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formula_6_2

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_2

Formula 6.2 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_2.Form6Dot2UtilizationRatio 

Form6Dot2UtilizationRatio(
    n_ed: KN, n_rd: KN, m_y_ed: KNM, m_y_rd: KNM, m_z_ed: KNM, m_z_rd: KNM
)

Bases: Formula

Class representing form 6.2 for the calculation of the utilization ratio [\(UC\)].

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

EN 1993-1-1:2005 art.6.2.1(7) - Formula (6.2)

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 [\(kNm\)].

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_2.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 1993-1-1:2005 art.6.2.1(7) - Formula (6.2)

    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 [$kNm$].

    Returns
    -------
    None
    """
    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_2005.chapter_6_ultimate_limit_state.formula_6_2.Form6Dot2UtilizationRatio.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for form 6.2.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_2.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for form 6.2."""
    numeric_equation = (
        rf"\frac{{{self.n_ed:.{n}f}}}{{{self.n_rd:.{n}f}}} + "
        rf"\frac{{{self.m_y_ed:.{n}f}}}{{{self.m_y_rd:.{n}f}}} + "
        rf"\frac{{{self.m_z_ed:.{n}f}}}{{{self.m_z_rd:.{n}f}}}"
    )
    return LatexFormula(
        return_symbol=r"UC",
        result=f"{self:.{n}f}",
        equation=r"\frac{N_{Ed}}{N_{Rd}} + \frac{M_{y,Ed}}{M_{y,Rd}} + \frac{M_{z,Ed}}{M_{z,Rd}}",
        numeric_equation=numeric_equation,
        comparison_operator_label="=",
    )