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formula_8_51

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_51

Formula 8.51 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_51.Form8Dot51ReducedBendingMomentResistance 

Form8Dot51ReducedBendingMomentResistance(
    mpl_y_rd: NMM, n: DIMENSIONLESS, a_w: DIMENSIONLESS
)

Bases: Formula

Class representing formula 8.51 for the calculation of [\(M_{N,y,Rd}\)].

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

EN 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.51)

Parameters:

  • mpl_y_rd (NMM) –

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

  • n (DIMENSIONLESS) –

    [\(n\)] Axial force ratio, see equation 8.50n (dimensionless).

  • a_w (DIMENSIONLESS) –

    [\(a_w\)] Reduction factor for the web (dimensionless), see equation 8.51aw.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_51.py 
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def __init__(
    self,
    mpl_y_rd: NMM,
    n: DIMENSIONLESS,
    a_w: DIMENSIONLESS,
) -> None:
    r"""[$M_{N,y,Rd}$] Calculation of the reduced bending moment [$Nmm$].

    EN 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.51)

    Parameters
    ----------
    mpl_y_rd : NMM
        [$M_{pl,y,Rd}$] Plastic bending moment resistance about the y-axis [$Nmm$].
    n : DIMENSIONLESS
        [$n$] Axial force ratio, see equation 8.50n (dimensionless).
    a_w : DIMENSIONLESS
        [$a_w$] Reduction factor for the web (dimensionless), see equation 8.51aw.
    """
    super().__init__()
    self.mpl_y_rd = mpl_y_rd
    self.n = n
    self.a_w = a_w

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_51.Form8Dot51ReducedBendingMomentResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.51.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_51.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.51."""
    _equation: str = r"\min \left( M_{pl,y,Rd} \cdot \frac{1 - n}{1 - 0.5 \cdot a_w}, M_{pl,y,Rd} \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"M_{pl,y,Rd}": f"{self.mpl_y_rd:.{n}f}",
            r" n": f" {self.n:.{n}f}",
            r"a_w": f"{self.a_w:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            r"M_{pl,y,Rd}": rf"{self.mpl_y_rd:.{n}f} \ Nmm",
            r" n": rf" {self.n:.{n}f}",
            r"a_w": rf"{self.a_w:.{n}f}",
        },
        unique_symbol_check=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=r"=",
        unit="Nmm",
    )