# Rangan and Joyce 1992

The results of tests performed on nine eccentrically loaded, slender, circular CFTs filled with high-strength concrete were reported. The two main test parameters were the slenderness ratio and the eccentricity of axial thrust. A simple method to calculate the strength of columns was presented and it showed good correlation with the test results reported in the paper and those reported by Neogi, Sen, and Chapman (1969).

## Contents

## Experimental Study, Discussion, and Results

All of the specimens failed at midheight due to the crushing of concrete in compression. The extreme tensile fibers in the steel did not reach yield for the low values of eccentricity, but did in the other cases. Extreme fiber compressive strains ranged from 0.002 to 0.004.

## Analytical Study

The method for calculating the axial load capacity of eccentrically loaded slender CFT columns was based upon the assumption that the failure load was reached when the maximum moment at midheight of the column was equal to the ultimate bending strength of the cross section at that location. This value was determined by iteratively computing the internal and external moments until equilibrium was established. The computation of the external moment included the effects of creep, initial eccentricity, and initial imperfections. The sum of the midheight deflections due to these effects and the deflection due to the load was multiplied by the axial load to get the external moment. The internal moment was computed by idealizing the cross-section. Linear strains over the cross-section were assumed with a maximum compressive strain of 0.003 in the concrete. Stress resultants acting at the centroids of the tensile (steel) and compressive (steel and concrete) regions were computed based on the distance to the neutral axis and the constitutive relation (Hognestad's parabola). The internal forces were computed based on these stress values multiplied by their respective areas. To relate the internal and external moments, the authors assumed a deflected shape in the form of a sine curve. Curvature was calculated by dividing the extreme fiber strain by the neutral axis distance. From this, deflection was calculated using the sine curve assumption and the midheight relationship between curvature and deflection. The neutral axis was adjusted until moment equilibrium was achieved.

## Comparison of Results

The results from the formula were conservative compared to the authors' tests and tests from other investigators. For columns with small eccentricities, the results were very conservative, probably due to assuming that the concrete crushed at a strain of 0.003. In reality, the more concentrically loaded columns will attain higher concrete strains. Neglecting the low eccentricity tests, the mean value of test/calculated for these 21 specimens was 1.08 with a coefficient of variation of 5% (1.17 and 16% for all 27 compared tests).

## References

- Rangan, B. V. and Joyce, M. (1992). “Strength of Eccentrically Loaded Slender Steel Tubular Columns Filled with High-Strength Concrete,” American Concrete Institute Structural Journal, Vol. 18, No. 6, pp. 676-681.