Lundberg and Galambos 1996

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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 (Pu/Po) 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.


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.