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formula_5_13

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_13

Formula 5.13 from EN 1993-5:2007 Chapter 5 - Ultimate limit state.

Classes:

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_13.Form5Dot13SimplifiedBucklingCheck 

Form5Dot13SimplifiedBucklingCheck(
    n_ed: KN,
    m_ed: KNM,
    a: MM2,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
    gamma_m1: DIMENSIONLESS,
    chi: DIMENSIONLESS,
    m_c_rd: KNM,
)

Bases: Formula

Class representing formula 5.13 for combined axial force and bending moment check. Only valid for class 1, 2 and 3.

Simplified buckling check for class 1, 2 and 3.

Provided that the boundary conditions are supplied by elements (anchor, earth support, capping beam, etc.) that give positional restraint corresponding to the non-sway buckling mode, this check may be used:

Parameters:

  • n_ed (KN) –

    [\(kN\)] Design axial force [\(kN\)].

  • m_ed (KNM) –

    [\(kNm\)] Design bending moment [\(kNm\)].

  • a (MM2) –

    [\(mm^2\)] Cross-sectional area [\(mm^2\)].

  • f_y (MPA) –

    [\(MPa\)] Yield strength of the material [\(MPa\)].

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial factor according to 5.1.1 (4) [\(-\)].

  • gamma_m1 (DIMENSIONLESS) –

    [\(\gamma_{M1}\)] Partial factor according to 5.1.1 (4) [\(-\)].

  • chi (DIMENSIONLESS) –

    [\(\chi\)] Buckling coefficient from 6.3.1.2 of EN 1993-1-1 [\(-\)].

  • m_c_rd (KNM) –

    [\(kNm\)] Design moment resistance of the cross-section [\(kNm\)]. See 5.2.2 (2). This can also be calculated using Form5Dot2DesignMomentResistanceClass1Or2 or Form5Dot3DesignMomentResistanceClass3.

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_13.py 
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def __init__(
    self,
    n_ed: KN,
    m_ed: KNM,
    a: MM2,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
    gamma_m1: DIMENSIONLESS,
    chi: DIMENSIONLESS,
    m_c_rd: KNM,
) -> None:
    r"""
    Simplified buckling check for class 1, 2 and 3.

    Provided that the boundary conditions are supplied by elements (anchor, earth support, capping beam, etc.)
    that give positional restraint corresponding to the non-sway buckling mode, this check may be used:

    Parameters
    ----------
    n_ed : KN
        [$kN$] Design axial force [$kN$].
    m_ed : KNM
        [$kNm$] Design bending moment [$kNm$].
    a : MM2
        [$mm^2$] Cross-sectional area [$mm^2$].
    f_y : MPA
        [$MPa$] Yield strength of the material [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial factor according to 5.1.1 (4) [$-$].
    gamma_m1 : DIMENSIONLESS
        [$\gamma_{M1}$] Partial factor according to 5.1.1 (4) [$-$].
    chi : DIMENSIONLESS
        [$\chi$] Buckling coefficient from 6.3.1.2 of EN 1993-1-1 [$-$].
    m_c_rd : KNM
        [$kNm$] Design moment resistance of the cross-section [$kNm$]. See 5.2.2 (2).
        This can also be calculated using Form5Dot2DesignMomentResistanceClass1Or2 or Form5Dot3DesignMomentResistanceClass3.
    """
    super().__init__()
    self.n_ed = n_ed
    self.m_ed = m_ed
    self.a = a
    self.f_y = f_y
    self.gamma_m0 = gamma_m0
    self.gamma_m1 = gamma_m1
    self.chi = chi
    self.m_c_rd = m_c_rd

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_13.Form5Dot13SimplifiedBucklingCheck.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 5.13.

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_13.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 5.13."""
    _equation: str = (
        r"\frac{N_{Ed}}{\chi \cdot (A \cdot f_{y} / \gamma_{M0}) \cdot \left( \frac{\gamma_{M0}}{\gamma_{M1}} \right)} + "
        r"1.15 \cdot \frac{M_{Ed}}{M_{c,Rd} \cdot \left( \frac{\gamma_{M0}}{\gamma_{M1}} \right)} \leq 1.0"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            "N_{Ed}": f"{self.n_ed:.{n}f}",
            "M_{Ed}": f"{self.m_ed:.{n}f}",
            "A": f"{self.a:.{n}f} / 10^6",
            "f_{y}": f"{self.f_y:.1f} \\cdot 10^3",
            "M_{c,Rd}": f"{self.m_c_rd:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.1f}",
            r"\gamma_{M1}": f"{self.gamma_m1:.1f}",
            r"\chi": f"{self.chi:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if self.__bool__() else "\\text{Not OK}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="\\to",
        unit="",
    )