Skip to content

formula_8_52af

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_52af

Formula 8.52af 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_52af.Form8Dot52afHollowSections 

Form8Dot52afHollowSections(a: MM2, h: MM, t: MM)

Bases: Formula

Class representing formula 8.52af for [\(a_f\)] in hollow sections.

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

EN 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.52af)

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_2022/chapter_8_ultimate_limit_state/formula_8_52af.py 
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
def __init__(
    self,
    a: MM2,
    h: MM,
    t: MM,
) -> None:
    r"""[$a_f$] Calculation of the reduction factor for hollow sections (dimensionless).

    EN 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.52af)

    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_2022.chapter_8_ultimate_limit_state.formula_8_52af.Form8Dot52afHollowSections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.52af.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_52af.py 
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.52af."""
    _equation: str = r"\min \left( \frac{A - 2 \cdot h \cdot t}{A}, 0.5 \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"A": f"{self.a:.{n}f}",
            r" h": f" {self.h:.{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" h": rf" {self.h:.{n}f} \ mm",
            r" t": rf" {self.t:.{n}f} \ mm",
        },
        unique_symbol_check=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_2022.chapter_8_ultimate_limit_state.formula_8_52af.Form8Dot52afWeldedBoxSections 

Form8Dot52afWeldedBoxSections(a: MM2, h: MM, t_w: MM)

Bases: Formula

Class representing formula 8.52af for [\(a_f\)] in welded box sections.

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

EN 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.52af)

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_2022/chapter_8_ultimate_limit_state/formula_8_52af.py 
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
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 1993-1-1:2022 art.8.2.9.1(6) - Formula (8.52af)

    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_2022.chapter_8_ultimate_limit_state.formula_8_52af.Form8Dot52afWeldedBoxSections.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.52af.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_52af.py 
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.52af."""
    _equation: str = r"\min \left( \frac{A - 2 \cdot h \cdot t_w}{A}, 0.5 \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"A": f"{self.a:.{n}f}",
            r" h": f" {self.h:.{n}f}",
            r"t_w": f"{self.t_w:.{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" h": rf" {self.h:.{n}f} \ mm",
            r"t_w": rf"{self.t_w:.{n}f} \ mm",
        },
        unique_symbol_check=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="-",
    )