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formula_5_8

codes.eurocode.en_1993_1_1_2005.chapter_5_structural_analysis.formula_5_8

Formula 5.8 from EN 1993-1-1:2005: Chapter 5 - Structural Analysis.

Classes:

codes.eurocode.en_1993_1_1_2005.chapter_5_structural_analysis.formula_5_8.Form5Dot8CheckSlenderness 

Form5Dot8CheckSlenderness(
    lambda_bar: DIMENSIONLESS, a: MM2, f_y: MPA, n_ed: N
)

Bases: ComparisonFormula

Class representing formula 5.8 for check of slenderness.

Check the slenderness ratio.

EN 1993-1-1:2005 art.5.3.2(6) - Formula (5.8)

Parameters:

  • lambda_bar (DIMENSIONLESS) –

    [\(\overline{\lambda}\)] In-plane non-dimensional slenderness calculated for the member considered as hinged at its ends [-].

  • a (MM2) –

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

  • f_y (MPA) –

    [\(f_y\)] Yield strength [\(MPa\)].

  • n_ed (N) –

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

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_5_structural_analysis/formula_5_8.py 
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def __init__(
    self,
    lambda_bar: DIMENSIONLESS,
    a: MM2,
    f_y: MPA,
    n_ed: N,
) -> None:
    r"""Check the slenderness ratio.

    EN 1993-1-1:2005 art.5.3.2(6) - Formula (5.8)

    Parameters
    ----------
    lambda_bar : DIMENSIONLESS
        [$\overline{\lambda}$] In-plane non-dimensional slenderness calculated for the member
        considered as hinged at its ends [-].
    a : MM2
        [$A$] Cross-sectional area [$mm^2$].
    f_y : MPA
        [$f_y$] Yield strength [$MPa$].
    n_ed : N
        [$N_{Ed}$] Design value of the compression force [$N$].
    """
    super().__init__()
    self.lambda_bar = lambda_bar
    self.a = a
    self.f_y = f_y
    self.n_ed = n_ed

codes.eurocode.en_1993_1_1_2005.chapter_5_structural_analysis.formula_5_8.Form5Dot8CheckSlenderness.unity_check property 

unity_check: float

Returns the unity check value.

codes.eurocode.en_1993_1_1_2005.chapter_5_structural_analysis.formula_5_8.Form5Dot8CheckSlenderness.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 5.8.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_5_structural_analysis/formula_5_8.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 5.8."""
    _equation: str = r"\left( \overline{\lambda} > 0.5 \sqrt{\frac{A \cdot f_{y}}{N_{Ed}}} \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\lambda": f"{self.lambda_bar:.{n}f}",
            "A": f"{self.a:.{n}f}",
            "f_{y}": f"{self.f_y:.{n}f}",
            "N_{Ed}": f"{self.n_ed:.{n}f}",
        },
        unique_symbol_check=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="",
    )