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formula_8_8n

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n

Formula 8.8N from EN 1992-1-1:2004: Chapter 8 - Detailing of reinforcement and prestressing tendons.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.Form8Dot8nAnchorageCapacityWeldedTransverseBar 

Form8Dot8nAnchorageCapacityWeldedTransverseBar(
    l_td: MM, diameter_t: MM, sigma_td: MPA, f_wd: KN
)

Bases: Formula

Class representing the formula 8.8N for the calculation of the anchorage capacity of welded transverse bar, welded on the inside of the main bar.

[\(F_{btd}\)] Anchorage capacity of welded transverse bar, welded on the inside of the main bar [\(kN\)].

Note: Value may be found in National Annex.

EN 1992-1-1:2004 art.8.6(2) - formula (8.8N)

Parameters:

  • l_td (MM) –

    [\(l_{td}\)] Design length of transverse bar [\(mm\)].

    [\(= 1.16 ⋅ ø_{t} ⋅ (f_{yd}/σ_{td})^{0.5} ≤ l_{t}\)]

    Use your own implementation of this formula or use the SubForm8Dot8nDesignLengthOfTransverseBar class.

  • diameter_t (MM) –

    [\(ø_{t}\)] Diameter of transverse bar [\(mm\)].

  • sigma_td (MPA) –

    [\(σ_{td}\)] Concrete stress [\(MPa\)].

    [\(=(f_{ctd}+σ_{cm})/y ≤ 3⋅f_{cd}\)]

    Use your own implementation of this formula or use the SubForm8Dot8nConcreteStress class.

  • f_wd (KN) –

    [\(F_{wd}\)] Design shear strength of weld (specified as a factor times [\(A_{s}⋅f_{yd}\)]; say [\(0.5⋅A_{s}⋅f_{yd}\)] where [\(A_{s}\)] is the cross-section of the anchored bar and fyd is its design yield strength) [\(kN\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def __init__(
    self,
    l_td: MM,
    diameter_t: MM,
    sigma_td: MPA,
    f_wd: KN,
) -> None:
    r"""[$F_{btd}$] Anchorage capacity of welded transverse bar, welded on the inside of the main bar [$kN$].

        Note: Value may be found in National Annex.

    EN 1992-1-1:2004 art.8.6(2) - formula (8.8N)

    Parameters
    ----------
    l_td: MM
        [$l_{td}$] Design length of transverse bar [$mm$].

        [$= 1.16 ⋅ ø_{t} ⋅ (f_{yd}/σ_{td})^{0.5} ≤ l_{t}$]

        Use your own implementation of this formula or use the SubForm8Dot8nDesignLengthOfTransverseBar class.
    diameter_t: MM
        [$ø_{t}$] Diameter of transverse bar [$mm$].
    sigma_td: MPA
        [$σ_{td}$] Concrete stress [$MPa$].

        [$=(f_{ctd}+σ_{cm})/y ≤ 3⋅f_{cd}$]

        Use your own implementation of this formula or use the SubForm8Dot8nConcreteStress class.
    f_wd: KN
        [$F_{wd}$] Design shear strength of weld (specified as a factor times [$A_{s}⋅f_{yd}$]; say [$0.5⋅A_{s}⋅f_{yd}$] where
        [$A_{s}$] is the cross-section of the anchored bar and fyd is its design yield strength)  [$kN$].
    """
    super().__init__()
    self.l_td = l_td
    self.diameter_t = diameter_t
    self.sigma_td = sigma_td
    self.f_wd = f_wd

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.Form8Dot8nAnchorageCapacityWeldedTransverseBar.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 8.8N.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 8.8N."""
    return LatexFormula(
        return_symbol=r"F_{btd}",
        result=f"{self:.{n}f}",
        equation=r"\min\left( l_{td} \cdot Ø_t \cdot \sigma_{td}, F_{wd} \right)",
        numeric_equation=rf"\min\left( {self.l_td:.{n}f} \cdot {self.diameter_t:.{n}f} "
        rf"\cdot {self.sigma_td:.{n}f} / 1000, {self.f_wd:.{n}f} \right)",
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.SubForm8Dot8nConcreteStress 

SubForm8Dot8nConcreteStress(
    f_ctd: MPA, sigma_cm: MPA, y_function: DIMENSIONLESS, f_cd: MPA
)

Bases: Formula

Class representing sub-formula for formula 8.8N, which calculates the concrete stress.

