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formula_6_40af

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_40af

Formula 6.40af 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_40af.Form6Dot40afHollowSections 

Form6Dot40afHollowSections(a: MM2, h: MM, t: MM)

Bases: Formula

Class representing formula 6.40af for [\(a_f\)] in hollow sections.

[\(a_f\)] Calculation of the reduction factor for hollow sections (dimensionless).

EN 1993-1-1:2005 art.6.2.9.1(5) - Formula (6.40af)

Parameters:

  • a (MM2) –

    [\(A\)] Total cross-sectional area [\(mm^2\)].

  • h (MM) –

    [\(h\)] Height of the section [\(mm\)].

  • t (MM) –

    [\(t\)] Thickness of the section [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_40af.py 
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def __init__(
    self,
    a: MM2,
    h: MM,
    t: MM,
) -> None:
    r"""[$a_f$] Calculation of the reduction factor for hollow sections (dimensionless).

    EN 1993-1-1:2005 art.6.2.9.1(5) - Formula (6.40af)

    Parameters
    ----------
    a : MM2
        [$A$] Total cross-sectional area [$mm^2$].
    h : MM
        [$h$] Height of the section [$mm$].
    t : MM
        [$t$] Thickness of the section [$mm$].
    """
    super().__init__()
    self.a = a
    self.h = h
    self.t = t

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_40af.Form6Dot40afHollowSections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.40af.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_40af.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.40af."""
    _equation: str = r"\min \left( \frac{A - 2 \cdot h \cdot t}{A}, 0.5 \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A": f"{self.a:.{n}f}",
            r" h": f" {self.h:.{n}f}",
            r" t": f" {self.t:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"A": rf"{self.a:.{n}f} \ mm^2",
            r" h": rf" {self.h:.{n}f} \ mm",
            r" t": rf" {self.t:.{n}f} \ mm",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"a_f",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"=",
        unit="-",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_40af.Form6Dot40afWeldedBoxSections 

Form6Dot40afWeldedBoxSections(a: MM2, h: MM, t_w: MM)

Bases: Formula

Class representing formula 6.40af for [\(a_f\)] in welded box sections.

[\(a_f\)] Calculation of the reduction factor for welded box sections (dimensionless).

EN 1993-1-1:2005 art.6.2.9.1(5) - Formula (6.40af)

Parameters:

  • a (MM2) –

    [\(A\)] Total cross-sectional area [\(mm^2\)].

  • h (MM) –

    [\(h\)] Height of the section [\(mm\)].

  • t_w (MM) –

    [\(t_w\)] Web thickness [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_40af.py 
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def __init__(
    self,
    a: MM2,
    h: MM,
    t_w: MM,
) -> None:
    r"""[$a_f$] Calculation of the reduction factor for welded box sections (dimensionless).

    EN 1993-1-1:2005 art.6.2.9.1(5) - Formula (6.40af)

    Parameters
    ----------
    a : MM2
        [$A$] Total cross-sectional area [$mm^2$].
    h : MM
        [$h$] Height of the section [$mm$].
    t_w : MM
        [$t_w$] Web thickness [$mm$].
    """
    super().__init__()
    self.a = a
    self.h = h
    self.t_w = t_w

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_40af.Form6Dot40afWeldedBoxSections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.40af.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_40af.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.40af."""
    _equation: str = r"\min \left( \frac{A - 2 \cdot h \cdot t_w}{A}, 0.5 \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A": f"{self.a:.{n}f}",
            r" h": f" {self.h:.{n}f}",
            r"t_w": f"{self.t_w:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"A": rf"{self.a:.{n}f} \ mm^2",
            r" h": rf" {self.h:.{n}f} \ mm",
            r"t_w": rf"{self.t_w:.{n}f} \ mm",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"a_f",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"=",
        unit="-",
    )