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formula_5_101

codes.eurocode.en_1992_2_2005.chapter_5_structural_analysis.formula_5_101

Formula 5.101 from EN 1992-2:2005: Chapter 5 - Structural Analysis.

Classes:

codes.eurocode.en_1992_2_2005.chapter_5_structural_analysis.formula_5_101.Form5Dot101Imperfections 

Form5Dot101Imperfections(theta_0: DIMENSIONLESS, alpha_h: DIMENSIONLESS)

Bases: Formula

Class representing formula 5.101 for the calculation of initial inclination imperfections, [\(\(\Theta_i\)\)].

[\(\(\Theta_i\)\)] Initial inclination imperfections, [\(\(\Theta_i\)\)], is a ratio between height and inclination of the member [\(\(-\)\)].

EN 1992-2:2005 art.5.2(5) - Formula (5.101)

Parameters:

  • theta_0 (DIMENSIONLESS) –

    [\(\(\Theta_0\)\)] Basic value [\(\(-\)\)]. Note: The value of [\(\(\Theta_0\)\)] for use in a Country may be found in its National Annex. The recommended value is 1/200 [\(\(-\)\)].

  • alpha_h (DIMENSIONLESS) –

    [\(\(\alpha_h\)\)] Reduction factor for length or height [\(\(-\)\)]. Use your own implementation of this value or use the SubForm5Dot101ReductionFactorLengthOrHeight class.

Source code in blueprints/codes/eurocode/en_1992_2_2005/chapter_5_structural_analysis/formula_5_101.py 
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def __init__(
    self,
    theta_0: DIMENSIONLESS,
    alpha_h: DIMENSIONLESS,
) -> None:
    r"""[$$\Theta_i$$] Initial inclination imperfections, [$$\Theta_i$$], is a ratio between height
    and inclination of the member [$$-$$].

    EN 1992-2:2005 art.5.2(5) - Formula (5.101)

    Parameters
    ----------
    theta_0 : DIMENSIONLESS
        [$$\Theta_0$$] Basic value [$$-$$].
        Note: The value of [$$\Theta_0$$] for use in a Country may be found in its National Annex.
        The recommended value is 1/200 [$$-$$].
    alpha_h : DIMENSIONLESS
        [$$\alpha_h$$] Reduction factor for length or height [$$-$$].
        Use your own implementation of this value or use the SubForm5Dot101ReductionFactorLengthOrHeight class.
    """
    super().__init__()
    self.theta_0 = theta_0
    self.alpha_h = alpha_h

codes.eurocode.en_1992_2_2005.chapter_5_structural_analysis.formula_5_101.Form5Dot101Imperfections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.101.

Source code in blueprints/codes/eurocode/en_1992_2_2005/chapter_5_structural_analysis/formula_5_101.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.101."""
    return LatexFormula(
        return_symbol=r"\theta_i",
        result=f"{self:.{n + 1}f}",
        equation=r"\theta_0 \cdot \alpha_h",
        numeric_equation=rf"{self.theta_0:.{n}f} \cdot {self.alpha_h:.{n}f}",
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_2_2005.chapter_5_structural_analysis.formula_5_101.Form5Dot101Sub1ReductionFactorLengthOrHeight 

Form5Dot101Sub1ReductionFactorLengthOrHeight(length: M)

Bases: Formula

Class representing sub-formula 5.101 for the calculation of the reduction factor for length or height, [\(\(\alpha_h\)\)].

[\(\(\alpha_h\)\)] Reduction factor for length or height [\(\(-\)\)].

The calculated value of [\(\(\alpha_h\)\)] is below 1.0.

NEN-EN 1992-2+C2:2005 art.5.2(105) - Formula (5.101)

Parameters:

  • length (M) –

    [\(\(length\)\)] Length or height [\(\(m\)\)].

Source code in blueprints/codes/eurocode/en_1992_2_2005/chapter_5_structural_analysis/formula_5_101.py 
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def __init__(
    self,
    length: M,
) -> None:
    r"""[$$\alpha_h$$] Reduction factor for length or height [$$-$$].

    The calculated value of [$$\alpha_h$$] is below 1.0.

    NEN-EN 1992-2+C2:2005 art.5.2(105) - Formula (5.101)

    Parameters
    ----------
    length : M
        [$$length$$] Length or height [$$m$$].
    """
    super().__init__()
    self.length = length

codes.eurocode.en_1992_2_2005.chapter_5_structural_analysis.formula_5_101.Form5Dot101Sub1ReductionFactorLengthOrHeight.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.101 subformula 1.

Source code in blueprints/codes/eurocode/en_1992_2_2005/chapter_5_structural_analysis/formula_5_101.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.101 subformula 1."""
    return LatexFormula(
        return_symbol=r"\alpha_h",
        result=f"{self:.{n}f}",
        equation=r"\min(2 / \sqrt{l}, 1)",
        numeric_equation=rf"\min( 2 / \sqrt{{{self.length:.{n}f}}}, 1)",
        comparison_operator_label="=",
    )