# Varma et al. 2000

This summary highlights the results presented in several papers and reports (Varma et al., 1998a, 1998b, 1998c, 1999; Varma, 2000; Varma et al., 2000, 2001a, 2001b, 2001c) on the behavior of square concrete-filled steel tubes manufactured from high strength materials. Both experimental and computational researches are presented.

## Experimental Study, Results and Discussions

Monotonic and cyclic loading tests were carried out on three-fourth-scale square CFTs. The main parameters of the experimental tests included the type of steel, the D/t ratio and the level of the axial load. Each specimen was filled with 15.95 ksi concrete. Either A500 Grade-B or A500 Grade-80 type of steel was used.

Four stub-column specimens were tested monotically under concentrated axial compression. Force controlled loading was applied and fix-fix support conditions were provided. The response of the columns up to the peak load was approximately linear. After the peak load, unloading was observed due to concrete crushing and local buckling of all four flanges. This was followed by a sudden decrease in axial load capacity due to extensive local buckling and concrete crushing. After this stage, the loading proceeded under displacement control and two trends were observed among the specimens. Most of the specimens underwent more plastic deformation while maintaining their remaining moment capacities. However, for one of the specimens, tearing of the seam weld took place and the moment capacity decreased with additional inelastic deformation.

Eight beam-column specimens were tested with constant axial load and monotically increasing end moments. Pin-pin support conditions were simulated by the test setup. Reduction in flexural stiffness was observed with the concrete cracking and concrete crushing. Steel yielding took place both in the compression and tension flanges before the peak moment. For only one specimen, steel yielding in tension flange occurred after the peak moment was reached and failure did not take place at the mid-height. This might be due to some problems associated with the test setup of this specimen. In most of the cases, concrete crushing took place before local buckling. Local buckling of the compression face and extensive concrete crushing were observed at the peak load This resulted in a decrease in the capacity. In later stages after the peak response, local buckling of the flanges propagated to the web. Tearing of the steel tube also occurred for some of the specimens.

Eight cyclic beam-column specimens were tested under a constant axial load and a cyclically varying lateral load. The base of the specimens was fixed and the lateral load was applied at the top. The elastic cycles were performed under load control. For the inelastic cycles, displacement-controlled loading was applied at seven displacement levels ranging from Δ_{y} to 8Δ_{y}. The yield displacement (Δ_{y}) for a cyclic specimen was estimated during the elastic cycles using its secant flexural stiffness. The flexural stiffness of the specimens started to decrease with concrete cracking and steel yielding. In some cases, concrete crushing took place earlier than local buckling, but generally the peak lateral load was reached with the occurrence of both concrete crushing and local buckling of the flanges. The local buckling propagated to the web with additional displacements. This caused rapid decrease in strength. Local buckling of the tube corners and tensile facture of the steel tube wall took place in the later stages of the loading.

For the stub-column tests, the specimens with lower D/t ratios were found to have larger axial stiffness. Increasing the grade of the steel caused an enhancement in the peak axial load, and the degree of improvement was higher for smaller D/t ratios. The AISC LRFD (1993), ACI (1995), and AIJ (1987) design code provisions gave conservative estimates for the axial compressive strength of the stub-column specimens except the one that failed by elastic local buckling. On the other hand, the Eurocode 4 (1996) estimates were not conservative for all the specimens. This was attributed to the fact that the reduction in concrete strength due to size and curing effects was not applied in Eurocode 4 (1996). The transformed axial stiffnesses were found to match with the experimental results accurately.

In the beam-column tests, the initial section flexural stiffnesses of the specimens were observed to decrease with increasing D/t ratio. However, no significant change occurred when the steel grade was varied. Using the moment-curvature response, the authors calculated a serviceability level section flexural stiffness as the secant section flexural stiffness corresponding to 60% of the peak moment. Excluding one specimen, it was found that the serviceability level flexural section stiffness increased for higher magnitude of axial loads. However, it decreased for greater D/t ratios. The initial section flexural stiffness and serviceability section flexural stiffness showed good correlation with the cracked and uncracked transformed section stiffnesses, respectively. The peak moment values for the specimens improved with a decrease in D/t ratio and an increase in steel grade. However, the amount of enhancement varied according to the inelastic response of the high strength steel without local buckling. The authors defined a curvature ductility ratio as the ratio of ultimate curvature to the yield curvature. They computed this value for each specimen and concluded that the specimens with lower D/t ratio and lower axial load showed more ductile behavior. However, steel strength did not affect this ratio. The test results for the beam-column specimens were compared to the AISC LRFD (1993), ACI (1995), AIJ (1997), and Eurocode 4 (1996) design code provisions, the ACI (1995) predictions showed the best correlation.

