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formula_6_70

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_70

Formula 6.70 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_70.Form6Dot70FatigueDamageFactor 

Form6Dot70FatigueDamageFactor(
    n_delta_sigma_i: list[MPA], capital_n_delta_sigma_i: list[MPA]
)

Bases: Formula

Class representing formula 6.70 for the calculation of the fatigue damage factor [\(D_{Ed}\)].

[D_{Ed}] The calculation of the fatigue damage factor [-].

EN 1992-1-1:2004 art.6.8.4(2) - Formula (6.70)

Parameters:

  • n_delta_sigma_i (list[MPA]) –

    [\(n(\Delta \sigma_i)\)] The applied number of cycles for a stress range [MPa].

  • capital_n_delta_sigma_i (list[MPA]) –

    [\(N(\Delta \sigma_i)\)] The resisting number of cycles for a stress range [MPa]

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_70.py 
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def __init__(self, n_delta_sigma_i: list[MPA], capital_n_delta_sigma_i: list[MPA]) -> None:
    r"""[D_{Ed}] The calculation of the fatigue damage factor [-].

    EN 1992-1-1:2004 art.6.8.4(2) - Formula (6.70)

    Parameters
    ----------
    n_delta_sigma_i : list[MPA]
        [$n(\Delta \sigma_i)$] The applied number of cycles for a stress range [MPa].
    capital_n_delta_sigma_i : list[MPA]
        [$N(\Delta \sigma_i)$] The resisting number of cycles for a stress range [MPa]

    Returns
    -------
    None
    """
    super().__init__()
    self.n_delta_sigma_i: list[MPA] = n_delta_sigma_i
    self.capital_n_delta_sigma_i: list[MPA] = capital_n_delta_sigma_i

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_70.Form6Dot70FatigueDamageFactor.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.70.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_70.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.70."""
    _equation: str = r"\sum_{i} \frac{n(\Delta \sigma_i)}{N(\Delta \sigma_i)} < 1"
    _numeric_equation: str = ""
    for n_idx, capital_n in zip(self.n_delta_sigma_i, self.capital_n_delta_sigma_i):
        _numeric_equation += f"\\frac{{{n_idx:.{n}f}}}{{{capital_n:.{n}f}}} + "
    _numeric_equation = _numeric_equation[:-3] + " < 1"
    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="",
    )