2.4.3.1 Model: Tensile Strength of Concrete

Model: Tensile Strength of Concrete

This model that is used to determine the effectiveness of concrete on tension between cracks is based on a defined stress-strain curve of concrete in the tension zone (parabola-rectangle diagram). The mathematical tensile strength is no fixed value but refers to the given strain in the governing steel (tension) fiber. The approach has been taken up in accordance with the specifications in [7] to the effect that the maximum tensile strength f_ctR decreases linearly to zero, starting at the defined crack strain until a yield strain ε_sy is reached in the governing steel fiber.

In several research projects (i.a. [8]), efforts were made to refine or modify the approach of Quast and adjust it on the basis of evaluated experiments.

The following figure illustrates the schematic approach.

The parabola-rectangle diagram for the tensile zone is determined according to the following formal relations:

$f_{ct,R}={\alpha }_{red}·f_{ct,\text{basic}}$

$v = \frac{f_{ct}}{f_{ct,R }}$

${\epsilon }_{cr} = \left|\frac{{\epsilon }_{c1}}{v}\right|$

$n_{ct}=1.05·E_{ctm}·\frac{{\epsilon }_{cr}}{f_{ct,R}}$

${\sigma }_{ct}=f_{ct,R}·\frac{{\epsilon }_{sy}-{\epsilon }_{s2}}{{\epsilon }_{sy}-{\epsilon }_{cr}} \text{with} {\epsilon }_{cr}\le {\epsilon }_{s2}\le {\epsilon }_{sy}$

where

• α_red : reduction factor of basic value of tensile strength
• f_ct,basic : basic value of tensile strength (e.g. f_ctm)
• f_ct,R : calculational tensile strength
• v : ratio of compressive to tensile strength
• ε_cr : calculational strain when f_cr,R is reached
• n_ct : exponent of parabola in tension zone
• σ_ct,R : calculational stress depending on governing strain of steel fibre
• ε_sy : calculational yield strain
• ε_s2 : strain of governing steel fiber