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formula_6_1

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_1

Formula 6.1 from NEN-EN 1993-1-1:2005: Chapter 6 - Ultimate limit state.

Classes:

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_1.Form6Dot1ElasticVerification 

Form6Dot1ElasticVerification(
    sigma_x_ed: MPA,
    sigma_z_ed: MPA,
    tau_ed: MPA,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
)

Bases: Formula

Class representing formula 6.1 for the elastic verification with the yield criterion.

Elastic verification with the yield criterion.

NEN-EN 1993-1-1+C2:2016 art.6.2.1(5) - Formula (6.1)

Parameters:

  • sigma_x_ed (MPA) –

    [\(\sigma_{x,\text{Ed}}\)] Design value of the longitudinal stress at the point of consideration [\(MPa\)].

  • sigma_z_ed (MPA) –

    [\(\sigma_{z,\text{Ed}}\)] Design value of the transverse stress at the point of consideration [\(MPa\)].

  • tau_ed (MPA) –

    [\(\tau_{\text{Ed}}\)] Design value of the shear stress at the point of consideration [\(MPa\)].

  • f_y (MPA) –

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

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial safety factor for the material [dimensionless].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_1.py 
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def __init__(
    self,
    sigma_x_ed: MPA,
    sigma_z_ed: MPA,
    tau_ed: MPA,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
) -> None:
    r"""Elastic verification with the yield criterion.

    NEN-EN 1993-1-1+C2:2016 art.6.2.1(5) - Formula (6.1)

    Parameters
    ----------
    sigma_x_ed : MPA
        [$\sigma_{x,\text{Ed}}$] Design value of the longitudinal stress at the point of consideration [$MPa$].
    sigma_z_ed : MPA
        [$\sigma_{z,\text{Ed}}$] Design value of the transverse stress at the point of consideration [$MPa$].
    tau_ed : MPA
        [$\tau_{\text{Ed}}$] Design value of the shear stress at the point of consideration [$MPa$].
    f_y : MPA
        [$f_y$] Yield strength of the material [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial safety factor for the material [dimensionless].
    """
    super().__init__()
    self.sigma_x_ed = sigma_x_ed
    self.sigma_z_ed = sigma_z_ed
    self.tau_ed = tau_ed
    self.f_y = f_y
    self.gamma_m0 = gamma_m0

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_1.Form6Dot1ElasticVerification.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.1.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_1.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.1."""
    _equation: str = (
        r"\left( \frac{\sigma_{x,\text{Ed}}}{f_y / \gamma_{M0}} \right)^2 "
        r"+ \left( \frac{\sigma_{z,\text{Ed}}}{f_y / \gamma_{M0}} \right)^2 "
        r"- \left( \frac{\sigma_{x,\text{Ed}}}{f_y / \gamma_{M0}} \right) "
        r"\left( \frac{\sigma_{z,\text{Ed}}}{f_y / \gamma_{M0}} \right) "
        r"+ 3 \left( \frac{\tau_{\text{Ed}}}{f_y / \gamma_{M0}} \right)^2 \leq 1"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\sigma_{x,\text{Ed}}": f"{self.sigma_x_ed:.{n}f}",
            r"\sigma_{z,\text{Ed}}": f"{self.sigma_z_ed:.{n}f}",
            r"\tau_{\text{Ed}}": f"{self.tau_ed:.{n}f}",
            r"f_y": f"{self.f_y:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.{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="",
    )