# Lai, Varma and Griffis 2016

## Comparison of Existing Studies and Experiments

This paper demonstrates and discusses tests performed on noncompact and slender CFT beam-columns, and compares this to the AISC bilinear axial force-bending moment interaction curves, as well as developing a finite element model to predict the behavior of CFT members. Members are classified as noncompact, compact, or slender depending on the slenderness ratio, which compares the width and the thickness of the members. This paper compares experimental tests from multiple sources, which include specimens of various cross sectional shape (circular, square, and rectangle), as well as various loading conditions. The experimental values are then compared to the predicted strength based on the AISC 360-10 P-M interaction equations. The comparisons indicate that the equations are extremely consrvative for most specimens, however are not overly conservative for rectangular specimens with relative strength ratio greater than 1. The equations are conservative because they do not account for the influence of axial compression on concrete cracking, and the beneficial contribution to the specimen’s flexural strength. The strength of CFT beam-columns depends on the slenderness ratio, the axial load ratio, the material strength ratio, and the member length. When the axial load level is low, flexural behavior dominates the structural response, however axial compression dominates when the axial load level is above the balance point. As the relative strength ratio increases, the CFT beam-column behavior becomes more like that of steel members, and becomes more like reinforced concrete members as the relative strength ratio decreases.

## Analytical Study

The finite element method models capable of predicting behavior of noncompact and slender CFT columns developed account for steel plasticity, local buckling, concrete cracking, geometric imperfections, and interactions between the steel tube and concrete infill. The contact interaction was modeled in both the normal and tangential directions, and the maximum interfacial shear stress was suggested by AISC 360-10. Cracking of concrete makes it difficult to obtain converged results using standard nonlinear solutions, such as the Newton, Newton-Raphson, and modified-Riks methods. An explicit dynamic analysis method was used as it can find solutions up to failure such as concrete in tension. Not all of the specimens presented in the prior section were modeled in the FEM model, as some specimens were tested under cyclic loading, thus 39 of 53 noncompact or slender sections were chosen to be modeled. The axial strength was defined by the maximum axial load applied, and the flexural strength was the bending strength corresponding to the maximum axial load. The effects of relative strength ratio and length were studied. When the material strength ratios increased while maintaining the slenderness ratio, the P-M interaction curves for both circular and rectangular CFT beam-columns are more similar to that of reinforced concrete members. The member length affects the second-order moments, however does not influence the stiffness. The length does not significantly influence the strength for rectangular beam-columns, however failure does occur earlier with increasing length due to local buckling. For circular beam-columns, strength marginally increases with length due to strain hardening. For both rectangular and circular specimens, the member length does not have a significant influence on the P-M interaction curves. This paper proposed three methods for interaction equations: Method A using polynomial equations, Method B uses a trilinear cure, and Method C uses a simplified bilinear curve. In conclusion, the methods presented in AISC 360-10 are conservative for the design of noncompact and slender CFT beam-columns, and equations can be updated for the P-M interaction curves, however further research is needed to verify the results.

## References

Lai, Z., Varma, A., Griffis, L. (2016). “Analysis and Design of Noncompact and Slender CFT Beam-Columns.” Journal of Structural Engineering 142(1),pp. 1-14 doi: 10.1061/(ASCE)ST.1943-541X.0001349