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formula_6_16

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_16

Formula 6.16 from EN 1993-1-1:2005: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_16.Form6Dot16CheckFlangeWithFastenerHoles 

Form6Dot16CheckFlangeWithFastenerHoles(
    a_f_net: MM2,
    f_u: MPA,
    gamma_m2: DIMENSIONLESS,
    a_f: MM2,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
)

Bases: Formula

Class representing formula 6.16 for the test of the stresses where there are fastener holes in the tension flange.

Test the stresses where there are fastener holes in the tension flange.

EN 1993-1-1:2005 art.6.2.5(4) - Formula (6.16)

Parameters:

  • a_f_net (MM2) –

    [\(A_{f,net}\)] Net area of the flange with fastener holes [mm^2].

  • f_u (MPA) –

    [\(f_{u}\)] Ultimate tensile strength of the material [MPa].

  • gamma_m2 (DIMENSIONLESS) –

    [\(\gamma_{M2}\)] Partial safety factor for ultimate limit state [-].

  • a_f (MM2) –

    [\(A_{f}\)] Gross area of the flange [mm^2].

  • f_y (MPA) –

    [\(f_{y}\)] Yield strength of the material [MPa].

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial safety factor for yield strength [-].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_16.py 
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def __init__(
    self,
    a_f_net: MM2,
    f_u: MPA,
    gamma_m2: DIMENSIONLESS,
    a_f: MM2,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
) -> None:
    r"""Test the stresses where there are fastener holes in the tension flange.

    EN 1993-1-1:2005 art.6.2.5(4) - Formula (6.16)

    Parameters
    ----------
    a_f_net : MM2
        [$A_{f,net}$] Net area of the flange with fastener holes [mm^2].
    f_u : MPA
        [$f_{u}$] Ultimate tensile strength of the material [MPa].
    gamma_m2 : DIMENSIONLESS
        [$\gamma_{M2}$] Partial safety factor for ultimate limit state [-].
    a_f : MM2
        [$A_{f}$] Gross area of the flange [mm^2].
    f_y : MPA
        [$f_{y}$] Yield strength of the material [MPa].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial safety factor for yield strength [-].
    """
    super().__init__()
    self.a_f_net = a_f_net
    self.f_u = f_u
    self.gamma_m2 = gamma_m2
    self.a_f = a_f
    self.f_y = f_y
    self.gamma_m0 = gamma_m0

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_16.Form6Dot16CheckFlangeWithFastenerHoles.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.16.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_16.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.16."""
    _equation: str = r"\left( \frac{A_{f,net} \cdot 0.9 \cdot f_{u}}{\gamma_{M2}} \geq \frac{A_{f} \cdot f_{y}}{\gamma_{M0}} \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A_{f,net}": f"{self.a_f_net:.{n}f}",
            r"f_{u}": f"{self.f_u:.{n}f}",
            r"\gamma_{M2}": f"{self.gamma_m2:.{n}f}",
            r"A_{f}": f"{self.a_f:.{n}f}",
            r"f_{y}": f"{self.f_y:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
        },
        False,
    )

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