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formula_8_41

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_41

Formula 8.41 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_41.Form8Dot41InclinationCompressionField 

Form8Dot41InclinationCompressionField(theta: DEG, theta_min: DEG)

Bases: DoubleComparisonFormula

Class representing formula 8.41 for checking inclination of the compression field in the web carrying shear.

Checking inclination of the compression field in the web carrying shear.

FprEN 1992-1-1:2023 art 8.2.3 (4) - Formula (8.41)

Parameters:

  • theta (DEG) –

    [\(\theta\)] Angle compression field [\(degrees\)].

  • theta_min (DEG) –

    [\(\theta_{min}\)] Minimum value of angle compression field [\(degrees\)]. Minimal inclination of the compression field theta_min for shear reinforcement of ductility class B or C. - cot_theta_min = 2.5 (theta = 21.8 deg) for ordinary reinforced members without axial force; - cot_theta_min = 3.0 (theta = 18.4) for members subjected to significant axial compressive force (average axial compressive stress >= |3 MPa| and provided that the depth of the compression chord x determined from a sectional analysis according to 8.1.1 and 8.1.2 is less than 0.25d. Interpolated values between 2.5 and 3.0 may be adopted for intermediate cases. For very high compressive forces (x > 0.25d), (11) can apply; - cot_theta_min = 2.5 - 0.1 * N_Ed / |V_Ed| >= 1.0 for members subjected to axial tension. For shear reinforcement of ductility class A, cot_theta_min shall be reduced by 20%.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_41.py 
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def __init__(self, theta: DEG, theta_min: DEG) -> None:
    r"""Checking inclination of the compression field in the web carrying shear.

    FprEN 1992-1-1:2023 art 8.2.3 (4) - Formula (8.41)

    Parameters
    ----------
    theta : DEG
        [$\theta$] Angle compression field [$degrees$].
    theta_min : DEG
        [$\theta_{min}$] Minimum value of angle compression field [$degrees$].
        Minimal inclination of the compression field theta_min for shear reinforcement of ductility class B or C.
        - cot_theta_min = 2.5 (theta = 21.8 deg) for ordinary reinforced members without axial force;
        - cot_theta_min = 3.0 (theta = 18.4) for members subjected to significant axial compressive force (average
          axial compressive stress >= |3 MPa| and provided that the depth of the compression chord x determined
          from a sectional analysis according to 8.1.1 and 8.1.2 is less than 0.25d. Interpolated values between
          2.5 and 3.0 may be adopted for intermediate cases. For very high compressive forces (x > 0.25d), (11)
          can apply;
        - cot_theta_min = 2.5 - 0.1 * N_Ed / |V_Ed| >= 1.0 for members subjected to axial tension.
        For shear reinforcement of ductility class A, cot_theta_min shall be reduced by 20%.
    """
    super().__init__()
    self.theta = theta
    self.theta_min = theta_min

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_41.Form8Dot41InclinationCompressionField.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 8.41.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_41.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 8.41."""
    _equation: str = r"1 \le \cot \left( \theta \right) \le \cot \left( \theta_{\min} \right)"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"\theta ": f"{self.theta:.{n}f} ",
            r"\theta_{\min} ": f"{self.theta_min:.{n}f} ",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"\theta ": rf"{self.theta:.{n}f} ^\circ",
            r"\theta_{\min} ": rf"{self.theta_min:.{n}f} ^\circ",
        },
        unique_symbol_check=False,
    )
    intermediate_result = rf"1 \le {cot(self.theta):.{n}f} \le {cot(self.theta_min):.{n}f}"

    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if bool(self) else r"\text{Not OK}",
        intermediate_result=intermediate_result,
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"\to",
        unit="",
    )