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2.4.3.2 Modified Characteristic Steel Curve

Modified Characteristic Steel Curve

The Tension Stiffening effect can also be taken into account by means of a modified characteristic steel curve. The approximate minor tangential stiffness (abrupt change in case of re-cracking) during crack development is determined by distinguishing between crack formation and final crack state.

Stress-strain curve of steel
Figure 2.24 Modified stress-strain curve of reinforcing steel according to [6]
Explanation

Uncracked – state I (0 < σs ≤ σsr)

εsm = εs1 

State of first crack formation (σsr < σs ≤ 1.3σsr)

εsm = εs2 - βt σs - σsr + 1.3 σsr - σs0.3 σsr εsr2 - εsr1 

State of final crack state (1.3 σsr < σs ≤ fy)

εsm = εs2 - βt εsr2 - εsr1 

Plastic steel yielding until failure (fy < σs ≤ ft)

εsm = εsy - βt εsr2 - εsr1 + δd 1 - σsrfy εs2 - εsy 

Descriptions:

    • εsm : mean steel strain
    • εsu : ultimate strain at failure of reinforced steel
    • εs1 : steel strain in uncracked state
    • εs2 : steel strain in cracked state (in crack)
    • εsr1 : steel strain in uncracked state with crack internal forces
    • εsr2 : steel strain in crack with crack internal forces
    • βt : factor for considering loading period or load repetitions
      • 0.40 short-term loading
      • 0.25 permanent load or frequent load changes
    • σsr : stress in tension reinforcement, calculated based on cracked cross-section for action combination resulting in first crack formation
    • σs : steel stress in cracked state (in crack) in [N/mm2]
    • σd : factor for considering ductility of reinforcement
      • 0.8 highly ductile steel
      • 0.6 normally ductile steel
Literatur
[6] Deutscher Ausschuss für Stahlbeton (Hrsg.): Heft 525 – Erläuterungen zu DIN 1045-1. Beuth Verlag GmbH, 2003.

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