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formula_8_58

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_58

Formula 8.58 from EN 1993-1-1:2022: Chapter 8 - Ultimate limit state.

Classes:

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_58.Form8Dot58LongitudinalStressClass4CrossSections 

Form8Dot58LongitudinalStressClass4CrossSections(
    sigma_x_ed: MPA, f_y: MPA, gamma_m0: DIMENSIONLESS
)

Bases: ComparisonFormula

Class representing formula 8.58 for Class 4 cross-sections: [\(\sigma_{x,Ed} \leq \frac{f_y}{\gamma_{M0}}\)].

Longitudinal stress check for Class 4 cross-sections in the absence of shear force. The maximum longitudinal stress [\(\sigma_{x,Ed}\)] should not exceed the yield strength divided by the partial safety factor [\(\frac{f_y}{\gamma_{M0}}\)].

EN 1993-1-1:2022 art. 8.2.9.3(1) - Formula (8.58)

Parameters:

  • sigma_x_ed (MPA) –

    [\(\sigma_{x,Ed}\)] Design value of the local longitudinal stress due to moment and axial force taking account of fastener holes where relevant [\(MPa\)].

  • f_y (MPA) –

    [\(f_y\)] Yield strength of the material [\(MPa\)].

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial safety factor for resistance of cross-sections [-].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_58.py 
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def __init__(
    self,
    sigma_x_ed: MPA,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
) -> None:
    r"""Longitudinal stress check for Class 4 cross-sections in the absence of shear force.
    The maximum longitudinal stress [$\sigma_{x,Ed}$] should not exceed the yield strength
    divided by the partial safety factor [$\frac{f_y}{\gamma_{M0}}$].

    EN 1993-1-1:2022 art. 8.2.9.3(1) - Formula (8.58)

    Parameters
    ----------
    sigma_x_ed : MPA
        [$\sigma_{x,Ed}$] Design value of the local longitudinal stress due to moment and axial force
        taking account of fastener holes where relevant [$MPa$].
    f_y : MPA
        [$f_y$] Yield strength of the material [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial safety factor for resistance of cross-sections [-].
    """
    super().__init__()
    self.sigma_x_ed = sigma_x_ed
    self.f_y = f_y
    self.gamma_m0 = gamma_m0

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_58.Form8Dot58LongitudinalStressClass4CrossSections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.58.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_58.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.58."""
    _equation: str = r"\sigma_{x,Ed} \leq \frac{f_y}{\gamma_{M0}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"\sigma_{x,Ed}": f"{self.sigma_x_ed:.{n}f}",
            r"f_y": f"{self.f_y:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            r"\sigma_{x,Ed}": rf"{self.sigma_x_ed:.{n}f} \ MPa",
            r"f_y": rf"{self.f_y:.{n}f} \ MPa",
            r"\gamma_{M0}": rf"{self.gamma_m0:.{n}f}",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if bool(self) else r"\text{Not OK}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"\to",
        unit=r"",
    )