 # RF-CONCRETE Members – Online Manual Version 5

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# 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  to the effect that the maximum tensile strength fctR decreases linearly to zero, starting at the defined crack strain until a yield strain εsy is reached in the governing steel fiber.

In several research projects (i.a. ), 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:

${n}_{ct}=1.05·{E}_{ctm}·\frac{{\epsilon }_{cr}}{{f}_{ct,R}}$

where

• αred : reduction factor of basic value of tensile strength
• fct,basic : basic value of tensile strength (e.g. fctm)
• fct,R : calculational tensile strength
• v : ratio of compressive to tensile strength
• εcr : calculational strain when fcr,R is reached
• nct : exponent of parabola in tension zone
• σct,R : calculational stress depending on governing strain of steel fibre
• εsy : calculational yield strain
• εs2 : strain of governing steel fiber
Literatur
  Deutscher Ausschuss für Stahlbetonbau (Hrsg.) Heft 415 – Programmgesteuerte Berechnung beliebiger Massivbauquerschnitte unter zweiachsiger Biegung mit Längskraft. Beuth Verlag GmbH, Berlin, 1990.  Pfeiffer, Uwe. Die nichtlineare Berechnung ebener Rahmen aus Stahl- oder Spannbeton mit Berücksichtigung der durch das Aufreißen bedingten Achsendehnung. Cuviller Verlag, Göttingen, 2004.