# Inai et al. 2000

In this paper, design equations to calculate the deformation capacity of circular and square CFT beam-columns were presented. For this purpose, a regression analysis was performed using the results of several experimental studies from the literature. The cyclic behavior of CFT beam-columns was also modeled.

## Analytical Study

A database of the experiments that were selected to make the statistical comparison with the design equations was prepared. The value of the chord rotation when the lateral load capacity drops to 95% of its peak value (R_{95}) was defined as the deformation capacity for a beam-column. The factors influencing the deformation capacity were D/t ratio, yield strength of steel, compressive strength of concrete, axial load ratio, and shear span over depth ratio. For each of these factors, the trend of deformation capacity was determined by regression analysis of the experiments in the database. For both circular and square specimens, the value of R95 was found to decrease as the D/t ratio and the axial load ratio got larger. No clear trend was observed for the yield strength of steel and compressive strength of concrete. Using the analysis results, equations to calculate R95 were proposed as follows (stress values are in MPa):

For circular CFT beam-columns:

For square CFT beam-columns:

where

The proposed equations were compared with the experimentally obtained values from the database and good correlation was achieved. The shear span-to-depth ratio did not exist in the equations, but it was found that the results from these equations already gave the average values when the effect of the shear span-to-depth ratio was introduced into the equations.

To model the cyclic deformation response of the CFT beam-columns, a tri-linear skeleton moment-rotation curve was developed. The curve started with a linear part at a slope of K_{e} (elastic stiffness) until M_{y}, which was defined as the short-time allowable flexural moment strength in AIJ (1987). It was followed by a second linear region with a milder slope up to Mu (the ultimate flexural strength). The third part of the curve was a horizontal line that terminated at the ultimate chord rotation angle (R_{u}). A stiffness degradation factor (αc) for the reduction in stiffness in the second part of the curve was defined. This factor was calculated by performing a statistical analysis of the experimental results, and it was taken as 0.65 for circular CFTs and 0.7 for square CFTs. The other factors required to define the skeleton curve were determined using available formulations from the literature. This model was used to estimate the cyclic response of specimens tested in the experimental studies. The hysteretic behavior was estimated well when chord rotation angles were smaller than 1%. However, energy dissipation capacity was overestimated for chord rotations outside of this range.

## References

Inai, E., Noguchi, T., Mori, O., and Fujimoto, T. (2000). “Deformation Capacity and Hysteretic Model of Concrete-Filled Steel Tubular Beam-Columns, Composite and Hybrid Structures, Proceedings of the Sixth ASCCS International Conference on Steel-Concrete Composite Structures, Xiao, Y. and Mahin, S. A. (eds.), Los Angeles, California, March 22-24, 2000, Association for International Cooperation and Research in Steel-Concrete Composite Structures, Los Angeles, California, pp. 605-612.