**2.5 Strength calculation of elements with spiral reinforcement**

The construction of CFST columns can be improved by placing spiral reinforcement in the concrete core (**Figure 2**). This will have a positive effect on the strength and survivability of columns. A spiral, installed at some distance from the inner surface of the steel tube, can also increase the fire resistance of columns. Experimental studies [10, 11, 20] confirm the high efficiency of such structures.

The widespread practical use of reinforced CFST columns is constrained by the lack of reliable methods for determining their strength. In work [12], a numerical finite element analysis of the load resistance of compressed CFST elements with spiral reinforcement was carried out. But empirical formulas were used here to determine the strength of concrete and lateral pressure on concrete in the limiting state.

The strength of short centrally compressed reinforced CFST column can be determined by formula:

$$N\_{\rm u0} = f\_{cc}A\_c + \sigma\_{\rm pz}A\_p + \sigma\_s A\_s,\tag{21}$$

where *σ<sup>s</sup>* is the compressive stress in longitudinal reinforcement in the limiting state of element;

*A*<sup>s</sup> is cross-sectional area of the longitudinal reinforcement.

Under the action of axial compressive force *N*, lateral pressure on the concrete takes place due to the restraining effect of the outer steel tube and spiral reinforcement. It is impossible to determine this pressure by the superposition principle, since the current problem is physically nonlinear. Therefore, the following calculation method is proposed.

First, the load resistance of a spirally reinforced concrete element that does not have an external steel tube is considered. As a result, the strength of concrete with confinement reinforcement *f* cs is calculated. At the second stage of the calculation, the interaction of this element and the outer steel shell is taken into account.

To determine the strength of the concrete core *f* cs, Eq. (15) and (16) are used with the replacement of *σ* by *σ*sc.

The value of relative lateral pressure *σsc* is calculated by the formula:

$$
\overline{\sigma}\_{\text{sc}} = \rho\_{\text{sc}} \frac{\sigma\_{\text{sc}}}{\gamma\_{\text{c}} f\_{\text{c}}},
\tag{22}
$$

where *ρ*sc is coefficient of confinement reinforcement by spirals;

**Figure 2.** *Reinforce concrete filled steel tube column construction.*

*Bearing Capacity of Concrete Filled Steel Tube Columns DOI: http://dx.doi.org/10.5772/intechopen.99650*

*σ*sc is tensile stress in the spiral reinforcement, which can be determined from the formula:

$$
\sigma\_{\rm s,c} = \varepsilon\_{\rm sc} E\_{\rm s,c} \le f\_{\rm y,c}, \tag{23}
$$

where *ε*sc is tensile strain of spiral reinforcement;

*E*s,c is modulus of elasticity of steel of spiral reinforcement;

*f* y,c is yield point of steel of spiral reinforcement.

The following formula for calculating the value *ε*sc by consecutive approximations is derived in the work [11]:

$$
\varepsilon\_{\rm sc} = -\frac{\nu\_{\rm xr}}{q \nu\_{\rm cs} E\_{\rm c}} f\_{\rm cs}, \tag{24}
$$

in which,

$$q = \mathbf{1} - \frac{E\_{\rm s,c}}{E\_{\rm c}} \rho\_{\rm sc} (\mathbf{1} - \nu\_{\rm rr}),\tag{25}$$

*ν*cs is the coefficient of elasticity at the maximum stress of concrete with confinement reinforcement.

The value *ν*cs is calculated using the formula:

$$
\nu\_{\rm cs} = \frac{f\_{\rm cs}}{\varepsilon\_{\rm cs} E\_{\rm c}},
\tag{26}
$$

where *ε*cs is the strain of concrete with confinement reinforcement at the maximum stress.

The values of coefficients of transverse deformations *υ*zr and *υ*rr are calculated using the formulas obtained in work [16]. The strain *ε*cs is calculated using the formula obtained below.

Then the strength of spirally reinforced concrete core *f* <sup>c</sup>с1, which has an outer steel shell, is determined. For this purpose the Eq. (15) is used, in the right-hand side of which the value *γ<sup>c</sup> f* <sup>c</sup> is substituted by *f* cs. The relative lateral pressure *σ*<sup>1</sup> depends on constructional coefficient *ξ*1, calculated by the formula:

$$\xi\_1 = \frac{f\_{\mathbf{y}} A\_{\mathbf{p}}}{f\_{\mathbf{cs}} A}.\tag{27}$$

The lateral pressure on the concrete from the steel tube acts outside the diameter of the spiral *d*eff. This pressure is calculated using the formula (20), but with the replacement of the coefficient *ξ* by *ξ*2. Constructive coefficient *ξ*<sup>2</sup> is determined from the formula (10) when the strength of concrete is *γ<sup>c</sup> f* <sup>c</sup>*:*

Depending on *σ*2, the strength of the concrete of the peripheral zone *f* <sup>c</sup>с<sup>2</sup> is calculated.

In order to simplify the calculations it is offered to use the averaged design compressive strength of concrete core *f* <sup>c</sup><sup>с</sup> for the method of limiting forces. It is determined from the formula:

$$f\_{\rm cc} = f\_{\rm cc2} (\mathbf{1} - \boldsymbol{\beta}\_{\rm c}^2) + f\_{\rm cc1} \boldsymbol{\beta}\_{\rm c}^2,\tag{28}$$

where *β*<sup>c</sup> is the coefficient determined using the formula *β*<sup>c</sup> ¼ *d*eff*=d*c.

The stress *σpz* in the steel tube is calculated by the following formula:

$$
\sigma\_{\rm pz} = \chi\_c f\_c \left[ \left( \xi\_2^2 - 3 \overline{\sigma}\_m^2 \right)^{1/2} - \overline{\sigma}\_m^2 \right] \frac{A}{A\_{\rm p}}, \tag{29}
$$

in which *σ<sup>m</sup>* – averaged value of relative lateral pressure of concrete core, calculated by the formula:

$$
\overline{\sigma}\_{m} = \overline{\sigma}\_{1}\beta\_{\text{c}} + \overline{\sigma}\_{2}(\mathbf{1} - \beta\_{\text{c}}).\tag{30}
$$

The compressive stress in the longitudinal reinforcement *σ*<sup>s</sup> should be determined from the condition of its combined deformation with the concrete core *ε<sup>s</sup>* ¼ *εсz*.
