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formula_8_5

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_5

Formula 8.5 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_5.Form8Dot5MinDeductionAreaStaggeredFastenerHoles 

Form8Dot5MinDeductionAreaStaggeredFastenerHoles(
    t: MM, n_1: DIMENSIONLESS, d_0: MM, s: Sequence[MM], p_2: Sequence[MM]
)

Bases: Formula

Class representing formula 8.5 for the calculation of the minimum area deduction for staggered fastener holes [\(\Delta A_{net,1}\)].

[\(\Delta A_{net,1}\)] Calculation of the area deduction for staggered fastener holes [\(mm^2\)].

EN 1993-1-1:2022 art.8.2.2.2 (4) b) - Formula (8.5) section (4) a) should be handled separately.

Parameters:

  • t (MM) –

    [\(t\)] Thickness [\(mm\)].

  • n_1 (DIMENSIONLESS) –

    [\(n_1\)] Number of holes extending in any diagonal or zig-zag line progressively across the member, see Figure 8.1 [\(-\)].

  • d_0 (MM) –

    [\(d_0\)] Diameter of hole [\(mm\)].

  • s (Sequence[MM]) –

    [\(s\)] Staggered pitch, the spacing of the centres of two consecutive holes in the chain measured parallel to the member axis [\(mm\)].

  • p_2 (Sequence[MM]) –

    [\(p_2\)] Spacing of the centres of the same two holes measured perpendicular to the member axis [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_5.py 
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def __init__(
    self,
    t: MM,
    n_1: DIMENSIONLESS,
    d_0: MM,
    s: Sequence[MM],
    p_2: Sequence[MM],
) -> None:
    r"""[$\Delta A_{net,1}$] Calculation of the area deduction for staggered fastener holes [$mm^2$].

    EN 1993-1-1:2022 art.8.2.2.2 (4) b) - Formula (8.5)
    section (4) a) should be handled separately.

    Parameters
    ----------
    t : MM
        [$t$] Thickness [$mm$].
    n_1 : DIMENSIONLESS
        [$n_1$] Number of holes extending in any diagonal or zig-zag line progressively across the member, see Figure 8.1 [$-$].
    d_0 : MM
        [$d_0$] Diameter of hole [$mm$].
    s : Sequence[MM]
        [$s$] Staggered pitch, the spacing of the centres of two consecutive holes in the
        chain measured parallel to the member axis [$mm$].
    p_2 : Sequence[MM]
        [$p_2$] Spacing of the centres of the same two holes measured perpendicular to the member axis [$mm$].
    """
    super().__init__()
    self.t = t
    self.n_1 = n_1
    self.d_0 = d_0
    self.s: Sequence[MM] = s
    self.p_2: Sequence[MM] = p_2

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_5.Form8Dot5MinDeductionAreaStaggeredFastenerHoles.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.5.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_5.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.5."""
    _equation: str = r"t \left( n_1 \cdot d_0 - \sum \frac{s^2}{4 \cdot p_2} \right)"
    _numeric_equation: str = (
        rf"{self.t:.{n}f} \left( {self.n_1:.{n}f} \cdot {self.d_0:.{n}f} - \left( \frac{{{self.s[0]:.{n}f}^2}}"
        rf"{{4 \cdot {self.p_2[0]:.{n}f}}}"
    )
    for s_i, p_2_i in zip(self.s[1:], self.p_2[1:]):
        _numeric_equation += rf" + \frac{{{s_i:.{n}f}^2}}{{4 \cdot {p_2_i:.{n}f}}}"
    _numeric_equation += r" \right) \right)"
    _numeric_equation_with_units: str = (
        rf"{self.t:.{n}f} \ mm \left( {self.n_1:.{n}f} \cdot {self.d_0:.{n}f} \ mm - \left( \frac{{{self.s[0]:.{n}f}^2 \ mm^2}}"
        rf"{{4 \cdot {self.p_2[0]:.{n}f} \ mm}}"
    )
    for s_i, p_2_i in zip(self.s[1:], self.p_2[1:]):
        _numeric_equation_with_units += rf" + \frac{{{s_i:.{n}f}^2 \ mm^2}}{{4 \cdot {p_2_i:.{n}f} \ mm}}"
    _numeric_equation_with_units += r" \right) \right)"
    return LatexFormula(
        return_symbol=r"\Delta A_{net,1}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="mm^2",
    )