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formula_e_4

codes.eurocode.en_1995_1_1_2023.appendix_e.formula_e_4

Formula E.4 from EN 1995-1-1:2023.

Classes:

  • FormEDot4DistanceToCentroidA2 –

    [\(\alpha_2\)] Distance between the centroid of the composite cross-section and the centroid of layer 2 of the cross-section.

codes.eurocode.en_1995_1_1_2023.appendix_e.formula_e_4.FormEDot4DistanceToCentroidA2 

FormEDot4DistanceToCentroidA2(
    e_i: list[MPA], a_i: list[MM2], gamma_i: list[DIMENSIONLESS], h_i: list[MM]
)

Bases: Formula

[\(\alpha_2\)] Distance between the centroid of the composite cross-section and the centroid of layer 2 of the cross-section.

[\((\alpha)_{2}\)] Effective bending stiffness, in [\(Nmm^2\)].

EN 1995-1-1:2023 art E.4(1) - Formula (E.1)

Parameters:

  • e_i (MPA) –

    [\(E_i\)] Modulus of elasticity of the i-numbered part of the cross-section [\(MPA\)].

  • a_i (MM2) –

    [\(A_i\)] Area of the i-numbered part of the cross-section [\(mm^2\)].

  • gamma_i (DIMENSIONLESS) –

    [\(\gamma_{i}\)] Factor for the efficiency of the mechanical connections of the respective i-numbered part of the cross-section [\(-\)].

  • h_i (MM) –

    [\(h_i\)] Depth of the i-th part of the cross-section [\(mm\)].

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1995_1_1_2023/appendix_e/formula_e_4.py 
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def __init__(self, e_i: list[MPA], a_i: list[MM2], gamma_i: list[DIMENSIONLESS], h_i: list[MM]) -> None:
    r"""[$(\alpha)_{2}$] Effective bending stiffness, in [$Nmm^2$].

    EN 1995-1-1:2023 art E.4(1) - Formula (E.1)

    Parameters
    ----------
    e_i : MPA
        [$E_i$] Modulus of elasticity of the i-numbered part of the cross-section [$MPA$].
    a_i : MM2
        [$A_i$] Area of the i-numbered part of the cross-section [$mm^2$].
    gamma_i : DIMENSIONLESS
        [$\gamma_{i}$] Factor for the efficiency of the mechanical connections of the respective i-numbered part of the cross-section [$-$].
    h_i : MM
        [$h_i$] Depth of the i-th part of the cross-section [$mm$].

    Returns
    -------
    None
    """
    super().__init__()
    self.e_i: list[MPA] = e_i
    self.gamma_i: list[MM2] = gamma_i
    self.a_i: list[DIMENSIONLESS] = a_i
    self.h_i: list[MM] = h_i

codes.eurocode.en_1995_1_1_2023.appendix_e.formula_e_4.FormEDot4DistanceToCentroidA2.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula E.4.

Source code in blueprints/codes/eurocode/en_1995_1_1_2023/appendix_e/formula_e_4.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula E.4."""
    n_up = 3
    den_eq_form = " + ".join([rf"\gamma_{i + 1} E_{i + 1} A_{i + 1}" for i in range(len(self.e_i))])
    denom = rf"2 \left({den_eq_form}\right)"

    numerator = r"\gamma_1 E_1 A_1 (h_1 + h_2)"
    if len(self.e_i) == n_up:
        numerator += r" - \gamma_3 E_3 A_3 (h_2 + h_3)"

    eq_form = rf"\frac{{{numerator}}}{{{denom}}}"

    e_istr = {f"E_{i + 1}": rf"{val:.{n}f} \cdot" for i, val in enumerate(self.e_i)}
    a_istr = {f"A_{i + 1}": rf"{val:.{n}f}" for i, val in enumerate(self.a_i)}
    gamma_istr = {rf"\gamma_{i + 1}": rf"{val:.{n}f} \cdot" for i, val in enumerate(self.gamma_i)}
    h_istr = {rf"h_{i + 1}": rf"{val:.{n}f}" for i, val in enumerate(self.h_i)}

    repl_symb = e_istr | a_istr | gamma_istr | h_istr
    return LatexFormula(
        return_symbol=r"\alpha_{2}",
        result=f"{self:.{n}f}",
        equation=eq_form,
        numeric_equation=latex_replace_symbols(eq_form, repl_symb, unique_symbol_check=False),
        comparison_operator_label="=",
    )