# Lundberg and Galambos 1996

The objective of this work (Lundberg, 1993; Lundberg and Galambos, 1996) was to determine the reliability index for composite columns and beam-columns, i.e., determine the probability that failure of a member will not occur. A large number of test results were analyzed to provide a statistical base for the reliability study. Results of steel-reinforced concrete shapes and rectangular and circular concrete-filled steel tubes were examined, the latter two of which will be highlighted in this summary.

## Discussion of Results

The experimental results were compared to the AISC LRFD Specification (1993) with the flexural and compressive resistance factors set to 1.0 to allow a direct comparison between the predicted and actual strengths. The data from 243 tests of circular CFTs (161 columns and 82 beam-columns) and 68 rectangular CFTs (16 columns and 52 beam-columns) was collected, tabulated, and analyzed. The analysis of the columns resulted in a mean ratio of test load to predicted load (P_{u}/P_{o}) of approximately 1.3 with a standard deviation of 0.23, reflecting the large scatter of the results. These values decrease if the results of the stub columns are omitted. Circular columns had a mean ratio of 1.5 with a standard deviation of 0.21 and rectangular columns had a mean ratio of 1.1 with a standard deviation of 0.12. A number of the rectangular sections had ultimate strength values below the AISC Specification. The beam-column tests exhibited a much larger scatter, producing a mean ratio of 1.5 with a large standard deviation of 0.36. The corresponding mean value and standard deviation values for the circular and rectangular beam-columns were approximately 1.6, 0.39 and 1.3, 0.21 respectively. The author concludes that the AISC Specifications are inconsistent and inadequate for CFT columns and beam-columns. The distributions of the test results were not normal and displayed a large amount of scatter, contributing to the difficulty in predicting CFT strength. The AISC approach for stub columns, which ignores the effect of confinement, was shown to be very conservative.

## References

Lundberg, J. E. and Galambos, T. V. (1996). “Load and Resistance Factor Design of Composite Columns,” Structural Safety, Vol. 18, No. 2-3, pp. 169-177.