Skip to content

formula_8_44

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_44

Formula 8.44 from FprEN-1992-1-1:2023: Chapter 8: Ultimate limit states (ULS).

Classes:

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_44.Form8Dot44StressCompressionField 

Form8Dot44StressCompressionField(
    tau_ed: MPA, theta: DEG, nu: DIMENSIONLESS, f_cd: MPA
)

Bases: Formula

Class representing formula 8.44 for the verification of the compression field stress.

The stress in the compression field in all cross-sections shall be verified according to: [\(\sigma_{cd} = \tau_{Ed}(\cot \theta + \tan \theta) \leq \nu \cdot f_{cd}\)]

Verification of the compression field stress.

FprEN 1992-1-1:2023 art. 8.2.3 - Formula (8.44)

Parameters:

  • tau_ed (MPA) –

    [\(\tau_{Ed}\)] Design value of the shear stress [\(MPa\)].

  • theta (DEG) –

    [\(\theta\)] Inclination angle of the compression strut [\(degrees\)].

  • nu (DIMENSIONLESS) –

    [\(\nu\)] Strength reduction factor for concrete cracked in shear (dimensionless).

  • f_cd (MPA) –

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

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_44.py 
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
def __init__(
    self,
    tau_ed: MPA,
    theta: DEG,
    nu: DIMENSIONLESS,
    f_cd: MPA,
) -> None:
    r"""Verification of the compression field stress.

    FprEN 1992-1-1:2023 art. 8.2.3 - Formula (8.44)

    Parameters
    ----------
    tau_ed : MPA
        [$\tau_{Ed}$] Design value of the shear stress [$MPa$].
    theta : DEG
        [$\theta$] Inclination angle of the compression strut [$degrees$].
    nu : DIMENSIONLESS
        [$\nu$] Strength reduction factor for concrete cracked in shear (dimensionless).
    f_cd : MPA
        [$f_{cd}$] Design value of the compressive strength of concrete [$MPa$].
    """
    super().__init__()
    self.tau_ed = tau_ed
    self.theta = theta
    self.nu = nu
    self.f_cd = f_cd

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_44.Form8Dot44StressCompressionField.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 8.44.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_44.py 
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 8.44."""
    _equation: str = r"\tau_{Ed} \cdot \left( \cot \left( \theta \right) + \tan \left( \theta \right) \right) \leq \nu \cdot f_{cd}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\tau_{Ed}": f"{self.tau_ed:.{n}f}",
            r"\theta": f"{self.theta:.{n}f}",
            r"\nu": f"{self.nu:.{n}f}",
            r"f_{cd}": f"{self.f_cd:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"\tau_{Ed}": rf"{self.tau_ed:.{n}f} \ MPa",
            r"\theta": rf"{self.theta:.{n}f} ^\circ",
            r"\nu": rf"{self.nu:.{n}f}",
            r"f_{cd}": rf"{self.f_cd:.{n}f} \ MPa",
        },
        False,
    )
    intermediate_result = (
        rf"{self._evaluate_pt1(tau_ed=self.tau_ed, theta=self.theta):.{n}f} \leq {self._evaluate_pt2(nu=self.nu, f_cd=self.f_cd):.{n}f}"
    )

    return LatexFormula(
        return_symbol=r"\sigma_{cd}",
        result=f"{self:.{n}f}",
        intermediate_result=intermediate_result,
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"=",
        unit="MPa",
    )