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formula_e_10

codes.eurocode.en_1995_1_1_2023.appendix_e.formula_e_10

Formula E.10 from EN 1995-1-1:2023.

Classes:

codes.eurocode.en_1995_1_1_2023.appendix_e.formula_e_10.FormEDot10ShearStressInLayer2 

FormEDot10ShearStressInLayer2(
    gamma_3: DIMENSIONLESS,
    e_2: MPA,
    e_3: MPA,
    a_3: MM2,
    alpha_2: MM,
    alpha_3: MM,
    h_2: MM,
    b_2: MM,
    v_d: N,
    ei_ef: NMM2,
)

Bases: Formula

Class representing formula E.10 for maximum shear stress in the cross-section, in the member web.

[\(\tau_{2,max}\)] maximum shear stress in the cross-section, in the member web (layer 2), in [\(MPa\)].

EN 1995-1-1:2023 art E.5(1) - Formula (E.10)

Parameters:

  • gamma_3 (DIMENSIONLESS) –

    [\(\gamma_3\)] Factor for the efficiency of the mechanical connections of 3-numbered part of cross-section [\(-\)].

  • e_2 (MPA) –

    [\(E_1\)] Modulus of elasticity of the 2-numbered part of the cross-section [\(MPA\)].

  • e_3 (MPA) –

    [\(E_2\)] Modulus of elasticity of the 3-numbered part of the cross-section [\(MPA\)].

  • a_3 (MM2) –

    [\(A_3\)] Area of the 3-numbered part of the cross-section [\(mm^2\)].

  • alpha_2 (MM2) –

    [\(\alpha_2\)] Distance between centroid of composite cross-section and centroid of 2-numbered part [\(mm^2\)].

  • alpha_3 (MM2) –

    [\(\alpha_3\)] Distance between centroid of composite cross-section and centroid of 2-numbered part [\(mm^2\)].

  • h_2 (MM) –

    [\(h_2\)] Depth of the 2-numbered part of the cross-section [\(mm\)].

  • b_2 (MM) –

    [\(b_2\)] Width of the 2-numbered part of the cross-section [\(mm\)].

  • v_d (N) –

    [\(V_d\)] Maximum design shear force in the member, regardless of the sign [\(N\)].

  • 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_10.py 
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def __init__(self, gamma_3: DIMENSIONLESS, e_2: MPA, e_3: MPA, a_3: MM2, alpha_2: MM, alpha_3: MM, h_2: MM, b_2: MM, v_d: N, ei_ef: NMM2) -> None:
    r"""[$\tau_{2,max}$] maximum shear stress in the cross-section, in the member web (layer 2), in [$MPa$].

    EN 1995-1-1:2023 art E.5(1) - Formula (E.10)

    Parameters
    ----------
    gamma_3 : DIMENSIONLESS
        [$\gamma_3$] Factor for the efficiency of the mechanical connections of 3-numbered part of cross-section [$-$].
    e_2 : MPA
        [$E_1$] Modulus of elasticity of the 2-numbered part of the cross-section [$MPA$].
    e_3 : MPA
        [$E_2$] Modulus of elasticity of the 3-numbered part of the cross-section [$MPA$].
    a_3 : MM2
        [$A_3$] Area of the 3-numbered part of the cross-section [$mm^2$].
    alpha_2 : MM2
        [$\alpha_2$] Distance between centroid of composite cross-section and centroid of 2-numbered part [$mm^2$].
    alpha_3 : MM2
        [$\alpha_3$] Distance between centroid of composite cross-section and centroid of 2-numbered part [$mm^2$].
    h_2 : MM
        [$h_2$] Depth of the 2-numbered part of the cross-section [$mm$].
    b_2 : MM
        [$b_2$] Width of the 2-numbered part of the cross-section [$mm$].
    v_d : N
        [$V_d$] Maximum design shear force in the member, regardless of the sign [$N$].
    ei_ef : NMM2
        [$(EI)_{ef}$] Effective bending stiffness, in [$Nmm^2$].

    Returns
    -------
    None
    """
    super().__init__()
    self.gamma_3 = gamma_3
    self.e_2 = e_2
    self.e_3 = e_3
    self.a_3 = a_3
    self.alpha_2 = alpha_2
    self.alpha_3 = alpha_3
    self.h_2 = h_2
    self.b_2 = b_2
    self.v_d = v_d
    self.ei_ef = ei_ef

codes.eurocode.en_1995_1_1_2023.appendix_e.formula_e_10.FormEDot10ShearStressInLayer2.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula E.10.

Source code in blueprints/codes/eurocode/en_1995_1_1_2023/appendix_e/formula_e_10.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula E.10."""
    eq_i = r"\left[\gamma_3 E_3 A_3 \alpha_3 + 0.5 E_2 b_2 \left(\frac{\alpha_2 + h_2}{2}\right)^2\right] \frac{V_d}{b_{2} EI_{ef}}"

    repl_symb = {
        r"\gamma_3": rf"{self.gamma_3:.{n}f}",
        r"E_2": rf"\cdot {self.e_2:.{n}f} \cdot",
        r"E_3": rf"\cdot {self.e_3:.{n}f} \cdot",
        r"A_3": rf"{self.a_3:.{n}f} \cdot",
        r"\alpha_3": rf"{self.alpha_3:.{n}f}",
        r"\alpha_2": rf"{self.alpha_2:.{n}f}",
        r"h_2": rf"{self.h_2:.{n}f}",
        r"b_{2}": rf"{self.b_2:.{n}f}",
        r"b_2": rf"{self.b_2:.{n}f}",
        r"V_d": rf"{self.v_d:.{n}f}",
        r"EI_{ef}": rf"\cdot {self.ei_ef:.{n}f}",
    }
    numeric_eq = latex_replace_symbols(eq_i, repl_symb)
    return LatexFormula(
        return_symbol=r"\tau_{2,max}", result=f"{self:.{n}f}", equation=eq_i, numeric_equation=numeric_eq, comparison_operator_label="="
    )