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formula_8_10

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_10

Formula 8.10 from EN 1992-1-1:2004: Chapter 8: Detailing of reinforcement and prestressing tendons.

Classes:

  • Form8Dot10DesignLapLength –

    Class representing formula 8.10 for the calculation of the design lap length [\(l_{0}\)] [\(mm\)].

  • SubForm8Dot10Alpha6 –

    Class representing the formula for the calculation of the coefficient [\(α_{6}\)].

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_10.Form8Dot10DesignLapLength 

Form8Dot10DesignLapLength(
    alpha_1: DIMENSIONLESS,
    alpha_2: DIMENSIONLESS,
    alpha_3: DIMENSIONLESS,
    alpha_5: DIMENSIONLESS,
    alpha_6: DIMENSIONLESS,
    l_b_rqd: MM,
    l_0_min: MM,
)

Bases: Formula

Class representing formula 8.10 for the calculation of the design lap length [\(l_{0}\)] [\(mm\)].

[\(l_{0}\)] Design lap length [\(mm\)].

EN 1992-1-1:2004 art.8.7.3(1) - Formula (8.10)

Parameters:

  • alpha_1 (DIMENSIONLESS) –

    [\(α_{1}\)] Coefficient for the effect of the form of the bars assuming adequate cover (see figure 8.1) [\(-\)].

    [\(= 1.0\)] for bars in compression.

    [\(= 1.0\)] for straight bars in tension.

    [\(= 1.0\)] if [\(c_{d} <= 3 ⋅ Ø\)] for bars other than straight in tension (see figure 8.1 (b), (c) and (d)).

    [\(= 0.7\)] if [\(c_{d} > 3 ⋅ Ø\)] for bars other than straight in tension (see figure 8.1 (b), (c) and (d)).

    Note: see figure 8.3 for values of [\(c_{d}\)].

  • alpha_2 (DIMENSIONLESS) –

    [\(α_{2}\)] Coefficient for the effect of minimum concrete cover (see figure 8.3) [\(-\)].

    [\(= 1.0\)] for bars in compression.

    [\(= 1 - 0.15 ⋅ (c_{d} - Ø) / Ø <= 1\)] with a minimum of 0.7 for straight bars in tension.

    [\(= 1 - 0.15 ⋅ (c_{d} - 3 ⋅ Ø) / Ø <= 1\)] with a minimum of 0.7 for bars other than straight in tension (see figure 8.1 (b), (c) and (d)).

    Note: see figure 8.3 for values of [\(c_{d}\)].

  • alpha_3 (DIMENSIONLESS) –

    [\(α_{3}\)] Coefficient for the effect of confinement by transverse reinforcement [\(-\)].

    [\(= 1.0\)] for bars in compression.

    [\(= 1 - K ⋅ λ <= 1\)] with a minimum of 0.7 for bars in tension.

    Where: [\(λ = (ΣA_{st} - ΣA_{st,min}) / A_{s}\)].

    Where: [\(ΣA_{st,min} = A_{s} ⋅ (σ_{sd}/f_{yd})\)]

    With [\(A_{s}\)] = area of one lapped bar [\(mm²\)].

    Note: see figure 8.4 for values of [\(K, A_{s}\)] and [\(A_{st}\)].

  • alpha_5 (DIMENSIONLESS) –

    [\(α_{5}\)] Coefficient for the effect of the pressure transverse to the plane of splitting along the design anchorage length [\(l_{bd}\)] (see 8.6) [\(-\)].

    [\(= 1 - 0.04 ⋅ p <= 1\)] with a minimum of 0.7 for all types of anchorage in compression.

    Where: p = transverse pressure at ultimate limit state along [\(l_{bd}\)] [\(MPa\)].

  • alpha_6 (DIMENSIONLESS) –

    [\(α_{6}\)] Coefficient for the effect of reinforcement ratio [\(-\)].

    [\(= (ρ_{1}/25)^{0.5} <= 1.5\)] with a minimum of 1.0.

    Where: [\(ρ_{1}\)] = reinforcement percentage lapped within [\(0,65 ⋅ l_{0}\)] from the centre of the lap length considered (see figure 8.8) [\(-\)].

