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formula_a_1

codes.eurocode.en_1993_1_9_2005.annex_a_determination_of_fatigue_load_parameters_and_verification_formats.formula_a_1

Formula A.1 from EN 1993-1-9:2005: Annex A - Determination of fatigue load parameters and verification formats.

Classes:

codes.eurocode.en_1993_1_9_2005.annex_a_determination_of_fatigue_load_parameters_and_verification_formats.formula_a_1.FormADot1DamageDuringDesignLife 

FormADot1DamageDuringDesignLife(
    n_e: list[DIMENSIONLESS], n_r: list[DIMENSIONLESS]
)

Bases: Formula

Class representing formula A.1 for the calculation of the damage during the design life [\(D_d\)].

[\(D_d\)] The calculation of the damage during the design life [\(-\)].

EN 1993-1-9:2005 art.A.5 - Formula (A.1)

Parameters:

  • n_e (list[DIMENSIONLESS]) –

    [\(n_E\)] Contains number of cycles associated with the stress range [\(\gamma_{Ff} \cdot \Delta\sigma_i\)] for each band i in the factored spectrum [\(-\)].

  • n_r (list[DIMENSIONLESS]) –

    [\(N_R\)] Contains the endurance (in cycles) obtained from the factored [\(\Delta\sigma_C / \gamma_{Mf} - n_r\)] curve for each stress range of [\(\gamma_{Ff} \cdot \Delta_i\)] [\(-\)].

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1993_1_9_2005/annex_a_determination_of_fatigue_load_parameters_and_verification_formats/formula_a_1.py 
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def __init__(self, n_e: list[DIMENSIONLESS], n_r: list[DIMENSIONLESS]) -> None:
    r"""[$D_d$] The calculation of the damage during the design life [$-$].

    EN 1993-1-9:2005 art.A.5 - Formula (A.1)

    Parameters
    ----------
    n_e : list[DIMENSIONLESS]
        [$n_E$] Contains number of cycles associated with the stress range [$\gamma_{Ff} \cdot \Delta\sigma_i$]
        for each band i in the factored spectrum [$-$].
    n_r : list[DIMENSIONLESS]
        [$N_R$] Contains the endurance (in cycles) obtained from the factored [$\Delta\sigma_C / \gamma_{Mf} - n_r$] curve for
        each stress range of [$\gamma_{Ff} \cdot \Delta_i$] [$-$].

    Returns
    -------
    None
    """
    super().__init__()
    self.n_e: list[DIMENSIONLESS] = n_e
    self.n_r: list[DIMENSIONLESS] = n_r

codes.eurocode.en_1993_1_9_2005.annex_a_determination_of_fatigue_load_parameters_and_verification_formats.formula_a_1.FormADot1DamageDuringDesignLife.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula A.1.

Source code in blueprints/codes/eurocode/en_1993_1_9_2005/annex_a_determination_of_fatigue_load_parameters_and_verification_formats/formula_a_1.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula A.1."""
    return LatexFormula(
        return_symbol=r"D_d",
        result=f"{self:.{n}f}",
        equation=r"\sum_{i}^{n} \frac{n_{Ei}}{N_Ri}",
        numeric_equation="".join(rf"\frac{{{self.n_e[i]:.{n}f}}}{{{self.n_r[i]:.{n}f}}} + " for i in range(len(self.n_r)))[:-3],
        comparison_operator_label="=",
    )