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formula_5_1

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_1

Formula 5.1 from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_1.Form5Dot1Imperfections 

Form5Dot1Imperfections(
    theta_0: DIMENSIONLESS, alpha_h: DIMENSIONLESS, alpha_m: DIMENSIONLESS
)

Bases: Formula

Class representing formula 5.1 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 1992-1-1:2004 art.5.2(5) - Formula (5.1)

Parameters:

  • theta_0 (float) –

    [\(\\Theta_0\)] 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 (float) –

    [\(\alpha_h\)] Reduction factor for length or height [-]. Use your own implementation of this value or use the SubForm5Dot1ReductionFactorLengthOrHeight class.

  • alpha_m (float) –

    [\(\alpha_m\)] Reduction factor for number of members [-]. Use your own implementation of this value or use the SubForm5Dot1ReductionFactorNumberOfMembers class.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_1.py 
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def __init__(
    self,
    theta_0: DIMENSIONLESS,
    alpha_h: DIMENSIONLESS,
    alpha_m: DIMENSIONLESS,
) -> None:
    r"""[$\\Theta_i$] Initial inclination imperfections, [$\\Theta_i$], is a ratio between height and inclination of the member [-].

    EN 1992-1-1:2004 art.5.2(5) - Formula (5.1)

    Parameters
    ----------
    theta_0 : float
        [$\\Theta_0$] 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 : float
        [$\alpha_h$] Reduction factor for length or height [-].
        Use your own implementation of this value or use the SubForm5Dot1ReductionFactorLengthOrHeight class.
    alpha_m : float
        [$\alpha_m$] Reduction factor for number of members [-].
        Use your own implementation of this value or use the SubForm5Dot1ReductionFactorNumberOfMembers class.
    """
    super().__init__()
    self.theta_0 = theta_0
    self.alpha_h = alpha_h
    self.alpha_m = alpha_m

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_1.Form5Dot1Imperfections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.1.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_1.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.1."""
    return LatexFormula(
        return_symbol=r"\theta_i",
        result=f"{self:.4f}",
        equation=r"\theta_0 \cdot \alpha_h \cdot \alpha_m",
        numeric_equation=rf"{self.theta_0:.{n}f} \cdot {self.alpha_h:.{n}f} \cdot {self.alpha_m:.{n}f}",
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_1.SubForm5Dot1ReductionFactorLengthOrHeight 

SubForm5Dot1ReductionFactorLengthOrHeight(length: M)

Bases: Formula

Class representing sub-formula 5.1 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 between 2/3 and 1.0.

EN 1992-1-1:2004 art.5.2(5) - Formula (5.1)

Parameters:

  • length (M) –

    [\(\text{length}\)] Length or height, see art.5.2(6) [\(m\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_1.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 between 2/3 and 1.0.

    EN 1992-1-1:2004 art.5.2(5) - Formula (5.1)

    Parameters
    ----------
    length : M
        [$\text{length}$] Length or height, see art.5.2(6) [$m$].
    """
    super().__init__()
    self.length = length

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_1.SubForm5Dot1ReductionFactorLengthOrHeight.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.1 subformula 1.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_1.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.1 subformula 1."""
    return LatexFormula(
        return_symbol=r"\alpha_h",
        result=f"{self:.{n}f}",
        equation=r"\min( \max(2 / \sqrt{l}; 2/3); 1)",
        numeric_equation=rf"\min( \max(2 / \sqrt{{{self.length:.{n}f}}}; 2/3); 1)",
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_1.SubForm5Dot1ReductionFactorNumberOfMembers 

SubForm5Dot1ReductionFactorNumberOfMembers(members: int)

Bases: Formula

Class representing sub-formula 5.1 for the calculation of the reduction factor for number of members, [\(\alpha_m\)].

[\(\alpha_m\)] Reduction factor for number of members [-].

EN 1992-1-1:2004 art.5.2(5) - Formula (5.1)

Parameters:

  • members (int) –

    [\(m\)] Number of vertical members contributing to the total effect [-].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_1.py 
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def __init__(
    self,
    members: int,
) -> None:
    r"""[$\alpha_m$] Reduction factor for number of members [-].

    EN 1992-1-1:2004 art.5.2(5) - Formula (5.1)

    Parameters
    ----------
    members : int
        [$m$] Number of vertical members contributing to the total effect [-].
    """
    super().__init__()
    self.members = members

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_1.SubForm5Dot1ReductionFactorNumberOfMembers.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.1 subformula 2.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_1.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.1 subformula 2."""
    return LatexFormula(
        return_symbol=r"\alpha_m",
        result=f"{self:.{n}f}",
        equation=r"\sqrt{0.5 \cdot ( 1 + 1 / m)}",
        numeric_equation=rf"\sqrt{{0.5 \cdot ( 1 + 1 / {self.members:.{n}f})}}",
        comparison_operator_label="=",
    )