# Kitada, Yoshida, and Nakai 1987

The elastoplastic behavior of short circular CFT columns was studied experimentally and compared to the values obtained from analytical methods proposed by other authors. The effect of the method of loading (i.e., load both materials, load the steel tube only, or load the concrete core only) was examined in detail as well as the effect of bond on the ductility and strength of the section. The study focused on a detailed examination of the triaxial stresses in the concrete and the biaxial stresses in the steel for the different loading methods and for the bonded and unbonded specimens.

## Experimental Study, Discussion, and Results

The test specimens were very short columns with variable parameters including the steel yield strength, the concrete compression strength, and the relative ratio of the two strengths. The specimens were loaded by three methods: 1) load both the concrete and the steel simultaneously such that the longitudinal strains in both materials are equal, 2) load the concrete core alone without applying axial compression on the tube, and 3) load the steel tube alone. The stresses in each specimen were analyzed using the Mises yield criterion which is defined by the following equation:

where σsl and σsc are the longitudinal and hoop stress, respectively, in the steel tube. For the different loading conditions, the authors plotted the stress path of the steel, i.e., the hoop stress versus the longitudinal stress, at different locations on the tube. Because the Poisson's ratio of the concrete is less than the corresponding ratio for steel in the elastic range, the concrete and steel do not interact and act independently of one another. At the crushing strain of the concrete, the lateral expansion of the concrete exceeds that of the steel and hoop stresses are induced in the steel tube, and corresponding triaxial stresses are induced in the concrete core. A failure curve proposed by Cai that was restated in this paper accurately described the relationship between the confining stress on the concrete and the axial compressive stress. This empirical equation is given by:

where σc is the ultimate axial compressive stress of encased concrete subjected to a uniform, radial compressive stress, σr. The failure of the section under this loading condition occurred at the ends of the specimen. Soon after yielding, the steel buckled locally and the concrete in the region of local buckling crushed.

When the concrete alone was loaded, little or no compressive stress was transferred to the steel tube at the ends of the specimen and the hoop stress predominantly occurs in these regions. At the midpoint of the tube, the longitudinal and hoop stresses increase proportionately until the steel yields. The axial compression at the middle of the tube was due to the friction between the two materials. For similar tests with a debonded interface, there was much less axial stress at the middle of the tube. Failure of the CFT columns for this loading case was initiated by crushing of the concrete at the midpoint of the section. The adjacent steel bulged outward, completing the failure.

The final loading method resulted in a column that performed in an manner similar to a hollow steel tube since there was little interaction between the two materials.

The load-deformation behavior of the tubes revealed that the axial capacity as computed by summing the individual strengths of the component materials largely underestimated the actual capacity of the section. The relationship between load and deformation is linear until the steel yields, at which point the concrete begins to undergo confinement and the stiffens of the member decreases substantially. For axial displacement beyond the yield point, the capacity of the section increases gradually, exhibiting good ductility. The method of loading did not affect the ultimate capacity of the section, except in the case of loading the steel alone in which case the concrete did not contribute any strength. Loading both materials simultaneously produced a slightly larger stiffness. The authors suggested that the calculation for the ultimate load of a short column proposed by Cai matched their results with sufficient accuracy. The equation is as follows:

## References

Kitada, T., Yoshida, Y., and Nakai, H. (1987). “Fundamental Study on Elastoplastic Behavior of Concrete Encased Steel Short Tubular Columns,” Memoirs of the Faculty of Engineering, Osaka City University, Osaka, Japan, Vol. 28, pp. 237-253.