# Nakahara, Sakino, and Inai 1998

In this paper, an analytical study was presented to estimate the response of short CFT square columns under concentric axial loading. Individual stress-strain relationships were proposed for steel and concrete and then they were superimposed. The analytical results were compared with the experiments from the available literature.

## Experimental Study

The specimens from the literature had D/t ratios varying from 15.5 to 73.9. The ranges for the compressive strength of concrete and the yield strength of steel were 3.68 to 13.21 ksi and 38 to 121.11 ksi, respectively. The L/D ratio of all the columns was 3.

In addition, the authors tested 4 CFT and 4 HT columns (see Nakahara and Sakino, 1998). The CFT columns had high strength concrete with compressive strength of 17.26 ksi. The yield strength of steel was varying from 44.96 to 113.28 ksi and the range of the D/t ratio was 31.3 to 64.7.

## Analytical Study

The analytical study was performed based on three conclusions of the authors from past experimental studies. Local buckling was assumed to reduce the capacity of the columns with large D/t ratios, the capacity increase that took place for the columns with low D/t ratios was attributed only to the strain hardening of the steel tube and, scale effect was introduced for the compressive strength of concrete.

For concrete in square CFT columns, a stress-strain relationship of confined concrete from the literature was adopted in the current study. The proposed model was similar to plain concrete in strength and it was similar to confined concrete in ductility. The yield strength of steel was assumed to affect the rate of strength degradation of concrete in post-peak region. Steel tube was considered to yield at large deformations and thus no restriction in steel strength was proposed. In the experiments, it was observed that the CFT columns had carried some axial load even in large deformation region. Therefore, concrete was assumed to carry 30% of its maximum stress in large deformation region.

Three stress-strain curves were proposed for steel tubes depending on the D/t ratio. For low D/t values, the steel tube was considered to experience strain hardening and the maximum strength was taken to be larger than the yield strength. In the case of the steel tubes with medium D/t values, the maximum strength was taken as equal to the yield strength. The maximum strength of the steel tubes with large D/t ratios was assumed to be smaller than the yield strength due to local buckling. The equation for the strain value corresponding to the end of strain-hardening region, for the steel tubes with low D/t values, was determined by a regression analysis of the test results. From the fact that CFT columns resisted some axial load in the large deformation range, the steel stress in each proposed model was assumed to remain constant following the falling branch after the peak strength. The authors named that region as the state of stability of CFT columns. In order to determine the strain value corresponding to the starting point of that region, the load-deformation curves of the tested CFT specimens were divided into 100 linear parts with a 0.04% strain increment. The strain interval with a tangent modulus smaller than 2% of the initial modulus of the column in absolute value and bigger than the tangent modulus of the previous interval was taken as the start of the state of stability. The corresponding strain value was used to calculate the stress value initiating the state of stability. The axial load at that strain level resisted by concrete was subtracted from the total axial load and the stress on steel tube was calculated. This stress value was determined for each specimen and then an equation was proposed by performing a regression analysis.

The analytical results matched accurately with the experimental load-deformation relationships of most of the specimens. However, the results for the high strength concrete specimens were not satisfactory and their axial load capacities were overestimated.

## References

Nakahara, H., Sakino, K. and Inai, E. (1998). “Analytical Model For Compressive Behavior of Concrete Filled Square Steel Tubular Columns,” Transactions of the Japan Concrete Institute, Vol. 20, pp. 171-178.