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formula_7_7

codes.eurocode.en_1995_1_1_2004.chapter_7_serviceability_limit_states.formula_7_7

Formula 7.7 from EN 1995-1-1:2004.

Classes:

  • Form7Dot7NumberOfFOVibrations –

    Class representing formula 7.7 for the calculations of the number of first-order vibrations with a natural frequency less than 40Hz.

codes.eurocode.en_1995_1_1_2004.chapter_7_serviceability_limit_states.formula_7_7.Form7Dot7NumberOfFOVibrations 

Form7Dot7NumberOfFOVibrations(
    f_1: HZ, b: M, length: M, ei_l: NM2_M, ei_b: NM2_M
)

Bases: Formula

Class representing formula 7.7 for the calculations of the number of first-order vibrations with a natural frequency less than 40Hz.

[\(n_{40}\)] The number of first-order vibrations with a natural frequency less than 40Hz [\(-\)].

EN 1995-1-1:2004 art 7.3.3(5) - Formula (7.7)

Parameters:

  • f_1 (HZ) –

    [\(f_{1}\)] Natural frequency of rectangular floor, laid freely on all four sides [\(Hz\)].

  • length (M) –

    [\(l\)] Span of the floor [\(m\)].

  • b (M) –

    [\(b\)] Width of the floor [\(m\)].

  • ei_l (NM2_M) –

    [\((EI)_{l}\)] Equivalent bending stiffness of the floor around the axis perpendicular to the longitudinal axis of the beam [\(Nm^{2}/m\)].

  • ei_b (NM2_M) –

    [\((EI)_{l}\)] Equivalent bending stiffness of the floor around the axis parallel to the longitudinal axis of the beam, with \(EI_{b} < EI_{l}\) [\(Nm^{2}/m\)].

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1995_1_1_2004/chapter_7_serviceability_limit_states/formula_7_7.py 
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def __init__(self, f_1: HZ, b: M, length: M, ei_l: NM2_M, ei_b: NM2_M) -> None:
    r"""[$n_{40}$] The number of first-order vibrations with a natural frequency less than 40Hz [$-$].

    EN 1995-1-1:2004 art 7.3.3(5) - Formula (7.7)

    Parameters
    ----------
    f_1 : HZ
        [$f_{1}$] Natural frequency of rectangular floor, laid freely on all four sides [$Hz$].
    length : M
        [$l$] Span of the floor [$m$].
    b : M
        [$b$] Width of the floor [$m$].
    ei_l : NM2_M
        [$(EI)_{l}$] Equivalent bending stiffness of the floor around the axis perpendicular to the longitudinal axis of the beam [$Nm^{2}/m$].
    ei_b : NM2_M
        [$(EI)_{l}$] Equivalent bending stiffness of the floor around the axis parallel to the longitudinal axis of the beam, with $EI_{b} < EI_{l}$ [$Nm^{2}/m$].

    Returns
    -------
    None
    """  # noqa: E501
    super().__init__()
    self.f_1 = f_1
    self.length = length
    self.b = b
    self.ei_l = ei_l
    self.ei_b = ei_b

codes.eurocode.en_1995_1_1_2004.chapter_7_serviceability_limit_states.formula_7_7.Form7Dot7NumberOfFOVibrations.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 7.7.

Source code in blueprints/codes/eurocode/en_1995_1_1_2004/chapter_7_serviceability_limit_states/formula_7_7.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 7.7."""
    eq_for: str = (
        r"\left\{\left ( \left (\frac{40}{f_1} \right )^2 -1 \right)\left ( \frac{b}{l } \right )^4 \frac{(EI)_l}{(EI)_b}\right\}^{0.25}"
    )
    repl_symb = {
        "(EI)_l": f"{self.ei_l:.{n}f}",
        "(EI)_b": f"{self.ei_b:.{n}f}",
        "f_1": f"{self.f_1:.{n}f}",
        "l ": f"{self.length:.{n}f}",
        "b": f"{self.b:.{n}f}",
    }
    return LatexFormula(
        return_symbol=r"n_{40}",
        result=f"{self:.{n}f}",
        equation=eq_for,
        numeric_equation=latex_replace_symbols(eq_for, repl_symb),
    )