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2.4.3 Tension Stiffening

Tension Stiffening

When parts of the reinforced concrete are cracked, we know from the design in the ultimate limit state that the tension forces occurring in the crack must be absorbed by the reinforcement only. Between two cracks, however, tension stresses are transferred into the concrete by means of the (movable) bond. Thus, in relation to the length of the structural component, the concrete participates in the absorption of internal tension forces, which leads to increased structural component stiffness. This effect is called effectiveness of concrete for tension between cracks or Tension Stiffening.

Figure 2.21 Stress and strain behavior between two primary cracks

This increase in the structural component stiffness due to tension stiffening can be considered in two ways:

  • After the crack formation, a remaining constant residual tension stress is represented in the concrete's stress-strain diagram. The residual tension stress is notably smaller than the concrete's tensile strength. Alternatively, it is possible to introduce modified stress-strain relations for the tension zone, which consider the concrete's effect on tension between cracks in the form of a descending branch in the graph after the tensile strength is reached. This procedure often proves to be sensible for numerical calculations.
  • The approach that is clearer and more conventional for practical designs is the modification of the "pure" stress-strain diagram of steel. A reduced steel strain εsm is applied in the considered cross-section, resulting from εs2 and a reduction term due to tension stiffening.
Figure 2.22 Considering the tension stiffening effect via
a) characteristic concrete curve or b) modified characteristic steel curve

In RF-CONCRETE Members, it is possible to consider the effect of Tension Stiffening by means of a modified characteristic curve for steel according to [6], as well as through a stress-strain curve for concrete in the tensile zone according to [7] and [8].

Advantages and disadvantages of these approaches and the functional application of the individual methods are described in detail in corresponding reference books (for example [8]).

[6] Deutscher Ausschuss für Stahlbeton (Hrsg.): Heft 525 – Erläuterungen zu DIN 1045-1. Beuth Verlag GmbH, 2003.
[7] Deutscher Ausschuss für Stahlbetonbau (Hrsg.) Heft 415 – Programmgesteuerte Berechnung beliebiger Massivbauquerschnitte unter zweiachsiger Biegung mit Längskraft. Beuth Verlag GmbH, Berlin, 1990.
[8] Pfeiffer, Uwe. Die nichtlineare Berechnung ebener Rahmen aus Stahl- oder Spannbeton mit Berücksichtigung der durch das Aufreißen bedingten Achsendehnung. Cuviller Verlag, Göttingen, 2004.

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