    Use your own implementation of this formula or use the :class:SubForm8Dot10Alpha6 class.

  • l_b_rqd (MM) –

    [\(l_{b,rqd}\)] Basic required anchorage length, for anchoring the force [\(A_{s} ⋅ σ_{sd}\)] in a straight bar assuming constant bond stress (formula 8.3) [\(mm\)].

    Use your own implementation for this value or use the :class:Form8Dot3RequiredAnchorageLength class.

  • l_0_min (MM) –

    [\(l_{0,min}\)] Minimum design lap length [\(mm\)].

    [\(= max(0.3 ⋅ α_{6} ⋅ l_{b,rqd}, 15 ⋅ Ø, 200)\)] (formula 8.11).

    Use your own implementation of this formula or use :class:Form8Dot11MinimumDesignLapLength class.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_10.py 
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def __init__(
    self,
    alpha_1: DIMENSIONLESS,
    alpha_2: DIMENSIONLESS,
    alpha_3: DIMENSIONLESS,
    alpha_5: DIMENSIONLESS,
    alpha_6: DIMENSIONLESS,
    l_b_rqd: MM,
    l_0_min: MM,
) -> None:
    r"""[$l_{0}$] Design lap length [$mm$].

    EN 1992-1-1:2004 art.8.7.3(1) - Formula (8.10)

    Parameters
    ----------
    alpha_1 : DIMENSIONLESS
        [$α_{1}$] Coefficient for the effect of the form of the bars assuming adequate cover (see figure 8.1) [$-$].

        [$= 1.0$] for bars in compression.

        [$= 1.0$] for straight bars in tension.

        [$= 1.0$] if [$c_{d} <= 3 ⋅ Ø$] for bars other than straight in tension (see figure 8.1 (b), (c) and (d)).

        [$= 0.7$] if [$c_{d} > 3 ⋅ Ø$] for bars other than straight in tension (see figure 8.1 (b), (c) and (d)).

        Note: see figure 8.3 for values of [$c_{d}$].
    alpha_2 : DIMENSIONLESS
        [$α_{2}$] Coefficient for the effect of minimum concrete cover (see figure 8.3) [$-$].

        [$= 1.0$] for bars in compression.

        [$= 1 - 0.15 ⋅ (c_{d} - Ø) / Ø <= 1$] with a minimum of 0.7 for straight bars in tension.

        [$= 1 - 0.15 ⋅ (c_{d} - 3 ⋅ Ø) / Ø <= 1$] with a minimum of 0.7 for bars other than straight in tension
        (see figure 8.1 (b), (c) and (d)).

        Note: see figure 8.3 for values of [$c_{d}$].
    alpha_3 : DIMENSIONLESS
        [$α_{3}$] Coefficient for the effect of confinement by transverse reinforcement [$-$].

        [$= 1.0$] for bars in compression.

        [$= 1 - K ⋅ λ <= 1$] with a minimum of 0.7 for bars in tension.

        Where: [$λ = (ΣA_{st} - ΣA_{st,min}) / A_{s}$].

        Where: [$ΣA_{st,min} = A_{s} ⋅ (σ_{sd}/f_{yd})$]

        With [$A_{s}$] = area of one lapped bar [$mm²$].

        Note: see figure 8.4 for values of [$K, A_{s}$] and [$A_{st}$].
    alpha_5 : DIMENSIONLESS
        [$α_{5}$] Coefficient for the effect of the pressure transverse to the plane of splitting along the design
        anchorage length [$l_{bd}$] (see 8.6) [$-$].

        [$= 1 - 0.04 ⋅ p <= 1$] with a minimum of 0.7 for all types of anchorage in compression.

        Where: p = transverse pressure at ultimate limit state along [$l_{bd}$] [$MPa$].
    alpha_6 : DIMENSIONLESS
        [$α_{6}$] Coefficient for the effect of reinforcement ratio [$-$].

        [$= (ρ_{1}/25)^{0.5} <= 1.5$] with a minimum of 1.0.

        Where: [$ρ_{1}$] = reinforcement percentage lapped within [$0,65 ⋅ l_{0}$] from the centre of the lap length
        considered (see figure 8.8) [$-$].

