | 335 | 300 | 600 | 518 |

3 | 40 | 2.0 | 60 | 412 | 345 | 911 | 821 |

4 | 40 | 2.4 | 70 | 496 | 400 | 1163 | 1043 |

5 | 50 | 2.4 | 40 | 335 | 345 | 804 | 761 |

6 | 50 | 2.0 | 50 | 275 | 400 | 738 | 651 |

7 | 50 | 1.6 | 60 | 496 | 235 | 929 | 793 |

8 | 50 | 1.2 | 70 | 412 | 300 | 790 | 709 |

9 | 60 | 1.6 | 40 | 412 | 400 | 740 | 666 |

10 | 60 | 1.2 | 50 | 496 | 345 | 754 | 673 |

11 | 60 | 2.4 | 60 | 275 | 300 | 779 | 681 |

12 | 60 | 2.0 | 335 | 235 | 235 | 837 | 763 |

13 | 70 | 2.0 | 40 | 496 | 300 | 908 | 811 |

14 | 70 | 2.4 | 50 | 412 | 235 | 801 | 705 |

15 | 70 | 1.2 | 60 | 335 | 400 | 670 | 571 |

16 | 70 | 1.6 | 70 | 275 | 345 | 700 | 601 |

The calculation results of range.

_{i} | _{0} | _{cu} | _{yo} | _{yi} | |
---|---|---|---|---|---|

_{u} | 46 | 205 | 149 | 256 | 59 |

_{f} | 57 | 189 | 142 | 226 | 47 |

According to Table

In this paper, five parameters (concrete strength, stainless steel yield strength, carbon steel strength, hollow ratio, and nominal steel ratio) are analyzed quantitatively by using the finite element model. At the same time, in order to compare the influence of different factors on the bearing capacity of short columns, this paper attempts to construct the parameter

It can be seen from Figure _{2} is 1), the corresponding ultimate loads are 523.62 kN, 559.29 kN, 607.33 kN, 653.18 kN, and 703.21 kN, which are increased by 34.3% (_{1} is 0.343), and the value of _{1} is 0.3368), and

(a)

As shown in Figure

(a)

The steel ratio increases from 0.0435 to 0.0898 (the nominal steel ratio is achieved by changing the thickness of stainless steel tube), which increases by 106.44%, and the corresponding limit load increases by 25.67% and

(a)

At present, there are few researches on the equation of bearing capacity of the CFSSAST columns, and the equation of failure load is not involved. This paper attempts to fit the equation of ultimate load and failure load on the basis of parameter analysis and relevant research.

Huang Hong put forward the equations of the bearing capacity of the CFDST columns (_{u}) through a lot of parameter analyses [_{scy} is the compound strength of outer steel tube and concrete; _{sco} is the sum of cross sectional area of outer steel tube and concrete; _{yi}, _{yo} and _{ck} are the yield strength of inner steel tube, yield strength of outer steel tube, and compressive strength of concrete, respectively; _{si}, _{so} and _{c} are the cross sectional areas of inner steel tube, outer steel tube, and concrete, respectively; _{n} are the steel ratio and nominal steel ratio, respectively; _{n} × (

According to the newly fitted equations, the ultimate loads of 137 different short columns (including 6 test short columns and 131 simulated short columns) are calculated, among which 97 (accounting for 70.8%) short columns have errors within 3%, with an average error of 0.89% and a standard deviation of 3.45%. The accuracy of the equation is enough for analysis.

The equation for calculating the failure load is still in the form of ultimate load (_{f}); that is, the equation is composed of two parts. One part is the compound failure load (

The failure loads of 137 different specimens are calculated by the equation. Among them, the 89 specimens have errors within 3%, accounting for 65.0%, the average error is 0.07%, and the standard deviation is 3.05%. These data prove the accuracy of the equation.

Take the model P1300-76-14 (eccentric compression column) as an example; the

To verify the rationality of the FE model, the errors of the simulated ultimate loads are obtained by comparing the simulated results with the experimental results, as shown in Table

Comparison of experimental data and simulated data.

