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formula_6_47

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47

Formula 6.47 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_47.Form6Dot47PunchingShearResistance 

Form6Dot47PunchingShearResistance(
    c_rd_c: DIMENSIONLESS,
    k: DIMENSIONLESS,
    rho_l: DIMENSIONLESS,
    f_ck: MPA,
    k_1: DIMENSIONLESS,
    sigma_cp: MPA,
    v_min: MPA,
)

Bases: Formula

Class representing formula 6.47 for the calculation of punching shear resistance, \(v_{Rd,c}\) of slabs and column bases without shear reinforcement.

\(v_{Rd,c}\) Calculation of punching shear resistance of slabs and column bases without shear reinforcement.

EN 1992-1-1:2004 art.6.4.4(1) - Formula (6.47).

The values of \(C_{Rd,c}\), \(v_{min}\), and \(k_1\) 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 \(k_1\) is \(0.1\).

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 [\(MPa\)].

  • k_1 (DIMENSIONLESS) –

    \(k_1\) Coefficient for concrete strength, recommended value 0.1 [-].

  • sigma_cp (MPA) –

    \(\sigma_{cp}\) Stress in the critical section as average of the two perpendicular directions, see equation SubForm6Dot47FactorSigmaCp [\(MPa\)].

  • 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_47.py 
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def __init__(
    self,
    c_rd_c: DIMENSIONLESS,
    k: DIMENSIONLESS,
    rho_l: DIMENSIONLESS,
    f_ck: MPA,
    k_1: DIMENSIONLESS,
    sigma_cp: MPA,
    v_min: MPA,
) -> None:
    r"""$v_{Rd,c}$ Calculation of punching shear resistance of slabs and column bases without shear reinforcement.

    EN 1992-1-1:2004 art.6.4.4(1) - Formula (6.47).

    The values of $C_{Rd,c}$, $v_{min}$, and $k_1$ 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 $k_1$ is $0.1$.

    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 [$MPa$].
    k_1 : DIMENSIONLESS
        $k_1$ Coefficient for concrete strength, recommended value 0.1 [-].
    sigma_cp : MPA
        $\sigma_{cp}$ Stress in the critical section as average of the two perpendicular directions, see
         equation SubForm6Dot47FactorSigmaCp [$MPa$].
    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.k_1 = k_1
    self.sigma_cp = sigma_cp
    self.v_min = v_min

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47.Form6Dot47PunchingShearResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.47.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.47."""
    _equation: str = (
        r"\max \left( C_{Rd,c} \cdot k \cdot (100 \cdot \rho_l \cdot f_{ck})^{1/3} "
        r"+ k_1 \cdot \sigma_{cp}, v_{min} + k_1 \cdot \sigma_{cp} \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"k_1": f"{self.k_1:.{n}f}",
            r"\sigma_{cp}": f"{self.sigma_cp:.{n}f}",
            r"v_{min}": f"{self.v_min:.{n}f}",
            r"k": f"{self.k:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"v_{Rd,c}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="MPa",
    )