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formula_7_11

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_11

Formula 7.11 from EN 1992-1-1:2004: Chapter 7 - Serviceability Limit State.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_11.Form7Dot11MaximumCrackSpacing 

Form7Dot11MaximumCrackSpacing(
    k_3: DIMENSIONLESS,
    c: MM,
    k_1: DIMENSIONLESS,
    k_2: DIMENSIONLESS,
    k_4: DIMENSIONLESS,
    diam: MM,
    rho_p_eff: DIMENSIONLESS,
)

Bases: Formula

Class representing formula 7.11 for the calculation of [\(s_{r,max}\)].

[\(s_{r,max}\)] Calculation of the maximum crack spacing [\(mm\)].

EN 1992-1-1:2004 art.7.3.4(3) - Formula (7.11)

Parameters:

  • k_3 (DIMENSIONLESS) –

    [\(k_3\)] Coefficient, the recommended value is 3.4 [\(-\)].

  • c (MM) –

    [\(c\)] Cover to the longitudinal reinforcement [\(mm\)].

  • k_1 (DIMENSIONLESS) –

    [\(k_1\)] Coefficient which takes account of the bond properties of the bonded reinforcement. Use 0.8 for high bond bars and 1.6 for bars with an effectively plain surface (e.g. prestressing tendons) [\(-\)].

  • k_2 (DIMENSIONLESS) –

    [\(k_2\)] Coefficient which takes account of the distribution of strain. Use 0.5 for bending, 1.0 for pure tension. For cases of eccentric tension or for local areas, intermediate values of k2 should be used which may be calculated with equation (7.13) [\(-\)] .

  • k_4 (DIMENSIONLESS) –

    [\(k_4\)] Coefficient, the recommended value is 0.425 [\(-\)].

  • diam (MM) –

    [\(diam\)] Bar diameter [\(mm\)]. Where a mixture of bar diameters is used in a section, an equivalent diameter, \(⌀_{eq}\), should be used. For a section with \(n_1\) bars of diameter \(⌀_1\) and \(n_2\) bars of diameter \(⌀_2\), expression (7.12) should be used to calculate \(⌀_{eq}\).

  • rho_p_eff (DIMENSIONLESS) –

    [\(\rho_{p,eff}\)] Effective reinforcement ratio [\(-\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_11.py 
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def __init__(
    self,
    k_3: DIMENSIONLESS,
    c: MM,
    k_1: DIMENSIONLESS,
    k_2: DIMENSIONLESS,
    k_4: DIMENSIONLESS,
    diam: MM,
    rho_p_eff: DIMENSIONLESS,
) -> None:
    r"""[$s_{r,max}$] Calculation of the maximum crack spacing [$mm$].

    EN 1992-1-1:2004 art.7.3.4(3) - Formula (7.11)

    Parameters
    ----------
    k_3 : DIMENSIONLESS
        [$k_3$] Coefficient, the recommended value is 3.4 [$-$].
    c : MM
        [$c$] Cover to the longitudinal reinforcement [$mm$].
    k_1 : DIMENSIONLESS
        [$k_1$] Coefficient which takes account of the bond properties of the bonded reinforcement.
        Use 0.8 for high bond bars and 1.6 for bars with an effectively plain surface
        (e.g. prestressing tendons) [$-$].
    k_2 : DIMENSIONLESS
        [$k_2$] Coefficient which takes account of the distribution of strain.
        Use 0.5 for bending, 1.0 for pure tension. For cases of eccentric tension or for local areas,
        intermediate values of k2 should be used which may be calculated with equation (7.13) [$-$] .
    k_4 : DIMENSIONLESS
        [$k_4$] Coefficient, the recommended value is 0.425 [$-$].
    diam : MM
        [$diam$] Bar diameter [$mm$]. Where a mixture of bar diameters is used in a section, an
        equivalent diameter, $⌀_{eq}$, should be used. For a section with $n_1$ bars of diameter $⌀_1$
        and $n_2$ bars of diameter $⌀_2$, expression (7.12) should be used to calculate $⌀_{eq}$.
    rho_p_eff : DIMENSIONLESS
        [$\rho_{p,eff}$] Effective reinforcement ratio [$-$].
    """
    super().__init__()
    self.k_3 = k_3
    self.c = c
    self.k_1 = k_1
    self.k_2 = k_2
    self.k_4 = k_4
    self.diam = diam
    self.rho_p_eff = rho_p_eff

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_11.Form7Dot11MaximumCrackSpacing.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 7.11.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_11.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 7.11."""
    _equation: str = r"k_3 \cdot c + k_1 \cdot k_2 \cdot k_4 \cdot \frac{⌀}{\rho_{p,eff}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"k_3": f"{self.k_3:.{n}f}",
            r"c ": f"{self.c:.{n}f} ",
            r"k_1": f"{self.k_1:.{n}f}",
            r"k_2": f"{self.k_2:.{n}f}",
            r"k_4": f"{self.k_4:.{n}f}",
            r"⌀": f"{self.diam:.{n}f}",
            r"\rho_{p,eff}": f"{self.rho_p_eff:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"s_{r,max}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm",
    )