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formula_6_2

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_2

Formula 6.2a 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_2.Form6Dot2ShearResistance 

Form6Dot2ShearResistance(
    c_rd_c: DIMENSIONLESS,
    k: DIMENSIONLESS,
    rho_l: DIMENSIONLESS,
    f_ck: MPA,
    k_1: DIMENSIONLESS,
    sigma_cp: MPA,
    b_w: MM,
    d: MM,
    v_min: N,
)

Bases: Formula

Class representing formula 6.2a for the calculation of the design value for the shear resistance, [\(V_{Rd,c}\)].

[\(V_{Rd,c}\)] Design value for the shear resistance [\(kN\)].

EN 1992-1-1:2004 art.6.2.2(1) - Formula (6.2a)

Parameters:

  • c_rd_c (DIMENSIONLESS) –

    [\(C_{Rd,c}\)] Coefficient for shear strength [\(-\)].

  • k (DIMENSIONLESS) –

    [\(k\)] Size effect factor [\(-\)].

  • rho_l (DIMENSIONLESS) –

    [\(\rho_l\)] Longitudinal reinforcement ratio [\(-\)].

  • f_ck (MPA) –

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

  • k_1 (DIMENSIONLESS) –

    [\(k_1\)] Coefficient for concrete [\(-\)].

  • sigma_cp (MPA) –

    [\(\sigma_{cp}\)] Compressive stress in the concrete [\(MPa\)].

  • b_w (MM) –

    [\(b_w\)] Width of the web [\(mm\)].

  • d (MM) –

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

  • v_min (N) –

    [\(v_{min}\)] shear capacity without rebar [\(N\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_2.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,
    b_w: MM,
    d: MM,
    v_min: N,
) -> None:
    r"""[$V_{Rd,c}$] Design value for the shear resistance [$kN$].

    EN 1992-1-1:2004 art.6.2.2(1) - Formula (6.2a)

    Parameters
    ----------
    c_rd_c : DIMENSIONLESS
        [$C_{Rd,c}$] Coefficient for shear strength [$-$].
    k : DIMENSIONLESS
        [$k$] Size effect factor [$-$].
    rho_l : DIMENSIONLESS
        [$\rho_l$] Longitudinal reinforcement ratio [$-$].
    f_ck : MPA
        [$f_{ck}$] Characteristic compressive strength of concrete [$MPa$].
    k_1 : DIMENSIONLESS
        [$k_1$] Coefficient for concrete [$-$].
    sigma_cp : MPA
        [$\sigma_{cp}$] Compressive stress in the concrete [$MPa$].
    b_w : MM
        [$b_w$] Width of the web [$mm$].
    d : MM
        [$d$] Effective depth [$mm$].
    v_min : N
        [$v_{min}$] shear capacity without rebar [$N$].
    """
    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.b_w = b_w
    self.d = d
    self.v_min = v_min

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_2.Form6Dot2ShearResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.2.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_2.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.2."""
    return LatexFormula(
        return_symbol=r"V_{Rd,c}",
        result=f"{self:.{n}f}",
        equation=r"\max(C_{Rd,c} \cdot k \cdot \left(100 \cdot \rho_l \cdot f_{ck}\right)^{1/3} + k_1 \cdot "
        r"\sigma_{cp}, v_{min} + k_1 \cdot \sigma_{cp}) \cdot b_w \cdot d",
        numeric_equation=rf"\max({self.c_rd_c:.{n}f} \cdot {self.k:.{n}f} \cdot \left(100 \cdot {self.rho_l:.{n}f} "
        rf"\cdot {self.f_ck:.{n}f}\right)^{{1/3}} + {self.k_1:.{n}f} \cdot {self.sigma_cp:.{n}f}, {self.v_min:.{n}f} + "
        rf"{self.k_1:.{n}f} \cdot {self.sigma_cp:.{n}f}) \cdot {self.b_w:.{n}f} \cdot {self.d:.{n}f}",
        comparison_operator_label="=",
        unit="N",
    )

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_2.Form6Dot2aSub1ThicknessFactor 

Form6Dot2aSub1ThicknessFactor(d: MM)

Bases: Formula

Class representing formula 6.2a for k, the thickness factor, [\(k\)].

[\(k\)] factor to take thickness into account [\(kN\)].

EN 1992-1-1:2004 art.6.2.2(1) - Formula (6.2a)

Parameters:

  • d (MM) –

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

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_2.py 
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def __init__(
    self,
    d: MM,
) -> None:
    r"""[$k$] factor to take thickness into account [$kN$].

    EN 1992-1-1:2004 art.6.2.2(1) - Formula (6.2a)

    Parameters
    ----------
    d : MM
        [$d$] Effective depth [$mm$].
    """
    super().__init__()
    self.d = d

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_2.Form6Dot2aSub1ThicknessFactor.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.2a Sub 1.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_2.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.2a Sub 1."""
    return LatexFormula(
        return_symbol=r"k",
        result=f"{self:.{n}f}",
        equation=r"\min(1 + \sqrt{\frac{200}{d}}, 2.0)",
        numeric_equation=rf"\min(1 + \sqrt{{\frac{{200}}{{{self.d:.{n}f}}}}}, 2.0)",
        comparison_operator_label="=",
        unit="-",
    )

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_2.Form6Dot2aSub2RebarRatio 

Form6Dot2aSub2RebarRatio(a_sl: MM2, b_w: MM, d: MM)

Bases: Formula

Class representing formula 6.2a for the tensile rebar ratio, [\(\rho_l\)].

[\(\rho_l\)] Tensile rebar ratio [\(-\)].

EN 1992-1-1:2004 art.6.2.2(1) - Formula (6.2a)

Parameters:

  • a_sl (MM2) –

    [\(A_{sl}\)] Area of tensile reinforcement [\(mm^2\)].

  • b_w (MM) –

    [\(b_w\)] Width of the web [\(mm\)].

  • d (MM) –

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

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_2.py 
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def __init__(
    self,
    a_sl: MM2,
    b_w: MM,
    d: MM,
) -> None:
    r"""[$\rho_l$] Tensile rebar ratio [$-$].

    EN 1992-1-1:2004 art.6.2.2(1) - Formula (6.2a)

    Parameters
    ----------
    a_sl : MM2
        [$A_{sl}$] Area of tensile reinforcement [$mm^2$].
    b_w : MM
        [$b_w$] Width of the web [$mm$].
    d : MM
        [$d$] Effective depth [$mm$].
    """
    super().__init__()
    self.A_sl = a_sl
    self.b_w = b_w
    self.d = d

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_2.Form6Dot2aSub2RebarRatio.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.2a Sub 2.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_2.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.2a Sub 2."""
    return LatexFormula(
        return_symbol=r"\rho_l",
        result=f"{self:.{n}f}",
        equation=r"\min( \frac{A_{sl}}{b_w \cdot d}, 0.02)",
        numeric_equation=rf"\min( \frac{{{self.A_sl:.{n}f}}}{{{self.b_w:.{n}f} \cdot {self.d:.{n}f}}}, 0.02)",
        comparison_operator_label="=",
        unit="-",
    )