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formula_5_15

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_15

Formula 5.15 from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_15.Form5Dot15EffectiveLengthBraced 

Form5Dot15EffectiveLengthBraced(
    k_1: DIMENSIONLESS, k_2: DIMENSIONLESS, height: M
)

Bases: Formula

Class representing formula 5.15 for the calculation of the effective length of braced members, [\(l_0\)].

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

EN 1992-1-1:2004 art.5.8.3.2(3) - Formula (5.15)

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 constraints [\(m\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_15.py 
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def __init__(self, k_1: DIMENSIONLESS, k_2: DIMENSIONLESS, height: M) -> None:
    r"""[$l_{0}$] Effective length for braced members [$m$].

    EN 1992-1-1:2004 art.5.8.3.2(3) - Formula (5.15)

    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 constraints [$m$].
    """
    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_15.Form5Dot15EffectiveLengthBraced.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.15.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_15.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.15."""
    return LatexFormula(
        return_symbol=r"l_0",
        result=f"{self:.{n}f}",
        equation=r"0.5 \cdot l \cdot \sqrt{\left(1+\frac{k_1}{0.45 + k_1}\right) \cdot \left(1 + \frac{k_2}{0.45 + k_2}\right)}",
        numeric_equation=rf"0.5 \cdot {self.height:.{n}f} \cdot \sqrt{{\left(1+\frac{{{self.k_1:.{n}f}}}{{0.45 + "
        rf"{self.k_1:.{n}f}}}\right) \cdot \left(1 + \frac{{{self.k_2:.{n}f}}}{{0.45 + {self.k_2:.{n}f}}}\right)}}",
        comparison_operator_label="=",
    )