Compressive behavior of concrete actively confined by metal strips, part B: analysis

Abstract

This paper presents analytical part of an investigation on the application of prestressed strips for concrete confinement. In this paper, an analytical model is proposed to predict the compressive stress–strain curve of strapped concrete as a function of the confinement level. The model was calibrated based on the experimental data of compressive tests which were described in part A of this paper. Various parameters are considered in the proposed model including volumetric ratio, yield strength and ultimate strain of confining material, shape of cross section, strength of plain concrete. Three key points were defined on the stress–stress curve of strapped concrete columns and applied in model definition including critical, yield and ultimate points. The model showed good capability in predicting the compressive stress–strain curve of tested strapped concrete specimens. The model is also compared to some of the conventional confinement models in prediction of the strength gained by post-tensioned strips. In addition, a plasticity model was applied in the nonlinear finite element analysis of prismatic and cylindrical tested specimens with various levels of confinement. It is shown that these models are able to predict the experimental results, reasonably.

Appendix A: The more accurate alternative for Eq. 11

As described in Sect. 3.4, an accurate equation for the pre-yield branch of the stress–strain curve must satisfy five constraints. Therefore, a forth order polynomial is required to simultaneously satisfy all of the constraints:

$$ Y = AX^{4} + BX^{3} + CX^{2} + DX + E $$

(17)

The coefficients of this polynomial are so obtained that it pass through origin, critical and yield points and also its slopes at the origin and yield point become equal with E _c and α, respectively. These coefficients were obtained as follows:

$$ \begin{gathered} A = {\frac{{f_{\text{cr}} - E_{\text{c}} \varepsilon_{\text{cr}} - {\frac{{\alpha - E_{\text{c}} }}{{2\varepsilon_{\text{cc}} }}}\varepsilon_{\text{cr}}^{2} + \left( {2\;{\frac{{\varepsilon_{\text{cr}}^{3} }}{{\varepsilon_{\text{cc}}^{3} }}} - 3\;{\frac{{\varepsilon_{\text{cr}}^{2} }}{{\varepsilon_{\text{cc}}^{2} }}}} \right)\left( {f_{\text{cc}} - \varepsilon_{\text{cc}} \left( {\alpha + E_{\text{c}} } \right)/2} \right)}}{{\varepsilon_{\text{cr}}^{2} \left( {\varepsilon_{\text{cr}}^{2} - 2\varepsilon_{\text{cr}} \varepsilon_{\text{cc}} + \varepsilon_{\text{cc}}^{2} } \right)}}}; \hfill \\ B = {\frac{{ - 2\left( {A\varepsilon_{\text{cc}}^{4} - \left( {\alpha + E_{\text{c}} } \right)\varepsilon_{\text{cc}} /2 + f_{\text{cc}} } \right)}}{{\varepsilon_{\text{cc}}^{3} }}}; \hfill \\ C = {\frac{{\alpha - E_{\text{c}} - 4A\varepsilon_{\text{cc}}^{3} - 3B\varepsilon_{\text{cc}}^{2} }}{{2\varepsilon_{\text{cc}} }}}; \hfill \\ D = E_{\text{c}} ; \hfill \\ E = 0 \hfill \\ \end{gathered} $$