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formula_6_45

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_45

Formula 6.45 from EN 1993-1-1:2005: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_45.Form6Dot45ReducedYieldStrength 

Form6Dot45ReducedYieldStrength(rho: DIMENSIONLESS, f_y: MPA)

Bases: Formula

Class representing formula 6.45 for the calculation of reduced yield strength for the shear area.

Reduced yield strength calculation for the shear area when shear force exceeds 50% of plastic shear resistance [\(MPa\)].

EN 1993-1-1:2005 art.6.2.10(3) - Formula (6.45)

Parameters:

  • rho (DIMENSIONLESS) –

    [\(\rho\)] Factor where \(\rho = (2V_{Ed} / V_{pl,Rd}-1)^2\) and \(V_{pl,Rd}\) is obtained from 6.2.6(2) [-].

  • f_y (MPA) –

    [\(f_y\)] Yield strength [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_45.py 
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def __init__(
    self,
    rho: DIMENSIONLESS,
    f_y: MPA,
) -> None:
    r"""Reduced yield strength calculation for the shear area when shear force exceeds 50% of plastic shear resistance [$MPa$].

    EN 1993-1-1:2005 art.6.2.10(3) - Formula (6.45)

    Parameters
    ----------
    rho : DIMENSIONLESS
        [$\rho$] Factor where $\rho = (2V_{Ed} / V_{pl,Rd}-1)^2$ and $V_{pl,Rd}$ is obtained from 6.2.6(2) [-].
    f_y : MPA
        [$f_y$] Yield strength [$MPa$].
    """
    super().__init__()
    self.rho = rho
    self.f_y = f_y

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_45.Form6Dot45ReducedYieldStrength.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.45.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_45.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.45."""
    _equation: str = r"(1 - \rho) \cdot f_y"

    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\rho": f"{self.rho:.{n}f}",
            r"f_y": f"{self.f_y:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"\rho": f"{self.rho:.{n}f}",
            r"f_y": rf"{self.f_y:.{n}f} \ MPa",
        },
        True,
    )

    return LatexFormula(
        return_symbol=r"f_{y,red}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="MPa",
    )