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formula_6_77

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_77

Formula 6.77 from EN 1992-1-1:2004: Chapter 6 - Ultimate limit state.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_77.Form6Dot77FatigueVerification 

Form6Dot77FatigueVerification(
    sigma_c_max: MPA, sigma_c_min: MPA, f_cd_fat: MPA, f_ck: MPA
)

Bases: Formula

Class representing formula 6.77 for the fatigue verification of concrete.

[\(\sigma_{Rd,max}\)] Fatigue verification for concrete [\(-\)].

EN 1992-1-1:2004 art.6.8.7(2) - Formula (6.77)

Parameters:

  • sigma_c_max (MPA) –

    [\(\sigma_{c,max}\)] Maximum compressive stress at a fibre under the frequent load combination [\(MPa\)].

  • sigma_c_min (MPA) –

    [\(\sigma_{c,min}\)] Minimum compressive stress at the same fibre where the maximum occurs [\(MPa\)].

  • f_cd_fat (MPA) –

    [\(f_{cd,fat}\)] Design compressive strength of concrete under fatigue [\(MPa\)].

  • f_ck (MPA) –

    [\(f_{ck}\)] Characteristic compressive strength of concrete [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_77.py 
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def __init__(
    self,
    sigma_c_max: MPA,
    sigma_c_min: MPA,
    f_cd_fat: MPA,
    f_ck: MPA,
) -> None:
    r"""[$\sigma_{Rd,max}$] Fatigue verification for concrete [$-$].

    EN 1992-1-1:2004 art.6.8.7(2) - Formula (6.77)

    Parameters
    ----------
    sigma_c_max : MPA
        [$\sigma_{c,max}$] Maximum compressive stress at a fibre under the frequent load combination [$MPa$].
    sigma_c_min : MPA
        [$\sigma_{c,min}$] Minimum compressive stress at the same fibre where the maximum occurs [$MPa$].
    f_cd_fat : MPA
        [$f_{cd,fat}$] Design compressive strength of concrete under fatigue [$MPa$].
    f_ck : MPA
        [$f_{ck}$] Characteristic compressive strength of concrete [$MPa$].
    """
    super().__init__()
    self.sigma_c_max = sigma_c_max
    self.sigma_c_min = sigma_c_min
    self.f_cd_fat = f_cd_fat
    self.f_ck = f_ck

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_77.Form6Dot77FatigueVerification.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.77.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_77.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.77."""
    _equation: str = (
        r"\frac{\sigma_{c,max}}{f_{cd,fat}} \leq \min\left(0.5 + 0.45 \cdot \frac{\sigma_{c,min}}{f_{cd,fat}}, \begin{cases} 0.9 & "
        r"\text{if } f_{ck} \leq 50 \\ 0.8 & \text{if } f_{ck} > 50 \end{cases}\right)"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\sigma_{c,max}": f"{self.sigma_c_max:.{n}f}",
            r"\sigma_{c,min}": f"{self.sigma_c_min:.{n}f}",
            "f_{cd,fat}": f"{self.f_cd_fat:.{n}f}",
            "f_{ck}": f"{self.f_ck:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if self.__bool__() else "\\text{Not OK}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="\\to",
        unit="",
    )