Concrete Core Strength and Deformability in Prestressed Concrete Filled Steel Tube Columns

The article reviews efficient methods of accomplishing stronger bonds between concrete and outer steel shell through transverse prestressing of the concrete core. Load-strain diagrams are provided for concrete subject to uniaxial and triaxial compression. The authors describe formulas of the basic parametric point, a vertex, of a deformation curve of triaxially compressed concrete. When making estimations using these formulas, the following is considered: long-term stressing of concrete, specifics of its behavior under triaxial compression, and whether it was prestressed.

Transverse prestressing of a concrete core is effective for providing stronger bonds between outer steel shell and concrete. The estimates suggest that satisfactory shearing resistance could be ensured at 1-3 MPa stressing even with zero bond between concrete and steel.
Suggested methods of concrete core prestressing are described in study [9]. According to the analysis found in that same study, long-term stressing of ready-mix concrete proves particularly useful. It improves concrete core structure. Stressing helps to reduce width of a concrete layer between pieces of aggregate creating a fine-grained structure of a cement stone with higher quality and distinctly smaller pores. As a result, strength of the source concrete improves. In the experiments [9], the stressing value was 2-3 MPa. At the same time, concrete strength increased by approximately 50-60%. Besides, being transferred through the concrete mix, stressing creates circumferential pre-tensile stress within a steel shell. Triaxial compression of a concrete core could be subsequently enabled at any level of its external loading.
Another method of concrete core prestressing is realized through self-stressing concrete energy [9][10][11]. This method is the simplest in terms of column production technology. However, it provides a less significant increase in concrete strength. In the work [12], it is shown that the most reliable method of determining CFST column carrying capacity is based on estimations using a stress-strain model of reinforced concrete. These estimations are based on diagrams of materials deformation. The most challenging task consists in plotting a diagram of concrete core deformation. What is more, concrete stress-strain behavior constantly changes with external compressive load increase.
Concrete deformation diagram is a descending curve. Numeric plotting of this diagram could be done with a multipoint method [9]. It is apparent that design parameters of a concrete deformation diagram determine, largely, the vertex coordinates -strength of three-dimensionally compressed concrete cc f and relative strain  To determine the strength of stressed concrete, the authors propose to use the following formula obtained in the work [13] : where c f is ultimate strength of concrete at axial compression, 1   is concrete composition-dependent factor, P is a value of effective stressing calculated using a formula (2) where co  is an estimated pressing value, f  is a reduction factor, which makes allowance for decline in long-term stressing efficiency with increasing source concrete strength, found through an empiric formula  and c f assume values in MPa. These formulas were practically tested for concretes of grades C20-C50. Value of the factor  should be revised on completion of testing of standard specimens of source and stressed concrete using formula (1).
Note that for self-stressing concrete c cp f f  should be adopted.
Strength of triaxially compressed concrete is defined using a formula where c  is a coefficient that incorporates increasing strength of concrete subject to triaxial Formula of relative lateral pressure of a steel shell on a concrete core in CFST limit state obtained through re-expression is written as where a, b are material factors determined through experiments (for heavy-weight concrete b=0.096 and а=0.5b); Then we use a value of structural factor of steel tube confined concrete  , calculated using a formula The other vertex coordinate of a concrete core deformation diagram is a relative longitudinal deformation 1 cc  (see figure 1). Value of this concrete core shortening deformation is determined with regard to a three-dimensional stress state. The obtained formula is written as where с E is a tangent concrete modulus of elasticity, m is an exponent quantity (statistical analysis has shown that best conformity with experimental data is achieved when ).

Summary
To conclude, formulas of the basic parametric point, a vertex, of a deformation curve of triaxially compressed concrete are proposed. These formulas make allowance for long-term stressing effect of concrete, and consider the specifics of its behavior under triaxial compression, including prestressing.