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formula_e_9

codes.eurocode.en_1995_1_1_2023.appendix_e.formula_e_9

Formula E.9 from EN 1995-1-1:2023.

Classes:

codes.eurocode.en_1995_1_1_2023.appendix_e.formula_e_9.FormEDot9BendingStressInILayer 

FormEDot9BendingStressInILayer(
    i: int, e_i: MPA, h_i: MM, m_yd: NMM, ei_ef: NMM2
)

Bases: Formula

Class representing formula E.9 for bending stress in the i-numbered part of the cross-section.

[\(\sigma_{m,i}\)] axial stress in the i-numbered part of the cross-section, in [\(MPa\)].

EN 1995-1-1:2023 art E.5(1) - Formula (E.9)

Parameters:

  • i (DIMENSIONLESS) –

    [\(i\)] Number of layer i of cross-section.

  • e_i (MPA) –

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

  • h_i (MM) –

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

  • m_yd (NMM) –

    [\(M_{y,d}\)] Design bending moment about y-axis [\(Nmm\)].

  • ei_ef (NMM2) –

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

Returns:

  • None –
Source code in blueprints/codes/eurocode/en_1995_1_1_2023/appendix_e/formula_e_9.py 
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def __init__(self, i: int, e_i: MPA, h_i: MM, m_yd: NMM, ei_ef: NMM2) -> None:
    r"""[$\sigma_{m,i}$] axial stress in the i-numbered part of the cross-section, in [$MPa$].

    EN 1995-1-1:2023 art E.5(1) - Formula (E.9)

    Parameters
    ----------
    i : DIMENSIONLESS
        [$i$] Number of layer i of cross-section.
    e_i : MPA
        [$E_i$] Modulus of elasticity of the i-numbered part of the cross-section [$MPA$].
    h_i : MM
        [$h_i$] Depth of the i-numbered part of the cross-section [$mm$].
    m_yd : NMM
        [$M_{y,d}$] Design bending moment about y-axis [$Nmm$].
    ei_ef : NMM2
        [$(EI)_{ef}$] Effective bending stiffness, in [$Nmm^2$].

    Returns
    -------
    None
    """
    super().__init__()
    self.e_i = e_i
    self.h_i = h_i
    self.m_yd = m_yd
    self.ei_ef = ei_ef
    self.i = i

codes.eurocode.en_1995_1_1_2023.appendix_e.formula_e_9.FormEDot9BendingStressInILayer.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula E.9.

Source code in blueprints/codes/eurocode/en_1995_1_1_2023/appendix_e/formula_e_9.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula E.9."""
    eq_i = f"\\frac{{0.5 E_{self.i} h_{self.i} M_{{yd}}}}{{EI_{{ef}}}}"

    repl_symb = {
        f"E_{self.i}": rf"\cdot {self.e_i:.{n}f} \cdot",
        f"h_{self.i}": rf"{self.h_i:.{n}f} \cdot",
        r"M_{yd}": rf"{self.m_yd:.{n}f}",
        r"EI_{ef}": rf"{self.ei_ef:.{n}f}",
    }
    numeric_eq = latex_replace_symbols(eq_i, repl_symb)
    return LatexFormula(
        return_symbol=rf"\sigma_{{{self.i}}}", result=f"{self:.{n}f}", equation=eq_i, numeric_equation=numeric_eq, comparison_operator_label="="
    )