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formula_7_2

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_2

Formula 7.2 and 7.2sub1 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_2.Form7Dot2StressDistributionCoefficient 

Form7Dot2StressDistributionCoefficient(
    sigma_c: MPA, k_1: DIMENSIONLESS, h: MM, f_ct_eff: MPA
)

Bases: Formula

Class representing formula 7.2 for the calculation of [\(k_c\)].

[\(k_c\)] Calculation of the coefficient for stress distribution for bending or bending combined with axial forces.

EN 1992-1-1:2004 art.7.3.2(2) - Formula (7.2)

Parameters:

  • sigma_c (MPA) –

    [\(\sigma_c\)] Compressive stress in the concrete, according to 7.4 [\(MPa\)].

  • k_1 (DIMENSIONLESS) –

    [\(k_1\)] Coefficient considering the effects of axial forces on the stress distribution, according to 7.2sub1 [\(-\)].

  • h (MM) –

    [\(h\)] Overall depth of the section [\(mm\)].

  • f_ct_eff (MPA) –

    [\(f_{ct,eff}\)] Mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_2.py 
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def __init__(
    self,
    sigma_c: MPA,
    k_1: DIMENSIONLESS,
    h: MM,
    f_ct_eff: MPA,
) -> None:
    r"""[$k_c$] Calculation of the coefficient for stress distribution for bending or bending combined with axial forces.

    EN 1992-1-1:2004 art.7.3.2(2) - Formula (7.2)

    Parameters
    ----------
    sigma_c : MPA
        [$\sigma_c$] Compressive stress in the concrete, according to 7.4 [$MPa$].
    k_1 : DIMENSIONLESS
        [$k_1$] Coefficient considering the effects of axial forces on the stress distribution, according to 7.2sub1 [$-$].
    h : MM
        [$h$] Overall depth of the section [$mm$].
    f_ct_eff : MPA
        [$f_{ct,eff}$] Mean value of the tensile strength of the concrete effective at the time when the
        cracks may first be expected to occur [$MPa$].
    """
    super().__init__()
    self.sigma_c = sigma_c
    self.k_1 = k_1
    self.h = h
    self.f_ct_eff = f_ct_eff

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_2.Form7Dot2StressDistributionCoefficient.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 7.2.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_2.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 7.2."""
    _equation: str = (
        r"min\left(0.4 \cdot \left(1 - \frac{\sigma_c}{k_1 \cdot \left(\frac{ h}{min( h, 1000)}\right) \cdot f_{ct,eff}}\right), 1\right)"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\sigma_c": f"{self.sigma_c:.{n}f}",
            r"k_1": f"{self.k_1:.{n}f}",
            r" h": f" {self.h:.{n}f}",
            r"f_{ct,eff}": f"{self.f_ct_eff:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"k_c",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_2.Form7Dot2Sub1AxialForceCoefficient 

Form7Dot2Sub1AxialForceCoefficient(n_ed: MPA, h: MM)

Bases: Formula

Class representing formula 7.2sub1 for the calculation of [\(k_1\)] factor.

[\(k_1\)] Calculation of the coefficient for stress distribution for bending or bending combined with axial forces.

EN 1992-1-1:2004 art.7.3.2(2) - Formula (7.2sub1)

Parameters:

  • n_ed (MPA) –

    [\(N_{Ed}\)] Axial force at the serviceability limit state acting on the part of the cross-section under consideration (compressive force positive). [\(N_{Ed}\)] should be determined considering the characteristic values of prestress and axial forces under the relevant combination of actions.

  • h (MM) –

    [\(h\)] Overall depth of the section [\(mm\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_2.py 
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def __init__(
    self,
    n_ed: MPA,
    h: MM,
) -> None:
    r"""[$k_1$] Calculation of the coefficient for stress distribution for bending or bending combined with axial forces.

    EN 1992-1-1:2004 art.7.3.2(2) - Formula (7.2sub1)

    Parameters
    ----------
    n_ed : MPA
        [$N_{Ed}$] Axial force at the serviceability limit state acting on the part of the cross-section
        under consideration (compressive force positive). [$N_{Ed}$] should be determined considering the characteristic
        values of prestress and axial forces under the relevant combination of actions.
    h : MM
        [$h$] Overall depth of the section [$mm$].
    """
    super().__init__()
    self.n_ed = n_ed
    self.h = h

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_2.Form7Dot2Sub1AxialForceCoefficient.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 7.2sub1.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_2.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 7.2sub1."""
    _equation: str = r"\begin{cases} 1.5 & \text{if } N_{Ed} > 0 \\ \frac{2 \cdot min(h, 1000)}{3 \cdot h} & \text{if } N_{Ed} \le 0 \end{cases}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            "N_{Ed}": f"{self.n_ed:.{n}f}",
            "h": f"{self.h:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"k_1",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )