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formula_12_5_6

codes.eurocode.en_1992_1_1_2004.chapter_12_plain_and_lightly_reinforced_concrete_structures.formula_12_5_6

Formula 12.5 and 12.6 from EN 1992-1-1:2004: Chapter 12 - Plain and Lightly Reinforced Concrete Structures.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_12_plain_and_lightly_reinforced_concrete_structures.formula_12_5_6.Form12Dot5And6PlainConcreteBendingResistance 

Form12Dot5And6PlainConcreteBendingResistance(
    f_ctd_pl: MPA,
    sigma_cp: MPA | Form12Dot3PlainConcreteShearStress,
    sigma_c_lim: MPA,
)

Bases: Formula

Class representing formula 12.5 and 12.6 for the calculation of the design bending resistance of plain concrete, :math:f_{cvd}.

EN 1992-1-1:2004 art.12.6.1 - Formula (12.5)

[:math:f_{cvd}] Design bending resistance of plain concrete [:math=MPa].

EN 1992-1-1:2004 art.12.6.1 - Formula (12.5)

Parameters:

  • f_ctd_pl (MPA) –

    [:math=f_{ctd,pl}] Design tensile strength of plain concrete [:math=MPa].

  • sigma_cp (MPA | Form12Dot3PlainConcreteShearStress) –

    [:math=\sigma_{cp}] Compressive stress [:math=MPa] or an instance of Form12Dot3PlainConcreteShearStress.

  • sigma_c_lim (MPA) –

    [:math=\sigma_{c,lim}] Limiting compressive stress [:math=MPa].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_12_plain_and_lightly_reinforced_concrete_structures/formula_12_5_6.py 
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def __init__(
    self,
    f_ctd_pl: MPA,
    sigma_cp: MPA | Form12Dot3PlainConcreteShearStress,
    sigma_c_lim: MPA,
) -> None:
    r"""[:math:`f_{cvd}`] Design bending resistance of plain concrete [:math=`MPa`].

    EN 1992-1-1:2004 art.12.6.1 - Formula (12.5)

    Parameters
    ----------
    f_ctd_pl : MPA
        [:math=`f_{ctd,pl}`] Design tensile strength of plain concrete [:math=`MPa`].
    sigma_cp : MPA | Form12Dot3PlainConcreteShearStress
        [:math=`\sigma_{cp}`] Compressive stress [:math=`MPa`] or an instance of Form12Dot3PlainConcreteShearStress.
    sigma_c_lim : MPA
        [:math=`\sigma_{c,lim}`] Limiting compressive stress [:math=`MPa`].
    """
    super().__init__()
    self.f_ctd_pl = f_ctd_pl
    self.sigma_cp = sigma_cp
    self.sigma_c_lim = sigma_c_lim

codes.eurocode.en_1992_1_1_2004.chapter_12_plain_and_lightly_reinforced_concrete_structures.formula_12_5_6.Form12Dot5And6PlainConcreteBendingResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 12.5. / 12.6.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_12_plain_and_lightly_reinforced_concrete_structures/formula_12_5_6.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 12.5. / 12.6."""
    result = self._evaluate(self.f_ctd_pl, self.sigma_cp, self.sigma_c_lim)
    comparison = Form12Dot4PlainConcreteShearStressComparison(self.sigma_cp, self.sigma_c_lim)
    if comparison:
        equation = r"\sqrt{f_{ctd, pl} ^ 2 + \sigma_{cp} \cdot f_{ctd, pl}}"
        numeric_equation = rf"\sqrt{{{self.f_ctd_pl:.{n}f} ^ 2 + {self.sigma_cp:.{n}f} \cdot {self.f_ctd_pl:.{n}f}}}"
    else:
        equation = r"\sqrt{f_{ctd, pl} ^ 2 + \sigma_{cp} \cdot f_{ctd, pl} - \left(\frac{\sigma_{cp} - \sigma_{c, lim}}{2}\right) ^ 2}"
        part1 = f"{self.f_ctd_pl:.{n}f} ^ 2"
        part2 = rf"{self.sigma_cp:.{n}f} \cdot {self.f_ctd_pl:.{n}f}"
        part3 = f"\\left(\\frac{{{self.sigma_cp:.{n}f} - {self.sigma_c_lim:.{n}f}}}{2}\\right) ^ 2"
        numeric_equation = rf"\sqrt{{{part1} + {part2} - {part3}}}"
    return LatexFormula(
        return_symbol=r"f_{cvd}",
        result=f"{result:.{n}f}",
        equation=equation,
        numeric_equation=numeric_equation,
        comparison_operator_label="=",
    )