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formula_6_71

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_71

Formula 6.71 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_71.Form6Dot71CriteriaBasedOnStressRange 

Form6Dot71CriteriaBasedOnStressRange(
    gamma_f_fat: DIMENSIONLESS,
    delta_sigma_s_equ_n_star: MPA,
    delta_sigma_rsk_n_star: MPA,
    gamma_s_fat: DIMENSIONLESS,
)

Bases: ComparisonFormula

Class representing formula 6.71 for the calculation of the fatigue criteria based on stress range.

[\(\text{CHECK}\)] Criteria met, based on damage accumulation.

NEN-EN 1993-1-1+C2:2011 art.6.8.5 - Formula (6.71)

Parameters:

  • gamma_f_fat (DIMENSIONLESS) –

    [\(\gamma_{F,fat}\)] Partial factor for fatigue actions [\(-\)].

  • delta_sigma_s_equ_n_star (MPA) –

    [\(\Delta\sigma_{s,equ}(N*)\)] Damage equivalent stress range for types of reinforcement and considering number of cycles N* [\(MPa\)].

  • delta_sigma_rsk_n_star (MPA) –

    [\(\Delta\sigma_{Rsk}(N*)\)] Stress range at N* cycles from the S-N curve in Figure 6.30 [\(MPa\)].

  • gamma_s_fat (DIMENSIONLESS) –

    [\(\gamma_{S,fat}\)] Partial factor for reinforcing or prestressing steel under fatigue loading [\(-\)].

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_71.py 
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def __init__(
    self,
    gamma_f_fat: DIMENSIONLESS,
    delta_sigma_s_equ_n_star: MPA,
    delta_sigma_rsk_n_star: MPA,
    gamma_s_fat: DIMENSIONLESS,
) -> None:
    r"""[$\text{CHECK}$] Criteria met, based on damage accumulation.

    NEN-EN 1993-1-1+C2:2011 art.6.8.5 - Formula (6.71)

    Parameters
    ----------
    gamma_f_fat : DIMENSIONLESS
        [$\gamma_{F,fat}$] Partial factor for fatigue actions [$-$].
    delta_sigma_s_equ_n_star : MPA
        [$\Delta\sigma_{s,equ}(N*)$] Damage equivalent stress range for types of reinforcement and considering number of cycles N* [$MPa$].
    delta_sigma_rsk_n_star : MPA
        [$\Delta\sigma_{Rsk}(N*)$] Stress range at N* cycles from the S-N curve in Figure 6.30 [$MPa$].
    gamma_s_fat : DIMENSIONLESS
        [$\gamma_{S,fat}$] Partial factor for reinforcing or prestressing steel under fatigue loading [$-$].

    Returns
    -------
    None
    """
    super().__init__()
    self.gamma_f_fat = gamma_f_fat
    self.delta_sigma_s_equ_n_star = delta_sigma_s_equ_n_star
    self.delta_sigma_rsk_n_star = delta_sigma_rsk_n_star
    self.gamma_s_fat = gamma_s_fat

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_71.Form6Dot71CriteriaBasedOnStressRange.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.71.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_71.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.71."""
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if self.__bool__() else "\\text{Not OK}",
        equation=r"\gamma_{F,fat} \cdot \Delta \sigma_{s,equ} (N^*) \leq \frac{\Delta \sigma_{Rsk} (N^*)}{\gamma_{s,fat}}",
        numeric_equation=(
            rf"{self.gamma_f_fat:.{n}f} \cdot {self.delta_sigma_s_equ_n_star:.{n}f} "
            rf"\leq \frac{{{self.delta_sigma_rsk_n_star:.{n}f}}}{{{self.gamma_s_fat:.{n}f}}}"
        ),
        comparison_operator_label=r"\rightarrow",
    )

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_71.Form6Dot71CriteriaBasedOnStressRangeLHS 

Form6Dot71CriteriaBasedOnStressRangeLHS(
    gamma_f_fat: DIMENSIONLESS, delta_sigma_s_equ_n_star: MPA
)

Bases: Formula

Class representing Left Hand Side of formula 6.71 for the calculation of the fatigue criteria based on stress range.

[\(\Delta\sigma_{Ed}\)] Loading side of equation [\(MPa\)].

NEN-EN 1993-1-1+C2:2011 art.6.8.5 - Formula (6.71)

Parameters:

  • gamma_f_fat (DIMENSIONLESS) –

    [\(\gamma_{F,fat}\)] Partial factor for fatigue actions [\(-\)].

