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formula_6_13

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_13

Formula 6.13 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_13.Form6Dot13ShearResistanceInclinedReinforcement 

Form6Dot13ShearResistanceInclinedReinforcement(
    a_sw: MM2, s: MM, z: MM, f_ywd: MPA, theta: DEG, alpha: DEG
)

Bases: Formula

Class representing formula 6.13 for the calculation of the shear resistance for members with inclined shear reinforcement, [\(V_{Rd,s}\)].

[\(V_{Rd,s}\)] Shear resistance for members with inclined shear reinforcement [\(N\)].

EN 1992-1-1:2004 art.6.2.3(4) - Formula (6.13)

Parameters:

  • a_sw (MM2) –

    [\(A_{sw}\)] Area of shear reinforcement [\(mm^2\)].

  • s (MM) –

    [\(s\)] Spacing of the shear reinforcement [\(mm\)].

  • z (MM) –

    [\(z\)] Lever arm [\(mm\)].

  • f_ywd (MPA) –

    [\(f_{ywd}\)] Design yield strength of the shear reinforcement [\(MPa\)].

  • theta (DEG) –

    [\(\theta\)] angle between the concrete compression strut and the beam axis perpendicular to the shear force [\(degrees\)].

  • alpha (DEG) –

    [\(\alpha\)] angle between shear reinforcement and the beam axis perpendicular to the shear force [\(degrees\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_13.py 
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def __init__(
    self,
    a_sw: MM2,
    s: MM,
    z: MM,
    f_ywd: MPA,
    theta: DEG,
    alpha: DEG,
) -> None:
    r"""[$V_{Rd,s}$] Shear resistance for members with inclined shear reinforcement [$N$].

    EN 1992-1-1:2004 art.6.2.3(4) - Formula (6.13)

    Parameters
    ----------
    a_sw : MM2
        [$A_{sw}$] Area of shear reinforcement [$mm^2$].
    s : MM
        [$s$] Spacing of the shear reinforcement [$mm$].
    z : MM
        [$z$] Lever arm [$mm$].
    f_ywd : MPA
        [$f_{ywd}$] Design yield strength of the shear reinforcement [$MPa$].
    theta : DEG
        [$\theta$] angle between the concrete compression strut and the beam axis perpendicular to the
        shear force [$degrees$].
    alpha : DEG
        [$\alpha$] angle between shear reinforcement and the beam axis perpendicular to the shear force [$degrees$].
    """
    super().__init__()
    self.a_sw = a_sw
    self.s = s
    self.z = z
    self.f_ywd = f_ywd
    self.theta = theta
    self.alpha = alpha

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_13.Form6Dot13ShearResistanceInclinedReinforcement.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.13.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_13.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.13."""
    return LatexFormula(
        return_symbol=r"V_{Rd,s}",
        result=f"{self:.{n}f}",
        equation=r"\frac{A_{sw}}{s} \cdot z \cdot f_{ywd} \cdot \left(\cot(\theta) + \cot(\alpha)\right) \cdot \sin(\alpha)",
        numeric_equation=rf"\frac{{{self.a_sw:.{n}f}}}{{{self.s:.{n}f}}} \cdot {self.z:.{n}f} \cdot {self.f_ywd:.{n}f} \cdot "
        rf"\left(\cot({self.theta:.{n}f}) + \cot({self.alpha:.{n}f})\right) \cdot \sin({self.alpha:.{n}f})",
        comparison_operator_label="=",
        unit="N",
    )