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formula_8_9

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_9

Formula 8.9 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_9.Form8Dot9AnchorageCapacityWeldedTransverseBarSmallDiameter 

Form8Dot9AnchorageCapacityWeldedTransverseBarSmallDiameter(
    f_wd: KN, diameter_t: MM, diameter_l: MM, a_s: MM2, f_cd: MPA
)

Bases: Formula

Class representing the formula 8.9 for the calculation of the anchorage capacity of a welded cross bar for nominal bar diameters smaller than 12 mm.

[\(F_{btd}\)] Anchorage capacity of a welded cross bar for nominal bar diameters smaller than 12 mm [\(kN\)].

EN 1992-1-1:2004 art.8.6(5) - formula 8.9

Parameters:

  • f_wd (KN) –

    [\(F_{wd}\)] Design shear strength of weld (specified as a factor times [\(A_{s} \cdot f_{yd}\)]; say [\(0.5 \cdot A_{s} \cdot f_{yd}\)] where [\(A_{s}\)] is the cross-section of the anchored bar and [\(f_{yd}\)] is its design yield strength) [\(kN\)].

  • diameter_t (MM) –

    [\(ø_{t}\)] Diameter of the transverse bar [\(mm\)].

    Note: [\(ø_{t} \leq 12\)] [\(mm\)].

  • diameter_l (MM) –

    [\(ø_{l}\)] Diameter of the bar to be anchored [\(mm\)].

    Note: [\(ø_{l} \leq 12\)] [\(mm\)].

  • a_s (MM2) –

    [\(A_{s}\)] Cross-section of the anchored bar [\(mm^{2}\)].

  • f_cd (MPA) –

    [\(f_{cd}\)] Design compressive strength of concrete [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_9.py 
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def __init__(
    self,
    f_wd: KN,
    diameter_t: MM,
    diameter_l: MM,
    a_s: MM2,
    f_cd: MPA,
) -> None:
    r"""[$F_{btd}$] Anchorage capacity of a welded cross bar for nominal bar diameters smaller than 12 mm [$kN$].

    EN 1992-1-1:2004 art.8.6(5) - formula 8.9

    Parameters
    ----------
    f_wd : KN
        [$F_{wd}$] Design shear strength of weld (specified as a factor times [$A_{s} \cdot f_{yd}$]; say [$0.5 \cdot A_{s} \cdot f_{yd}$]
        where [$A_{s}$] is the cross-section of the anchored bar and [$f_{yd}$] is its design yield strength)  [$kN$].
    diameter_t : MM
        [$ø_{t}$] Diameter of the transverse bar [$mm$].

        Note: [$ø_{t} \leq 12$] [$mm$].
    diameter_l : MM
        [$ø_{l}$] Diameter of the bar to be anchored [$mm$].

        Note: [$ø_{l} \leq 12$] [$mm$].
    a_s : MM2
        [$A_{s}$] Cross-section of the anchored bar [$mm^{2}$].
    f_cd : MPA
        [$f_{cd}$] Design compressive strength of concrete [$MPa$].
    """
    super().__init__()
    self.f_wd = f_wd
    self.diameter_t = diameter_t
    self.diameter_l = diameter_l
    self.a_s = a_s
    self.f_cd = f_cd

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_9.Form8Dot9AnchorageCapacityWeldedTransverseBarSmallDiameter.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 8.9.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_9.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 8.9."""
    return LatexFormula(
        return_symbol=r"F_{btd}",
        result=f"{self:.{n}f}",
        equation=r"\min \left( F_{wd}, 16 \cdot A_s \cdot f_{cd} \cdot \frac{Ø_t}{Ø_l} \right)",
        numeric_equation=(
            rf"\min \left( {self.f_wd:.{n}f}, 1000 \cdot 16 \cdot {self.a_s:.{n}f} \cdot {self.f_cd:.{n}f} \cdot "
            rf"\frac{{{self.diameter_t:.{n}f}}}{{{self.diameter_l:.{n}f}}} \right)"
        ),
        comparison_operator_label="=",
    )