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formula_8_46

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_46

Formula 8.46 from EN 1993-1-1:2022: Chapter 8 - Ultimate Limit State.

Classes:

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_46.Form8Dot46CheckAxialForceY 

Form8Dot46CheckAxialForceY(
    n_ed: N, h_w: MM, t_w: MM, f_y: MPA, gamma_m0: DIMENSIONLESS
)

Bases: ComparisonFormula

Class representing formula 8.46 for checking axial force about the y-y axis.

For doubly symmetrical I- and H-sections or other flanges sections, allowance need not be made for the effect of the axial force on the plastic resistance moment about the y-y axis when 8.45 and 8.46 are satisfied.

EN 1993-1-1:2022 art.8.2.9.1(4) - Formula (8.46)

Parameters:

  • n_ed (N) –

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

  • h_w (MM) –

    [\(h_w\)] Web height [\(mm\)].

  • t_w (MM) –

    [\(t_{w}\)] Web thickness [\(mm\)].

  • f_y (MPA) –

    [\(f_{y}\)] Yield strength [\(MPa\)].

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial safety factor [-].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_46.py 
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def __init__(
    self,
    n_ed: N,
    h_w: MM,
    t_w: MM,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
) -> None:
    r"""For doubly symmetrical I- and H-sections or other flanges sections,
    allowance need not be made for the effect of the axial force on the
    plastic resistance moment about the y-y axis when 8.45 and 8.46 are satisfied.

    EN 1993-1-1:2022 art.8.2.9.1(4) - Formula (8.46)

    Parameters
    ----------
    n_ed : N
        [$N_{Ed}$] Design axial force [$N$].
    h_w : MM
        [$h_w$] Web height [$mm$].
    t_w : MM
        [$t_{w}$] Web thickness [$mm$].
    f_y : MPA
        [$f_{y}$] Yield strength [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial safety factor [-].
    """
    super().__init__()
    self.n_ed = n_ed
    self.h_w = h_w
    self.t_w = t_w
    self.f_y = f_y
    self.gamma_m0 = gamma_m0

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_46.Form8Dot46CheckAxialForceY.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.46.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_46.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.46."""
    _equation: str = r"N_{Ed} \leq \frac{0.5 \cdot h_{w} \cdot t_{w} \cdot f_{y}}{\gamma_{M0}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"N_{Ed}": f"{self.n_ed:.{n}f}",
            r"h_{w}": f"{self.h_w:.{n}f}",
            r"t_{w}": f"{self.t_w:.{n}f}",
            r"f_{y}": f"{self.f_y:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            r"N_{Ed}": rf"{self.n_ed:.{n}f} \ N",
            r"h_{w}": rf"{self.h_w:.{n}f} \ mm",
            r"t_{w}": rf"{self.t_w:.{n}f} \ mm",
            r"f_{y}": rf"{self.f_y:.{n}f} \ MPa",
            r"\gamma_{M0}": rf"{self.gamma_m0:.{n}f}",
        },
        unique_symbol_check=True,
    )
    return LatexFormula(
        return_symbol="CHECK",
        result="OK" if bool(self) else "\\text{Not OK}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="\\to",
        unit="",
    )