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formula_6_31

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_31

Formula 6.31 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_31.Form6Dot31CheckBendingAndAxialForce 

Form6Dot31CheckBendingAndAxialForce(m_ed: NMM, m_n_rd: NMM)

Bases: Formula

Class representing formula 6.31 for bending and axial force.

Check the bending and axial force criterion.

EN 1993-1-1:2005 art.6.2.9.1 - Formula (6.31)

Parameters:

  • m_ed (NMM) –

    [\(M_{Ed}\)] Design value of the applied bending moment [\(Nmm\)].

  • m_n_rd (NMM) –

    [\(M_{N,Rd}\)] Design plastic moment resistance reduced due to the axial force \(N_{Ed}\) [\(Nmm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_31.py 
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def __init__(
    self,
    m_ed: NMM,
    m_n_rd: NMM,
) -> None:
    r"""Check the bending and axial force criterion.

    EN 1993-1-1:2005 art.6.2.9.1 - Formula (6.31)

    Parameters
    ----------
    m_ed : NMM
        [$M_{Ed}$] Design value of the applied bending moment [$Nmm$].
    m_n_rd : NMM
        [$M_{N,Rd}$] Design plastic moment resistance reduced due to the axial force $N_{Ed}$ [$Nmm$].
    """
    super().__init__()
    self.m_ed = m_ed
    self.m_n_rd = m_n_rd

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_31.Form6Dot31CheckBendingAndAxialForce.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.31.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_31.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.31."""
    _equation: str = r"M_{Ed} \leq M_{N,Rd}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            "M_{Ed}": f"{self.m_ed:.{n}f}",
            "M_{N,Rd}": f"{self.m_n_rd:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            "M_{Ed}": rf"{self.m_ed:.{n}f} \ Nmm",
            "M_{N,Rd}": rf"{self.m_n_rd:.{n}f} \ Nmm",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if self.__bool__() else "\\text{Not OK}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="\\to",
        unit="",
    )