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formula_8_44

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_44

Formula 8.44 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_44.Form8Dot44MNrdRectangular 

Form8Dot44MNrdRectangular(m_pl_rd: NMM, n_ed: N, n_pl_rd: N)

Bases: Formula

Class representing formula 8.44 for the calculation of [\(M_{N,Rd}\)].

[\(M_{N,Rd}\)] Calculation of the reduced plastic moment for rectangular solid section without fastener holes [\(Nmm\)].

EN 1993-1-1:2022 art.8.2.9.1(3) - Formula (8.44)

Parameters:

  • m_pl_rd (NMM) –

    [\(M_{pl,Rd}\)] Plastic moment resistance of the section [\(Nmm\)].

  • n_ed (N) –

    [\(N_{Ed}\)] Design axial force [\(N\)].

  • n_pl_rd (N) –

    [\(N_{pl,Rd}\)] Plastic axial resistance of the section [\(N\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_44.py 
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def __init__(
    self,
    m_pl_rd: NMM,
    n_ed: N,
    n_pl_rd: N,
) -> None:
    r"""[$M_{N,Rd}$] Calculation of the reduced plastic moment for rectangular solid section without fastener holes [$Nmm$].

    EN 1993-1-1:2022 art.8.2.9.1(3) - Formula (8.44)

    Parameters
    ----------
    m_pl_rd : NMM
        [$M_{pl,Rd}$] Plastic moment resistance of the section [$Nmm$].
    n_ed : N
        [$N_{Ed}$] Design axial force [$N$].
    n_pl_rd : N
        [$N_{pl,Rd}$] Plastic axial resistance of the section [$N$].
    """
    super().__init__()
    self.m_pl_rd = m_pl_rd
    self.n_ed = n_ed
    self.n_pl_rd = n_pl_rd

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_44.Form8Dot44MNrdRectangular.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.44.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_44.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.44."""
    _equation: str = r"M_{pl,Rd} \cdot \left[ 1 - \left( \frac{N_{Ed}}{N_{pl,Rd}} \right)^2 \right]"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"M_{pl,Rd}": f"{self.m_pl_rd:.{n}f}",
            r"N_{Ed}": f"{self.n_ed:.{n}f}",
            r"N_{pl,Rd}": f"{self.n_pl_rd:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            r"M_{pl,Rd}": rf"{self.m_pl_rd:.{n}f} \ Nmm",
            r"N_{Ed}": rf"{self.n_ed:.{n}f} \ N",
            r"N_{pl,Rd}": rf"{self.n_pl_rd:.{n}f} \ N",
        },
        unique_symbol_check=True,
    )
    return LatexFormula(
        return_symbol=r"M_{N,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",
    )