Skip to content

formula_7_19

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_19

Formula 7.19 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_19.Form7Dot19DistributionCoefficient 

Form7Dot19DistributionCoefficient(
    beta: DIMENSIONLESS, sigma_sr: MPA, sigma_s: MPA
)

Bases: Formula

Class representing formula 7.19 for the calculation of [\(\zeta\)].

[\(\zeta\)] Calculation of the distribution coefficient, 0 for uncracked sections [\(\zeta\)].

Note: \(\sigma_{sr} / \sigma_{s}\) may be replaced by \(M_{cr} / M\) for flexure or \(N_{cr} / N\) for pure tension, where \(M_{cr}\) is the cracking moment and \(N_{cr}\) is the cracking force.

EN 1992-1-1:2004 art.7.4.3(3) - Formula (7.19)

Parameters:

  • beta (DIMENSIONLESS) –

    [\(\beta\)] Coefficient taking account of the influence of the duration of the loading or of repeated loading on the average strain. For short-term loading, [\(\beta\)] = 1.0. For sustained loads or many cycles of repeated loading [\(\beta\)] = 0.5 [\(-\)].

  • sigma_sr (MPA) –

    [\(\sigma_{sr}\)] Stress in the tension reinforcement calculated on the basis of a cracked section under the loading conditions causing first cracking [\(MPa\)].

  • sigma_s (MPA) –

    [\(\sigma_{s}\)] Stress in the tension reinforcement calculated on the basis of a cracked section under loading conditions causing first cracking [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_19.py 
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
def __init__(
    self,
    beta: DIMENSIONLESS,
    sigma_sr: MPA,
    sigma_s: MPA,
) -> None:
    r"""[$\zeta$] Calculation of the distribution coefficient, 0 for uncracked sections [$\zeta$].

    Note: $\sigma_{sr} / \sigma_{s}$ may be replaced by $M_{cr} / M$ for flexure or $N_{cr} / N$ for pure tension,
    where $M_{cr}$ is the cracking moment and $N_{cr}$ is the cracking force.

    EN 1992-1-1:2004 art.7.4.3(3) - Formula (7.19)

    Parameters
    ----------
    beta : DIMENSIONLESS
        [$\beta$] Coefficient taking account of the influence of the duration of the loading or of
        repeated loading on the average strain. For short-term loading, [$\beta$] = 1.0. For sustained loads or
        many cycles of repeated loading [$\beta$] = 0.5 [$-$].
    sigma_sr : MPA
        [$\sigma_{sr}$] Stress in the tension reinforcement calculated on the basis of a
        cracked section under the loading conditions causing first cracking [$MPa$].
    sigma_s : MPA
        [$\sigma_{s}$] Stress in the tension reinforcement calculated on the basis of a cracked section under
        loading conditions causing first cracking [$MPa$].
    """
    super().__init__()
    self.beta = beta
    self.sigma_sr = sigma_sr
    self.sigma_s = sigma_s

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_19.Form7Dot19DistributionCoefficient.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 7.19.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_19.py 
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 7.19."""
    _equation: str = r"1 - \beta \left(\frac{\sigma_{sr}}{\sigma_{s}}\right)^2"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\beta": f"{self.beta:.{n}f}",
            r"\sigma_{sr}": f"{self.sigma_sr:.{n}f}",
            r"\sigma_{s}": f"{self.sigma_s:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\zeta",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )