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formula_6_50

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_50

Formula 6.50 from EN 1992-1-1:2004: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_50.Form6Dot50PunchingStressResistance 

Form6Dot50PunchingStressResistance(
    c_rd_c: DIMENSIONLESS,
    k: DIMENSIONLESS,
    rho_l: DIMENSIONLESS,
    f_ck: MPA,
    d: MM,
    a: MM,
    v_min: MPA,
)

Bases: Formula

Class representing formula 6.50 for the calculation of punching stress resistance [\(v_{Rd}\)] of slabs and column bases without shear reinforcement.

[\(v_{Rd}\)] Calculation of punching stress resistance of slabs and column bases without shear reinforcement.

EN 1992-1-1:2004 art.6.4.4(2) - Formula (6.50)

The values of \(C_{Rd,c}\), \(v_{min}\), and \(k\) for use in a country may be found in its national annex. The recommended value for \(C_{Rd,c}\) is \(0.18 / \gamma_c\), for \(v_{min}\) is given by Expression (6.3N), and that for \(k\) is \(1.0\).

Parameters:

  • c_rd_c (DIMENSIONLESS) –

    \(C_{Rd,c}\) Coefficient for punching shear resistance, recommended value \(0.18 / \gamma_c\) [-].

  • k (DIMENSIONLESS) –

    \(k\) Size effect factor, see equation SubForm6Dot47FactorK [-].

  • rho_l (DIMENSIONLESS) –

    \(\rho_l\) Longitudinal reinforcement ratio, see equation SubForm6Dot47FactorRhoL [-].

  • f_ck (MPA) –

    \(f_{ck}\) Characteristic compressive strength of concrete [\(MPa\)].

  • d (MM) –

    \(d\) Effective depth [\(mm\)].

  • a (MM) –

    \(a\) Distance from the periphery of the column to the control perimeter considered [\(mm\)].

  • v_min (MPA) –

    \(v_{min}\) Minimum shear stress capacity concrete, recommended value with Expression (6.3N) [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_50.py 
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def __init__(
    self,
    c_rd_c: DIMENSIONLESS,
    k: DIMENSIONLESS,
    rho_l: DIMENSIONLESS,
    f_ck: MPA,
    d: MM,
    a: MM,
    v_min: MPA,
) -> None:
    r"""[$v_{Rd}$] Calculation of punching stress resistance of slabs and column bases without shear reinforcement.

    EN 1992-1-1:2004 art.6.4.4(2) - Formula (6.50)

    The values of $C_{Rd,c}$, $v_{min}$, and $k$ for use in a country may be found in its national annex.
    The recommended value for $C_{Rd,c}$ is $0.18 / \gamma_c$, for $v_{min}$ is given by Expression (6.3N),
    and that for $k$ is $1.0$.

    Parameters
    ----------
    c_rd_c : DIMENSIONLESS
        $C_{Rd,c}$ Coefficient for punching shear resistance, recommended value $0.18 / \gamma_c$ [-].
    k : DIMENSIONLESS
        $k$ Size effect factor, see equation SubForm6Dot47FactorK [-].
    rho_l : DIMENSIONLESS
        $\rho_l$ Longitudinal reinforcement ratio, see equation SubForm6Dot47FactorRhoL [-].
    f_ck : MPA
        $f_{ck}$ Characteristic compressive strength of concrete [$MPa$].
    d : MM
        $d$ Effective depth [$mm$].
    a : MM
        $a$ Distance from the periphery of the column to the control perimeter considered [$mm$].
    v_min : MPA
        $v_{min}$ Minimum shear stress capacity concrete, recommended value with Expression (6.3N) [$MPa$].
    """
    super().__init__()
    self.c_rd_c = c_rd_c
    self.k = k
    self.rho_l = rho_l
    self.f_ck = f_ck
    self.d = d
    self.a = a
    self.v_min = v_min

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_50.Form6Dot50PunchingStressResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.50.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_50.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.50."""
    _equation: str = (
        r"\max \left( C_{Rd,c} \cdot k \cdot \left( 100 \cdot \rho_l \cdot f_{ck} \right)^{\frac{1}{3}} "
        r"\cdot \frac{2 \cdot d}{a}, v_{min} \cdot \frac{2 \cdot d}{a} \right)"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"C_{Rd,c}": f"{self.c_rd_c:.{n}f}",
            r"\rho_l": f"{self.rho_l:.{n}f}",
            r"f_{ck}": f"{self.f_ck:.{n}f}",
            r" d": f" {self.d:.{n}f}",
            r"{a": "{" + f"{self.a:.{n}f}",
            r"v_{min}": f"{self.v_min:.{n}f}",
            r"k": f"{self.k:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"C_{Rd,c}": rf"{self.c_rd_c:.3f}",
            r"\rho_l": rf"{self.rho_l:.3f}",
            r"f_{ck}": rf"{self.f_ck:.3f} \ MPa",
            r" d": rf" {self.d:.3f} \ mm",
            r"{a": "{" + rf"{self.a:.3f} \ mm",
            r"v_{min}": rf"{self.v_min:.3f} \ MPa",
            r"k": rf"{self.k:.3f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"v_{Rd}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="MPa",
    )