# SSRC, Tast Group 20, 1979

This paper proposed design equations for composite members (both concrete-filled steel tubes and concrete-encased steel shapes). Short and slender columns under pure axial load and beam-columns under combined axial load and bending were examined. Included were a number of design equations and an appendix documenting previous tests and comparing them to the allowable loads formulas proposed.

## Design Formulation

Short Axially Loaded Columns. SSRC used a conservative approach to determine the amount of axial capacity for a given CFT section. The modified allowable stress for CFT columns was expressed as:

with fy < 55 ksi to prevent the concrete from crushing before the steel yields. Fifty-five ksi corresponds to an axial strain of 0.0018, the strain at which concrete fails in compression. Using a steel yield stress below 55 ensures that the steel will yield at a smaller strain than 0.0018, producing a desirable ductile failure. The above equation superimposes the individual strengths of the concrete and the steel tube, but it does not account for any confinement effect of the steel tube on the concrete, which is a conservative approach. Limits were placed on the D/t ratio such that the section will not buckle locally before the yield strength is reached. For rectangular sections this D/t limit was established as

and for circular sections:

The SSRC specification also requires that only concrete strengths between 3 ksi and 8 ksi be used.

Slender Axially Loaded Columns. The slenderness of a column is a function of its modulus of elasticity, E, its moment of inertia, I, and its length, L. While these values are easily obtained for a steel section, the task is not straightforward for CFTs. Concrete is an inhomogeneous material and its E varies with sustained loads. Also, tensile cracking significantly reduces the effective stiffness of the concrete, even when it is confined within a tube. To account for this, the SSRC council imposed a reduction factor of 0.4 on the initial stiffness of the concrete. This accounts for both creep and tensile cracking. They expressed the total modified modulus of elasticity of the concrete-filled steel tube as:

The modified values of E may be incorporated into column curves, which reflect the relationship between thrust capacity and column slenderness.

Beams and Beam-Columns. Axial capacity in a column is greatest in the absence of any bending moment. Likewise, a member's greatest moment capacity occurs without any axial load applied. In this case, the SSRC recommends using only the moment capacity of the steel tube in calculating the member's resistance:

where Ss is the section modulus of the steel tube alone. For beam-columns, the allowable loads are expressed in terms of an interaction equation which requires that the sum of the axial stress ratio squared and the stress ratios due to bending in the x and y directions be less than 1. To account for secondary moments, the stress ratios due to bending were modified by a moment magnifier as in the AISC Specification.

## Comparison of Results

A number of CFT tests were compared to the design formulas for both types of loading. The average value of the ratio between test load and allowable load was an acceptable 2.26 for axially loaded CFTs and varied from 1.90 to 2.50 for the eccentrically loaded beam-columns.