# Cai 1991

Twenty-seven circular CFT columns with non-uniform moment distribution diagrams were tested and the results were briefly described. The main parameters were the slenderness ratio, eccentricity ratio, and the ratio of the smaller to larger end moments. A method was described to convert a column with a non-uniform moment distribution to an equivalent column with uniform moment distribution. This formulation was the main thrust of the paper.

## Experimental Study

Of the 27 tests performed, 18 were columns bent in single curvature with eccentricity only at one end; the remainder were bent in double curvature with two opposite end eccentricities. These experiments served as test data for the theoretical study, namely to obtain values for the parameters that will subsequently be defined.

## Theoretical Discussion

The ultimate strength of a circular CFT column was proposed as follows:

Po is the ultimate strength of a axially loaded stub column, Φl is a strength reduction factor due to the slenderness ratio, and Φe is a strength reduction factor due to the eccentricity ratio (the ratio of eccentricity to the radius of the concrete core). Five types of moment distribution were described and quantified using a parameter β equal to the ratio of the smaller end moment to the larger end moment. Standard columns were defined as columns with equal end moments bent in single (β = 1) or double curvature (β = -1). The remaining three types had unequal end moments --one type was bent in single curvature (0 < β < 1), one in double curvature (β < 0), and the third was the special case of zero moment at one end (β = 0). To convert an unequal moment distribution to an equal one, the authors applied an equivalent-length factor K (less than 1) and replaced the unequal moments with uniform ones equal to the larger moment. Values of K were determined experimentally for β = -1 and β = 0 (k must equal 1 for β = 1) and then interpolated for intermediate values. Using the value of K, the eccentricity ratio in the above equation was modified. As shown in a previous paper by the author, the load-moment interaction equation based on the above parameters may be expressed as:

for an eccentricity ratio less than or equal to 1.55 and

for eccentricity ratios greater than 1.55. The paper illustrated an interaction curve based on these formulas and limits on the strength reduction factors.

## Comparison of Results

For ultimate load, the results of the experimental method and the computation using the above approach showed good correlation: the ratio of Pu/Po varied from 0.935 to 1.161.

## References

Cai, S.-H. (1991). “Influence of Moment Distribution Diagram on Load-Carrying Capacity of Concrete-Filled Steel Tubular Columns,” Proceedings of the Third International Conference on Steel-Concrete Composite Structures, Wakabayashi, M. (ed.), Fukuoka, Japan, September 26-29, 1991, Association for International Cooperation and Research in Steel-Concrete Composite Structures, pp. 113-118.