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formula_5_39

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_39

Formula 5.39 from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_39.Form5Dot39SimplifiedCriterionBiaxialBending 

Form5Dot39SimplifiedCriterionBiaxialBending(
    m_edz: KNM, m_rdz: KNM, m_edy: KNM, m_rdy: KNM, a: DIMENSIONLESS
)

Bases: Formula

Class representing formula 5.39 for simplified criterion for biaxial bending.

Simplified criterion for biaxial bending.

EN 1992-1-1:2004 art.5.8.9(4) - Formula (5.39)

Parameters:

  • m_edz (KNM) –

    [\(M_{Edz}\)] Design moment including second order moment in z-direction [\(kNm\)].

  • m_rdz (KNM) –

    [\(M_{Rdz}\)] Design moment resistance in z-direction [\(kNm\)].

  • m_edy (KNM) –

    [\(M_{Edy}\)] Design moment including second order moment in y-direction [\(kNm\)].

  • m_rdy (KNM) –

    [\(M_{Rdy}\)] Design moment resistance in y-direction [\(kNm\)].

  • a (DIMENSIONLESS) –

    [\(a\)] Exponent for the interaction formula, for circular and elliptical cross sections: a = 2, for rectangular see table [-].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_39.py 
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def __init__(
    self,
    m_edz: KNM,
    m_rdz: KNM,
    m_edy: KNM,
    m_rdy: KNM,
    a: DIMENSIONLESS,
) -> None:
    r"""Simplified criterion for biaxial bending.

    EN 1992-1-1:2004 art.5.8.9(4) - Formula (5.39)

    Parameters
    ----------
    m_edz : KNM
        [$M_{Edz}$] Design moment including second order moment in z-direction [$kNm$].
    m_rdz : KNM
        [$M_{Rdz}$] Design moment resistance in z-direction [$kNm$].
    m_edy : KNM
        [$M_{Edy}$] Design moment including second order moment in y-direction [$kNm$].
    m_rdy : KNM
        [$M_{Rdy}$] Design moment resistance in y-direction [$kNm$].
    a : DIMENSIONLESS
        [$a$] Exponent for the interaction formula, for circular and elliptical cross sections: a = 2, for rectangular see table [-].
    """
    super().__init__()
    self.m_edz = m_edz
    self.m_rdz = m_rdz
    self.m_edy = m_edy
    self.m_rdy = m_rdy
    self.a = a

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_39.Form5Dot39SimplifiedCriterionBiaxialBending.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.39.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_39.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.39."""
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if self.__bool__() else "\\text{Not OK}",
        equation=r"\left( \frac{M_{Edz}}{M_{Rdz}} \right)^{a} + \left( \frac{M_{Edy}}{M_{Rdy}} \right)^{a} \leq 1",
        numeric_equation=rf"\left( \frac{{{self.m_edz:.{n}f}}}{{{self.m_rdz:.{n}f}}} \right)^{{{self.a:.{n}f}}} + "
        rf"\left( \frac{{{self.m_edy:.{n}f}}}{{{self.m_rdy:.{n}f}}} \right)^{{{self.a:.{n}f}}} \leq 1",
        comparison_operator_label="\\to",
        unit="",
    )