Regression equations for circular CFST columns carrying capacity evaluation

Abstract. Within the last decades, a considerable amount of experimental studies have been carried out by numerous researchers across the world with the purpose to study the carrying capacity of concrete-filled steel tubular (CFST) columns and evaluation of their stressed-strained state. The array of the obtained results have allowed designing a mathematical model to determine the maximum carrying capacity value of such constructions using the methods of mathematical statistics. The authors obtained three types of regression equations for short and long circular CFST columns with different geometrical and physical properties under axial compression. Statistical quality of the obtained models was verified by both regression equation quality in general and statistical significance of the equation parameters. The comparison of the obtained carrying capacity values with the results calculated by Eurocode 4 and AIJ methodologies allows making a conclusion on the sufficient calculation accuracy of the designed mathematical models.


Introduction
Since the steel concrete columns have been commonly used in the civil engineering, the issues of research of their carrying capacity and evaluation of the stressed-strained state still remain very important today.The extensive experimental data set on carrying capacity of the columns under various loading conditions assembled within the latest decades by the researchers across the world has enabled to study the behaviour of the columns using the techniques of mathematical statistics [1][2][3][4][5][6].
The authors of this research have built mathematical models to evaluate the maximum carrying capacity of circular CFST columns under axial compression.One of the most widely used statistical techniques was used for this purpose, namely, regression analysis [7].
Initially, two models were supposed to be built for circular CFST short (L/D < 4) and long (L/D ≥ 4) columns, where L, Dlength and outer diameter of the column, respectively.
However, analysis of the obtained results showed that in case of the long columns it would be preferable to consider separately the samples with the casing thickness t < 2.5 mm and those with the thickness t ≥ 2.5 mm.

CFST long thick-walled columns
In the second case, circular CFST columns with the casing thickness at least 2. +0.2322
In general, the statistical significance of the regression equations is verified with the Fisher criterion, while the statistical significance of the equation parameters is verified with the Student criterion.
The performed mathematical analysis of the obtained models, as well as comparison of the results with the carrying capacity value of the circular CFST columns calculated using the DYN-WIND'2017 51 methods of Eurocode 4 [8] and Architecture Institute of Japan (AIJ) [9] allow to make a conclusion that the degree of confidence of the regression equations (1) ÷( 3) is sufficiently high.

Table 1 .
Confidence intervals for regression equation parameters with probability P = 0.95 are shown in Table1.Confidence intervals.

Table 2 .
and mean approximation error are given Quality parameters of the models.