Skip to content

formula_8_26

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_26

Formula 8.26 from FprEN 1992-1-1:2023: Chapter 8: Ultimate limit states (ULS).

Classes:

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_26.Form8Dot26AngleBetweenPrincipalShearForceAndXAxis 

Form8Dot26AngleBetweenPrincipalShearForceAndXAxis(v_ed_x: N_MM, v_ed_y: N_MM)

Bases: Formula

Class representing formula 8.26 for the calculation of the angle between the principal shear force and the x-axis in planar members.

[\(\alpha_v\)] Angle between the principal shear force and the x-axis [\(degrees\)].

FprEN 1992-1-1:2023 (E) art 8.2.1 (5) - Formula (8.26)

Both components are taken as magnitudes, consistent with Formulas (8.21) to (8.24), which use the same two quantities. The result therefore lies between 0 and 90 degrees. The standard gives no rule for [\(v_{Ed,x} = 0\)], for which the ratio is undefined, so that input is rejected.

Parameters:

  • v_ed_x (N_MM) –

    [\(v_{Ed,x}\)] Out-of-plane design shear force per unit width acting on the cross-section perpendicular to the x direction [\(N/mm\)].

  • v_ed_y (N_MM) –

    [\(v_{Ed,y}\)] Out-of-plane design shear force per unit width acting on the cross-section perpendicular to the y direction [\(N/mm\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_26.py 
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
def __init__(self, v_ed_x: N_MM, v_ed_y: N_MM) -> None:
    r"""[$\alpha_v$] Angle between the principal shear force and the x-axis [$degrees$].

    FprEN 1992-1-1:2023 (E) art 8.2.1 (5) - Formula (8.26)

    Both components are taken as magnitudes, consistent with Formulas (8.21) to (8.24), which use the same
    two quantities. The result therefore lies between 0 and 90 degrees. The standard gives no rule for
    [$v_{Ed,x} = 0$], for which the ratio is undefined, so that input is rejected.

    Parameters
    ----------
    v_ed_x : N_MM
        [$v_{Ed,x}$] Out-of-plane design shear force per unit width acting on the cross-section perpendicular
        to the x direction [$N/mm$].
    v_ed_y : N_MM
        [$v_{Ed,y}$] Out-of-plane design shear force per unit width acting on the cross-section perpendicular
        to the y direction [$N/mm$].
    """
    super().__init__()
    self.v_ed_x = v_ed_x
    self.v_ed_y = v_ed_y

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_26.Form8Dot26AngleBetweenPrincipalShearForceAndXAxis.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.26.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_26.py 
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.26."""
    _equation: str = r"\arctan\left(\frac{v_{Ed,y}}{v_{Ed,x}}\right)"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"v_{Ed,x}": f"{self.v_ed_x:.{n}f}",
            r"v_{Ed,y}": f"{self.v_ed_y:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"v_{Ed,x}": rf"{self.v_ed_x:.{n}f} \ N/mm",
            r"v_{Ed,y}": rf"{self.v_ed_y:.{n}f} \ N/mm",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"\alpha_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="degrees",
    )