  • delta_sigma_s_equ_n_star (MPA) –

    [\(\Delta\sigma_{s,equ}(N*)\)] Damage equivalent stress range for types of reinforcement and considering number of cycles N* [\(MPa\)].

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_71.py 
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def __init__(
    self,
    gamma_f_fat: DIMENSIONLESS,
    delta_sigma_s_equ_n_star: MPA,
) -> None:
    r"""[$\Delta\sigma_{Ed}$] Loading side of equation [$MPa$].

    NEN-EN 1993-1-1+C2:2011 art.6.8.5 - Formula (6.71)

    Parameters
    ----------
    gamma_f_fat : DIMENSIONLESS
        [$\gamma_{F,fat}$] Partial factor for fatigue actions [$-$].
    delta_sigma_s_equ_n_star : MPA
        [$\Delta\sigma_{s,equ}(N*)$] Damage equivalent stress range for types of reinforcement and considering number of cycles N* [$MPa$].

    Returns
    -------
    None
    """
    super().__init__()
    self.gamma_f_fat = gamma_f_fat
    self.delta_sigma_s_equ_n_star = delta_sigma_s_equ_n_star

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_71.Form6Dot71CriteriaBasedOnStressRangeLHS.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for left hand side formula 6.71.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_71.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for left hand side formula 6.71."""
    return LatexFormula(
        return_symbol=r"\Delta \sigma_{Ed}",
        result=f"{self:.{n}f}",
        equation=r"\gamma_{F,fat} \cdot \Delta \sigma_{s,equ} (N^*)",
        numeric_equation=rf"{self.gamma_f_fat:.{n}f} \cdot {self.delta_sigma_s_equ_n_star:.{n}f}",
        comparison_operator_label=r"=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_71.Form6Dot71CriteriaBasedOnStressRangeRHS 

Form6Dot71CriteriaBasedOnStressRangeRHS(
    delta_sigma_rsk_n_star: MPA, gamma_s_fat: DIMENSIONLESS
)

Bases: Formula

Class representing Right Hand Side of formula 6.71 for the calculation of the fatigue criteria based on stress range.

[\(\Delta\sigma_{Rd}\)] Resistance side of equation [\(MPa\)].

NEN-EN 1993-1-1+C2:2011 art.6.8.5 - Formula (6.71)

Parameters:

  • delta_sigma_rsk_n_star (MPA) –

    [\(\Delta\sigma_{Rsk}(N*)\)] Stress range at N* cycles from the S-N curve in Figure 6.30 [\(MPa\)].

  • gamma_s_fat (DIMENSIONLESS) –

    [\(\gamma_{S,fat}\)] Partial factor for reinforcing or prestressing steel under fatigue loading [\(-\)].

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_71.py 
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def __init__(
    self,
    delta_sigma_rsk_n_star: MPA,
    gamma_s_fat: DIMENSIONLESS,
) -> None:
    r"""[$\Delta\sigma_{Rd}$] Resistance side of equation [$MPa$].

    NEN-EN 1993-1-1+C2:2011 art.6.8.5 - Formula (6.71)

    Parameters
    ----------
    delta_sigma_rsk_n_star : MPA
        [$\Delta\sigma_{Rsk}(N*)$] Stress range at N* cycles from the S-N curve in Figure 6.30 [$MPa$].
    gamma_s_fat : DIMENSIONLESS
        [$\gamma_{S,fat}$] Partial factor for reinforcing or prestressing steel under fatigue loading [$-$].

    Returns
    -------
    None
    """
    super().__init__()
    self.delta_sigma_rsk_n_star = delta_sigma_rsk_n_star
    self.gamma_s_fat = gamma_s_fat

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_71.Form6Dot71CriteriaBasedOnStressRangeRHS.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for right hand side formula 6.71.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_71.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for right hand side formula 6.71."""
    return LatexFormula(
        return_symbol=r"\Delta \sigma_{Rd}",
        result=f"{self:.{n}f}",
        equation=r"\frac{\Delta \sigma_{Rsk} (N^*)}{\gamma_{s,fat}}",
        numeric_equation=rf"\frac{{{self.delta_sigma_rsk_n_star:.{n}f}}}{{{self.gamma_s_fat:.{n}f}}}",
        comparison_operator_label=r"=",
    )