[\(σ_{td}\)] Concrete stress [\(MPa\)].

EN 1992-1-1:2004 art.8.6(2) - [\(σ_{td}\)]

Parameters:

  • f_ctd (MPA) –

    [\(f_{ctd}\)] Design tensile strength of concrete [\(MPa\)].

  • sigma_cm (MPA) –

    [\(σ_{cm}\)] Compression in the concrete perpendicular to both bars (mean value) [\(MPa\)].

  • y_function (DIMENSIONLESS) –

    [\(y\)] A function [\(-\)]

    [\(= 0.015 + 0.14 ⋅ exp(-0.18⋅x)\)]

    Use your own implementation of this formula or use the SubForm8Dot8nFunctionY class.

  • f_cd (MPA) –

    [\(f_{cd}\)] Design value compressive strength of concrete [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def __init__(
    self,
    f_ctd: MPA,
    sigma_cm: MPA,
    y_function: DIMENSIONLESS,
    f_cd: MPA,
) -> None:
    r"""[$σ_{td}$] Concrete stress [$MPa$].

    EN 1992-1-1:2004 art.8.6(2) - [$σ_{td}$]

    Parameters
    ----------
    f_ctd: MPA
        [$f_{ctd}$] Design tensile strength of concrete [$MPa$].
    sigma_cm: MPA
        [$σ_{cm}$] Compression in the concrete perpendicular to both bars (mean value) [$MPa$].
    y_function: DIMENSIONLESS
        [$y$] A function [$-$]

        [$= 0.015 + 0.14 ⋅ exp(-0.18⋅x)$]

        Use your own implementation of this formula or use the SubForm8Dot8nFunctionY class.
    f_cd: MPA
        [$f_{cd}$] Design value compressive strength of concrete [$MPa$].
    """
    super().__init__()
    self.f_ctd = f_ctd
    self.sigma_cm = sigma_cm
    self.y_function = y_function
    self.f_cd = f_cd

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.SubForm8Dot8nConcreteStress.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 8.8N concrete stress.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 8.8N concrete stress."""
    return LatexFormula(
        return_symbol=r"\sigma_{td}",
        result=f"{self:.{n}f}",
        equation=r"\min\left( 3 \cdot f_{cd}, \frac{f_{ctd} + \sigma_{cm}}{y} \right)",
        numeric_equation=(
            rf"\min\left(3 \cdot {self.f_cd:.{n}f}, \frac{{{self.f_ctd:.{n}f} " rf"+ {self.sigma_cm:.{n}f}}}{{{self.y_function:.{n}f}}} \right)"
        ),
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.SubForm8Dot8nDesignLengthOfTransverseBar 

SubForm8Dot8nDesignLengthOfTransverseBar(
    diameter_t: MM, f_yd: MPA, sigma_td: MPA, l_t: MM
)

Bases: Formula

Class representing sub-formula for formula 8.8N, which calculates the design length of the transverse bar.

[\(l_{td}\)] Design length of transverse bar [\(mm\)].

EN 1992-1-1:2004 art.8.6(2) - [\(l_{td}\)]

Parameters:

  • diameter_t (MM) –

    [\(ø_{t}\)] Diameter of transverse bar [\(mm\)].

  • f_yd (MPA) –

    [\(f_{yd}\)] Design yield strength of bar [\(MPa\)].

  • sigma_td (MPA) –

    [\(σ_{td}\)] Concrete stress [\(MPa\)].

    [\(=(f_{ctd}+σ_{cm})/y ≤ 3⋅f_{cd}\)]

    Use your own implementation of this formula or use the SubForm8Dot8nConcreteStress class.

  • l_t (MM) –

    [\(l_{t}\)] Length of transverse bar, but not more than the spacing of bars to be anchored [\(mm\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def __init__(
    self,
    diameter_t: MM,
    f_yd: MPA,
    sigma_td: MPA,
    l_t: MM,
) -> None:
    r"""[$l_{td}$] Design length of transverse bar [$mm$].

    EN 1992-1-1:2004 art.8.6(2) - [$l_{td}$]

    Parameters
    ----------
    diameter_t: MM
        [$ø_{t}$] Diameter of transverse bar [$mm$].
    f_yd: MPA
        [$f_{yd}$] Design yield strength of bar [$MPa$].
    sigma_td: MPA
        [$σ_{td}$] Concrete stress [$MPa$].

