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formula_8_21

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_21

Formula 8.21 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_21.Form8Dot21DesignShearForcePerUnitWidth 

Form8Dot21DesignShearForcePerUnitWidth(v_ed_x: N_MM, v_ed_y: N_MM)

Bases: Formula

Class representing formula 8.21 for the calculation of the design shear force per unit width in planar members with out-of-plane shear forces acting in two directions.

[\(v_{Ed}\)] Design shear force per unit width in planar members [\(N/mm\)].

FprEN 1992-1-1:2023 (E) art 8.2.1 (5) - Formula (8.21)

Both components enter squared, so the sign of either of them does not reach the result. They are components of a shear force vector and the standard places no restriction on their sign, so a negative one is accepted and gives the same result as its positive counterpart.

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_21.py 
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def __init__(self, v_ed_x: N_MM, v_ed_y: N_MM) -> None:
    r"""[$v_{Ed}$] Design shear force per unit width in planar members [$N/mm$].

    FprEN 1992-1-1:2023 (E) art 8.2.1 (5) - Formula (8.21)

    Both components enter squared, so the sign of either of them does not reach the result. They are
    components of a shear force vector and the standard places no restriction on their sign, so a negative
    one is accepted and gives the same result as its positive counterpart.

    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_21.Form8Dot21DesignShearForcePerUnitWidth.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.21.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_21.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.21."""
    _equation: str = r"\sqrt{\left(v_{Ed,x}\right)^2 + \left(v_{Ed,y}\right)^2}"
    _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"v_{Ed}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="N/mm",
    )