Skip to content

formula_6_8

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_8

Formula 6.8 from EN 1992-1-1:2004: Chapter 6 - Ultimate Limit State.

Classes:

  • Form6Dot8ShearResistance –

    Class representing formula 6.8 for the calculation of the shear resistance, \(V_{Rd,s}\).

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_8.Form6Dot8ShearResistance 

Form6Dot8ShearResistance(a_sw: MM2, s: MM, z: MM, f_ywd: MPA, theta: DEG)

Bases: Formula

Class representing formula 6.8 for the calculation of the shear resistance, \(V_{Rd,s}\).

[\(V_{Rd,s}\)] Shear resistance [\(N\)].

EN 1992-1-1:2004 art.6.2.3(3) - Formula (6.8)

Parameters:

  • a_sw (MM2) –

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

  • s (MM) –

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

  • 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 [\(degrees\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_8.py 
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
def __init__(
    self,
    a_sw: MM2,
    s: MM,
    z: MM,
    f_ywd: MPA,
    theta: DEG,
) -> None:
    r"""[$V_{Rd,s}$] Shear resistance [$N$].

    EN 1992-1-1:2004 art.6.2.3(3) - Formula (6.8)

    Parameters
    ----------
    a_sw : MM2
        [$A_{sw}$] Cross-sectional area of the shear reinforcement [$mm^2$].
    s : MM
        [$s$] Spacing of the stirrups [$mm$].
    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 [$degrees$].
    """
    super().__init__()
    self.a_sw = a_sw
    self.s = s
    self.z = z
    self.f_ywd = f_ywd
    self.theta = theta

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_8.Form6Dot8ShearResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.8.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_8.py 
63
64
65
66
67
68
69
70
71
72
73
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.8."""
    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 \cot(\theta)",
        numeric_equation=rf"\frac{{{self.a_sw:.{n}f}}}{{{self.s:.{n}f}}} \cdot {self.z:.{n}f} \cdot "
        rf"{self.f_ywd:.{n}f} \cdot \cot({self.theta:.{n}f})",
        comparison_operator_label="=",
        unit="N",
    )