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formula_6_39

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_39

Formula 6.39 from EN 1992-1-1:2004: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_39.Form6Dot39BetaCoefficient 

Form6Dot39BetaCoefficient(
    k: DIMENSIONLESS, m_ed: NMM, v_ed: N, u_1: MM, w_1: MM2
)

Bases: Formula

Class representing formula 6.39 for the calculation of the beta coefficient, [\(\beta\)].

[\(\beta\)] Beta coefficient [\(-\)].

EN 1992-1-1:2004 art.6.4.3(3) - Formula (6.39)

Parameters:

  • k (DIMENSIONLESS) –

    [\(k\)] Coefficient dependent on the ratio between the column dimensions c1 and c2 [\(-\)].

  • m_ed (NMM) –

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

  • v_ed (N) –

    [\(V_{Ed}\)] Design value of the applied shear force [\(N\)].

  • u_1 (MM) –

    [\(u_1\)] Length of the basic control perimeter [\(mm\)].

  • w_1 (MM2) –

    [\(W_1\)] Distribution of shear as illustrated in Figure 6.19 [\(mm^2\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_39.py 
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def __init__(
    self,
    k: DIMENSIONLESS,
    m_ed: NMM,
    v_ed: N,
    u_1: MM,
    w_1: MM2,
) -> None:
    r"""[$\beta$] Beta coefficient [$-$].

    EN 1992-1-1:2004 art.6.4.3(3) - Formula (6.39)

    Parameters
    ----------
    k : DIMENSIONLESS
        [$k$] Coefficient dependent on the ratio between the column dimensions c1 and c2 [$-$].
    m_ed : NMM
        [$M_{Ed}$] Design value of the applied moment [$Nmm$].
    v_ed : N
        [$V_{Ed}$] Design value of the applied shear force [$N$].
    u_1 : MM
        [$u_1$] Length of the basic control perimeter [$mm$].
    w_1 : MM2
        [$W_1$] Distribution of shear as illustrated in Figure 6.19 [$mm^2$].
    """
    super().__init__()
    self.k = k
    self.m_ed = m_ed
    self.v_ed = v_ed
    self.u_1 = u_1
    self.w_1 = w_1

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_39.Form6Dot39BetaCoefficient.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.39.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_39.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.39."""
    return LatexFormula(
        return_symbol=r"\beta",
        result=f"{self:.{n}f}",
        equation=r"1 + k \cdot \frac{M_{Ed}}{V_{Ed}} \cdot \frac{u_1}{W_1}",
        numeric_equation=rf"1 + {self.k:.{n}f} \cdot \frac{{{self.m_ed:.{n}f}}}{{{self.v_ed:.{n}f}}} \cdot \frac{{{self.u_1:.{n}f}}}{{{self.w_1:.{n}f}}}",  # noqa: E501
        comparison_operator_label="=",
        unit="-",
    )