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formula_6_3

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_3

Formula 6.3 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_3.Form6Dot3MinDeductionAreaStaggeredFastenerHoles 

Form6Dot3MinDeductionAreaStaggeredFastenerHoles(
    t: MM, n: MM, d_0: MM, s: Sequence[MM], p: Sequence[MM]
)

Bases: Formula

Class representing formula 6.3 for the calculation of the minimum area deduction for staggered fastener holes [\(A_{deduction}\)].

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

EN 1993-1-1:2005 art.6.2.2.2 (4) b) - Formula (6.3) section (4) a) should be handled separately.

Parameters:

  • t (MM) –

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

  • n (MM) –

    [\(n\)] Number of holes extending in any diagonal or zig-zag line progressively across the member, see Figure 6.1 [\(mm\)].

  • 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 (Sequence[MM]) –

    [\(p\)] 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_2005/chapter_6_ultimate_limit_state/formula_6_3.py 
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def __init__(
    self,
    t: MM,
    n: MM,
    d_0: MM,
    s: Sequence[MM],
    p: Sequence[MM],
) -> None:
    """[$A_{deduction}$] Calculation of the area deduction for staggered fastener holes [$mm^2$].

    EN 1993-1-1:2005 art.6.2.2.2 (4) b) - Formula (6.3)
    section (4) a) should be handled separately.

    Parameters
    ----------
    t : MM
        [$t$] Thickness [$mm$].
    n : MM
        [$n$] Number of holes extending in any diagonal or zig-zag line progressively across the member, see Figure 6.1 [$mm$].
    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 : Sequence[MM]
        [$p$] Spacing of the centres of the same two holes measured perpendicular to the member axis [$mm$].
    """
    super().__init__()
    self.t = t
    self.n = n
    self.d_0 = d_0
    self.s: Sequence[MM] = s
    self.p: Sequence[MM] = p

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_3.Form6Dot3MinDeductionAreaStaggeredFastenerHoles.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.3.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_3.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.3."""
    _equation: str = r"t \left( n \cdot d_0 - \sum \frac{s^2}{4 \cdot p} \right)"
    _numeric_equation: str = (
        rf"{self.t:.{n}f} \left( {self.n:.{n}f} \cdot {self.d_0:.{n}f} - \left( \frac{{{self.s[0]:.{n}f}^2}}"
        rf"{{4 \cdot {self.p[0]:.{n}f}}}"
    )
    for s_i, p_i in zip(self.s[1:], self.p[1:]):
        _numeric_equation += rf" + \frac{{{s_i:.{n}f}^2}}{{4 \cdot {p_i:.{n}f}}}"
    _numeric_equation += r" \right) \right)"
    return LatexFormula(
        return_symbol=r"A_{deduction}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )