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formula_6_44

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_44

Formula 6.44 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_44.Form6Dot44CombinedCompressionBendingClass4CrossSections 

Form6Dot44CombinedCompressionBendingClass4CrossSections(
    n_ed: N,
    a_eff: MM2,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
    m_y_ed: NMM,
    e_ny: MM,
    w_eff_y_min: MM3,
    m_z_ed: NMM,
    e_nz: MM,
    w_eff_z_min: MM3,
)

Bases: ComparisonFormula

Class representing formula 6.44 for cross-sections of class 4.

Combined compression and bending check for Class 4 cross-sections. The combined utilization from axial force and bending moments should not exceed unity.

EN 1993-1-1:2005 art. 6.2.9.3 (2) - Formula (6.44)

Parameters:

  • n_ed (N) –

    [\(N_{Ed}\)] Design value of the axial force [\(N\)].

  • a_eff (MM2) –

    [\(A_{eff}\)] Effective area of the cross-section when subjected to uniform compression [\(mm^2\)].

  • f_y (MPA) –

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

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial safety factor for resistance of cross-sections [-].

  • m_y_ed (NMM) –

    [\(M_{y,Ed}\)] Design value of the bending moment about the y-axis [\(Nmm\)].

  • e_ny (MM) –

    [\(e_{Ny}\)] Shift of the centroidal y-axis when the cross-section is subjected to compression only [\(mm\)].

  • w_eff_y_min (MM3) –

    [\(W_{eff,y,min}\)] Effective section modulus (corresponding to the fibre with the maximum elastic stress) about the y-axis [\(mm^3\)].

  • m_z_ed (NMM) –

    [\(M_{z,Ed}\)] Design value of the bending moment about the z-axis [\(Nmm\)].

  • e_nz (MM) –

    [\(e_{Nz}\)] Shift of the centroidal z-axis when the cross-section is subjected to compression only [\(mm\)].

  • w_eff_z_min (MM3) –

    [\(W_{eff,z,min}\)] Effective section modulus (corresponding to the fibre with the maximum elastic stress) about the z-axis [\(mm^3\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_44.py 
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def __init__(
    self,
    n_ed: N,
    a_eff: MM2,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
    m_y_ed: NMM,
    e_ny: MM,
    w_eff_y_min: MM3,
    m_z_ed: NMM,
    e_nz: MM,
    w_eff_z_min: MM3,
) -> None:
    r"""Combined compression and bending check for Class 4 cross-sections.
    The combined utilization from axial force and bending moments should not exceed unity.

    EN 1993-1-1:2005 art. 6.2.9.3 (2) - Formula (6.44)

    Parameters
    ----------
    n_ed : N
        [$N_{Ed}$] Design value of the axial force [$N$].
    a_eff : MM2
        [$A_{eff}$] Effective area of the cross-section when subjected to uniform compression [$mm^2$].
    f_y : MPA
        [$f_y$] Yield strength of the material [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial safety factor for resistance of cross-sections [-].
    m_y_ed : NMM
        [$M_{y,Ed}$] Design value of the bending moment about the y-axis [$Nmm$].
    e_ny : MM
        [$e_{Ny}$] Shift of the centroidal y-axis when the cross-section is subjected to compression only [$mm$].
    w_eff_y_min : MM3
        [$W_{eff,y,min}$] Effective section modulus (corresponding to the fibre with the maximum elastic stress) about the y-axis [$mm^3$].
    m_z_ed : NMM
        [$M_{z,Ed}$] Design value of the bending moment about the z-axis [$Nmm$].
    e_nz : MM
        [$e_{Nz}$] Shift of the centroidal z-axis when the cross-section is subjected to compression only [$mm$].
    w_eff_z_min : MM3
        [$W_{eff,z,min}$] Effective section modulus (corresponding to the fibre with the maximum elastic stress) about the z-axis [$mm^3$].
    """
    super().__init__()
    self.n_ed = n_ed
    self.a_eff = a_eff
    self.f_y = f_y
    self.gamma_m0 = gamma_m0
    self.m_y_ed = m_y_ed
    self.e_ny = e_ny
    self.w_eff_y_min = w_eff_y_min
    self.m_z_ed = m_z_ed
    self.e_nz = e_nz
    self.w_eff_z_min = w_eff_z_min

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_44.Form6Dot44CombinedCompressionBendingClass4CrossSections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.44.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_44.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.44."""
    _equation: str = (
        r"\frac{N_{Ed}}{A_{eff} \cdot f_y / \gamma_{M0}} + "
        r"\frac{M_{y,Ed} + N_{Ed} \cdot e_{Ny}}{W_{eff,y,min} \cdot f_y / \gamma_{M0}} + "
        r"\frac{M_{z,Ed} + N_{Ed} \cdot e_{Nz}}{W_{eff,z,min} \cdot f_y / \gamma_{M0}} \leq 1"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"N_{Ed}": f"{self.n_ed:.{n}f}",
            r"A_{eff}": f"{self.a_eff:.{n}f}",
            r"f_y": f"{self.f_y:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
            r"M_{y,Ed}": f"{self.m_y_ed:.{n}f}",
            r"e_{Ny}": f"{self.e_ny:.{n}f}",
            r"W_{eff,y,min}": f"{self.w_eff_y_min:.{n}f}",
            r"M_{z,Ed}": f"{self.m_z_ed:.{n}f}",
            r"e_{Nz}": f"{self.e_nz:.{n}f}",
            r"W_{eff,z,min}": f"{self.w_eff_z_min:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"N_{Ed}": rf"{self.n_ed:.{n}f} \ N",
            r"A_{eff}": rf"{self.a_eff:.{n}f} \ mm^2",
            r"f_y": rf"{self.f_y:.{n}f} \ MPa",
            r"\gamma_{M0}": rf"{self.gamma_m0:.{n}f}",
            r"M_{y,Ed}": rf"{self.m_y_ed:.{n}f} \ Nmm",
            r"e_{Ny}": rf"{self.e_ny:.{n}f} \ mm",
            r"W_{eff,y,min}": rf"{self.w_eff_y_min:.{n}f} \ mm^3",
            r"M_{z,Ed}": rf"{self.m_z_ed:.{n}f} \ Nmm",
            r"e_{Nz}": rf"{self.e_nz:.{n}f} \ mm",
            r"W_{eff,z,min}": rf"{self.w_eff_z_min:.{n}f} \ mm^3",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if bool(self) else r"\text{Not OK}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"\to",
        unit="",
    )