# Tsuda, Matsui, and Mino 1996

An experimental study conducted on circular and square CFT beam-columns was presented in two companion papers (see also Matsui et al., 1995). The behavior of CFT specimens was examined under axial loading and combined axial and flexural loading. Columns having a wide range of L/D ratios were tested. The experimental results were compared with AIJ (1987, 1990) and CIDECT (1994) design code provisions.

## Experimental Study Results and Discussions

There were two series of experiments. In the first series, forty-eight CFT and twelve HT columns were tested. The CFT specimens were subjected to monotonic concentrically and eccentrically applied axial loads. The main parameters were L/D ratio and magnitude of eccentricity. The L/D ratios ranged between 4 and 30. The maximum value of eccentricity for square and circular specimens were 4.9 in. and 4.1 in., respectively. The D/t ratio was selected as 33 for the square specimens and 37 for the circular specimens. The nominal yield strength of steel was 58.0 ksi and the nominal compressive strength of concrete was 4.3 ksi. Pinned-end conditions were used in the test setup.

For the first series of experiments, it was observed that the specimens having a higher magnitude of eccentricity exhibited lower axial strength and larger mid-height deflection. The effect of eccentricity decreased for high L/D ratios. The columns with L/D ratios less than 18 achieved the plastic moment capacity. The circular specimens in this range even exhibited larger capacities due to the confinement effect. For square specimens, the confinement effect was not observed. The capacities of the columns having L/D ratios above 18 could not attain the plastic capacity due instability effects.

In the second series of experiments, twenty CFT columns were tested under constant axial and cyclic horizontal loading. The main parameters were L/D ratio and the axial load ratio. The L/D ratio was varied between 6 and 24. The axial load ratio (P/P_{o}) ranged from 0.2 to 0.7. The D/t ratio and material properties were kept the same as in first series of experiments. The cantilever columns were fixed at the bottom and free at the top. Displacement-controlled loading was applied at the free end of the columns. For axial load ratios greater than 0.5, square columns showed rapid deterioration in strength. Circular columns showed stable and ductile hysteresis loops even for high slenderness and high axial load ratios.

## Analytical Study

A modified AIJ method was developed to calculate the capacity of slender CFT columns. It was different from the AIJ (1987, 1990) method of calculating the capacity of the concrete portion of a CFT, and a new concrete column interaction equation was proposed. It was based on an elasto-plastic analysis that was conducted using a Newmark iteration method in which a sine curve is assumed as the deflected shape of the beam-column. The modified AIJ method agreed with experimental results of the first series of experiments when the L/D ratio was between 8 and 30. However, the test results were underestimated when the L/D was smaller than 4. This trend was most notable for circular columns and it was attributed to the effects of confinement and strain hardening, which in the proposed analytical method were not taken into account explicitly. On the other hand, the AIJ (1987, 1990) method was generally conservative. The CIDECT (1994) design provisions gave almost the same capacities as the modified AIJ method for L/D ratios between 12 and 30. This method had more accurate results for short circular columns, as concrete confinement was accounted for. In the second series of experiments, the columns with L/D ratios smaller than 9 achieved their cross-section strength. Both the AIJ (1987, 1990) and modified AIJ methods predicted most of the experimental results conservatively. It was pointed out that the design equations for CFT beam-columns having no restraint for joint translation should be reviewed.

## References

Tsuda, K., Matsui, C., and Mino, E. (1996). “Strength and Behavior of Slender Concrete Filled Steel Tubular Columns,” Stability Problems in Designing, Construction and Rehabilitation of Metal Structures, Proccedings of the Fifth International Colloquium on Structural Stability, SSRC IC/BRASIL ’96, Rio de Janerio, Brasil, August 5-7, 1996, Structural Stability Research Council, Bethlehem, Pennsylvania, pp. 489-500.