# Elchalakani, Zhao, and Grzebieta 2001

The flexural behavior of circular CFTs was investigated. Twelve CFT beams were tested under pure bending. The strength, deformation capacity, and energy dissipation of the specimens were monitored and compared with those of hollow tubes tested by the author and reported in the literature. The authors recommended a D/t ratio for circular CFT beams to achieve their plastic moments. Moreover, they proposed a formulation to calculate the moment capacity of circular CFT sections.

## Experimental Study, Results and Discussions

The testing machine for these monotonic experiments was displacement-controlled and had the capability of applying constant moment at the mid-length of the specimens without creating any significant axial load or shear force. Nine compact specimens had D/t ratios smaller than 40 while the D/t ratios for the three slender specimens varied between 74 and 110. The average measured yield strength of steel and compressive strength of concrete were 60.77 ksi and 3.39 ksi, respectively. The L/D ratio for the slender specimens was approximately 5.4, versus ranging from 7.9 to 23.7 for the compact specimens.The compact specimens did not undergo any local buckling or tension fracture. The moment-curvature and moment-rotation responses of the specimens indicated that the ductility and energy absorption capacity improved due to the concrete infill. The improvement was more pronounced for the compact specimens with the higher D/t ratios. The moment strength was also greater than the equivalent hollow tubes and the amount of enhancement, which was again more apparent in the case of higher D/t ratios, ranged from 3% to 37%. The ovalization of the specimens due to radial distortion was approximately 1% and it did not affect the test results significantly.

The general moment-rotation response of the slender specimens was represented by a series of linear and non-linear curves. According to the idealized moment-rotation response, the response curve became nonlinear when the rotation was equal to θy. At a rotation level of 1.5θy, initiation of local buckling was observed. Following this stage, the specimens underwent strain hardening in the tension region. Later, local buckling began to increase and a gradual reduction in strength took place until failure. For one specimen, failure was sudden and the gradual reduction in strength was not observed. This was attributed to the early fracture at the seam weld as it was applied below the centroid of the steel tube. For the others, failure occurred with fracture at the outermost tension fiber, with the crack propagating towards the neutral axis.

The bond between the steel and concrete was also examined. No abrupt change in the moment-curvature response was noticed and this showed that slip did not occur between the steel and concrete. It was suggested that an a/d ratio of 2.7 was sufficient to ensure no slip.

## Analytical Study

To obtain a limiting slenderness and D/t ratio for transition between compact and slender sections, a slenderness parameter (α) and rotation capacity formula were selected from literature. These two quantities were calculated for each specimen using the following equations:

A rotation capacity versus slenderness parameter graph for the tested specimens had a clear transition point between compact and slender sections. The slenderness parameter corresponding to that point was taken as the slenderness parameter limit (αp) and it was inserted into the equation for slenderness of the sections. The limiting D/t ratio and plastic slenderness limit (λp) for 60.77 ksi steel were then calculated as 112 and 188, respectively.

The limiting D/t ratio was about 14% greater than the limits calculated according to the AIJ (1987) design code provisions if measured steel yield strength was used. This was attributed to the presence axial force in the experiments that were used to derive the equations in AIJ (1987).

By assuming perfect bond and performing a rectangular stress block analysis, an equation to calculate the moment strength of the CFT sections was proposed. Good correlation was obtained with the experimental results and the moment strength values from EC4 (1992) and CIDECT (1995) procedures.

## References

Elchalakani, M., Zhao, X. L., and Grzebieta, R. H. (2001). “Concrete-Filled Circular Steel Tubes Subjected to Pure Bending.” Journal of Constructional Steel Research, 57(11), 1141–1168. doi:10.1016/S0143-974X(01)00035-9