# Tomii, Matsui, and Sakino 1973

This paper presented a very thorough review of the knowledge of CFT behavior to date. Topics of discussion included axially loaded short and long columns, the behavior and design of beam-columns subjected to combined axial load, bending moment, and shearing force, and connection types and their behavior.

A number of advantages of CFTs were cited in the paper's introductory section: the load-carrying capacity of the member is increased without increasing the member size; the tube provides ideally-placed reinforcement; thinner steel tubes may be used since the concrete core forces all local buckling modes outward, delaying the onset of local buckling; the tube prevents concrete spalling which increases member ductility; in precast members, the tube protects the concrete during shipment; the tube serves as the concrete formwork in construction; and CFTs will have a higher fire resistance and require less fireproofing than hollow tubes because the concrete has a larger thermal capacity than air.

## Theoretical Discussion

Short Axially Loaded Columns. The shape of the CFT (i.e., circular or rectangular) will affect the axial behavior of the CFT. The relationship between axial load and longitudinal strain illustrates the marked decrease in capacity in the inelastic region for rectangular tubes. The decrease is not, however, evident for circular tubes due to the greater degree of confinement. Also, the thinner the tube and the higher the concrete strength, the steeper the descending branch of the axial load-longitudinal strain curve. Most importantly, though, the CFT displays a greater ductility and strength than the sum of the individual ductilities and strengths of the constituent materials due to the interaction between the steel and the concrete.

The authors described short CFT column behavior as occurring in two phases. The first phase is the elastic phase, in which the Poisson's ratio of concrete (0.16 to 0.25) is lower than that for steel (0.3). Provided the bond between the concrete and steel does not break down, the concrete's smaller lateral expansion will pull the steel inward, inducing compressive hoop stresses in the tube and tensile lateral stresses in the concrete. The behavior in this region is similar to the sum of the individual behaviors of the constituent materials and the authors suggested that modulus of elasticity of the CFT may be dervied from uniaxial stress conditions.

In the second phase of loading, the longitudinal strain reaches a point at which the concrete undergoes volumetric expansion and its lateral expansion exceeds the lateral expansion of the steel. This occurs at a longitudinal strain of approximately 0.002. At this point in the loading, the concrete will be triaxially confined in compression and tensile hoop stresses will exist in the steel tube. The authors suggested that both the concrete's strength and ductility will increase for both circular and rectangular CFTs due to the confinement. The augmented concrete strength was calculated for circular tubes as follows:

where is the lateral pressure exerted on the concrete. This value is calculated by:

where γsc is the hoop stress in the steel tube. Based on failure theory, for an existing hoop stress in the inelastic range, the longitudinal stress, γsl, will be less than fy. The reduction in the yield strength of the steel tube in the presence of a hoop stress is, however, offset by the increase in the strength of the concrete. The modified calculation of the ultimate axial strength accounting for these effects is:

Assuming no lateral interaction occurs, the ultimate axial load may be conservatively calculated by:

Long Axially Loaded Columns. The authors stated that the effects of confinement do not affect the behavior of long, or slender, columns, which fail by buckling before longitudinal strains become large enough for interaction between the material sto take place. Two types of buckling may occur: slender columns will fail by elastic buckling; and intermediate length columns will fail by inelastic buckling.

The failure load for a CFT column failing by elastic buckling may be computed by the following formula:

The critical buckling load, Pcr, is calculated using a stiffness that is simply the sum of the individual stiffnesses of the concrete and steel. The above formula may be modified for CFT columns failing by inelastic buckling by replacing the respective elastic moduli with tangent moduli. The resulting equation is:

A second, similar method of computing the ultimate load for inelastic columns assumes that the concrete core and the steel tube act as independent columns. The buckling load is calculated by summing the individual tangent modulus loads of the concrete core and the steel tube. Both of these methods require that the stress-strain relationships of the materials by known. These properties are often obtained from stub column tests. The tangent modulus load of the steel tube has been typically calculated using the AISC design code and the concrete core tangent modulus load has been typically derived using Hognestad's parabolic stress-strain curve.

Beam-Columns. CFT members subjected to a combination of axial load and bending moment sustain large deformations without spalling of the concrete or local buckling of the steel. For CFTs with an L/D ratio larger than 15, the load-deflection relationship may be accurately calculated using the uniaxial stress-strain relationships of the steel and the concrete. The member may show increased strength and ductility due to confinement, however, as the axial load increases. The effects of confinement in these cases will be larger in circular CFTs than in rectangular CFTs.

The authors proposed the following formulas to compute the initial composite stiffness of a CFT beam-column, which is used in the analysis and design of beam-columns. For an applied axial load 0≤P≤0.5Po,

And for 0.5Po≤P≤Po, the above equation is modified as follows:

where the modulus of elasticity of the concrete, Ec, is calculated by:

To analyze the overall behavior of a CFT beam-column, i.e., in a moment-curvature analysis, the effects of confinement should be considered. The ultimate bending strength of a CFT beam-column, however, may be accurately calculated using a modified stress block computation such as the ACI method for reinforced concrete members.

To account for the complicated effects of slenderness in the design of CFT beam-columns, approximate methods are often used. The authors discussed the method in the Architectural Institute of Japan (AIJ) code. The maximum slenderness ratio, λ, must not exceed 100. For λ, 50≤λ≤100, the working loads are multiplied by a factor, Φ:

The slenderness ratio, λ, is calculated as the unsupported length of the beam column divided by the effective minimum radius of gyration of the section. For circular members, the radius of gyration is taken as 0.25*D; for rectangular, 0.29*D.

Beam-Columns Subjected to Shearing Force. CFT beam-columns demonstrate excellent shear resistance. For low axial loads, the shear capacity of a CFT will increase with increasing load due to the strain hardening of the steel. Additionally, the authors stated that CFT beam-columns do not fail in shear even under high axial loads. Experiments have shown that in the presence of a moment gradient, the ductility and ultimate strength of the section increase. The authors offerred no explanation of this phenomenon. To calculate the initial composite stiffness for shearing force, the authors proposed the following equation:

## Further Reasearch

The authors listed several additional topics that require further investigation. These include: investigating the elasto-plastic behavior of CFTs by examining the stress-strain characteristics of confined concrete and biaxially-stressed steel; studying the effect of end conditions and load transfer on the behavior of CFT members; investigating the hysteretic behavior of CFTs subjected to alternately repeated loading; and, finally, investigating the behavior of frames subjected to lateral force.