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formula_6_64

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_64

Formula 6.64 from EN 1992-1-1:2004: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_64.Form6Dot64BondFactor 

Form6Dot64BondFactor(a_s: MM2, a_p: MM2, xi: DIMENSIONLESS, d_s: MM, d_p: MM)

Bases: Formula

Class representing formula 6.64 for the calculation of [\(\eta\)].

[\(\eta\)] Calculation of [\(\eta\)].

EN 1992-1-1:2004 art.6.8.2(2) - Formula (6.64)

Parameters:

  • a_s (MM2) –

    [\(A_s\)] Area of reinforcing steel [\(mm^2\)].

  • a_p (MM2) –

    [\(A_P\)] Area of prestressing tendon or tendons [\(mm^2\)].

  • xi (DIMENSIONLESS) –

    [\(\xi\)] ratio of bond strength between bonded tendons and ribbed steel in concrete. The value is subject to the relevant European Technical Approval. In the absence of this the values given in Table 6.2 may be used. [-].

  • d_s (MM) –

    [\(⌀_s\)] Largest diameter of reinforcement [\(mm\)].

  • d_p (MM) –

    [\(⌀_P\)] Diameter or equivalent diameter of prestressing steel [\(mm\)]. \(⌀_P = 1.6 \cdot \sqrt{A_P}\) for bundles \(⌀_P = 1.75 \cdot ⌀_wire}\) for single 7 wire strands where \(⌀_wire\) is the wire diameter \(⌀_P = 1.20 \cdot ⌀_wire}\) for single 3 wire strands where \(⌀_wire\) is the wire diameter

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_64.py 
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def __init__(
    self,
    a_s: MM2,
    a_p: MM2,
    xi: DIMENSIONLESS,
    d_s: MM,
    d_p: MM,
) -> None:
    r"""[$\eta$] Calculation of [$\eta$].

    EN 1992-1-1:2004 art.6.8.2(2) - Formula (6.64)

    Parameters
    ----------
    a_s : MM2
        [$A_s$] Area of reinforcing steel [$mm^2$].
    a_p : MM2
        [$A_P$] Area of prestressing tendon or tendons [$mm^2$].
    xi : DIMENSIONLESS
        [$\xi$] ratio of bond strength between bonded tendons and ribbed steel in concrete. The value is subject to the
        relevant European Technical Approval. In the absence of this the values given in Table 6.2 may be used. [-].
    d_s : MM
        [$⌀_s$] Largest diameter of reinforcement [$mm$].
    d_p : MM
        [$⌀_P$] Diameter or equivalent diameter of prestressing steel [$mm$].
        $⌀_P = 1.6 \cdot \sqrt{A_P}$ for bundles
        $⌀_P = 1.75 \cdot ⌀_wire}$ for single 7 wire strands where $⌀_wire$ is the wire diameter
        $⌀_P = 1.20 \cdot ⌀_wire}$ for single 3 wire strands where $⌀_wire$ is the wire diameter
    """
    super().__init__()
    self.a_s = a_s
    self.a_p = a_p
    self.xi = xi
    self.d_s = d_s
    self.d_p = d_p

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_64.Form6Dot64BondFactor.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.64.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_64.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.64."""
    _equation: str = r"\frac{A_s + A_P}{A_s + A_P \cdot \sqrt{\xi \cdot ⌀_s / ⌀_P}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A_s": f"{self.a_s:.{n}f}",
            r"A_P": f"{self.a_p:.{n}f}",
            r"\xi": f"{self.xi:.{n}f}",
            r"⌀_s": f"{self.d_s:.{n}f}",
            r"⌀_P": f"{self.d_p:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\eta",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )