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formula_8_32

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_32

Formula 8.32 from EN 1993-1-1:2022: Chapter 8 - Ultimate Limit State.

Classes:

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_32.Form8Dot32VplTRdChannelSection 

Form8Dot32VplTRdChannelSection(
    tau_t_ed: MPA, f_y: MPA, gamma_m0: DIMENSIONLESS, tau_w_ed: MPA, v_pl_rd: N
)

Bases: Formula

Class representing formula 8.32 for the calculation of [\(V_{pl,T,Rd}\)].

[\(V_{pl,T,Rd}\)] Calculation of the shear resistance for channel sections [\(N\)].

EN 1993-1-1:2022 art.8.2.7(9) - Formula (8.32)

Parameters:

  • tau_t_ed (MPA) –

    [\(\tau_{Ed}\)] Design shear stress due to St. Venant torsion [\(MPa\)].

  • f_y (MPA) –

    [\(f_y\)] Yield strength of the material [\(MPa\)].

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial safety factor for resistance of cross-sections.

  • tau_w_ed (MPA) –

    [\(\tau_{w,Ed}\)] Design shear stress due to warping [\(MPa\)].

  • v_pl_rd (N) –

    [\(V_{pl,Rd}\)] Plastic shear resistance [\(N\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_32.py 
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def __init__(
    self,
    tau_t_ed: MPA,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
    tau_w_ed: MPA,
    v_pl_rd: N,
) -> None:
    r"""[$V_{pl,T,Rd}$] Calculation of the shear resistance for channel sections [$N$].

    EN 1993-1-1:2022 art.8.2.7(9) - Formula (8.32)

    Parameters
    ----------
    tau_t_ed : MPA
        [$\tau_{Ed}$] Design shear stress due to St. Venant torsion [$MPa$].
    f_y : MPA
        [$f_y$] Yield strength of the material [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial safety factor for resistance of cross-sections.
    tau_w_ed : MPA
        [$\tau_{w,Ed}$] Design shear stress due to warping [$MPa$].
    v_pl_rd : N
        [$V_{pl,Rd}$] Plastic shear resistance [$N$].
    """
    super().__init__()
    self.tau_t_ed = tau_t_ed
    self.f_y = f_y
    self.gamma_m0 = gamma_m0
    self.tau_w_ed = tau_w_ed
    self.v_pl_rd = v_pl_rd

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_32.Form8Dot32VplTRdChannelSection.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.32.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_32.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.32."""
    _equation: str = (
        r"\left( \sqrt{1 - \frac{\tau_{t,Ed}}{1.25 \cdot \left( f_y / \sqrt{3} \right) / \gamma_{M0}}} - "
        r"\frac{\tau_{w,Ed}}{\left( f_y / \sqrt{3} \right) / \gamma_{M0}} \right) \cdot V_{pl,Rd}"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"\tau_{t,Ed}": f"{self.tau_t_ed:.{n}f}",
            r"f_y": f"{self.f_y:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
            r"\tau_{w,Ed}": f"{self.tau_w_ed:.{n}f}",
            r"V_{pl,Rd}": f"{self.v_pl_rd:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            r"\tau_{t,Ed}": rf"{self.tau_t_ed:.{n}f} \ MPa",
            r"f_y": rf"{self.f_y:.{n}f} \ MPa",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
            r"\tau_{w,Ed}": rf"{self.tau_w_ed:.{n}f} \ MPa",
            r"V_{pl,Rd}": rf"{self.v_pl_rd:.{n}f} \ N",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"V_{pl,T,Rd}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="N",
    )