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formula_6_54

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_54

Formula 6.54 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_54.Form6Dot54BucklingResistanceOfMembersInBending 

Form6Dot54BucklingResistanceOfMembersInBending(m_ed: NMM, m_b_rd: NMM)

Bases: ComparisonFormula

Class representing formula 6.54 for buckling resistance.

[\(\frac{M_{Ed}}{M_{b,Rd}} \leq 1.0\)]

Buckling resistance check for laterally unrestrained members.

Members subject to major axis bending.

EN 1993-1-1:2005 art. 6.3.2.1 (1) - Formula (6.54)

Parameters:

  • m_ed (NMM) –

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

  • m_b_rd (NMM) –

    [\(M_{b,Rd}\)] Design buckling resistance moment [\(Nmm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_54.py 
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def __init__(
    self,
    m_ed: NMM,
    m_b_rd: NMM,
) -> None:
    r"""Buckling resistance check for laterally unrestrained members.

    Members subject to major axis bending.

    EN 1993-1-1:2005 art. 6.3.2.1 (1) - Formula (6.54)

    Parameters
    ----------
    m_ed : NMM
        [$M_{Ed}$] Design value of the moment [$Nmm$].
    m_b_rd : NMM
        [$M_{b,Rd}$] Design buckling resistance moment [$Nmm$].
    """
    super().__init__()
    self.m_ed = m_ed
    self.m_b_rd = m_b_rd

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_54.Form6Dot54BucklingResistanceOfMembersInBending.unity_check property 

unity_check: float

Returns the unity check value.

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_54.Form6Dot54BucklingResistanceOfMembersInBending.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.54.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_54.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.54."""
    _equation: str = r"\frac{M_{Ed}}{M_{b,Rd}} \leq 1.0"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"M_{Ed}": f"{self.m_ed:.{n}f}",
            r"M_{b,Rd}": f"{self.m_b_rd:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"M_{Ed}": rf"{self.m_ed:.{n}f} \ Nmm",
            r"M_{b,Rd}": rf"{self.m_b_rd:.{n}f} \ Nmm",
        },
        False,
    )
    _intermediate_result: str = rf"\left( {self.unity_check:.{n}f} \leq 1.0 \right)"
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if bool(self) else r"\text{Not OK}",
        intermediate_result=_intermediate_result,
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"\to",
        unit="",
    )