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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 [7] 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 the result is an increase in line with 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 [8] 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 [7]), the axial force will be kept constant for the calculation of crack moments. This case would be applicable, for example, in case of an acting prestress. 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: