# Varma, Ricles, Sause & Lu. 2000, 2001, 2002, 2004

The behavior of square CFT beam-columns subjected to constant axial load and cyclically varying flexural loading was investigated (Varma et al. 2002), and the effects of d/t, yield stress, and axial load level was studied. Crushing of concrete and cyclic local buckling occurred and the elastic section flexural stiffness decreased due to tension cracking of the concrete.

## Experimental Study, Results, and Discussion

Eight CFT specimens with constant square cross section were created using different d/t ratios and steel yield stress. High strength concrete was used, and two types of steel were used: A500 Grade-80 and A500 Grade-B. Specimens were tested at an axial load capacity of .1 or .2 Po. The length of all of the specimens were kept constant, and the specimens were fixed at the base and subjected to a constant axial load and cyclically varying lateral load at the top, free to rotate about the base. The axial load was applied with a hollow core hydraulic jack, an axial loading beam, and two axial tension rods. The lateral load was applied by imposing cyclically varying displacements at the top of the specimen using a hydraulic ram. Linear variable displacement transducers were used to measure the displacements, which were used to determine second-order bending moments, and rotation was measured using rotation meters that were mounted on the tension rods. The rotations were used to determine the curvature. The specimens were also loaded and tested laterally, and the tests consisted of both elastic and inelastic cycles. Each test consisted of two cycles at each lateral load level, and the secant flexural stiffness of the specimen was used to determine the yield level lateral displacement (Δy). For the inelastic cycles, the displacement was kept under control at displacement levels of 1.0,1.5, 2.0, 3.0, 5.0, 7.0, 8.0, and 11.0Δy. One elastic half cycle was imposed after each set of inelastic cycles to determine if the elastic stiffness of the specimen had changed. The significant events that occur during the cyclic tests are A) concrete goes into tension, B) steel tube flanges yield in compression, C) extreme concrete compression fiber reaches cylinder failure strain, D) steel tube flanges yield in tension, E) initial crushing of concrete, F) local buckling of steel flange, G) local buckling of steel webs, H) local buckling of steel tube corners, and I) tension cracking or fracture of steel tube corners. Event F occurred at the point when the longitudinal strain at the center of the steel section deviated significantly from the strain at the corners. The specimens with .2Po behaved similarly, and the flexural stiffness decreased with increasing lateral displacements beyond Δy due to concrete cracking and steel tube yielding. Local buckling of the tube flanges (Event F) occurred during the 2.0Δy test, and the steel tube fractured (event I) during the 7.0Δy test, and the test was concluded. Extensive crushing of the concrete was observed at the base of the tube. Many of the specimens with .1Po behaved similarly as well, and local buckling of the steel flanges occurred during the 1.5Δy test, whereas tension fracture of the steel occurred during the 7.0Δy test, and the test was concluded here. Although the behavior of the specimens was similar, the order of events A-I varied between tests depending on specimen parameters. An equation for the moment at mid height was used to determine the cyclic moment-curvature response. Curvature was determined using an equation with the central difference method and the rotations from the experimental testing. The moment-curvature responses were used to determine the initial-section flexural stiffness, the serviceability-section flexural stiffness, the moment capacity, and the cyclic curvature ductility. The lateral load- lateral displacement responses were used to determine the displacement ductility of the systems. It was observed that increasing the yield stress of the steel, or the axial load level does not have a significant influence of the initial flexural stiffness, whereas increasing the b/t ratio of the steel results in a slight reduction of the initial flexural stiffness. The specimens with smaller b/t ratios have a greater ratio of initial to gross section modulus due to a greater area of steel. The moment capacity of the specimens increased with an increase of the nominal yield stress of the steel, however increasing the b/t ratio while maintaining the yield stress and load level decreases the moment capacity. The curvature ductility of the specimens decreases significantly with an increase in load level, whereas the b/t ratio and yield stress have a small influence on the curvature ductility at higher load levels, and reduced the ductility at lower load levels. The energy dissipated due to flexural loading by each specimen was determined with an equation as well as the lateral load-displacement response. The energy dissipated due to axial load was also determined using an equation with axial load and axial shortening at each step as parameters. The total energy dissipated can now be calculated as the sum of the energy dissipated due to flexural and axial loading. In conclusion, cyclic loading does not have a significant effect on the flexural stiffness and moment capacity, and the initial and service level flexural stiffness can be calculated accurately using the uncracked transformed and cracked transformed section properties.

## References

Varma, A., Ricles, J., 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 130 (2), February, pp. 209-318 doi:10.1061/(ASCE)0733-9445(2004)130:2(169)