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formula_8_15

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_15

Formula 8.15 from EN 1992-1-1:2004: Chapter 8: Detailing of reinforcement and prestressing tendons.

Classes:

  • Form8Dot15PrestressTransferStress –

    Class representing formula 8.15 for the calculation of the constant bond stress at which prestress is assumed to be transferred to the

  • SubForm8Dot15EtaP1 –

    Class representing sub-formula 8.15 for the calculation of the coefficient that takes into account the type of tendon and the bond situation

  • SubForm8Dot15TensileStrengthAtRelease –

    Class representing sub-formula 8.15 for the calculation of the design tensile value of strength at time of release (see 3.1.2(8) and

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_15.Form8Dot15PrestressTransferStress 

Form8Dot15PrestressTransferStress(
    eta_p1: DIMENSIONLESS, eta_1: DIMENSIONLESS, f_ctd_t: MPA
)

Bases: Formula

Class representing formula 8.15 for the calculation of the constant bond stress at which prestress is assumed to be transferred to the concrete, at the release of tendons.

[\(f_{bpt}\)] Constant bond stress at which prestress is assumed to be transferred to the concrete [\(MPa\)]. EN 1992-1-1:2004 art.8.10.2.2(1) - Formula (8.15).

Parameters:

  • eta_p1 (DIMENSIONLESS) –

    [\(\eta_{p1}\)] Coefficient that takes into account the type of tendon and the bond situation at release [\(-\)]. = 2.7 for indented wires. = 3.2 for 3 and 7-wire strands Use your own implementation for this value or use :class:SubForm8Dot15EtaP1 class.

  • eta_1 (DIMENSIONLESS) –

    [\(\eta_1\)] Coefficient related to the quality of the bond condition and the position of bar during concreting (see Figure 8.2) [\(-\)]. = 1 when 'good' conditions are obtained; = 0.7 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 :class:SubForm8Dot2CoefficientQualityOfBond class.

  • f_ctd_t (MPA) –

    [\(f_{ctd}(t)\)] Design tensile value of strength at time of release [\(MPa\)]. = [\(\alpha_{ct} \cdot 0.7 \cdot f_{ctm}(t) / \gamma_{c}\)] (see 3.1.2(9) and 3.1.6(2)P) Use your own implementation for this value or use :class:SubForm8Dot15TensileStrengthAtRelease class.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_15.py 
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def __init__(
    self,
    eta_p1: DIMENSIONLESS,
    eta_1: DIMENSIONLESS,
    f_ctd_t: MPA,
) -> None:
    r"""[$f_{bpt}$] Constant bond stress at which prestress is assumed to be transferred to the concrete [$MPa$].
    EN 1992-1-1:2004 art.8.10.2.2(1) - Formula (8.15).

    Parameters
    ----------
    eta_p1 : DIMENSIONLESS
        [$\eta_{p1}$] Coefficient that takes into account the type of tendon and the bond situation at release [$-$].
        = 2.7 for indented wires.
        = 3.2 for 3 and 7-wire strands
        Use your own implementation for this value or use :class:`SubForm8Dot15EtaP1` class.
    eta_1 : DIMENSIONLESS
        [$\eta_1$] Coefficient related to the quality of the bond condition and the position of bar during concreting (see Figure 8.2) [$-$].
        = 1 when 'good' conditions are obtained;
        = 0.7 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 :class:`SubForm8Dot2CoefficientQualityOfBond` class.
    f_ctd_t : MPA
        [$f_{ctd}(t)$] Design tensile value of strength at time of release [$MPa$].
        = [$\alpha_{ct} \cdot 0.7 \cdot f_{ctm}(t) / \gamma_{c}$] (see 3.1.2(9) and 3.1.6(2)P)
        Use your own implementation for this value or use :class:`SubForm8Dot15TensileStrengthAtRelease` class.
    """
    super().__init__()
    self.eta_p1 = eta_p1
    self.eta_1 = eta_1
    self.f_ctd_t = f_ctd_t

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_15.Form8Dot15PrestressTransferStress.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 8.15.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_15.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 8.15."""
    return LatexFormula(
        return_symbol=r"f_{bpt}",
        result=f"{self:.{n}f}",
        equation=r"\eta_{p1} \cdot \eta_1 \cdot f_{ctd}(t)",
        numeric_equation=rf"{self.eta_p1:.{n}f} \cdot {self.eta_1:.{n}f} \cdot {self.f_ctd_t:.{n}f}",
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_15.SubForm8Dot15EtaP1 

SubForm8Dot15EtaP1(type_of_wire: str)

Bases: Formula

Class representing sub-formula 8.15 for the calculation of the coefficient that takes into account the type of tendon and the bond situation at release.

