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formula_6_40

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_40

Formula 6.40 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_40.Form6Dot40ReducedBendingMomentResistance 

Form6Dot40ReducedBendingMomentResistance(
    mpl_z_rd: NMM, n: DIMENSIONLESS, a_f: DIMENSIONLESS
)

Bases: Formula

Class representing formula 6.40 for the calculation of [\(M_{N,z,Rd}\)].

[\(M_{N,z,Rd}\)] Calculation of the reduced bending moment [\(Nmm\)].

EN 1993-1-1:2005 art.6.2.9.1(5) - Formula (6.40)

Parameters:

  • mpl_z_rd (NMM) –

    [\(M_{pl,z,Rd}\)] Plastic bending moment resistance about the z-axis [\(Nmm\)].

  • n (DIMENSIONLESS) –

    [\(n\)] Axial force ratio, see equation 6.38n (dimensionless).

  • a_f (DIMENSIONLESS) –

    [\(a_f\)] Reduction factor for the flange (dimensionless).

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_40.py 
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def __init__(
    self,
    mpl_z_rd: NMM,
    n: DIMENSIONLESS,
    a_f: DIMENSIONLESS,
) -> None:
    r"""[$M_{N,z,Rd}$] Calculation of the reduced bending moment [$Nmm$].

    EN 1993-1-1:2005 art.6.2.9.1(5) - Formula (6.40)

    Parameters
    ----------
    mpl_z_rd : NMM
        [$M_{pl,z,Rd}$] Plastic bending moment resistance about the z-axis [$Nmm$].
    n : DIMENSIONLESS
        [$n$] Axial force ratio, see equation 6.38n (dimensionless).
    a_f : DIMENSIONLESS
        [$a_f$] Reduction factor for the flange (dimensionless).
    """
    super().__init__()
    self.mpl_z_rd = mpl_z_rd
    self.n = n
    self.a_f = a_f

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_40.Form6Dot40ReducedBendingMomentResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.40.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_40.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.40."""
    _equation: str = r"\min \left( M_{pl,z,Rd} \cdot \frac{1 - n}{1 - 0.5 \cdot a_f}, M_{pl,z,Rd} \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"M_{pl,z,Rd}": f"{self.mpl_z_rd:.{n}f}",
            r" n": f" {self.n:.{n}f}",
            r"a_f": f"{self.a_f:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"M_{pl,z,Rd}": rf"{self.mpl_z_rd:.{n}f} \ Nmm",
            r" n": rf" {self.n:.{n}f}",
            r"a_f": rf"{self.a_f:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"M_{N,z,Rd}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"=",
        unit="Nmm",
    )