When the cyclic test results were compared to the monotonic beam-column tests, the moment capacity was found to be approximately the same, but the peak moment of the cyclic specimens decreased more quickly. The initial flexural stiffness of the cyclic specimens was not affected by the axial load ratio and the steel strength. However, increasing the D/t ratio reduced the initial flexural stiffness. On the other hand, a high axial load ratio increased the contribution of concrete to the behavior and this resulted in a higher secant flexural stiffness. When the effects of steel grade and D/t ratio on moment capacity were examined, it was found that the increase in steel strength enhanced the moment capacity but the level of improvement was higher for the specimens with a lower D/t ratio. A decrease in the D/t ratio also improved the capacity, and the level of improvement was better for the specimens with a lower grade of steel. From the test results, curvature ductility of the specimens was also investigated. The curvature ductility was calculated for the failure segment at the base of the specimens. It was defined as the average value of the ratio of the post-peak curvature at 90% of the peak moment to the pre-peak curvature at the same moment level. For high axial loads, a significant decrease in curvature ductility was observed. When the axial load level was high, the influence of D/t ratio and steel strength on the curvature ductility was low. For low levels of axial load, increasing the D/t ratio and steel strength decreased the curvature ductility. When the section elastic flexural stiffness was examined, it was found to be close to the transformed section stiffness at early stages of loading. Due to concrete cracking and local buckling, the elastic stiffness decreased to values below the flexural stiffness of the steel tube alone. The energy dissipated throughout the test was calculated from the lateral load and lateral displacement response, as well as, from the cyclic moment curvature response of the failure segment. It was found that most of the energy was dissipated through flexure in the failure segment. The energy dissipation was low for specimens with high axial load level and larger D/t ratio. It was not affected noticeably by the grade of the steel. Axial shortening of the cyclic specimens was also monitored throughout the test. The axial shortening started at an earlier stage of loading and resulted in a larger permanent deformation for the specimens with a low level of axial load compared to the ones with a high level of axial load. The test results were compared to the AISC LRFD (1993), ACI (1995), AIJ (1997), and Eurocode 4 (1996) design code provisions, and the ACI (1995) predictions again showed the best correlation.

## Analytical Study

Three-dimensional finite element analyses of the stub columns were done using the finite element program ABAQUS. The finite element models were able to account for local buckling, confinement, and composite interaction. In the analyses, one fourth of the CFT cross section was modeled and the Modified Riks Algorithm was executed with displacement control. For the steel tubes, S-4 shell elements were selected. The stress-strain response obtained from the coupon tests in the experimental study was used as the uniaxial constitutive steel model. In the elastic range, an isotropic multiaxial constitutive steel model was used, and in the inelastic range, a plasticity-based multiaxial constitutive model utilizing a Von-Mises yield surface was selected. The concrete was modeled by 3D continuum elements. The stress strain relationships obtained from the cylinder compression tests were taken as the uniaxial constitutive concrete model. An elastic isotropic multiaxial constitutive model and a plasticity-based multiaxial constitutive model using a 2-parameter Drucker-Prager compression yield surface were chosen for the concrete in the elastic and inelastic ranges, respectively. The composite behavior between the concrete and the steel was modeled by uniaxial gap contact elements to account for the transverse interaction. Rigidly plastic springs were generated for simulating the bond between concrete and steel. Due to the confining pressure from the corners of the square tube, the concrete has core regions in a state of tri-axial stress. The inelastic multiaxial constitutive concrete model was calibrated for these regions by adjusting the two parameters accounting for the effect of confinement on the yield surface and the effect of confinement on the plastic strain tensor. For this purpose, an equation from the literature to predict the strength of the confined concrete was used. The calibration of the concrete model for the non-core regions in biaxial stress state was not done due to lack of experimental data. The first finite element analysis was conducted without introducing any imperfection in the specimen. In the elastic range, Poisson’s ratio for the steel was greater than that of the concrete. This resulted in gap opening and no interaction between the steel and the concrete. In the inelastic range, contact forces developed between the steel and the concrete. This caused composite action to initiate. The confinement of the concrete occurred and tensile circumferential stresses developed in the steel. These stresses reduced the longitudinal compressive capacity of the steel tube. The peak load was reached due to inelastic response of the steel and concrete without any local buckling. The peak loads were overestimated and the post-peak responses were not close to the experimental results. The second finite element analysis was conducted by assuming an imperfection at the mid-height of the column. The type of the imperfection was determined from the local buckling pattern of the hollow steel tubes. The correlation of the analysis results with the experimental values for the peak loads and elastic axial stiffnesses were good. However, a failure segment formed at the imperfection region due to longitudinal strain concentration. The formation of the failure segment caused elastic unloading of the remaining sections, which reduced the axial ductility of the columns. As a result, post peak response predicted by the finite element analysis was not convergent to the experimental results. The third finite element analysis was performed for the failure segments in the imperfection region. Inelastic behavior of the steel and concrete was observed but the failure was due to local buckling. The response of the failure segments were combined with the response of the remaining elastically unloaded parts to get the overall response of the column specimens. The calculated response was close to the experimental behavior.

