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formula_8_19

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_19

Formula 8.19 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_19.Form8Dot19CheckBendingMoment 

Form8Dot19CheckBendingMoment(m_ed: NMM, m_c_rd: NMM)

Bases: ComparisonFormula

Class representing formula 8.19 for the test of the bending moment.

Check the bending moment.

EN 1993-1-1:2022 art.8.2.5(1) - Formula (8.19)

Parameters:

  • m_ed (NMM) –

    [\(M_{Ed}\)] Design bending moment [\(Nmm\)].

  • m_c_rd (NMM) –

    [\(M_{c,Rd}\)] The design resistance for bending about one principal axis of a cross-section [\(Nmm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_19.py 
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def __init__(
    self,
    m_ed: NMM,
    m_c_rd: NMM,
) -> None:
    r"""Check the bending moment.

    EN 1993-1-1:2022 art.8.2.5(1) - Formula (8.19)

    Parameters
    ----------
    m_ed : NMM
        [$M_{Ed}$] Design bending moment [$Nmm$].
    m_c_rd : NMM
        [$M_{c,Rd}$] The design resistance for bending about one principal axis of a cross-section [$Nmm$].
    """
    super().__init__()
    self.m_ed = m_ed
    self.m_c_rd = m_c_rd

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_19.Form8Dot19CheckBendingMoment.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.19.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_19.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.19."""
    _equation: str = r"\frac{M_{Ed}}{M_{c,Rd}} \leq 1.0"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            "M_{Ed}": f"{self.m_ed:.{n}f}",
            "M_{c,Rd}": f"{self.m_c_rd:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            "M_{Ed}": rf"{self.m_ed:.{n}f} \ Nmm",
            "M_{c,Rd}": rf"{self.m_c_rd:.{n}f} \ Nmm",
        },
        unique_symbol_check=False,
    )
    _intermediate_result: str = rf"\left( {self.lhs:.{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="",
    )