 # RF-CONCRETE Members – Online Manual Version 5

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# 4.2.2 Tension Stiffening

### Tension Stiffening

The specifications for the Tension Stiffening Effect (effectiveness of concrete between cracks) can be defined separately for the ultimate limit state, the serviceability limit state, and for fire resistance.

Tension Stiffening Approach
Concrete (residual) tensile strength

The approach is based on a residual tensile strength of concrete described by Quast  that is defined depending on the governing strain of the steel fibre within the tension zone. This approach is represented graphically in chapter 2.4.3.1.

Modified steel characteristic diagram

As described in chapter 2.4.3.2, the Tension Stiffening Effect can also be considered through a modified characteristic steel curve. The computing time will be slightly increased, because in addition to the sole calculation in cracked sections (state II ), the analysis requires a calculation in the uncracked state, as well as a determination of crack internal forces.

Without tension stiffening

If the Tension Stiffening Effect is not taken into account, the program will simply distinguish between cracked and uncracked zones: In uncracked zones, the program calculates using the concrete's corresponding stiffness in uncracked sections (state I, considering the provided longitudinal reinforcement). In cracked zones, it calculates with the stiffnesses available in pure state II.

Tension Stiffening

The calculation values of the concrete tensile strength determine the exponent of the parabola area in a way that results in an increase affine to the compression zone (Ecm = Ectm).

Effective Tensile Strength fct,R

To take the appropriate safety level into account, it is possible to select one of the following strengths for the concrete tensile strength to be applied:

• fctm : mean axial tensile strength
• fctk; 0.05 : characteristic value of 5%-quantile of tensile strength
• ftk; 0.95 : characteristic value of 95%-quantile of axial tensile strength
Adjustment Factor of Tensile Strength fct,R

The value for the concrete tensile strength fct,R applied for calculation can be influenced by an adjustment factor. Thus, it is possible to consider boundary conditions such as existing damage.

Pfeiffer  suggests a reduction to 60 % of the tensile strengths (default setting).

Normal force as initial force

This check box is important for the calculation of crack internal forces: If it is selected (not possible for method by Quast ), the axial force will be kept constant for the calculation of crack moments. This case is applicable in case of an acting prestress, for example. If it is clear, the entire load vector will be considered for the calculation of the crack internal forces.

Concrete Material - Calculation Parameters

The Standard Values of the concrete parameters are preset (see chapter 2.4.3.1). After clearing the check box (fourth table column), you can directly influence the stress-strain curve of the tension zone. As the values are interdependent, the corresponding columns are adjusted accordingly after a modification.

This dialog section manages the load duration factors β for applying the reduction term (εsr2 - εsr1), that is the strains of the governing steel fibres for the crack internal forces in the cracked or uncracked state (see chapter 2.4.3.2). The factor β depends on the time of load duration:

When applying a Modified characteristic steel diagram, you can use the check box to decide if a load case is considered a Permanent Load or short-time load.

For load combinations, the applied factor β2 represents the average of the respective β2-values of the load cases contained in the combination.

When designing compression elements, you generally have to use the Tension Stiffening model by Quast. The residual tension force can be influenced by the Adjustment Factor of Tensile Strength fct,R.

The Tension Stiffening model with the modified characteristic steel curve is based on a distinction between cracked (M > Mcr) and uncracked zones (M < Mcr): In the uncracked zone, the program calculates linear-elastically using a constant modulus of elasticity for concrete (Ecm,eff). In the case of predominant compression, however, considerably expanded curvatures occur for minor moment loadings due to the nonlinear diagram of the concrete's stress-strain curve. Thus, results may be very much on the unsafe side.

Literature
  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.