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formula_8_35

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_35

Formula 8.35 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_35.Form8Dot35MaximumShearStressResistance 

Form8Dot35MaximumShearStressResistance(tau_rdc_0: MPA, a_cs_0: MM, d: MM)

Bases: Formula

Class representing formula 8.35 for the calculation of the upper bound of the shear stress resistance used in Formula (8.32).

[\(\tau_{Rdc,max}\)] Maximum shear stress resistance [\(MPa\)].

FprEN 1992-1-1:2023 (E) art 8.2.2 (5) - Formula (8.35)

The printed upper bound of [\(2.7 \cdot \tau_{Rdc,0}\)] is implemented as a minimum.

Parameters:

  • tau_rdc_0 (MPA) –

    [\(\tau_{Rdc,0}\)] Design value of the shear stress resistance without the effect of compressive normal forces according to Formula (8.33), see Form8Dot33ShearStressResistanceWithoutAxialForce [\(MPa\)].

  • a_cs_0 (MM) –

    [\(a_{cs,0}\)] Effective shear span determined according to Formula (8.30), without considering in [\(M_{Ed}\)] and [\(V_{Ed}\)] the effect of prestressing or external load that produces the compressive axial force [\(mm\)].

  • d (MM) –

    [\(d\)] Effective depth [\(mm\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_35.py 
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def __init__(self, tau_rdc_0: MPA, a_cs_0: MM, d: MM) -> None:
    r"""[$\tau_{Rdc,max}$] Maximum shear stress resistance [$MPa$].

    FprEN 1992-1-1:2023 (E) art 8.2.2 (5) - Formula (8.35)

    The printed upper bound of [$2.7 \cdot \tau_{Rdc,0}$] is implemented as a minimum.

    Parameters
    ----------
    tau_rdc_0 : MPA
        [$\tau_{Rdc,0}$] Design value of the shear stress resistance without the effect of compressive
        normal forces according to Formula (8.33), see Form8Dot33ShearStressResistanceWithoutAxialForce [$MPa$].
    a_cs_0 : MM
        [$a_{cs,0}$] Effective shear span determined according to Formula (8.30), without considering in
        [$M_{Ed}$] and [$V_{Ed}$] the effect of prestressing or external load that produces the compressive
        axial force [$mm$].
    d : MM
        [$d$] Effective depth [$mm$].
    """
    super().__init__()
    self.tau_rdc_0 = tau_rdc_0
    self.a_cs_0 = a_cs_0
    self.d = d

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_35.Form8Dot35MaximumShearStressResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.35.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_35.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.35."""
    _equation: str = (
        r"\min\left(2.15 \cdot \tau_{Rdc,0} \cdot \left(\frac{a_{cs,0}}{d}\right)^{\frac{1}{6}}, "
        r"2.7 \cdot \tau_{Rdc,0}\right)"
    )
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"\tau_{Rdc,0}": f"{self.tau_rdc_0:.{n}f}",
            r"a_{cs,0}": f"{self.a_cs_0:.{n}f}",
            r"{d}": "{" + f"{self.d:.{n}f}" + "}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"\tau_{Rdc,0}": rf"{self.tau_rdc_0:.{n}f} \ MPa",
            r"a_{cs,0}": rf"{self.a_cs_0:.{n}f} \ mm",
            r"{d}": "{" + rf"{self.d:.{n}f} \ mm" + "}",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"\tau_{Rdc,max}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="MPa",
    )