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formula_7_16_ab

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_16_ab

Formula 7.16a/b from EN 1992-1-1:2004: Chapter 7 - Serviceability limit state.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_16_ab.Form7Dot16ReferenceReinforcementRatio 

Form7Dot16ReferenceReinforcementRatio(f_ck: MPA)

Bases: Formula

Class representing formula 7.16 for the calculation of [\(\rho_0\)].

[\(\rho_0\)] Reference reinforcement ratio [\(-\)].

EN 1992-1-1:2004 art.7.4.2(2) - Formula (7.16)

Parameters:

  • f_ck (MPA) –

    [\(f_{ck}\)] Characteristic compressive strength of concrete [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_16_ab.py 
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def __init__(
    self,
    f_ck: MPA,
) -> None:
    r"""[$\rho_0$] Reference reinforcement ratio [$-$].

    EN 1992-1-1:2004 art.7.4.2(2) - Formula (7.16)

    Parameters
    ----------
    f_ck : MPA
        [$f_{ck}$] Characteristic compressive strength of concrete [$MPa$].
    """
    super().__init__()
    self.f_ck = f_ck

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_16_ab.Form7Dot16ReferenceReinforcementRatio.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 7.16_rho_0.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_16_ab.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 7.16_rho_0."""
    _equation: str = r"\sqrt{f_{ck}} \cdot 10^{-3}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"f_{ck}": f"{self.f_ck:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\rho_0",
        result=f"{self:.6f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_16_ab.Form7Dot16abSpanDepthRatio 

Form7Dot16abSpanDepthRatio(
    capital_k: DIMENSIONLESS,
    f_ck: MPA,
    rho: DIMENSIONLESS,
    rho_0: DIMENSIONLESS,
    rho_prime: DIMENSIONLESS,
)

Bases: Formula

Class representing formula 7.16a/b for the calculation of the limit span/depth ratio.

[\(\frac{l}{d}\)] Limit span/depth ratio [\(-\)].

EN 1992-1-1:2004 art.7.4.2(2) - Formula (7.16a and 7.16b)

Parameters:

  • capital_k (DIMENSIONLESS) –

    [\(K\)] Factor to take into account the different structural systems [\(-\)].

  • f_ck (MPA) –

    [\(f_{ck}\)] Characteristic compressive strength of concrete [\(MPa\)].

  • rho (DIMENSIONLESS) –

    [\(\rho\)] Required tension reinforcement ratio at mid-span to resist the moment due to the design loads (at support for cantilevers) [\(-\)].

  • rho_0 (DIMENSIONLESS) –

    [\(\rho_0\)] Reference reinforcement ratio [\(\sqrt{f_{ck}} \cdot 10^{-3}\)] [\(-\)].

  • rho_prime (DIMENSIONLESS) –

    [\(\rho'\)] Required compression reinforcement ratio at mid-span to resist the moment due to design loads (at support for cantilevers) [\(-\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_16_ab.py 
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def __init__(
    self,
    capital_k: DIMENSIONLESS,
    f_ck: MPA,
    rho: DIMENSIONLESS,
    rho_0: DIMENSIONLESS,
    rho_prime: DIMENSIONLESS,
) -> None:
    r"""[$\frac{l}{d}$] Limit span/depth ratio [$-$].

    EN 1992-1-1:2004 art.7.4.2(2) - Formula (7.16a and 7.16b)

    Parameters
    ----------
    capital_k : DIMENSIONLESS
        [$K$] Factor to take into account the different structural systems [$-$].
    f_ck : MPA
        [$f_{ck}$] Characteristic compressive strength of concrete [$MPa$].
    rho : DIMENSIONLESS
        [$\rho$] Required tension reinforcement ratio at mid-span to resist the moment
        due to the design loads (at support for cantilevers) [$-$].
    rho_0 : DIMENSIONLESS
        [$\rho_0$] Reference reinforcement ratio [$\sqrt{f_{ck}} \cdot 10^{-3}$] [$-$].
    rho_prime : DIMENSIONLESS
        [$\rho'$] Required compression reinforcement ratio at mid-span to resist the moment
        due to design loads (at support for cantilevers) [$-$].
    """
    super().__init__()
    self.capital_k = capital_k
    self.f_ck = f_ck
    self.rho = rho
    self.rho_0 = rho_0
    self.rho_prime = rho_prime

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_16_ab.Form7Dot16abSpanDepthRatio.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 7.16a/b.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_16_ab.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 7.16a/b."""
    _equation: str = (
        r"\begin{cases} K \cdot \left[11 + 1.5 \cdot \sqrt{f_{ck}} \cdot \frac{\rho_0}{\rho} + "
        r"3.2 \cdot \sqrt{f_{ck}} \cdot \left(\frac{\rho_0}{\rho} - 1\right)^{3/2}\right] & \text{if } \rho \leq \rho_0 \\ "
        r"K \cdot \left[11 + 1.5 \cdot \sqrt{f_{ck}} \cdot \frac{\rho_0}{\rho - \rho'} + "
        r"\frac{1}{12} \cdot \sqrt{f_{ck}} \cdot \sqrt{\frac{\rho'}{\rho_0}}\right] & \text{if } \rho > \rho_0 \end{cases}"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"K": f"{self.capital_k:.{n}f}",
            r"f_{ck}": f"{self.f_ck:.{n}f}",
            r"\rho_0": f"{self.rho_0:.{n + 1}f}",
            r"\rho'": f"{self.rho_prime:.{n + 1}f}",
            r"\rho": f"{self.rho:.{n + 1}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\frac{l}{d}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )