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formula_7_5

codes.eurocode.en_1995_1_1_2004.chapter_7_serviceability_limit_states.formula_7_5

Formula 7.5 from EN 1995-1-1:2004.

Classes:

codes.eurocode.en_1995_1_1_2004.chapter_7_serviceability_limit_states.formula_7_5.Form7Dot5NaturalFrequency 

Form7Dot5NaturalFrequency(length: M, ei_l: NM2_M, m: KG_M2)

Bases: Formula

Class representing formula 7.5 for the calculation of natural frequency [\(f_{1}\)].

[\(f_{1}\)] The natural frequency [\(Hz\)].

EN 1995-1-1:2004 art 7.3.3(4) - Formula (7.5)

Parameters:

  • length (M) –

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

  • ei_l (NM2_M) –

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

  • m (KG_M2) –

    [\(m\)] Mass per unit area [\(kg/m^{2}\)].

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1995_1_1_2004/chapter_7_serviceability_limit_states/formula_7_5.py 
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def __init__(self, length: M, ei_l: NM2_M, m: KG_M2) -> None:
    r"""[$f_{1}$] The natural frequency [$Hz$].

    EN 1995-1-1:2004 art 7.3.3(4) - Formula (7.5)

    Parameters
    ----------
    length : M
        [$l$] Span of the floor [$m$].
    ei_l : NM2_M
        [$(EI)_{l}$] Equivalent plate bending stiffness of the floor around the axis perpendicular to the
        longitudinal axis of the beam [$Nm^{2}/m$].
    m : KG_M2
        [$m$] Mass per unit area [$kg/m^{2}$].

    Returns
    -------
    None
    """
    super().__init__()
    self.length = length
    self.ei_l = ei_l
    self.m = m

codes.eurocode.en_1995_1_1_2004.chapter_7_serviceability_limit_states.formula_7_5.Form7Dot5NaturalFrequency.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 7.5.

Source code in blueprints/codes/eurocode/en_1995_1_1_2004/chapter_7_serviceability_limit_states/formula_7_5.py 
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def latex(self, n: int = 2) -> LatexFormula:  # noqa: ARG002
    """Returns LatexFormula object for formula 7.5."""
    eq1: str = r"\frac{\pi}{2 \cdot l^{2}} \cdot \sqrt{\frac{(EI)_{l}}{m}}"
    repl_symb = {"m": f"{self.m:.{2}f}", " l": f" {self.length:.{2}f}", "(EI)_{l}": f"{self.ei_l:.{2}f}"}
    return LatexFormula(
        return_symbol=r"f_{1}",
        result=f"{self:.{2}f}",
        equation=eq1,
        numeric_equation=latex_replace_symbols(eq1, repl_symb),
        comparison_operator_label="=",
    )