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formula_6_15

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_15

Formula 6.15 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_15.Form6Dot15ShearReinforcementResistance 

Form6Dot15ShearReinforcementResistance(
    a_sw_max: MM2,
    f_ywd: MPA,
    b_w: MM,
    s: MM,
    alpha_cw: DIMENSIONLESS,
    nu_1: DIMENSIONLESS,
    f_cd: MPA,
    alpha: DEG,
)

Bases: Formula

Class representing formula 6.15 for checking the shear reinforcement resistance.

Check the shear reinforcement resistance.

EN 1992-1-1:2004 art.6.2.3(4) - Formula (6.15)

Parameters:

  • a_sw_max (MM2) –

    [\(A_{sw,max}\)] The cross-sectional area of the shear reinforcement [\(mm^2\)].

  • f_ywd (MPA) –

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

  • b_w (MM) –

    [\(b_{w}\)] Width of the web [\(mm\)].

  • s (MM) –

    [\(s\)] Spacing of the stirrups [\(mm\)].

  • alpha_cw (DIMENSIONLESS) –

    [\(\alpha_{cw}\)] Coefficient taking account of the state of stress in the compression chord [\(-\)].

  • nu_1 (DIMENSIONLESS) –

    [\(\nu_{1}\)] Strength reduction factor for concrete cracked in shear [\(-\)].

  • f_cd (MPA) –

    [\(f_{cd}\)] Design value of concrete compressive strength [\(MPa\)].

  • 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_15.py 
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def __init__(
    self,
    a_sw_max: MM2,
    f_ywd: MPA,
    b_w: MM,
    s: MM,
    alpha_cw: DIMENSIONLESS,
    nu_1: DIMENSIONLESS,
    f_cd: MPA,
    alpha: DEG,
) -> None:
    r"""Check the shear reinforcement resistance.

    EN 1992-1-1:2004 art.6.2.3(4) - Formula (6.15)

    Parameters
    ----------
    a_sw_max : MM2
        [$A_{sw,max}$] The cross-sectional area of the shear reinforcement [$mm^2$].
    f_ywd : MPA
        [$f_{ywd}$] Design yield strength of the shear reinforcement [$MPa$].
    b_w : MM
        [$b_{w}$] Width of the web [$mm$].
    s : MM
        [$s$] Spacing of the stirrups [$mm$].
    alpha_cw : DIMENSIONLESS
        [$\alpha_{cw}$] Coefficient taking account of the state of stress in the compression chord [$-$].
    nu_1 : DIMENSIONLESS
        [$\nu_{1}$] Strength reduction factor for concrete cracked in shear [$-$].
    f_cd : MPA
        [$f_{cd}$] Design value of concrete compressive strength [$MPa$].
    alpha : DEG
        [$\alpha$] Angle between shear reinforcement and the beam axis perpendicular to the shear force [$degrees$].
    """
    super().__init__()
    self.a_sw_max = a_sw_max
    self.f_ywd = f_ywd
    self.b_w = b_w
    self.s = s
    self.alpha_cw = alpha_cw
    self.nu_1 = nu_1
    self.f_cd = f_cd
    self.alpha = alpha

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_15.Form6Dot15ShearReinforcementResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.15.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_15.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.15."""
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if self.__bool__() else "\\text{Not OK}",
        equation=r"\frac{A_{sw,max} \cdot f_{ywd}}{b_{w} \cdot s} \leq \frac{\frac{1}{2} \cdot \alpha_{cw} "
        r"\cdot \nu_{1} \cdot f_{cd}}{\sin(\alpha)}",
        numeric_equation=rf"\frac{{{self.a_sw_max:.{n}f} \cdot {self.f_ywd:.{n}f}}}{{{self.b_w:.{n}f} \cdot "
        rf"{self.s:.{n}f}}} \leq \frac{{\frac{{1}}{{2}} \cdot {self.alpha_cw:.{n}f} \cdot {self.nu_1:.{n}f} "
        rf"\cdot {self.f_cd:.{n}f}}}{{\sin({self.alpha:.{n}f})}}",
        comparison_operator_label="\\to",
        unit="",
    )