# Ichinohe et al. 1991

The elasto-plastic behavior of CFT circular specimens constructed of high-strength steel tubes and high-strength concrete was examined by performing 11 tests to determine moment-curvature relations and 9 tests to determine the shear in specimens subjected to bending. The tests were conducted both monotonically and cyclically and included an axial load. The authors defined a limiting D/t ratio below which specimens were free from moment degradation due to local buckling. The authors also defined a limiting axial force ratio above which excessive axial deformation under a cyclic load would occur, leading to a loss of building frame stability. The paper also proposed an analytical method to explain the elasto-plastic behavior of the columns.

## Experimental Study, Discussion and Results

The following parameters were used in the tests: D/t, P/P_{o}, λ, annealing or no annealing, and loading pattern. The first group of tests, the moment-curvature tests, were performed by loading a horizontally-oriented, simply-supported specimen axially and transversely at approximately the third points along the specimen's length. In the monotonic moment-curvature tests, decreasing the D/t or P/P_{o} ratio delayed local buckling and steepened the slope of the increasing moment in the plastic zone. All specimens with D/t less than or equal to 53 showed an increasing moment after local buckling with no degradation. However, a specimen with D/t equal 71 did show degradation. Therefore, a critical bifurcation point exists between these two values. Under cyclic loads, all specimens exhibited good energy absorption and little or no moment degradation. The second group of tests, the shear bending tests, again consisted of a horizontally oriented, simply-supported member loaded axially and transversely. This time the transverse load was applied via a beam framing into the member at mid-length. The connection of the beam and the tested specimen formed a rigid joint at the load point. Therefore, each half of the beam was treated as an axially loaded cantilever; the rigid joint at the midpoint of the specimen served as the fixed end of each half, and the simply-supported ends simulated the free ends of a cantilever. For these shear-bending tests, if the average axial force ratio P/P_{o} was less than or equal to 0.5, the deformation due to P had little influence on stability, even though P was temporarily increased to 0.7*P_{o} by the overturning moment.

## Analytical Study

The proposed analytical method was a mechanics-based analytical method which tried to model the behavior of concrete-filled steel tubes. The model assumed biaxial stress in the steel and triaxial stress in the concrete, and hence confinement of the concrete. The ratio of hoop stress to longitudinal stress in the steel was found experimentally to be 0.5 to 0.6 on the tension face and between 0 and 0.5 on the compression face. Using these experimental values and the von Mises yield criterion to relate the longitudinal and hoop stresses, the authors obtained the stress-strain relationship in the plastic region. The concrete stress-strain relationships were adopted from Park and Priestly. The moment-curvature relationship was obtained by numerical integration based on Navier's hypothesis. The moment-rotation was obtained by integrating the calculated moment-curvature along the axis of the member. The load-deformation relationship of the column was traced favorably by this method over the elasto-plastic region (the region between first yield and the full plasticity of the steel tube). The shear bending test was mimicked well showing that both the moment-curvature and shear bending tests may be evaluated with the same moment-curvature relationship.

## References

Ichinohe, Y., Matsutani, T., Nakajima, M., Ueda, H., and Takada, K. (1991). “Elasto-Plastic Behavior of Concrete Filled Steel Circular Columns,” 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. 131-136.