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formula_6_55

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_55

Formula 6.55 from 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_55.Form6Dot55DesignBucklingResistanceMoment 

Form6Dot55DesignBucklingResistanceMoment(
    chi_lt: DIMENSIONLESS, w_y: MM3, f_y: MPA, gamma_m1: DIMENSIONLESS
)

Bases: Formula

Class representing formula 6.55 for the calculation of [\(M_{b,Rd}\)].

[\(M_{b,Rd}\)] Design buckling resistance moment [\(Nmm\)].

EN 1993-1-1:2005 art.6.3.2.1(3) - Formula (6.55)

Parameters:

  • chi_lt (DIMENSIONLESS) –

    [\(\chi_{LT}\)] Reduction factor for lateral-torsional buckling [-].

  • w_y (MM3) –

    [\(W_y\)] Appropriate section modulus [\(mm^3\)].

  • f_y (MPA) –

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

  • gamma_m1 (DIMENSIONLESS) –

    [\(\gamma_{M1}\)] Partial factor for resistance of members to instability [-].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_55.py 
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def __init__(
    self,
    chi_lt: DIMENSIONLESS,
    w_y: MM3,
    f_y: MPA,
    gamma_m1: DIMENSIONLESS,
) -> None:
    r"""[$M_{b,Rd}$] Design buckling resistance moment [$Nmm$].

    EN 1993-1-1:2005 art.6.3.2.1(3) - Formula (6.55)

    Parameters
    ----------
    chi_lt : DIMENSIONLESS
        [$\chi_{LT}$] Reduction factor for lateral-torsional buckling [-].
    w_y : MM3
        [$W_y$] Appropriate section modulus [$mm^3$].
    f_y : MPA
        [$f_y$] Yield strength of the material [$MPa$].
    gamma_m1 : DIMENSIONLESS
        [$\gamma_{M1}$] Partial factor for resistance of members to
        instability [-].
    """
    super().__init__()
    self.chi_lt = chi_lt
    self.w_y = w_y
    self.f_y = f_y
    self.gamma_m1 = gamma_m1

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_55.Form6Dot55DesignBucklingResistanceMoment.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.55.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_55.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.55."""
    _equation: str = r"\chi_{LT} \cdot W_y \cdot \frac{f_y}{\gamma_{M1}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\chi_{LT}": f"{self.chi_lt:.{n}f}",
            r"W_y": f"{self.w_y:.{n}f}",
            r"f_y": f"{self.f_y:.{n}f}",
            r"\gamma_{M1}": f"{self.gamma_m1:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"\chi_{LT}": f"{self.chi_lt:.3f}",
            r"W_y": rf"{self.w_y:.3f} \ mm^3",
            r"f_y": rf"{self.f_y:.3f} \ MPa",
            r"\gamma_{M1}": f"{self.gamma_m1:.3f}",
        },
        True,
    )
    return LatexFormula(
        return_symbol=r"M_{b,Rd}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="Nmm",
    )