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formula_8_2

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_2

Formula 8.2 from EN 1992-1-1:2004: Chapter 8: Detailing of reinforcement and prestressing tendons.

Classes:

  • Form8Dot2UltimateBondStress –

    Class representing formula 8.2 for the calculation of the design value of the ultimate bond stress for ribbed bars.

  • SubForm8Dot2CoefficientBarDiameter –

    Class representing sub-formula for formula 8.2, which calculates the coefficient 'η2' which is dependent on the bar diameter.

  • SubForm8Dot2CoefficientQualityOfBond –

    Class representing sub-formula for formula 8.2, which calculates the coefficient 'η1' which is dependent on the quality of the bond.

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_2.Form8Dot2UltimateBondStress 

Form8Dot2UltimateBondStress(
    eta_1: DIMENSIONLESS, eta_2: DIMENSIONLESS, f_ctd: MPA
)

Bases: Formula

Class representing formula 8.2 for the calculation of the design value of the ultimate bond stress for ribbed bars.

[\(f_{bd}\)] The design value of the ultimate bond stress for ribbed bars [\(-\)].

EN 1992-1-1:2004 art.8.4.2(2) - Formula (8.2)

Parameters:

  • eta_1 (DIMENSIONLESS) –

    [\(η_1\)] coefficient related to the quality of the bond condition and the position of the bar during concreting (see Figure 8.2) [\(-\)]. = [\(1\)] when ‘good’ conditions are obtained; = [\(1\)] other cases and for bars in structural elements built with slip-forms, unless it can be shown that ‘good’ bond conditions exist; Use your own implementation of this formula or use the SubForm8Dot2CoefficientQualityOfBond class.

  • eta_2 (DIMENSIONLESS) –

    [\(η_2\)] A factor related to the bar diameter [\(-\)]. = [\(1\)] for bars with a diameter ≤ [\(32 \text{mm}\)]; = [\((132 - Ø) / 100\)] for bars with a diameter > [\(32 \text{mm}\)]. Use your own implementation of this value or use the SubForm8Dot2CoefficientBarDiameter class.

  • f_ctd (MPA) –

    [\(f_{ctd}\)] Design tensile strength of concrete according to art.3.1.6(2) [\(MPa\)]. Due to the increasing brittleness of higher strength concrete, [\(f_{ctk,0,05}\)] should be limited here to the value for C60/75, unless it can be verified that the average bond strength increases above this limit.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_2.py 
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def __init__(
    self,
    eta_1: DIMENSIONLESS,
    eta_2: DIMENSIONLESS,
    f_ctd: MPA,
) -> None:
    r"""[$f_{bd}$] The design value of the ultimate bond stress for ribbed bars [$-$].

    EN 1992-1-1:2004 art.8.4.2(2) - Formula (8.2)

    Parameters
    ----------
    eta_1 : DIMENSIONLESS
        [$η_1$] coefficient related to the quality of the bond condition and the position of the bar during concreting (see Figure 8.2) [$-$].
        = [$1$] when ‘good’ conditions are obtained;
        = [$1$] other cases and for bars in structural elements built with slip-forms, unless it can be shown that ‘good’ bond conditions
        exist;
        Use your own implementation of this formula or use the SubForm8Dot2CoefficientQualityOfBond class.
    eta_2 : DIMENSIONLESS
        [$η_2$] A factor related to the bar diameter [$-$].
        = [$1$] for bars with a diameter ≤ [$32 \text{mm}$];
        = [$(132 - Ø) / 100$] for bars with a diameter > [$32 \text{mm}$].
        Use your own implementation of this value or use the SubForm8Dot2CoefficientBarDiameter class.
    f_ctd : MPA
        [$f_{ctd}$] Design tensile strength of concrete according to art.3.1.6(2) [$MPa$].
        Due to the increasing brittleness of higher strength concrete, [$f_{ctk,0,05}$] should be limited here to the value for C60/75, unless
        it can be verified that the average bond strength increases above this limit.
    """
    super().__init__()
    self.eta_1 = eta_1
    self.eta_2 = eta_2
    self.f_ctd = f_ctd

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_2.Form8Dot2UltimateBondStress.latex 

latex(n: int = 2) -> LatexFormula

Returns a representation of the formula in LaTeX format.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_2.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns a representation of the formula in LaTeX format."""
    return LatexFormula(
        return_symbol=r"f_{bd}",
        result=f"{self:.{n}f}",
        equation=r"2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd}",
        numeric_equation=rf"2.25 \cdot {self.eta_1:.{n}f} \cdot {self.eta_2:.{n}f} \cdot {self.f_ctd:.{n}f}",
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_2.SubForm8Dot2CoefficientBarDiameter 

SubForm8Dot2CoefficientBarDiameter(diameter: MM)

Bases: Formula

Class representing sub-formula for formula 8.2, which calculates the coefficient 'η2' which is dependent on the bar diameter.

[\(η_2\)] Coefficient that depends on the bar diameter [\(-\)].

EN 1992-1-1:2004 art.8.4.2(2) - [\(η_2\)]

Parameters:

  • diameter (MM) –

    [\(Ø\)] Diameter of the bar [\(mm\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_2.py 
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def __init__(self, diameter: MM) -> None:
    r"""[$η_2$] Coefficient that depends on the bar diameter [$-$].

    EN 1992-1-1:2004 art.8.4.2(2) - [$η_2$]

    Parameters
    ----------
    diameter : MM
        [$Ø$] Diameter of the bar [$mm$].
    """
    super().__init__()
    self.diameter = diameter

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_2.SubForm8Dot2CoefficientBarDiameter.latex 

latex(n: int = 2) -> LatexFormula

Returns a LatexFormula object for this formula.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_2.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns a LatexFormula object for this formula."""
    numerical_equation = "1.00" if self.diameter <= 32 else f"(132 - {self.diameter}) / 100"

    return LatexFormula(
        return_symbol=r"\eta_2",
        result=f"{self:.{n}f}",
        equation=r"\begin{matrix} 1.0 & \text{for }Ø ≤ 32 \\ (132 - Ø) / 100 & \text{for }Ø > 32  \end{matrix}",
        numeric_equation=numerical_equation,
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_2.SubForm8Dot2CoefficientQualityOfBond 

SubForm8Dot2CoefficientQualityOfBond(bond_quality: str)

Bases: Formula

Class representing sub-formula for formula 8.2, which calculates the coefficient 'η1' which is dependent on the quality of the bond.

[\(η_1\)] Coefficient that depends on the type of cement [\(-\)].

EN 1992-1-1:2004 art.8.4.2(2) - η1

Parameters:

  • bond_quality (str) –

    Quality of the bond. = 'good' for a good bond condition.; = 'other' for other cases and for bars in structural elements built with slip-forms, unless it can be shown that ‘good’ bond conditions exist.;

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_2.py 
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def __init__(self, bond_quality: str) -> None:
    r"""[$η_1$] Coefficient that depends on the type of cement [$-$].

    EN 1992-1-1:2004 art.8.4.2(2) - η1

    Parameters
    ----------
    bond_quality : str
        Quality of the bond.
            = 'good' for a good bond condition.;
            = 'other' for other cases and for bars in structural elements built with slip-forms, unless it can be shown that ‘good’ bond
            conditions exist.;
    """
    super().__init__()
    self.bond_quality = bond_quality