# Elremaily and Azizinamini 2002

This paper presents the results of six cyclic beam-columns tests as well as an analytical model for the cross section strength of circular CFTs. The effect of axial load, D/t ratio, and concrete compressive strength were investigated in the tests. The analytical model emphasized the multiaxial behavior of the materials.

## Experimental Study, Results, and Discussion

Six circular CFT beam-column specimens were selected to be approximately 2/3 scale of columns for a typical prototype building. The diameter of all of the specimens was 12.75 in. with a D/t ratio of 51 or 34. The columns were subjected to constant axial load between 0.2 and 0.4 of the column squash load as well as a cyclic lateral load. The lateral load was applied to a rigid stub at mid-height of the column, the stub was intended to simulate the effect of a rigid floor system intersecting the beam column. For all specimens, an outward indent, or bulge, formed adjacent to the stub. This bulge initiated at the compression face of the column but grew with the load cycles to form a complete ring around the beam-column. The typical failure mode was a tensile fracture at the bulge. Axial shortening of the specimens was noted and attributed to the formation of the bulge.

The load-deflection curves show full hysteretic loops without a significant drop in the strength (as exhibited by the lateral load). The authors noted that the thicker tubes produced fuller hysteretic loops. A study of the stiffness degradation was also performed. The effective stiffness was calculated from the slope of the load-deflection curve and an analytical equation which included second order effects. The results indicated that the transformed stiffness (EI_{trans} = E_{c}I_{c} + E_{s}I_{s}) was a good approximation for initial stiffness and that the stiffness degraded as much as 40% during the experiment.

## Analytical Study

The authors selected a moment-curvature approach for the analytical cross section model. The section was divided into rectangular strips and for a given level of axial load, the ultimate moment capacity was calculated iteratively. The uniaxial stress-strain models of both the steel and the concrete were chosen to represent the multiaxial behavior existing within the beam-column. A concrete constitutive model by Mander was used with the confining stress taken as a function of the hoop stress in the steel tube. The steel constitutive model was derived from the Von Mises’ yield criterion noting the steel hoop stress. The six specimens from the current paper along with 37 other specimens reported by Furlong and Morino in referenced papers were used to calibrate the model and find an appropriate average value for the hoop stress. A hoop stress equal to 0.1 F_{y} was determined to fit the data the best.

## References

Elremaily, A. and Azizinamini, A. (2002). “Behavior and Strength of Circular Concrete-Filled Tube Columns,” Journal of Constructional Steel Research, Vol. 58, pp. 1567-1591.