Skip to content

formula_5_12

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_12

Formula 5.12 from EN 1993-5:2007: Chapter 5 - Ultimate Limit States.

Classes:

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_12.Form5Dot12ElasticCriticalLoad 

Form5Dot12ElasticCriticalLoad(e: MPA, i: MM4, beta_d: DIMENSIONLESS, l: MM)

Bases: Formula

Class representing formula 5.12 for the calculation of the elastic critical load, [\(N_{cr}\)].

[\(N_{cr}\)] Elastic critical load [\(N\)].

EN 1993-5:2007 art.5.2.3 - Formula (5.12)

Parameters:

  • e (MPA) –

    [\(E\)] Modulus of elasticity [\(MPa\)].

  • i (MM4) –

    [\(I\)] Moment of inertia [\(mm^4\)].

  • beta_d (DIMENSIONLESS) –

    [\(\beta_D\)] Reduction factor, see 6.4 [\(-\)].

  • l (MM) –

    [\(l\)] the buckling length, determined according to Figure 5-2 for a free or partially fixed earth support or according to Figure 5-3 for a fixed earth support. [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_12.py 
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
def __init__(
    self,
    e: MPA,
    i: MM4,
    beta_d: DIMENSIONLESS,
    l: MM,  # noqa: E741
) -> None:
    r"""[$N_{cr}$] Elastic critical load [$N$].

    EN 1993-5:2007 art.5.2.3 - Formula (5.12)

    Parameters
    ----------
    e : MPA
        [$E$] Modulus of elasticity [$MPa$].
    i : MM4
        [$I$] Moment of inertia [$mm^4$].
    beta_d : DIMENSIONLESS
        [$\beta_D$] Reduction factor, see 6.4 [$-$].
    l : MM
        [$l$] the buckling length, determined according to Figure 5-2 for a free or partially fixed earth
        support or according to Figure 5-3 for a fixed earth support. [$mm$].
    """
    super().__init__()
    self.e = e
    self.i = i
    self.beta_d = beta_d
    self.l = l

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_12.Form5Dot12ElasticCriticalLoad.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.12.

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_12.py 
64
65
66
67
68
69
70
71
72
73
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.12."""
    return LatexFormula(
        return_symbol=r"N_{cr}",
        result=f"{self:.{n}f}",
        equation=r"\frac{E \cdot I \cdot \beta_D \cdot \pi^2}{l^2}",
        numeric_equation=rf"\frac{{{self.e:.{n}f} \cdot {self.i:.{n}f} \cdot {self.beta_d:.{n}f} \cdot \pi^2}}{{{self.l:.{n}f}^2}}",
        comparison_operator_label="=",
        unit="N",
    )