        Use your own implementation of this formula or use the :class:`SubForm8Dot10Alpha6` class.
    l_b_rqd : MM
        [$l_{b,rqd}$] Basic required anchorage length, for anchoring the force [$A_{s} ⋅ σ_{sd}$] in a straight bar assuming constant
        bond stress (formula 8.3) [$mm$].

        Use your own implementation for this value or use the :class:`Form8Dot3RequiredAnchorageLength` class.
    l_0_min : MM
        [$l_{0,min}$] Minimum design lap length [$mm$].

        [$= max(0.3 ⋅ α_{6} ⋅ l_{b,rqd}, 15 ⋅ Ø, 200)$] (formula 8.11).

        Use your own implementation of this formula or use :class:`Form8Dot11MinimumDesignLapLength` class.
    """
    super().__init__()
    self.alpha_1 = alpha_1
    self.alpha_2 = alpha_2
    self.alpha_3 = alpha_3
    self.alpha_5 = alpha_5
    self.alpha_6 = alpha_6
    self.l_b_rqd = l_b_rqd
    self.l_0_min = l_0_min

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_10.Form8Dot10DesignLapLength.latex 

latex(n: int = 2) -> LatexFormula

Returns a LatexFormula representation of the formula.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_10.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns a LatexFormula representation of the formula."""
    return LatexFormula(
        return_symbol=r"l_{0}",
        result=f"{self:.{n}f}",
        equation=latex_max_curly_brackets(r"\alpha_1 \cdot \alpha_2 \cdot \alpha_3 \cdot \alpha_5 \cdot \alpha_6 \cdot l_{b,rqd}", r"l_{0,min}"),
        numeric_equation=latex_max_curly_brackets(
            rf"{self.alpha_1:.{n}f} \cdot {self.alpha_2:.{n}f} \cdot {self.alpha_3:.{n}f} \cdot "
            rf"{self.alpha_5:.{n}f} \cdot {self.alpha_6:.{n}f} \cdot {self.l_b_rqd:.{n}f}",
            f"{self.l_0_min:.{n}f}",
        ),
        comparison_operator_label="=",
    )

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_10.SubForm8Dot10Alpha6 

SubForm8Dot10Alpha6(rho_1: DIMENSIONLESS)

Bases: Formula

Class representing the formula for the calculation of the coefficient [\(α_{6}\)].

[\(α_{6}\)] Coefficient for the effect of reinforcement ratio [\(-\)].

EN 1992-1-1:2004 art.8.7.3(1) - Formula (8.8)

Parameters:

  • rho_1 (DIMENSIONLESS) –

    [\(ρ_{1}\)] Reinforcement percentage lapped within [\(0,65 ⋅ l_{0}\)] from the centre of the lap length considered (see figure 8.8) [\(-\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_10.py 
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def __init__(self, rho_1: DIMENSIONLESS) -> None:
    r"""[$α_{6}$] Coefficient for the effect of reinforcement ratio [$-$].

    EN 1992-1-1:2004 art.8.7.3(1) - Formula (8.8)

    Parameters
    ----------
    rho_1 : DIMENSIONLESS
        [$ρ_{1}$] Reinforcement percentage lapped within [$0,65 ⋅ l_{0}$] from the centre of the lap length
        considered (see figure 8.8) [$-$].
    """
    super().__init__()
    self.rho_1 = rho_1

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_10.SubForm8Dot10Alpha6.latex 

latex(n: int = 2) -> LatexFormula

Returns a LatexFormula representation of the formula.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_10.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns a LatexFormula representation of the formula."""
    argument_1_formula = r"\left(\frac{\rho_1}{25}\right)^{0.5}"
    numerical_argument_1 = rf"\left(\frac{{{self.rho_1:.{n}f}}}{{25}}\right)^{{0.5}}"
    return LatexFormula(
        return_symbol=r"\alpha_6",
        result=f"{self:.{n}f}",
        equation=f"{latex_max_curly_brackets(latex_min_curly_brackets(argument_1_formula, '1.5'), '1')}",
        numeric_equation=f"{latex_max_curly_brackets(latex_min_curly_brackets(numerical_argument_1, '1.5'), '1')}",
        comparison_operator_label="=",
    )