[\(\eta_{p1}\)] Coefficient that takes into account the type of tendon and the bond situation at release [\(-\)].

EN 1992-1-1:2004 art.8.10.2.2(1) - Formula (8.15)

Parameters:

  • type_of_wire (str) –

    Type of wire.

    = 'indented' for indented wires;

    = '3_7_wire_strands' for 3 and 7-wire strands;

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_15.py 
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def __init__(
    self,
    type_of_wire: str,
) -> None:
    r"""[$\eta_{p1}$] Coefficient that takes into account the type of tendon and the bond situation at release [$-$].

    EN 1992-1-1:2004 art.8.10.2.2(1) - Formula (8.15)

    Parameters
    ----------
    type_of_wire : str
        Type of wire.

        = 'indented' for indented wires;

        = '3_7_wire_strands' for 3 and 7-wire strands;
    """
    super().__init__()
    self.type_of_wire = type_of_wire

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_15.SubForm8Dot15EtaP1.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for the first subformula of formula 8.15.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_15.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for the first subformula of formula 8.15."""
    return LatexFormula(
        return_symbol=r"\eta_{p1}",
        result=f"{self:.{n}f}",
        equation=r"type\;of\;wire",
        numeric_equation=f"{self.type_of_wire}".replace(" ", r"\;"),
        comparison_operator_label=r"\rightarrow",
    )

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_15.SubForm8Dot15TensileStrengthAtRelease 

SubForm8Dot15TensileStrengthAtRelease(
    alpha_ct: DIMENSIONLESS, f_ctm_t: MPA, gamma_c: DIMENSIONLESS
)

Bases: Formula

Class representing sub-formula 8.15 for the calculation of the design tensile value of strength at time of release (see 3.1.2(8) and 3.1.6(2)P).

[\(f_{ctd}(t)\)] Design tensile value of strength at time of release [\(MPa\)].

EN 1992-1-1:2004 art.8.10.2.2(1) - Formula (8.15)

Parameters:

  • alpha_ct (DIMENSIONLESS) –

    [\(\alpha_{ct}\)] coefficient taking account of long term effects on the tensile strength and of unfavourable effects, resulting from the way the load is applied. [\(-\)].

    Value may be found in national annex. Recommended value: 1.0

  • f_ctm_t (MPA) –

    [\(f_{ctm}(t)\)] Mean value of tensile strength at time of release (see formula 3.4) [\(MPa\)].

    Use your own implementation for this value or use :class:Form3Dot4DevelopmentTensileStrength class.

  • gamma_c (DIMENSIONLESS) –

    [\(\gamma_{c}\)] Partial safety factor for concrete [\(-\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_15.py 
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def __init__(
    self,
    alpha_ct: DIMENSIONLESS,
    f_ctm_t: MPA,
    gamma_c: DIMENSIONLESS,
) -> None:
    r"""[$f_{ctd}(t)$] Design tensile value of strength at time of release [$MPa$].

    EN 1992-1-1:2004 art.8.10.2.2(1) - Formula (8.15)

    Parameters
    ----------
    alpha_ct : DIMENSIONLESS
        [$\alpha_{ct}$] coefficient taking account of long term effects on the tensile strength and of unfavourable effects, resulting from the
        way the load is applied. [$-$].

        Value may be found in national annex. Recommended value: 1.0
    f_ctm_t : MPA
        [$f_{ctm}(t)$] Mean value of tensile strength at time of release (see formula 3.4) [$MPa$].

        Use your own implementation for this value or use :class:`Form3Dot4DevelopmentTensileStrength` class.
    gamma_c : DIMENSIONLESS
        [$\gamma_{c}$] Partial safety factor for concrete [$-$].
    """
    super().__init__()
    self.alpha_ct = alpha_ct
    self.f_ctm_t = f_ctm_t
    self.gamma_c = gamma_c

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_15.SubForm8Dot15TensileStrengthAtRelease.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for the second subformula of formula 8.15.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_15.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for the second subformula of formula 8.15."""
    return LatexFormula(
        return_symbol=r"f_{ctd}(t)",
        result=f"{self:.{n}f}",
        equation=r"\frac{\alpha_{ct} \cdot 0.7 \cdot f_{ctm}(t)}{\gamma_c}",
        numeric_equation=rf"\frac{{{self.alpha_ct:.{n}f} \cdot 0.7 \cdot {self.f_ctm_t:.{n}f}}}{{{self.gamma_c:.{n}f}}}",
        comparison_operator_label="=",
    )