Specimen number | Mean value of experimental ultimate load (kN) | Mean value of simulated ultimate load (kN) | Error (%) |
---|---|---|---|

P800-50-4 | 653 | 669.93 | 2.59 |

P800-76-14 | 436 | 406.41 | −6.79 |

P800-89-45 | 200 | 218.83 | 9.42 |

P1300-50-4 | 556 | 554.34 | −0.30 |

P1300-76-14 | 380 | 358.98 | −5.53 |

P1300-89-45 | 201 | 193.98 | −3.49 |

P1800-50-4 | 492 | 487.19 | −0.98 |

P1800-76-14 | 300 | 305.07 | 1.69 |

P1800-89-45 | 181 | 169.49 | −6.36 |

In order to further explain the mutations of the stressing state of the eccentric compression columns, several cross sections are selected for analysis. They are section A (in the middle of column), section D (at the end), and sections B and C (B and C are sections of trisection of sections A and D), where section B is closer to section A. It can be seen from Figure

(a) Transverse strain − _{j} curves of different sections. (b) Slope of transverse strain − _{j} curves of different sections.

Similar to the axial compression column, model P1300-76-14 is selected for analyzing the stress change of eccentric compression column during the whole loading process. The stress contour maps corresponding to four representative loads are selected for analysis. The four loads are (1) point A: elastoplastic critical load, (2) point B: failure load, (3) point C: ultimate load, and (4) point D: load corresponding to 30% reduction of bearing capacity, respectively (Figure

Figure

The longitudinal stress contour maps of the stainless steel tube. (a) Point A. (b) Point B. (c) Point C. (d) Point D.

The stress of concrete at four points is different from that of stainless steel tube, as shown in Figure

The longitudinal stress contour maps of the concrete. (a) Point A. (b) Point B. (c) Point C. (d) Point D.

According to the principle of single variable, the influences of 7 factors on the bearing capacity of eccentrically loaded columns are analyzed, including nominal steel ratio, slenderness ratio, hollow ratio, concrete strength, stainless steel strength, carbon steel strength, and load eccentricity. In order to ensure the reliability of simulated results, the level of each parameter should be maintained at the experimental level.

Figures

(a) _{j} − Middle point deflection of the columns curves under different nominal steel ratio. (b)

As shown in Figure

(a)

The hollow ratio increases by 199.6% (from 0.273 to 0.818), and the corresponding ultimate load decreases by 28.56% and the

(a) _{j} − Middle point deflection of the columns curves under different hollow ratio. (b)

The analysis of other parameters is the same as above, and the comprehensive comparison of the

Based on the experiment and a large number of simulation parameter analyses, Tao et al. [_{u} is the axial bearing capacity of the column; _{u} is the flexural capacity of the column; _{s} and _{c} are the modulus elasticity of steel tube and concrete, respectively; _{so}, _{si} and _{c} are the section moments of inertia of outer, inner steel tubes, and concrete, respectively; _{1}. The only difference between the CFSSAST column in this paper and the CFDST column is that the outer steel tube changes from carbon steel to stainless steel, so it is assumed that the relationship between _{1} and the ultimate bearing capacity of CFSSAST column under eccentric compression (

The equation of failure load is still in the form of ultimate load; that is, the failure load is deduced by using ultimate load. Through parameter analysis, the equation of failure load is as follows:

This study reveals the stressing state characteristics of the CFSSAST columns under eccentric compression and axial compression. Based on the experimental data, the

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Sijin Liu, Wei Wang, and Baisong Yang conceived the study and were responsible for the design and development of the data analysis. Wei Wang and Sijin Liu were responsible for data collection, analysis, and interpretation. Lingxian Yang and Guorui Sun helped perform the analysis with constructive discussions. Baisong Yang wrote the original draft of the article. Baisong Yang and Wei Wang equally contributed to this manuscript as co first author.

The authors would like to express their gratitude to Xiaofei Wen for carrying out the excellent experiment of CFSSAST columns and giving the complete experimental data. The authors would also like to thank the members of the HIT 504 office for their selfless help and useful suggestions.