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formula_6_36

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_36

Formula 6.36 from EN 1993-1-1:2005: Chapter 6 - Ultimate limit state.

Classes:

  • Form6Dot36MomentReduction –

    Class representing formula 6.36 for the calculation of reduced bending moment when axially loaded.

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_36.Form6Dot36MomentReduction 

Form6Dot36MomentReduction(mpl_y_rd: NMM, a: DIMENSIONLESS, n: DIMENSIONLESS)

Bases: Formula

Class representing formula 6.36 for the calculation of reduced bending moment when axially loaded.

[\(M_{N,y,Rd}\)] Reduced bending moment [\(Nmm\)].

EN 1993-1-1:2005 art.6.2.9.1(5) - Formula (6.36)

Parameters:

  • mpl_y_rd (NMM) –

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

  • a (DIMENSIONLESS) –

    Reduction factor for cross-sectional area, see formula 6.38a (Form6Dot38A) [-].

  • n (DIMENSIONLESS) –

    Axial force ratio, see formula 6.38n (Form6Dot38N) [-].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_36.py 
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def __init__(
    self,
    mpl_y_rd: NMM,
    a: DIMENSIONLESS,
    n: DIMENSIONLESS,
) -> None:
    r"""[$M_{N,y,Rd}$] Reduced bending moment [$Nmm$].

    EN 1993-1-1:2005 art.6.2.9.1(5) - Formula (6.36)

    Parameters
    ----------
    mpl_y_rd : NMM
        [$M_{pl,y,Rd}$] Plastic bending moment about the y-axis [$Nmm$].
    a : DIMENSIONLESS
        Reduction factor for cross-sectional area, see formula 6.38a (`Form6Dot38A`) [-].
    n : DIMENSIONLESS
        Axial force ratio, see formula 6.38n (`Form6Dot38N`) [-].
    """
    super().__init__()
    self.mpl_y_rd = mpl_y_rd
    self.a = a
    self.n = n

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_36.Form6Dot36MomentReduction.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.36.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_36.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.36."""
    _equation: str = r"\min\left(M_{pl,y,Rd}, M_{pl,y,Rd} \cdot (1 - n) / (1 - 0.5 \cdot a)\right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            "M_{pl,y,Rd}": f"{self.mpl_y_rd:.{n}f}",
            " n": f" {self.n:.{n}f}",
            "a": f"{self.a:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            "M_{pl,y,Rd}": rf"{self.mpl_y_rd:.{n}f} \ Nmm",
            " n": rf" {self.n:.{n}f}",
            "a": rf"{self.a:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"M_{N,y,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",
    )