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formula_7_9

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_9

Formula 7.9 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_9.Form7Dot9EpsilonSmMinusEpsilonCm 

Form7Dot9EpsilonSmMinusEpsilonCm(
    sigma_s: MPA,
    k_t: DIMENSIONLESS,
    f_ct_eff: MPA,
    rho_p_eff: DIMENSIONLESS,
    e_s: MPA,
    e_cm: MPA,
)

Bases: Formula

Class representing formula 7.9 for the calculation of [\(\epsilon_{sm} - \epsilon_{cm}\)].

[\(\epsilon_{sm} - \epsilon_{cm}\)] Calculation of the strain difference [\(\epsilon\)].

EN 1992-1-1:2004 art.7.3.4(2) - Formula (7.9)

Parameters:

  • sigma_s (MPA) –

    [\(\sigma_s\)] Stress in the reinforcement [\(MPa\)].

  • k_t (DIMENSIONLESS) –

    [\(k_t\)] Factor dependent on the duration of the load, 0.6 for short term loading, 0.4 for long term loading [\(-\)].

  • f_ct_eff (MPA) –

    [\(f_{ct,eff}\)] Effective tensile strength of concrete [\(MPa\)].

  • rho_p_eff (DIMENSIONLESS) –

    [\(\rho_{p,eff}\)] Effective reinforcement ratio, see equation 7.10 [\(-\)].

  • e_s (MPA) –

    [\(e_s\)] Modulus of elasticity of reinforcement [\(MPa\)].

  • e_cm (MPA) –

    [\(e_{cm}\)] Modulus of elasticity of concrete [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_9.py 
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def __init__(
    self,
    sigma_s: MPA,
    k_t: DIMENSIONLESS,
    f_ct_eff: MPA,
    rho_p_eff: DIMENSIONLESS,
    e_s: MPA,
    e_cm: MPA,
) -> None:
    r"""[$\epsilon_{sm} - \epsilon_{cm}$] Calculation of the strain difference [$\epsilon$].

    EN 1992-1-1:2004 art.7.3.4(2) - Formula (7.9)

    Parameters
    ----------
    sigma_s : MPA
        [$\sigma_s$] Stress in the reinforcement [$MPa$].
    k_t : DIMENSIONLESS
        [$k_t$] Factor dependent on the duration of the load, 0.6 for short term loading, 0.4 for long term loading [$-$].
    f_ct_eff : MPA
        [$f_{ct,eff}$] Effective tensile strength of concrete [$MPa$].
    rho_p_eff : DIMENSIONLESS
        [$\rho_{p,eff}$] Effective reinforcement ratio, see equation 7.10 [$-$].
    e_s : MPA
        [$e_s$] Modulus of elasticity of reinforcement [$MPa$].
    e_cm : MPA
        [$e_{cm}$] Modulus of elasticity of concrete [$MPa$].
    """
    super().__init__()
    self.sigma_s = sigma_s
    self.k_t = k_t
    self.f_ct_eff = f_ct_eff
    self.rho_p_eff = rho_p_eff
    self.e_s = e_s
    self.e_cm = e_cm
    self.alpha_e = e_s / e_cm

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_9.Form7Dot9EpsilonSmMinusEpsilonCm.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 7.9.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_9.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 7.9."""
    _equation: str = (
        r"\max\left("
        r"\frac{\sigma_s - k_t \cdot \frac{f_{ct,eff}}{\rho_{p,eff}} \cdot \left(1 + \frac{E_s}{E_{cm}} \cdot \rho_{p,eff}\right)}{E_s}; "
        r"\frac{0.6 \cdot \sigma_s}{E_s}"
        r"\right)"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\sigma_s": f"{self.sigma_s:.{n}f}",
            r"k_t": f"{self.k_t:.{n}f}",
            r"f_{ct,eff}": f"{self.f_ct_eff:.{n}f}",
            r"\rho_{p,eff}": f"{self.rho_p_eff:.{n}f}",
            r"E_s": f"{self.e_s:.{n}f}",
            r"E_{cm}": f"{self.e_cm:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\epsilon_{sm} - \epsilon_{cm}",
        result=f"{self:.6f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )