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formula_5_16

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_16

Formula 5.16 from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_16.Form5Dot16EffectiveLengthUnbraced 

Form5Dot16EffectiveLengthUnbraced(
    k_1: DIMENSIONLESS, k_2: DIMENSIONLESS, height: M
)

Bases: Formula

Class representing formula 5.16 for the calculation of effective length of unbraced members, [\(l_0\)].

[\(l_{0}\)] Effective length for unbraced members [\(m\)].

EN 1992-1-1:2004 art.5.8.3.2(3) - Formula (5.16)

Parameters:

  • k_1 (DIMENSIONLESS) –

    [\(k_{1}\)] Relative flexibility of rotational constraint at end 1 [\(-\)].

  • k_2 (DIMENSIONLESS) –

    [\(k_{2}\)] Relative flexibility of rotational constraint at end 2 [\(-\)].

  • height (M) –

    [\(l\)] Clear height of compression member between end constraint [\(m\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_16.py 
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def __init__(self, k_1: DIMENSIONLESS, k_2: DIMENSIONLESS, height: M) -> None:
    r"""[$l_{0}$] Effective length for unbraced members [$m$].

    EN 1992-1-1:2004 art.5.8.3.2(3) - Formula (5.16)

    Parameters
    ----------
    k_1 : DIMENSIONLESS
        [$k_{1}$] Relative flexibility of rotational constraint at end 1 [$-$].
    k_2 : DIMENSIONLESS
        [$k_{2}$] Relative flexibility of rotational constraint at end 2 [$-$].
    height : M
        [$l$] Clear height of compression member between end constraint [$m$].
    """
    super().__init__()
    self.k_1 = k_1
    self.k_2 = k_2
    self.height = height

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_16.Form5Dot16EffectiveLengthUnbraced.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.16.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_16.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.16."""
    return LatexFormula(
        return_symbol=r"l_0",
        result=f"{self:.{n}f}",
        equation=r"l \cdot max\left\{"
        r"\sqrt{1+10 \cdot \frac{k_1 \cdot k_2}{k_1+k_2}}; "
        r"\left(1+\frac{k_1}{1 + k_1}\right) \cdot \left(1 + \frac{k_2}{1 + k_2}\right) \right\}",
        numeric_equation=rf"{self.height:.{n}f} \cdot max\left\{{"
        rf"\sqrt{{1+10 \cdot \frac{{{self.k_1:.{n}f} \cdot {self.k_2:.{n}f}}}{{{self.k_1:.{n}f}+{self.k_2:.{n}f}}}}}; "
        rf"\left(1+\frac{{{self.k_1:.{n}f}}}{{1 + {self.k_1:.{n}f}}}\right) \cdot "
        rf"\left(1 + \frac{{{self.k_2:.{n}f}}}{{1 + {self.k_2:.{n}f}}}\right) \right\}}",
        comparison_operator_label="=",
    )