# Han, Huo, and Wang 2007

## Analytical Study

A nonlinear finite-element analysis model and experimental test were developed in this paper to analyze load vs. deformation graphs for steel beam to concrete- filled steel tubular column connections. Six tests were also performed according to ISO-834 to verify the model. Each specimen consisted of a concrete filled steel tube (CFST) column with two steel beam segments in cruciform arrangement. This is meant to represent an interior joint in a building. The specimen height was 61.81” and three of which had circular cross section while the remainder had square. Other parameters were measured including fire duration time (0 or 90 min), axial load level, and beam-column strength ratio. Strips of steel tubes and sheets were tested in tension to determine yield strength and the modulus of elasticity. Additional strips were exposed to spire and tested in tension to determine the same values. The specimens exhibited mild change in the modulus of elasticity for mild steel after fire exposure. Five of the six specimens were simultaneously exposed to standard ISO-834 fire condition for 90 minutes, in which the start temperature was 20°C and were not protected during exposure. The temperature was not measured due to financial constraints, and the specimens were left to cool down. The specimens were then tested under both constant axial load and cyclically increasing flexural load. A rigid stub was attached to prevent local failure, and a lateral load was applied. Curvature gauges, strain gauges and displacement transducers were attached to measure displacement, strain and curvature. A pin-pin connection was simulated using cylindrical bearings which had freedom to rotate in-plane. All of the test specimens behaved in a ductile manner, and it was observed that the specimens failed under local buckling at the compression flanges closest to the exterior ring. The beam webs also failed under local buckling as the lateral displacement increased. All of the fire-exposed test specimens failed due to reduction in the lateral load bearing capacity. It was also observed that the steel tube separated from the concrete in the square cross- section tubes, however did not occur in the circular tubes.

The FEA model is under the assumptions that plane sections remain plane during loading; no slip displacement occurs between the steel and concrete within the CFST; shear force on structural deformation is neglected; and only plane frame action is considered. The equilibrium equations were determined using Lagrangian procedures, and at a certain applied load, an incremental displacement was assumed, ad the axial and flexural deformations can be obtained. Material tangent and geometric stiffness matrices were defined. Assumed hysteric moment vs. curvature curves for steel beam and CFST columns were used to calculate parameters in the matrices. Similar methods can be used to assemble the elements internal force vector. The incremental displacements under each imbalanced load are used to solve for the imbalanced load vector using the internal force vector, the load vector, and the fixed load vector. This process is iterated until the imbalanced load is negligible compared to the applied load. The comparison between the FEA model and the experimental test displays that the predicted lateral load resistance is consistently lower than the predicted values, thus the predicted values from the model are safe, and the model can be used to accurately predict the load-displacement curves.

## References

Han, L., Huo, J., Wang, Y., (2007). “Behavior of Steel Beam to Concrete-Filled Steel Tubular Column Connections after Exposure to Fire” Journal of Structural Engineering, 133 (6), June.