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formula_8_37

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_37

Formula 8.37 from EN 1993-1-1:2022: Chapter 8 - Ultimate Limit State.

Classes:

  • Form8Dot37Rho –

    Class representing formula 8.37 for the calculation of [\(\rho\)], where no torsion is present.

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_37.Form8Dot37Rho 

Form8Dot37Rho(v_ed: N, v_c_rd: N)

Bases: Formula

Class representing formula 8.37 for the calculation of [\(\rho\)], where no torsion is present.

[\(\rho\)] Calculation of the reduction factor, where no torsion is present [\(\text{dimensionless}\)].

EN 1993-1-1:2022 art.8.2.8(4) - Formula (8.37)

Parameters:

  • v_ed (N) –

    [\(V_{Ed}\)] Design shear force [\(N\)].

  • v_c_rd (N) –

    [\(V_{pl,Rd}\)] Plastic shear resistance, obtained from 8.2.6(2) [\(N\)]. Note, see also 8.2.8(4)

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_37.py 
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def __init__(
    self,
    v_ed: N,
    v_c_rd: N,
) -> None:
    r"""[$\rho$] Calculation of the reduction factor, where no torsion is present [$\text{dimensionless}$].

    EN 1993-1-1:2022 art.8.2.8(4) - Formula (8.37)

    Parameters
    ----------
    v_ed : N
        [$V_{Ed}$] Design shear force [$N$].
    v_c_rd : N
        [$V_{pl,Rd}$] Plastic shear resistance, obtained from 8.2.6(2) [$N$].
        Note, see also 8.2.8(4)
    """
    super().__init__()
    self.v_ed = v_ed
    self.v_c_rd = v_c_rd

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_37.Form8Dot37Rho.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.37.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_37.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.37."""
    _equation: str = (
        r"\begin{cases} "
        r"0 & \text{if } V_{Ed} \leq 0.5 \cdot V_{c,Rd} \\ "
        r"\left( \frac{2 \cdot V_{Ed}}{V_{c,Rd}} - 1 \right)^2 & \text{if } V_{Ed} > 0.5 \cdot V_{c,Rd} "
        r"\end{cases}"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"V_{Ed}": f"{self.v_ed:.{n}f}",
            r"V_{c,Rd}": f"{self.v_c_rd:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            r"V_{Ed}": rf"{self.v_ed:.{n}f} \ N",
            r"V_{c,Rd}": rf"{self.v_c_rd:.{n}f} \ N",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"\rho",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="-",
    )