Skip to content

formula_8_14

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_14

Formula 8.14 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_14.Form8Dot14DesignPlasticResistanceGrossCrossSection 

Form8Dot14DesignPlasticResistanceGrossCrossSection(
    a: MM2, f_y: MPA, gamma_m0: DIMENSIONLESS
)

Bases: Formula

Class representing formula 8.14 for the calculation of [\(N_{pl,Rd}\)].

[\(N_{pl,Rd}\)] Calculation of the design plastic resistance of the gross cross-section [\(N\)].

EN 1993-1-1:2022 art.8.2.3(2) - Formula (8.14)

Parameters:

  • a (MM2) –

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

  • f_y (MPA) –

    [\(f_y\)] Yield strength of the material [\(MPa\)].

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial safety factor for resistance of cross-sections, irrespective of the class.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_14.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,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
) -> None:
    r"""[$N_{pl,Rd}$] Calculation of the design plastic resistance of the gross cross-section [$N$].

    EN 1993-1-1:2022 art.8.2.3(2) - Formula (8.14)

    Parameters
    ----------
    a : MM2
        [$A$] Gross cross-sectional area [$mm^2$].
    f_y : MPA
        [$f_y$] Yield strength of the material [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial safety factor for resistance of cross-sections, irrespective of the class.
    """
    super().__init__()
    self.a = a
    self.f_y = f_y
    self.gamma_m0 = gamma_m0

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_14.Form8Dot14DesignPlasticResistanceGrossCrossSection.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.14.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_14.py 
52
53
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
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.14."""
    _equation: str = r"\frac{A \cdot f_y}{\gamma_{M0}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A": f"{self.a:.{n}f}",
            r"f_y": f"{self.f_y:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"A": rf"{self.a:.{n}f} \ mm^2",
            r"f_y": rf"{self.f_y:.{n}f} \ MPa",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"N_{pl,Rd}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="N",
    )