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formula_9_11

codes.eurocode.en_1992_1_1_2004.chapter_9_detailling_and_specific_rules.formula_9_11

Formula 9.11 from EN 1992-1-1:2004: Chapter 9 - Detailing and specific rules.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_9_detailling_and_specific_rules.formula_9_11.Form9Dot11MinimumShearReinforcement 

Form9Dot11MinimumShearReinforcement(
    alpha: DEG, s_r: MM, s_t: MM, f_ck: MPA, f_yk: MPA
)

Bases: Formula

Class representing the formula 9.11 for the calculation of the minimum shear reinforcement.

[\(\(A_{sw,min}\)\)] Minimum shear reinforcement [\(\(mm^2\)\)].

The spirit of the equation is to calculate the shear reinforcement area. The formula is converted such that it actually does that, as opposed to the presentation in the Eurocode which only checks if the area is sufficient with a boolean result.

EN 1992-1-1:2004 art.9.4.3(2) - Formula (9.11)

Parameters:

  • alpha (DEG) –

    [\(\(\alpha\)\)] Angle between the shear reinforcement and the main steel [\(\(^\circ\)\)].

  • s_r (MM) –

    [\(\(s_r\)\)] Spacing of shear links in the radial direction [\(\(mm\)\)].

  • s_t (MM) –

    [\(\(s_t\)\)] Spacing of shear links in the tangential direction [\(\(mm\)\)].

  • f_ck (MPA) –

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

  • f_yk (MPA) –

    [\(\(f_{yk}\)\)] Characteristic yield strength of reinforcement [\(\(MPa\)\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_9_detailling_and_specific_rules/formula_9_11.py 
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def __init__(
    self,
    alpha: DEG,
    s_r: MM,
    s_t: MM,
    f_ck: MPA,
    f_yk: MPA,
) -> None:
    r"""[$$A_{sw,min}$$] Minimum shear reinforcement [$$mm^2$$].

    The spirit of the equation is to calculate the shear reinforcement area. The formula is converted such that
    it actually does that, as opposed to the presentation in the Eurocode which only checks if the area is sufficient
    with a boolean result.

    EN 1992-1-1:2004 art.9.4.3(2) - Formula (9.11)

    Parameters
    ----------
    alpha : DEG
        [$$\alpha$$] Angle between the shear reinforcement and the main steel [$$^\circ$$].
    s_r : MM
        [$$s_r$$] Spacing of shear links in the radial direction [$$mm$$].
    s_t : MM
        [$$s_t$$] Spacing of shear links in the tangential direction [$$mm$$].
    f_ck : MPA
        [$$f_{ck}$$] Characteristic compressive strength of concrete [$$MPa$$].
    f_yk : MPA
        [$$f_{yk}$$] Characteristic yield strength of reinforcement [$$MPa$$].
    """
    super().__init__()
    self.alpha = alpha
    self.s_r = s_r
    self.s_t = s_t
    self.f_ck = f_ck
    self.f_yk = f_yk

codes.eurocode.en_1992_1_1_2004.chapter_9_detailling_and_specific_rules.formula_9_11.Form9Dot11MinimumShearReinforcement.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 9.11.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_9_detailling_and_specific_rules/formula_9_11.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 9.11."""
    _equation: str = (
        r"\frac{0.08 \cdot \sqrt{f_{ck}}}{f_{yk}} \cdot \frac{s_r \cdot s_t}{1.5 \cdot "
        r"\sin(\alpha) + \cos(\alpha)}"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\alpha": f"{self.alpha:.{n}f}",
            "s_r": f"{self.s_r:.{n}f}",
            "s_t": f"{self.s_t:.{n}f}",
            "f_{ck}": f"{self.f_ck:.{n}f}",
            "f_{yk}": f"{self.f_yk:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"A_{sw,min}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )