# Schneider 1998

In this paper, the author presented an experimental study and results from a three-dimensional finite element analysis on the behavior of circular, square, and rectangular CFTs. The response of short columns under concentric axial load was investigated. The results were compared with the AISC LRFD (1993) design code provisions.

## Experimental Study Results and Discussions

Three circular, five square, and six rectangular specimens were tested under monotonic axial load. The columns were simply supported. The D/t ratio of the specimens varied from 17 to 50. The nominal yield strength of steel and nominal compressive strength of concrete were 46 ksi and 2.9 ksi, respectively. The L/D ratios ranged between 4 and 5. The tubes were annealed and free from residual stresses.

The specimens showed different post-yield behaviors depending on their shape and D/t ratio. All of the circular specimens achieved hardening type post-yield response. Among rectangular and square specimens, two specimens that had the lowest D/t ratios also exhibited hardening behavior in their post-yield response. However, most of the other specimens underwent softening post-yield response.

The ductility level of the specimens was defined as the ratio of axial deformation at any point during the load history over the axial deformation at the point of yielding. If the yield point of the specimens were not clear, it was obtained by a 0.2% offset rule. No local buckling was observed before yielding of the columns. The local buckling of the circular specimens took place when the ductility levels were more than 10. For the square and rectangular hardening specimens, the ductility level at local buckling was between 6 to 8. In the case of the softening specimens, local buckling ductility levels were less than 6. The hardening columns underwent large deformations up to ductility levels greater than 10 before they reached the ultimate axial load. For the hardening specimens, it was found that the peak axial load was up to 1.41 times their yield load. On the other hand, for the softening specimens, the ductility level at the peak axial load was less than 2 and the peak axial load was approximately 1.07 times greater than the yield load. The increase in peak axial load observed in the tests was attributed to the confinement effect, and it was larger for circular sections.

The load carried by the steel section alone throughout the test was calculated from the longitudinal strain values of the steel tube. For thick sections, the load share of the steel tube maintained a constant value until yield load. However, it was found to increase in the case of thin sections. After yielding, the load carried by the steel tube was observed to decrease in strain hardening type specimens. The opposite trend was observed for the strain softening specimens. For most of the columns, circumferential strain over longitudinal strain ratios were close to Poisson’s ratio of steel until 92% of yield load and then they were observed to increase up to 15%. This was indicative of concrete confinement. Local buckling was observed for every specimen and it was more intense in the case of large D/t values. The concrete at the locally buckled parts was investigated and generally it was observed to flow plastically without any granulation.

The axial strengths of the specimens were calculated by the method in the AISC LRFD (1993) specification. Good correlation was achieved with an average value of 1.08 for measured over predicted load ratios. These ratios exhibited large scatter with respect to column slenderness, λc, in AISC LRFD (1993) provisions. However, their correlation with respect to D/t ratios was better.

## Analytical Study

The test specimens were analyzed using three-dimensional finite element analysis, through the use of ABAQUS. The same model was used to investigate the response of larger scale CFT columns that were common in current construction practice. Brick elements for the concrete core and shell elements for the steel tube were utilized. The available concrete material model in ABAQUS was selected, and it was assumed to represent adequately a low amount of confinement prior to yielding of the CFT column. The Von Mises yield criterion and the Prandtl-Resuss flow rule were chosen for the steel. No strain-hardening was assumed. The interaction between the steel and concrete was simulated by gap elements, and the coefficient of friction between the steel and concrete was assumed to be 0.25. Both the elastic and inelastic response of the specimens were closely correlated by the computational results, and the computational and experimental local buckling patterns were found to be similar. In addition to the experimental specimens, fifteen more finite element models for circular CFT columns were analyzed, covering D/t ratios ranging from 10 to 85. In these models, three different diameters of 2.7 in., 14.2 in., and 28.4 in. were selected. The nominal yield strength of the steel was taken as 46.0 ksi and the nominal concrete compressive strength was taken as 4.5 ksi in the analyses. The L/D ratio was chosen as 5. The column slenderness parameter, λc, in the AISC LRFD (1993) provisions for all of the steel tubes was approximately equal to 0.2. From the computational results, it was found that both the concrete and steel developed their compressive yield stresses when the CFT member reached its yield strength, which was calculated by a 0.2% offset rule for the analytical model . In the case of large diameter specimens, the steel tube could not develop its yield strength due to the detrimental effect of the biaxial stresses. From the concrete stress values at the peak axial load, the concrete strength enhancement due to confinement was found to be about 30% for small diameter specimens and 15% for large diameter specimens. The computational yield strengths of all of these specimens were also compared with the axials strengths predicted by the AISC LRFD (1993) provisions. It was found that for small diameter specimens, the ratio of the computational strength over design strength decreased with increasing D/t values. In the case of large diameter specimens, the predictions were close to the analysis results for small D/t values while the analysis results were overestimated for large D/t values.

## References

Schneider, S. P. (1998). “Axially Loaded Concrete-Filled Steel Tubes,” Journal of Structural Engineering, ASCE, Vol. 124, No. 10, October, pp. 1125-1138.