Skip to content

formula_8_1

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_1

Formula 8.1 from EN 1992-1-1:2004: Chapter 8 Detailing of reinforcement and prestressing tendons.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_1.Form8Dot1RequiredMinimumMandrelDiameter 

Form8Dot1RequiredMinimumMandrelDiameter(
    f_bt: KN, a_b: MM, diameter: MM, f_cd: MPA
)

Bases: Formula

Class representing formula 8.1 for the calculation of the required minimum mandrel diameter if it needs to be checked to avoid concrete failure.

[\(\Ø_{m,min}\)] minimum mandrel diameter if it needs to be checked to avoid concrete failure [\(MM\)].

EN 1992-1-1:2004 art.8.3(3) - Formula (8.1)

Parameters:

  • f_bt (KN) –

    [\(F_{bt}\)] Tensile force from ultimate loads in a bar or group of bars in contact at the start of a bend [\(kN\)].

  • a_b (MM) –

    [\(a_b\)] Half of the centre-to-centre distance between bars (or groups of bars) perpendicular to the plane of the bend for a given bar (or group of bars in contact). For a bar or group of bars adjacent to the face of the member, [\(a_b\)] should be taken as the cover plus [\(\Ø/2\)] [\(mm\)].

  • diameter (MM) –

    [\(\Ø\)] Diameter of reinforcing bar [\(mm\)].

  • f_cd (MPA) –

    [\(f_{cd}\)] Design value of concrete compressive stress [\(MPa\)]. Note: The value of [\(f_{cd}\)] should not be taken greater than that for concrete class C55/67.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_1.py 
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
46
47
48
def __init__(
    self,
    f_bt: KN,
    a_b: MM,
    diameter: MM,
    f_cd: MPA,
) -> None:
    r"""[$\Ø_{m,min}$] minimum mandrel diameter if it needs to be checked to avoid concrete failure [$MM$].

    EN 1992-1-1:2004 art.8.3(3) - Formula (8.1)

    Parameters
    ----------
    f_bt: KN
        [$F_{bt}$] Tensile force from ultimate loads in a bar or group of bars in contact at the start of a bend  [$kN$].
    a_b: MM
        [$a_b$] Half of the centre-to-centre distance between bars (or groups of bars) perpendicular
        to the plane of the bend for a given bar (or group of bars in contact).
        For a bar or group of bars adjacent to the face of the member, [$a_b$] should be taken as the cover plus [$\Ø/2$] [$mm$].
    diameter: MM
        [$\Ø$] Diameter of reinforcing bar [$mm$].
    f_cd: MPA
        [$f_{cd}$] Design value of concrete compressive stress [$MPa$].
        Note: The value of [$f_{cd}$] should not be taken greater than that for concrete class C55/67.
    """
    super().__init__()
    self.f_bt = f_bt
    self.a_b = a_b
    self.diameter = diameter
    self.f_cd = f_cd

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_1.Form8Dot1RequiredMinimumMandrelDiameter.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.1.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_1.py 
66
67
68
69
70
71
72
73
74
75
76
77
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.1."""
    return LatexFormula(
        return_symbol=r"Ø_{m,min}",
        result=f"{self:.{n}f}",
        equation=r"\frac{F_{bt} \left( \frac{1}{a_b} + \frac{1}{2 \cdot Ø} \right) }{f_{cd}}",
        numeric_equation=(
            rf"\frac{{{self.f_bt:.{n}f} \cdot 1000 \cdot \left( \frac{{1}}{{{self.a_b:.{n}f}}}"
            rf" + \frac{{1}}{{2 \cdot {self.diameter:.{n}f}}} \right)}}{{{self.f_cd:.{n}f}}}"
        ),
        comparison_operator_label="=",
    )