# Furlong 1968

Design formulas and graphs (both the author's and those of AISC and ACI) were presented for columns and beam-columns based on axial load capacity, flexural strength, and flexural stiffness. Bond between the steel and concrete in CFTs was examined in detail, and creep and residual stresses were also examined. Experimental results from a range of different investigations, including the author's own, were compared with the theoretical and design formulations.

## Contents

## Experimental Study, Discussion, and Results

*Bond*. Initial eccentric load tests performed by the author exhibited a stiffness much less than the value computed based on a design formula using transformed areas. The assumption in the formula that plane sections remain plane in bending, and therefore that bond between the materials exists, may have contributed to this discrepancy. To examine this assumption, tests were performed to determine the influence of bond on the behavior of the specimens. Greased and non-greased tubes were tested to determine the strength contribution of the bond between the steel and concrete. For the axial load tests, the load-strain curves for “bonded” and “unbonded” were very similar. This was expected since the longitudinal strains in both materials should parallel one another. Surprisingly, however, the curves were also similar for the bending tests, which revealed that bond contributed little or no strength to the ungreased, or “bonded” member. Even at low stress the bond could not prevent sliding. Little change in behavior occurred between the “bonded” and “unbonded” specimens regardless of the tube shape, concrete strength, or wall thickness. The author was confident that bond existed at the beginning of the test in the non-greased specimens. Therefore the bond must have broken at low loads to permit separation of the wall and the core. The only sustained interaction seemed to be the physical pressure between the two materials.

*Residual Stresses*. Tests on steel coupons taken from the tubes showed extensive residual stresses in cold-rolled and welded steel. The presence of residual stresses caused a “softening”, or decreases in the elastic stiffness well before the yield point, translating into proportional limits that were in some cases as low as 50% of nominal yield.

*Creep*. Creep, as indicated by reductions of load over time, became prominent after longitudinal steel yielding. The author suggested that the ultimate strength under sustained loading could be 10% higher than the incremental test loads obtained.

## Theoretical Discussion

*Stiffness*. Since it was shown that little interaction between the materials took place, the author presented a basic formula for computing the composite stiffness of a CFT member:

EI=E_cI_c+E_sI_s

The modulus of elasticity for concrete was computed by the standard ACI formula:

To account for the softening of the steel due to residual stresses, the author used a steel modulus of elasticity Es equal to 25*10^6 psi. The author's final formulation based on the gross moment of inertia of the cross section was:

where α is the ratio between the steel area and the gross area. A similar formulation was used to compute the axial stiffness, E*A. The CFTs behaved much like reinforced concrete. Stiffness increased with the amount of axial load prior to bending. Then at about 50% of axial capacity, the measured flexural stiffness decreased because the stiffness of plain concrete drops sharply for stresses above 0.50* f'c. To account for the stiffness reduction of the concrete at higher axial loads, the author further modified the above stiffness function by the factor:

for axial load P between 0.50*Po and Po, where Po is the squash load.

*Strength*. The author presented the formulas derived in Furlong (1967) and reiterated the accuracy obtained by treating the section as reinforced concrete when analyzing the interaction functions. He also presented quite accurate equations for long columns under pure axial loading, but these will have limited application in practice since moments almost always exist.

## Comparison of Results

The accuracy of the theoretical formulation for stiffness was as much as 25% off from the experimental results, and the author suggested that his formulas, though convenient, be used only as a crude approximation.

## Further Research

The author suggested the following topics of study: connection details, fabrication techniques, and the investigation of the behavior and economy of high-strength concrete (8000+ psi).

## References

Furlong, R. W. (1968). “Design of Steel-Encased Concrete Beam Columns,” Journal of the Structural Division, ASCE, Vol. 94, No. ST1, pp. 267-281.