        [$=(f_{ctd}+σ_{cm})/y ≤ 3⋅f_{cd}$]

        Use your own implementation of this formula or use the SubForm8Dot8nConcreteStress class.
    l_t: MM
        [$l_{t}$] Length of transverse bar, but not more than the spacing of bars to be anchored [$mm$].
    """
    super().__init__()
    self.diameter_t = diameter_t
    self.f_yd = f_yd
    self.sigma_td = sigma_td
    self.l_t = l_t

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.SubForm8Dot8nDesignLengthOfTransverseBar.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 8.8N transverse bar.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 8.8N transverse bar."""
    return LatexFormula(
        return_symbol=r"l_{td}",
        result=f"{self:.{n}f}",
        equation=r"\min\left(l_t, 1.16 \cdot Ø_t \cdot ({\frac{f_{yd}}{\sigma_{td}}})^{0.5} \right)",
        numeric_equation=(
            rf"\min\left({self.l_t:.{n}f}, 1.16 \cdot {self.diameter_t:.{n}f} \cdot "
            rf"({{\frac{{{self.f_yd:.{n}f}}}{{{self.sigma_td:.{n}f}}}}})^{{0.5}} \right)"
        ),
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.SubForm8Dot8nFunctionX 

SubForm8Dot8nFunctionX(cover: MM, diameter_t: MM)

Bases: Formula

Class representing sub-formula for formula 8.8N, which calculates the function x.

[\(x\)] A function accounting for the geometry [\(-\)].

EN 1992-1-1:2004 art.8.6(2) - [\(x\)]

Parameters:

  • cover (MM) –

    [\(c\)] Concrete cover perpendicular to both bars [\(mm\)].

  • diameter_t (MM) –

    [\(ø_{t}\)] Diameter of transverse bar [\(mm\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def __init__(
    self,
    cover: MM,
    diameter_t: MM,
) -> None:
    r"""[$x$] A function accounting for the geometry [$-$].

    EN 1992-1-1:2004 art.8.6(2) - [$x$]

    Parameters
    ----------
    cover: MM
        [$c$] Concrete cover perpendicular to both bars [$mm$].
    diameter_t: MM
        [$ø_{t}$] Diameter of transverse bar [$mm$].
    """
    super().__init__()
    self.cover = cover
    self.diameter_t = diameter_t

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.SubForm8Dot8nFunctionX.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 8.8N x-function.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 8.8N x-function."""
    return LatexFormula(
        return_symbol=r"x",
        result=f"{self:.{n}f}",
        equation=r"2 \cdot \frac{c}{Ø_t}",
        numeric_equation=rf"2 \cdot \frac{{{self.cover:.{n}f}}}{{{self.diameter_t:.{n}f}}}",
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.SubForm8Dot8nFunctionY 

SubForm8Dot8nFunctionY(x_function: DIMENSIONLESS)

Bases: Formula

Class representing sub-formula for formula 8.8N, which calculates the function y.

[\(y\)] A function [\(-\)].

EN 1992-1-1:2004 art.8.6(2) - [\(y\)]

Parameters:

  • x_function (DIMENSIONLESS) –

    [\(x\)] A function accounting for the geometry [\(-\)]

    [\(= 2⋅(c/ø_{t}) + 1\)]

    Use your own implementation of this formula or use the SubForm8Dot8nFunctionX class.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def __init__(
    self,
    x_function: DIMENSIONLESS,
) -> None:
    r"""[$y$] A function [$-$].

    EN 1992-1-1:2004 art.8.6(2) - [$y$]

    Parameters
    ----------
    x_function: DIMENSIONLESS
        [$x$] A function accounting for the geometry [$-$]

        [$= 2⋅(c/ø_{t}) + 1$]

        Use your own implementation of this formula or use the SubForm8Dot8nFunctionX class.
    """
    super().__init__()
    self.x_function = x_function

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_8n.SubForm8Dot8nFunctionY.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 8.8N y-function.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_8n.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 8.8N y-function."""
    return LatexFormula(
        return_symbol=r"y",
        result=f"{self:.{n}f}",
        equation=r"0.015 + 0.14 \cdot e^{-0.18 \cdot x}",
        numeric_equation=rf"0.015 + 0.14 \cdot e^{{-0.18 \cdot {self.x_function:.{n}f}}}",
        comparison_operator_label="=",
    )