# Tsuji, Nakashima, and Morita 1991

The interaction between the steel and concrete in CFTs subjected to axial compressive loads was examined. Considering a triaxial state of stress for concrete and a biaxial state of stress for steel, the authors derived separate constitutive equations for the two materials in an attempt to mimic the behavior of CFTs. Using these constitutive relationships, the authors plotted axial load versus axial strain. Finally, axial compression tests were carried out on short CFTs and compared to the theoretical results derived from the constitutive equations.

## Contents

## Experimental Study, Discussion, and Results

The limited number of experiments performed resulted in ultimate strengths beyond those predicted by summing the individual strengths of the CFT components. This indicated the presence of interaction between the steel and concrete. Up to a strain of 0.001, the apparent Poisson's ratio (measured as the relationship between the strains in the longitudinal and circumferential direction) remained constant at about 0.3. As strains increased to 0.003, the apparent Poisson's ratio increased from 0.3 to 0.8. Beyond this point, Poisson's ratio remained constant at 0.8 for additional strain. These values of Poisson's ratio were used in the concrete stress formulation described below. It was also found that significant strength gains were achieved due to the interaction of the steel and the concrete. The strength corresponding to the 0.2% offset strain and the strength at 2.0% strain were 16% and 33% larger, respectively than the strengths obtained by simply summing the individual strength contributions of the two materials.

## Analytical Study

Using constitutive equations, the authors attempted to model the interactive behavior of the concrete and steel in CFTs. The Drucker-Prager yield condition in strain space was employed for analysis of the concrete. The associated flow rule was adopted whereby plastic strain vectors are normal to the yield surface specified by the Drucker-Prager equation. It was also assumed that only plastic flow occurs in the plastic range, and that there is no fracture. The stress versus strain relationship for the steel tube followed the von Mises yield criterion and the Prandtl-Reuss isotropic hardening rule. In analyzing the behavior of axially loaded CFTs, the authors looked at the experimental behavior to gauge the amount of interaction. For strains less than 0.001, where Poisson's ratio began to increase, no contact existed between the materials and simple superposition of stresses was made. For additional straining, the concrete became inelastic and contacted the steel, initiating interaction between the materials. Beyond the point of interaction, the longitudinal stresses in the concrete and the steel remained equal, as did the circumferential and radial strains in the steel and concrete, respectively. The authors imposed an equation of equilibrium for this condition to relate the stress of the steel in the circumferential direction (σsc) and the radial stress in the concrete (σc):

where D is the tube diameter and t is the thickness of the tube.

## Comparison of Results

The experimental and analytical results both showed smooth axial force versus axial strain curves, indicating stability in the section. The effectiveness of the analytical procedure was demonstrated by the general agreement with the experimental results.

## References

Tsuji, B., Nakashima, M., and Morita, S. (1991). “Axial Compression Behavior of Concrete Filled Circular Steel Tubes,” Proceedings of the Third International Conference on Steel-Concrete Composite Structures, Wakabayashi, M. (ed.), Fukuoka, Japan, September 26-29, 1991, Association for International Cooperation and Research in Steel-Concrete Composite Structures, pp. 19-24.