# Gardner and Jacobson 1967

The authors investigated axially loaded CFT compression members both experimentally and theoretically. The results were compared to ACI (American Concrete Institute 318-63) and NBC (National Building Code of Canada, 1965), as well as tests performed by Klöppel and Goder (1957). They attempted to predict the ultimate load of short CFTs and the buckling load of long CFTs. The data for the theoretical analysis of the long CFTs was obtained from an experimentally-derived load-deflection curve based on tests of a stub column with the same cross sectional dimensions. Furlong and Knowles wrote a discussion of this paper, parts of which were included in this summary.

## Contents

## Experimental Study, Results, and Discussion

At least two columns of each different tube size were tested and for each long column size a corresponding stub column was tested. Both the long columns and the stub columns first yielded in the longitudinal direction. Some interaction existed between the materials, as the CFT had a greater ultimate strength than the sum of the individual steel and concrete components. A limited investigation into the effects of varying the end conditions on the stub columns was conducted by alternately loading the steel only, the concrete only, and then both materials together. These results were tabulated but no general trends were cited in the discussion.

## Theoretical Discussion

The authors discussed theoretical and design formulas from previous investigations, i.e., Considère, Russell, Klöppel and Goder, and others, and summarized some of their work.

## Short Axially Loaded CFTs

A very detailed discussion of short column behavior was presented. The authors described the stress state of the CFT as load was applied. Initially, Poisson's ratio for steel (0.283) exceeded that of the concrete (0.15-0.25) and no confinement existed. As the load increased, the lateral strains in the concrete “caught up” to the strains in the steel, i.e., the Poisson's ratio of the concrete reached and then exceeded that of the steel. At this point, the tube began to restrain the concrete core and the hoop stress in the tube became tensile. At failure, the steel augmented the concrete strength as expressed by the equation

where k is an experimentally determined empirical factor with a value of about 4 and *r is the radial pressure on the concrete. The authors presented the following formula to represent the total load on the column:

## Long Axially Loaded CFTs

The buckling strength of a long column may be determined by the tangent modulus formula:

Est and Ect are the respective steel and concrete tangent moduli. The steel modulus was obtained from tension tests and the concrete properties were found by using a stub column test. This approach poses a problem because the loads carried individually by the steel and concrete must be known.

## Design Formulation

ACI and NBC used the following formula to determine the allowable load:

The steel must have a yield strength of at least 33000 psi and . The results of this formulation are discussed in the following section.

## Comparison of Results

Results were given for the experimental ultimate loads, the tangent modulus formula, and the ACI-NBC method. The long column tests revealed that the tangent modulus formula conservatively predicts the results within 0 to 16.8%. But the method required a stub column test to determine Ect. The ACI-NBC implied a load factor at failure of 2.5, but experimental factors ranged from 3.37 to 5.13. For stub columns, the axial load showed good agreement. However, the authors cautioned against using their theoretical formulation because the full triaxial concrete strength was not developed in the tests. They stated that the additional section strength shown in the experiments was probably due more in part to the steel going into strain hardening, rather than the concrete being triaxially confined.

## References

Gardner, N. J. and Jacobson, E. R. (1967). “Structural Behavior of Concrete Filled Steel Tubes,” Journal of the American Concrete Institute, Vol. 64, No. 11, pp. 404-413.