# Zhang and Shahrooz 1997

In this report, analytical models for cross-section strength of square CFTs and the corresponding concrete and steel stress-strain relationships were presented. The analytical models were implemented for the specimens of past and current experimental studies and the results were compared with the measured values. Member behavior was also investigated. It was captured by numerical techniques using reliable cross-section responses and compared with the experimental findings. In addition, an experimental study for two square CFT beam-columns was also presented.

## Experimental Study

Two square CFTs were subjected to combined axial force and flexure. The axial load was the main parameter of the experiment. One of the specimens was subjected to an axial load of 0.18Po. The second one was not subjected to any axial load. The D/t ratio was 32 and the L/D ratio was 4.8 for both of the specimens. The average measured steel yield strength and compressive concrete core strength were 53.67 ksi and 6.05 ksi, respectively. The columns were tested in a horizontal position and the supports were pin-ended. After maintaining the constant axial load, transverse loads were applied at two points along the specimen length. The specimens were loaded and unloaded to a zero transverse load to examine the stiffness degradation throughout the loading history. The strain distribution along the mid-span, vertical deflections, and support rotations were measured.

Both specimens failed by inelastic flexural buckling. The column tested without axial load exhibited higher strength and more stable post-peak behavior. In both tests, the strain distribution along the mid-span showed that most of the steel was yielded close to the top and bottom fibers.

## Analytical Study

The cross section types used in the experimental studies by Furlong (1967, 1968), Tomii and Sakino (1979b) and Fujimoto et al. (1995) were analyzed using six different analytical models. In the first two models, the ACI (1995) standard stress block approach developed for reinforced concrete members was implemented. A fiber approach was chosen for the remaining ones and concrete and steel stress-strain curves varied for each analytical model. The effects of cold working and residual stresses on cross- section strength were examined separately.

The cross-section strengths calculated by the standard ACI method matched closely with the measured values of Furlong (1967, 1968) and Tomii and Sakino (1979b). However, they did not estimate the Fujimoto et al. (1995) results well due to the high strength steel utilized in those specimens. The fiber models improved the analytical results for the tests of Furlong (1967, 1968) and Tomii and Sakino (1979b) only marginally. However, they estimated the results by Fujimoto et al. (1995) better than the standard ACI (1995) method. Moment-curvature-thrust analysis was also made with the fiber models for the tests of Tomii and Sakino (1979b) and good correlation was obtained with the experimentally obtained curves, even in the post-peak region. Among the fiber models, the concrete and steel stress-strain relationships varied to study the effects like concrete confinement and local buckling of steel tube. To account for confinement effect, the concrete model of Tomii and Sakino (1979b) and the concrete model of Inai and Sakino (1996) were implemented in the third and fourth analytical models, respectively. In the former concrete model, the confinement effect depended on D/t ratio alone while in the latter one, confinement was effected by both D/t ratio and yield strength of steel. The analysis results showed better correlation with the experiments for the concrete model of Tomii and Sakino (1979b) and it was recommended to be used. In the fifth and sixth analysis types, different compressive steel properties were used to account for local buckling. However, the results showed that the effect of local buckling was not so significant due to the low D/t ratio of the cross sections studied.

The increase in strength at the corner regions because of cold working was modeled in several of the analyses by selecting different material properties in these portions of the cross section. Two sets of moment curvature-thrust analyses were performed for a sample cross section. In the first analysis, cold working was neglected, while in the second analysis, cold working was accounted for. It was determined that the moment strength was affected by approximately 5% at an axial load of 0.60P0, and the difference was even more negligible when high strength materials were utilized. For residual stresses, two types of residual stress distribution was assumed on a sample cross section and moment-curvature-thrust analysis were performed. It was found that the residual stresses caused reduction in cross-sectional stiffness. The effect of residual stresses was greater when the axial load was large. The authors proposed a conservative residual stress distribution and recommended it to be used if the actual distribution was not available.

Using the strain distributions at the peak points along the backbone of the load-deflection curves of the two tested CFT beam-columns, moment-curvature-thrust diagrams were generated at the mid-span of the CFTs. The flexural stiffness of the specimens was computed from the linear portion of these diagrams. A fiber model employing the concrete model of Tomii and Sakino (1979b) and measured stress-strain relations for the steel was then implemented to obtain the analytical moment-curvature-thrust relations of the specimens. Good correlation was obtained between the experimental and analytical moment-curvature-thrust diagrams. The initial flexural stiffness calculated from the fiber analysis matched with the measured stiffness of the column tested under axial load. However, the measured initial stiffness was underestimated for the column having no axial load. For the column tested under axial load, the loss of stiffness observed after a moment of 1505 kip-inches was not noticeable in the analytical results. This was attributed to the softening of the steel as a result of the subsequent loading and unloading process applied to the specimens. The moment-curvature-thrust relationships from the fiber analysis were then integrated numerically and load-displacement curves were obtained. For the specimens having axial load, second order effects were accounted for. The analytical load-displacement curves showed good correlation with the experimental results. However, the analytical results indicated a loss in initial stiffness at a higher load as compared to the experimental stiffness of the specimens. This was again attributed to the softening of the steel.

## References

Zhang, W. and Shahrooz, B. M. (1997). “Analytical and Experimental Studies into Behavior of Concrete-Filled Tubular Columns,” Report No. UC-CII 97/01, Cincinnati Infrastructure Institute, Department of Civil and Environmental Engineering, University of Cincinnati, College of Engineering, Cincinnati, Ohio, May.