# Kawaguchi et al. 1993

The results of 26 square cantilever beam-column tests were presented. Twelve HT tests and 14 CFT tests were conducted. Each specimen was loaded axially and subjected to an alternately repeated transverse load at the top of the beam-column. The effect of filling the steel tubes with concrete on the energy dissipation capacity and the number of load repetitions the member could withstand was discussed. The strength deterioration of the specimens due to local buckling of the steel tube was also investigated. A number of detailed hysteretic curves including an indication of the point of local buckling were presented as well. The parameters that were varied in the tests included the D/t ratio, the axial load ratio, and the amount of lateral displacement the beam-column was subjected to, expressed as the ratio Δmax/Δcr

## Experimental Study, Discussion, and Results

Each specimen was loaded transversely until the specified displacement, Δmax, was reached. This value was varied from 0.6Δcr to 1.3Δcr for different tests. After the specified displacement was reached in one direction, the load was reversed and the beam-column was displaced an equal amount in the opposite direction. Ten cycles of alternately repeated load were applied at this constant displacement amplitude. The displacement at the occurrence of local buckling decreased with an increase in axial load. The magnitude of the displacement at which local buckling of the steel tube occurs was 1.4 times greater for the concrete-filled tube than for the hollow tube for a D/t ratio of 22.1, and 1.9 times greater for D/t = 31.3. The hollow tubes could not, in some cases, sustain sufficient axial strength to undergo 10 cycles without failure. The concrete-filled tubes exhibited less strength deterioration and more energy dissipation capacity than comparable hollow tubes. Plots of the maximum strength versus load cycle showed how the CFT was able to sustain its strength, reaching a steady state after local buckling, while the hollow tube's maximum strength dropped, sometimes significantly, with each cycle due to strength deterioration. Although the concrete did not contribute much strength in bending, it increased the energy dissipation mainly by delaying the onset of local buckling of the tube. The value of the axial strain at the occurrence of the local buckling was not greatly affected by the axial load ratio.

## Analytical Study

Stress-strain curves and corresponding formulas were presented to model the behavior of the individual components of the CFT. The formulas for the steel traced linear elastic and linear strain-hardening curves with a curvilinear elasto-plastic portion between the two linear curves. Also presented was a function tracing the degradation following local buckling. The concrete curve followed Popovics's relation and it was assumed that the maximum strength was maintained due to confinement. The beam-column was modeled by dividing the cross-section into fiber elements to determine load-deflection and moment-curvature diagrams analytically. The model of the beam-column cross-section consisted of two types of fibers: a series of fibers in the tube and a series of fibers, each of which is a transverse layer, to model the concrete. It was assumed that the stress in each concrete layer was uniformly distributed and plane sections remained plane after bending. The true value of the centroidal strain (calculated from a given curvature) satisfying equilibrium with the applied axial force was obtained by a trial and error method. From the strains, the moment in the section was calculated, giving the moment-curvature relationship. The transverse load-displacement relation was calculated assuming that the deformable portion of the beam-column was located over a width D at the base of the specimen and the remainder of the beam-column was rigid. Once a moment-curvature relation was established, the applied transverse load could be calculated without trial and error from the deflection. The deflection was obtained from a formula expressing it in terms of the deformable length D and the amount of curvature at the base:

where L is the member length and Φ is the base curvature. The calculation of the transverse load H followed:

where M(Φ) is the moment as a function of curvature and P is the applied axial load. The analytical method presented predicted the experimental behavior well. However, it did not model the Bauschinger effect, i.e., the gradual softening of the stiffness beyond the elastic region.

## References

Kawaguchi, J., Morino, S., Atsumi, H., and Yamamoto, S. (1993). “Strength Deterioration Behavior of Concrete-Filled Steel Tubular Beam-Columns,” Composite Construction in Steel and Concrete II, Proceedings of the Engineering Foundation Conference, Easterling, W. S. and Roddis, W. M. (eds.), Potosi, Missouri, June 14-19, 1992, ASCE, New York, New York, pp. 825-839.