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formula_8_42

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_42

Formula 8.42 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_42.Form8Dot42ShearStressResistanceReinforcement 

Form8Dot42ShearStressResistanceReinforcement(
    rho_w: DIMENSIONLESS, f_ywd: MPA, theta: DEG
)

Bases: Formula

Class representing formula 8.42 for the shear stress resistance perpendicular to the longitudinal member axis in case of yielding of the shear reinforcement.

FprEN 1992-1-1:2023 art. 8.2.3 (5) - Formula (8.42)

Formula

[\(\tau_{Rd,sy} = \rho_w \cdot f_{ywd} \cdot \cot \theta\)]

Parameters:

  • rho_w (DIMENSIONLESS) –

    [\(\rho_w\)] Shear reinforcement ratio (dimensionless). Defined in formula (8.42).

  • f_ywd (MPA) –

    [\(f_{ywd}\)] Design yield strength of the shear reinforcement (\(MPa\)).

  • theta (DEG) –

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

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_42.py 
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def __init__(
    self,
    rho_w: DIMENSIONLESS,
    f_ywd: MPA,
    theta: DEG,
) -> None:
    super().__init__()
    self.rho_w = rho_w
    self.f_ywd = f_ywd
    self.theta = theta

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_42.Form8Dot42ShearStressResistanceReinforcement.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.42.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_42.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.42."""
    _equation: str = r"\rho_w \cdot f_{ywd} \cdot \cot \left( \theta \right)"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"\rho_w": f"{self.rho_w:.{n}f}",
            r"f_{ywd}": f"{self.f_ywd:.{n}f}",
            r"\theta": f"{self.theta:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"\rho_w": rf"{self.rho_w:.{n}f}",
            r"f_{ywd}": rf"{self.f_ywd:.{n}f} \ MPa",
            r"\theta": rf"{self.theta:.{n}f} ^\circ",
        },
        unique_symbol_check=True,
    )
    intermediate_result = rf"{self.rho_w:.{n}f} \cdot {self.f_ywd:.{n}f} \cdot {cot(self.theta):.{n}f}"

    return LatexFormula(
        return_symbol=r"\tau_{Rd,sy}",
        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="=",
        unit="MPa",
    )