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formula_8_25

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_25

Formula 8.25 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_25.Form8Dot25EffectiveDepthFromPrincipalShearForce 

Form8Dot25EffectiveDepthFromPrincipalShearForce(
    d_x: MM,
    d_y: MM,
    alpha_v: DEG | None = None,
    v_ed_x: N_MM | None = None,
    v_ed_y: N_MM | None = None,
)

Bases: Formula

Class representing formula 8.25 for the calculation of the effective depth of planar members, as an alternative to formulas 8.22, 8.23 and 8.24.

[\(d\)] Effective depth of planar members, taken from the direction of the principal shear force [\(mm\)].

FprEN 1992-1-1:2023 (E) art 8.2.1 (5) - Formula (8.25)

This is the alternative offered by the standard to Formulas (8.22), (8.23) and (8.24), not an equivalent of them.

The angle can be supplied in either of the two ways the standard offers. Give [\(\alpha_v\)] directly, or give the two shear forces and let Formula (8.26) produce it. At least one of the two routes is required; an [\(\alpha_v\)] that is given directly always wins, since the standard prints Formula (8.26) as what the angle "may be taken as" and so leaves room for a directly determined direction of the principal shear force.

Parameters:

  • d_x (MM) –

    [\(d_x\)] Effective depth in the x direction [\(mm\)].

  • d_y (MM) –

    [\(d_y\)] Effective depth in the y direction [\(mm\)].

  • alpha_v (DEG, default: None ) –

    [\(\alpha_v\)] Angle between the principal shear force and the x-axis, which may be taken according to Formula (8.26), see Form8Dot26AngleBetweenPrincipalShearForceAndXAxis. Leave it out to have it computed from the two shear forces instead. It lies between 0 and 90 degrees, as Formula (8.26) can produce nothing else [\(degrees\)].

  • v_ed_x (N_MM, default: None ) –

    [\(v_{Ed,x}\)] Out-of-plane design shear force per unit width perpendicular to the x direction. Used only when [\(\alpha_v\)] is left out, and taken as a magnitude [\(N/mm\)].

  • v_ed_y (N_MM, default: None ) –

    [\(v_{Ed,y}\)] Out-of-plane design shear force per unit width perpendicular to the y direction. Used only when [\(\alpha_v\)] is left out, and taken as a magnitude [\(N/mm\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_25.py 
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def __init__(
    self,
    d_x: MM,
    d_y: MM,
    alpha_v: DEG | None = None,
    v_ed_x: N_MM | None = None,
    v_ed_y: N_MM | None = None,
) -> None:
    r"""[$d$] Effective depth of planar members, taken from the direction of the principal shear force [$mm$].

    FprEN 1992-1-1:2023 (E) art 8.2.1 (5) - Formula (8.25)

    This is the alternative offered by the standard to Formulas (8.22), (8.23) and (8.24), not an
    equivalent of them.

    The angle can be supplied in either of the two ways the standard offers. Give [$\alpha_v$] directly, or
    give the two shear forces and let Formula (8.26) produce it. At least one of the two routes is
    required; an [$\alpha_v$] that is given directly always wins, since the standard prints Formula (8.26)
    as what the angle "may be taken as" and so leaves room for a directly determined direction of the
    principal shear force.

    Parameters
    ----------
    d_x : MM
        [$d_x$] Effective depth in the x direction [$mm$].
    d_y : MM
        [$d_y$] Effective depth in the y direction [$mm$].
    alpha_v : DEG, optional
        [$\alpha_v$] Angle between the principal shear force and the x-axis, which may be taken according
        to Formula (8.26), see Form8Dot26AngleBetweenPrincipalShearForceAndXAxis. Leave it out to have it
        computed from the two shear forces instead. It lies between 0 and 90 degrees, as Formula (8.26) can
        produce nothing else [$degrees$].
    v_ed_x : N_MM, optional
        [$v_{Ed,x}$] Out-of-plane design shear force per unit width perpendicular to the x direction. Used
        only when [$\alpha_v$] is left out, and taken as a magnitude [$N/mm$].
    v_ed_y : N_MM, optional
        [$v_{Ed,y}$] Out-of-plane design shear force per unit width perpendicular to the y direction. Used
        only when [$\alpha_v$] is left out, and taken as a magnitude [$N/mm$].
    """
    super().__init__()
    self.d_x = d_x
    self.d_y = d_y
    self.v_ed_x = v_ed_x
    self.v_ed_y = v_ed_y
    self.alpha_v = self._angle(alpha_v, v_ed_x, v_ed_y)

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_25.Form8Dot25EffectiveDepthFromPrincipalShearForce.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.25.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_25.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.25."""
    _equation: str = r"d_x \cdot \cos^2(\alpha_v) + d_y \cdot \sin^2(\alpha_v)"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"d_x": f"{self.d_x:.{n}f}",
            r"d_y": f"{self.d_y:.{n}f}",
            r"\alpha_v": f"{self.alpha_v:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"d_x": rf"{self.d_x:.{n}f} \ mm",
            r"d_y": rf"{self.d_y:.{n}f} \ mm",
            r"\alpha_v": rf"{self.alpha_v:.{n}f} \ degrees",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"d",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="mm",
    )