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formula_6_29rho

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_29rho

Formula 6.29rho from EN 1993-1-1:2005: Chapter 6 - Ultimate Limit State.

Classes:

  • Form6Dot29Rho –

    Class representing formula 6.29rho for the calculation of [\(\rho\)], where no torsion is present.

  • Form6Dot29RhoWithTorsion –

    Class representing formula 6.29rho with torsion for the calculation of [\(\rho\)].

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_29rho.Form6Dot29Rho 

Form6Dot29Rho(v_ed: N, v_pl_rd: N)

Bases: Formula

Class representing formula 6.29rho for the calculation of [\(\rho\)], where no torsion is present.

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

EN 1993-1-1:2005 art.6.2.10(3) - Formula (6.29rho)

Parameters:

  • v_ed (N) –

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

  • v_pl_rd (N) –

    [\(V_{pl,Rd}\)] Plastic shear resistance, obtained from 6.2.6(2) [\(N\)]. Note, see also 6.2.10(3)

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_29rho.py 
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def __init__(
    self,
    v_ed: N,
    v_pl_rd: N,
) -> None:
    r"""[$\rho$] Calculation of the reduction factor, where no torsion is present [$\text{dimensionless}$].

    EN 1993-1-1:2005 art.6.2.10(3) - Formula (6.29rho)

    Parameters
    ----------
    v_ed : N
        [$V_{Ed}$] Design shear force [$N$].
    v_pl_rd : N
        [$V_{pl,Rd}$] Plastic shear resistance, obtained from 6.2.6(2) [$N$].
        Note, see also 6.2.10(3)
    """
    super().__init__()
    self.v_ed = v_ed
    self.v_pl_rd = v_pl_rd

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_29rho.Form6Dot29Rho.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.29rho.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_29rho.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.29rho."""
    _equation: str = (
        r"\begin{cases} "
        r"0 & \text{if } V_{Ed} \leq 0.5 \cdot V_{pl,Rd} \\ "
        r"\left( \frac{2 \cdot V_{Ed}}{V_{pl,Rd}} - 1 \right)^2 & \text{if } V_{Ed} > 0.5 \cdot V_{pl,Rd} "
        r"\end{cases}"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"V_{Ed}": f"{self.v_ed:.{n}f}",
            r"V_{pl,Rd}": f"{self.v_pl_rd:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"V_{Ed}": rf"{self.v_ed:.{n}f} \ N",
            r"V_{pl,Rd}": rf"{self.v_pl_rd:.{n}f} \ N",
        },
        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="-",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_29rho.Form6Dot29RhoWithTorsion 

Form6Dot29RhoWithTorsion(v_ed: N, v_pl_t_rd: N)

Bases: Formula

Class representing formula 6.29rho with torsion for the calculation of [\(\rho\)].

[\(\rho\)] Calculation of the reduction factor with torsion [\(\text{dimensionless}\)].

EN 1993-1-1:2005 art.6.2.7(4) - Formula (6.29rho with torsion)

Parameters:

  • v_ed (N) –

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

  • v_pl_t_rd (N) –

    [\(V_{pl,T,Rd}\)] Plastic shear resistance with torsion [\(N\)]. Note, see also 6.2.7

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_29rho.py 
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def __init__(
    self,
    v_ed: N,
    v_pl_t_rd: N,
) -> None:
    r"""[$\rho$] Calculation of the reduction factor with torsion [$\text{dimensionless}$].

    EN 1993-1-1:2005 art.6.2.7(4) - Formula (6.29rho with torsion)

    Parameters
    ----------
    v_ed : N
        [$V_{Ed}$] Design shear force [$N$].
    v_pl_t_rd : N
        [$V_{pl,T,Rd}$] Plastic shear resistance with torsion [$N$].
        Note, see also 6.2.7
    """
    super().__init__()
    self.v_ed = v_ed
    self.v_pl_t_rd = v_pl_t_rd

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_29rho.Form6Dot29RhoWithTorsion.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.29rho with torsion.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_29rho.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.29rho with torsion."""
    _equation: str = (
        r"\begin{cases} "
        r"0 & \text{if } V_{Ed} \leq 0.5 \cdot V_{pl,T,Rd} \\ "
        r"\left( \frac{2 \cdot V_{Ed}}{V_{pl,T,Rd}} - 1 \right)^2 & \text{if } V_{Ed} > 0.5 \cdot V_{pl,T,Rd} "
        r"\end{cases}"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"V_{Ed}": f"{self.v_ed:.{n}f}",
            r"V_{pl,T,Rd}": f"{self.v_pl_t_rd:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"V_{Ed}": rf"{self.v_ed:.{n}f} \ N",
            r"V_{pl,T,Rd}": rf"{self.v_pl_t_rd:.{n}f} \ N",
        },
        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="-",
    )