Fiber-based finite element models were developed for the monotonic beam-column specimens in DRAIN-2DX. The inelastic responses of the specimens were mostly affected by the 12 in. length failure segments. Therefore, fiber-based models were developed for these failure segments. The tensile uniaxial stress-strain curve for steel was adopted from the coupon test results. To determine the uniaxial compressive stress-strain curves of the steel and concrete fibers, 3D finite element analysis of the failure segments were conducted in ABAQUS under axial compression. The analysis method was similar to the one presented above for the stub column specimens. Then, using the analysis results of each finite element, effective compressive stress-strain curves were defined and used for the steel and concrete fibers. These models implicitly accounted for the effects of concrete confinement, local buckling and biaxial stress state in steel tube. The fiber-based analysis results estimated the moment capacity and M versus ф response of the monotonic beam-column specimens with reasonable accuracy. The cyclic beam-column specimens were also analyzed with the fiber-based finite element method. The uniaxial stress-strain curves of the monotonic beam-column specimens were adopted for the envelopes of the cyclic stress-strain curves of the cyclic beam-column specimens. The same cyclic loading history in the experiments was utilized in the analysis. Interaction curves were generated by analyzing the specimens under various axial load levels. The theoretical results showed good correlation with the experimental moment capacities and M versus ф responses of the cyclic beam-column specimens.

## References

Varma, A. H., Hull, B. K., Ricles, J. M., Sause, R., and Lu, L. W. (1998a). “Behavior of High Strength Square CFT Columns,” Proceedings of the Sixth U.S. National Conference on Earthquake Engineering, Seattle, Washington, May 31-June 4, 1998, Earthquake Engineering Research Institute, Oakland, California.

Varma, A. H., Hull, B. K., Ricles, J. M., Sause, R., and Lu, L. W. (1998b). “Experimental Studies of High Strength CFT Beam-Columns,” Proceedings of the Fifth Pacific Structural Steel Conference, Seoul, Korea, October, Volume 2, pp. 893-900.

Varma, A. H., Ricles, J. M., Sause, R., Hull, B. K., and Lu, L.-W. (1998c). “Behavior of High Strength Square CFT Columns,” ATLSS Report No. 98-10, Department of Civil and Environmental Engineering, Lehigh University, Bethlehem, Pennsylvania.

Varma, A. H., Hull, B. K., Ricles, J. M., Sause, R., and Lu, L.-W. (1999). “High Strength Square CFT Columns: An Experimental Perspective,” Proceedings of the Annual Technical Session and Meeting, Atlanta, Georgia, September 21-23, 1998, Structural Stability Research Council, Gainesville, Florida, pp. 205-218.

Varma, A. H. (2000). “Seismic Behavior, Analysis, and Design of High Strength Square Concrete Filled Steel Tube (CFT) Columns,” Ph.D. dissertation, Department of Civil Engineering, Lehigh University, Bethlehem, Pennsylvania, November.

Varma, A. H., Ricles, J. M., Sause, R., and Lu, L.-W. (2000). “Seismic Behavior of High Strength Square CFT Beam-Columns,” Composite and Hybrid Structures, Proceedings of the Sixth ASCCS International Conference on Steel-Concrete Composite Structures, Xiao, Y. and Mahin, S. A. (eds.), Los Angeles, California, March 22-24, 2000, Association for International Cooperation and Research in Steel-Concrete Composite Structures, Los Angeles, California, pp. 547-556.

Varma, A. H., Ricles, J. M., Sause, R., Hull, B. K., and Lu, L. W. (2000). “An Experimental Evaluation of High-Strength Square CFT Columns,” Composite and Hybrid Systems, ACI SP-196, Aboutaha, R. S. and Bracci, J . M. (eds.), American Concrete Institute, Farmington Hills, Michigan.

Varma, A. H., Sause, R., and Ricles, J. M. (2001a). “FEM Analysis of High Strength Square CFT Columns,” Proceedings of the Annual Technical Session and Meeting, Memphis, Tennessee, July 24-26, 2000, Structural Stability Research Council, Gainseville, Florida, 272-287.

Varma, A. H., Ricles, J. M., Sause, R., Hull, B. K., and Lu, L.-W. (2001b). “An Experimental Evaluation of High Strength Square CFT Columns,” ACI SP-196, Special Publication on Composite Steel-Reinforced Concrete Structures -- In Honor of the Late Dr. Walter P. Moore, Jr., Aboutaha, R. S. and Bracci, J. M. (eds.), American Concrete Institute, Detroit, Michigan, pp. 51-86.

Varma, A. H., Ricles, J. M., and Sause, R. (2001c). “Seismic Behavior of High Strength Square CFT Beam-Columns,” Proceedings of the 2001 Annual Technical Session and Meeting, Fort Lauderdale, Florida, May 9-12, 2001, Structural Stability Research Council, Gainesville, Florida, 2001, pp. 459-480.

Varma, A. H., Ricles, J. M., Sause, R., and Lu, L.-W. (2002). “Experimental Behavior of High Strength Square Concrete-Filled Steel Tube Beam-Columns,” Journal of Structural Engineering, ASCE, Vol. 128, No. 3, March, pp. 309-318.

Varma, A. H., Ricles, J. M., Sause, R., and Lu, L.-W. (2004). “Seismic Behavior and Design of High-Strength Square Concrete-Filled Steel Tube Beam Columns,” Journal of Structural Engineering, ASCE, Vol. 130, No. 2, February, pp. 169-179.