Skip to content

formula_6_25

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_25

Formula 6.25 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_25.Form6Dot25DesignShearResistance 

Form6Dot25DesignShearResistance(
    c: DIMENSIONLESS,
    mu: DIMENSIONLESS,
    f_ctd: MPA,
    sigma_n: MPA,
    a_s: MM2,
    a_i: MM2,
    f_yd: MPA,
    alpha: DEG,
    nu: DIMENSIONLESS,
    f_cd: MPA,
)

Bases: Formula

Class representing formula 6.25 for the calculation of the design shear resistance at the interface, [\(v_{Rdi}\)].

[\(v_{Rdi}\)] Design shear resistance at the interface [\(MPa\)].

EN 1992-1-1:2004 art.6.2.5(1) - Formula (6.25)

Parameters:

  • c (DIMENSIONLESS) –

    [\(c\)] Factor which depends on the roughness of the interface, see (2) [\(-\)].

  • mu (DIMENSIONLESS) –

    [\(\mu\)] Factor which depends on the roughness of the interface, see (2) [\(-\)].

  • f_ctd (MPA) –

    [\(f_{ctd}\)] Design tensile strength of concrete, as defined in 3.1.6 (2)P [\(MPa\)].

  • sigma_n (MPA) –

    [\(\sigma_{n}\)] Stress per unit area caused by the minimum external normal force across the interface [\(MPa\)].

  • a_s (MM2) –

    [\(A_{s}\)] Area of reinforcement crossing the interface [\(mm^2\)].

  • a_i (MM2) –

    [\(A_{i}\)] Area of the joint [\(mm^2\)].

  • f_yd (MPA) –

    [\(f_{yd}\)] Design yield strength of reinforcement [\(MPa\)].

  • alpha (DEG) –

    [\(\alpha\)] Angle of the interface, limited by 45° ≤ α ≤ 90° [\(degrees\)].

  • nu (DIMENSIONLESS) –

    [\(\nu\)] Strength reduction factor [\(-\)].

  • f_cd (MPA) –

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

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_25.py 
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
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
def __init__(
    self,
    c: DIMENSIONLESS,
    mu: DIMENSIONLESS,
    f_ctd: MPA,
    sigma_n: MPA,
    a_s: MM2,
    a_i: MM2,
    f_yd: MPA,
    alpha: DEG,
    nu: DIMENSIONLESS,
    f_cd: MPA,
) -> None:
    r"""[$v_{Rdi}$] Design shear resistance at the interface [$MPa$].

    EN 1992-1-1:2004 art.6.2.5(1) - Formula (6.25)

    Parameters
    ----------
    c : DIMENSIONLESS
        [$c$] Factor which depends on the roughness of the interface, see (2) [$-$].
    mu : DIMENSIONLESS
        [$\mu$] Factor which depends on the roughness of the interface, see (2) [$-$].
    f_ctd : MPA
        [$f_{ctd}$] Design tensile strength of concrete, as defined in 3.1.6 (2)P [$MPa$].
    sigma_n : MPA
        [$\sigma_{n}$] Stress per unit area caused by the minimum external normal force across the interface [$MPa$].
    a_s : MM2
        [$A_{s}$] Area of reinforcement crossing the interface [$mm^2$].
    a_i : MM2
        [$A_{i}$] Area of the joint [$mm^2$].
    f_yd : MPA
        [$f_{yd}$] Design yield strength of reinforcement [$MPa$].
    alpha : DEG
        [$\alpha$] Angle of the interface, limited by 45° ≤ α ≤ 90° [$degrees$].
    nu : DIMENSIONLESS
        [$\nu$] Strength reduction factor [$-$].
    f_cd : MPA
        [$f_{cd}$] Design compressive strength of concrete [$MPa$].
    """
    super().__init__()
    self.c = c
    self.mu = mu
    self.f_ctd = f_ctd
    self.sigma_n = sigma_n
    self.a_s = a_s
    self.a_i = a_i
    self.f_yd = f_yd
    self.alpha = alpha
    self.nu = nu
    self.f_cd = f_cd

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_25.Form6Dot25DesignShearResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.25.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_25.py 
103
104
105
106
107
108
109
110
111
112
113
114
115
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.25."""
    return LatexFormula(
        return_symbol=r"v_{Rdi}",
        result=f"{self:.{n}f}",
        equation=r"\min \left( c \cdot f_{ctd} + \mu \cdot \sigma_{n} + \frac{A_{s}}{A_{i}} \cdot f_{yd} \cdot "
        r"(\mu \cdot \sin(\alpha) + \cos(\alpha)); 0.5 \cdot \nu \cdot f_{cd} \right)",
        numeric_equation=rf"\min \left( {self.c:.{n}f} \cdot {self.f_ctd:.{n}f} + {self.mu:.{n}f} \cdot {self.sigma_n:.{n}f} "
        rf"+ \frac{{{self.a_s:.{n}f}}}{{{self.a_i:.{n}f}}} \cdot {self.f_yd:.{n}f} \cdot ({self.mu:.{n}f} \cdot \sin({self.alpha:.{n}f}) "
        rf"+ \cos({self.alpha:.{n}f})); 0.5 \cdot {self.nu:.{n}f} \cdot {self.f_cd:.{n}f} \right)",
        comparison_operator_label="=",
        unit="MPa",
    )