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formula_8_51aw

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_51aw

Formula 8.51aw 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_51aw.Form8Dot51awHollowSections 

Form8Dot51awHollowSections(a: MM2, b: MM, t: MM)

Bases: Formula

Class representing formula 8.51aw for [\(a_w\)] in hollow sections.

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

EN 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.51aw)

Parameters:

  • a (MM2) –

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

  • b (MM) –

    [\(b\)] Width of the section [\(mm\)].

  • t (MM) –

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

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_51aw.py 
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def __init__(
    self,
    a: MM2,
    b: MM,
    t: MM,
) -> None:
    r"""[$a_w$] Calculation of the reduction factor for hollow sections (dimensionless).

    EN 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.51aw)

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

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_51aw.Form8Dot51awHollowSections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.51aw.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_51aw.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.51aw."""
    _equation: str = r"\min \left( \frac{A - 2 \cdot b \cdot t}{A}, 0.5 \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"A": f"{self.a:.{n}f}",
            r"b": f"{self.b:.{n}f}",
            r" t": f" {self.t:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            r"A": rf"{self.a:.{n}f} \ mm^2",
            r"b": rf"{self.b:.{n}f} \ mm",
            r" t": rf" {self.t:.{n}f} \ mm",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"a_w",
        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_2022.chapter_8_ultimate_limit_state.formula_8_51aw.Form8Dot51awWeldedBoxSections 

Form8Dot51awWeldedBoxSections(a: MM2, b: MM, t_f: MM)

Bases: Formula

Class representing formula 8.51aw for [\(a_w\)] in welded box sections.

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

EN 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.51aw)

Parameters:

  • a (MM2) –

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

  • b (MM) –

    [\(b\)] Width of the section [\(mm\)].

  • t_f (MM) –

    [\(t_f\)] Flange thickness [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_51aw.py 
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def __init__(
    self,
    a: MM2,
    b: MM,
    t_f: MM,
) -> None:
    r"""[$a_w$] Calculation of the reduction factor for welded box sections (dimensionless).

    EN 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.51aw)

    Parameters
    ----------
    a : MM2
        [$A$] Total cross-sectional area [$mm^2$].
    b : MM
        [$b$] Width of the section [$mm$].
    t_f : MM
        [$t_f$] Flange thickness [$mm$].
    """
    super().__init__()
    self.a = a
    self.b = b
    self.t_f = t_f

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_51aw.Form8Dot51awWeldedBoxSections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.51aw.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_51aw.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.51aw."""
    _equation: str = r"\min \left( \frac{A - 2 \cdot b \cdot t_f}{A}, 0.5 \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"A": f"{self.a:.{n}f}",
            r"b": f"{self.b:.{n}f}",
            r"t_f": f"{self.t_f:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            r"A": rf"{self.a:.{n}f} \ mm^2",
            r"b": rf"{self.b:.{n}f} \ mm",
            r"t_f": rf"{self.t_f:.{n}f} \ mm",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"a_w",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label=r"=",
        unit="-",
    )