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formula_8_3

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_3

Formula 8.3 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_3.Form8Dot3UtilizationRatio 

Form8Dot3UtilizationRatio(
    n_ed: KN, n_rd: KN, m_y_ed: KNM, m_y_rd: KNM, m_z_ed: KNM, m_z_rd: KNM
)

Bases: ComparisonFormula

Class representing formula 8.3 for the calculation of the utilization ratio [\(UC\)].

[\(UC\)] The calculation of the utilization ratio [\(-\)].

EN 1993-1-1:2022 art.8.2.1(7) - Formula (8.3)

Parameters:

  • n_ed (KN) –

    [\(N_{Ed}\)] Contains the design axial force [\(kN\)].

  • n_rd (KN) –

    [\(N_{Rd}\)] Contains the design axial resistance [\(kN\)].

  • m_y_ed (KNM) –

    [\(M_{y,Ed}\)] Contains the design moment about the y-axis [\(kNm\)].

  • m_y_rd (KNM) –

    [\(M_{y,Rd}\)] Contains the design moment resistance about the y-axis [\(kNm\)].

  • m_z_ed (KNM) –

    [\(M_{z,Ed}\)] Contains the design moment about the z-axis [\(kNm\)].

  • m_z_rd (KNM) –

    [\(M_{z,Rd}\)] Contains the design moment resistance about the z-axis [\(kNm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_3.py 
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def __init__(
    self,
    n_ed: KN,
    n_rd: KN,
    m_y_ed: KNM,
    m_y_rd: KNM,
    m_z_ed: KNM,
    m_z_rd: KNM,
) -> None:
    r"""
    [$UC$] The calculation of the utilization ratio [$-$].

    EN 1993-1-1:2022 art.8.2.1(7) - Formula (8.3)

    Parameters
    ----------
    n_ed : KN
        [$N_{Ed}$] Contains the design axial force [$kN$].
    n_rd : KN
        [$N_{Rd}$] Contains the design axial resistance [$kN$].
    m_y_ed : KNM
        [$M_{y,Ed}$] Contains the design moment about the y-axis [$kNm$].
    m_y_rd : KNM
        [$M_{y,Rd}$] Contains the design moment resistance about the y-axis [$kNm$].
    m_z_ed : KNM
        [$M_{z,Ed}$] Contains the design moment about the z-axis [$kNm$].
    m_z_rd : KNM
        [$M_{z,Rd}$] Contains the design moment resistance about the z-axis [$kNm$].
    """
    super().__init__()
    self.n_ed = n_ed
    self.n_rd = n_rd
    self.m_y_ed = m_y_ed
    self.m_y_rd = m_y_rd
    self.m_z_ed = m_z_ed
    self.m_z_rd = m_z_rd

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_3.Form8Dot3UtilizationRatio.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for form 8.3.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_3.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for form 8.3."""
    _equation: str = r"\frac{N_{Ed}}{N_{Rd}} + \frac{M_{y,Ed}}{M_{y,Rd}} + \frac{M_{z,Ed}}{M_{z,Rd}} \leq 1.0"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"N_{Ed}": f"{self.n_ed:.{n}f}",
            r"N_{Rd}": f"{self.n_rd:.{n}f}",
            r"M_{y,Ed}": f"{self.m_y_ed:.{n}f}",
            r"M_{y,Rd}": f"{self.m_y_rd:.{n}f}",
            r"M_{z,Ed}": f"{self.m_z_ed:.{n}f}",
            r"M_{z,Rd}": f"{self.m_z_rd:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"N_{Ed}": rf"{self.n_ed:.{n}f} \ kN",
            r"N_{Rd}": rf"{self.n_rd:.{n}f} \ kN",
            r"M_{y,Ed}": rf"{self.m_y_ed:.{n}f} \ kNm",
            r"M_{y,Rd}": rf"{self.m_y_rd:.{n}f} \ kNm",
            r"M_{z,Ed}": rf"{self.m_z_ed:.{n}f} \ kNm",
            r"M_{z,Rd}": rf"{self.m_z_rd:.{n}f} \ kNm",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"CHECK",
        result=rf"{self.lhs:.{n}f} \to OK" if bool(self) else rf"{self.lhs:.{n}f} \to \text{{Not OK}}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"\to",
    )