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formula_6_9

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_9

Formula 6.9 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_9.Form6Dot9MaximumShearResistance 

Form6Dot9MaximumShearResistance(
    b_w: MM,
    z: MM,
    f_cd: MPA,
    nu_1: DIMENSIONLESS,
    alpha_cw: DIMENSIONLESS,
    theta: DEG,
)

Bases: Formula

Class representing formula 6.9 for the calculation of the maximum shear resistance, \(V_{Rd,max}\).

[\(V_{Rd,max}\)] Maximum shear resistance [\(N\)].

EN 1992-1-1:2004 art.6.2.3(3) - Formula (6.9)

Parameters:

  • b_w (MM) –

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

  • z (MM) –

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

  • f_cd (MPA) –

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

  • nu_1 (DIMENSIONLESS) –

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

  • alpha_cw (DIMENSIONLESS) –

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

  • theta (DEG) –

    [\(\theta\)] Angle between the concrete compression strut 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_9.py 
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def __init__(
    self,
    b_w: MM,
    z: MM,
    f_cd: MPA,
    nu_1: DIMENSIONLESS,
    alpha_cw: DIMENSIONLESS,
    theta: DEG,
) -> None:
    r"""[$V_{Rd,max}$] Maximum shear resistance [$N$].

    EN 1992-1-1:2004 art.6.2.3(3) - Formula (6.9)

    Parameters
    ----------
    b_w : MM
        [$b_{w}$] Width of the web of the beam [$mm$].
    z : MM
        [$z$] Lever arm [$mm$].
    f_cd : MPA
        [$f_{cd}$] Design value of concrete compressive strength [$MPa$].
    nu_1 : DIMENSIONLESS
        [$\nu_{1}$] Strength reduction factor for concrete cracked in shear [-].
    alpha_cw : DIMENSIONLESS
        [$\alpha_{cw}$] Coefficient taking account of the state of the stress in the compression chord [-].
    theta : DEG
        [$\theta$] Angle between the concrete compression strut and the beam axis perpendicular to the shear force [$degrees$].
    """
    super().__init__()
    self.b_w = b_w
    self.z = z
    self.f_cd = f_cd
    self.nu_1 = nu_1
    self.alpha_cw = alpha_cw
    self.theta = theta

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_9.Form6Dot9MaximumShearResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.9.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_9.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.9."""
    return LatexFormula(
        return_symbol=r"V_{Rd,max}",
        result=f"{self:.{n}f}",
        equation=r"\alpha_{cw} \cdot b_{w} \cdot z \cdot \nu_{1} \cdot \frac{f_{cd}}{\cot(\theta) + \tan(\theta)}",
        numeric_equation=rf"{self.alpha_cw:.{n}f} \cdot {self.b_w:.{n}f} \cdot {self.z:.{n}f} \cdot {self.nu_1:.{n}f} \cdot"
        rf" \frac{{{self.f_cd:.{n}f}}}{{\cot({self.theta:.{n}f}) + \tan({self.theta:.{n}f})}}",
        comparison_operator_label="=",
        unit="N",
    )