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formula_7_21

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_21

Formula 7.21 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_21.Form7Dot21CurvatureDueToShrinkage 

Form7Dot21CurvatureDueToShrinkage(
    epsilon_cs: DIMENSIONLESS,
    es: MPA,
    ec_eff: MPA,
    capital_s: MM3,
    capital_i: MM4,
)

Bases: Formula

Class representing formula 7.21 for the calculation of [\(\frac{1}{r_{cs}}\)].

[\(\frac{1}{r_{cs}}\)] Calculation of the curvature due to shrinkage [\(mm^{-1}\)].

S and i should be calculated for the uncracked condition and the fully cracked condition, the final curvature being assessed by use of Expression (7.18).

EN 1992-1-1:2004 art.7.4.3(6) - Formula (7.21)

Parameters:

  • epsilon_cs (DIMENSIONLESS) –

    [\(\epsilon_{cs}\)] Free shrinkage strain, see 3.1.4.

  • es (MPA) –

    [\(E_s\)] Modulus of elasticity of the reinforcement [\(MPa\)].

  • ec_eff (MPA) –

    [\(E_{c,eff}\)] Effective modulus of elasticity of the concrete [\(MPa\)].

  • capital_s (MM3) –

    [\(S\)] First moment of area of the reinforcement about the centroid of the section [\(mm^3\)].

  • capital_i (MM4) –

    [\(I\)] Second moment of area of the section [\(mm^4\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_21.py 
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def __init__(
    self,
    epsilon_cs: DIMENSIONLESS,
    es: MPA,
    ec_eff: MPA,
    capital_s: MM3,
    capital_i: MM4,
) -> None:
    r"""[$\frac{1}{r_{cs}}$] Calculation of the curvature due to shrinkage [$mm^{-1}$].

    S and i should be calculated for the uncracked condition and the fully cracked condition, the
    final curvature being assessed by use of Expression (7.18).

    EN 1992-1-1:2004 art.7.4.3(6) - Formula (7.21)

    Parameters
    ----------
    epsilon_cs : DIMENSIONLESS
        [$\epsilon_{cs}$] Free shrinkage strain, see 3.1.4.
    es : MPA
        [$E_s$] Modulus of elasticity of the reinforcement [$MPa$].
    ec_eff : MPA
        [$E_{c,eff}$] Effective modulus of elasticity of the concrete [$MPa$].
    capital_s : MM3
        [$S$] First moment of area of the reinforcement about the centroid of the section [$mm^3$].
    capital_i : MM4
        [$I$] Second moment of area of the section [$mm^4$].
    """
    super().__init__()
    self.epsilon_cs = epsilon_cs
    self.es = es
    self.ec_eff = ec_eff
    self.capital_s = capital_s
    self.capital_i = capital_i

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_21.Form7Dot21CurvatureDueToShrinkage.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 7.21.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_21.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 7.21."""
    _equation: str = r"\epsilon_{cs} \cdot \frac{E_s}{E_{c,eff}} \cdot \frac{S}{I}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\epsilon_{cs}": f"{self.epsilon_cs:.{n + 1}f}",
            r"E_s": f"{self.es:.{n}f}",
            r"E_{c,eff}": f"{self.ec_eff:.{n}f}",
            r"S": f"{self.capital_s:.{n}f}",
            r"I": f"{self.capital_i:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\frac{1}{r_{cs}}",
        result=f"{self:.{n + 3}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^{-1}",
    )