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formula_6_28

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_28

Formula 6.28 from EN 1992-1-1:2004: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_28.Form6Dot28RequiredCrossSectionalArea 

Form6Dot28RequiredCrossSectionalArea(
    u_k: MM, f_yd: MPA, t_ed: NMM, a_k: MM2, theta: DEG
)

Bases: Formula

Class representing formula 6.28 for the calculation of the required cross-sectional area of the longitudinal reinforcement. The description of the equation states that it is used to calculate the total reinforcement area. Therefore the calculation has been rewritten to find the solution to that question, [\(\Sigma A_{sl}\)].

[\(\Sigma A_{sl}\)] Required cross-sectional area of the longitudinal reinforcement [\(mm^2\)].

EN 1992-1-1:2004 art.6.3.2(3) - Formula (6.28)

Parameters:

  • u_k (MM) –

    [\(u_k\)] Perimeter of the area A_k [\(mm\)].

  • f_yd (MPA) –

    [\(f_{yd}\)] Design yield stress of the longitudinal reinforcement [\(MPa\)].

  • t_ed (NMM) –

    [\(T_{Ed}\)] Design value of the torsional moment [\(Nmm\)].

  • a_k (MM2) –

    [\(A_k\)] Area enclosed by the centre-lines of the connecting walls, including inner hollow areas [\(mm^2\)].

  • theta (DEG) –

    [\(\theta\)] Angle of compression struts (see Figure 6.5) [\(degrees\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_28.py 
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def __init__(
    self,
    u_k: MM,
    f_yd: MPA,
    t_ed: NMM,
    a_k: MM2,
    theta: DEG,
) -> None:
    r"""[$\Sigma A_{sl}$] Required cross-sectional area of the longitudinal reinforcement [$mm^2$].

    EN 1992-1-1:2004 art.6.3.2(3) - Formula (6.28)

    Parameters
    ----------
    u_k : MM
        [$u_k$] Perimeter of the area A_k [$mm$].
    f_yd : MPA
        [$f_{yd}$] Design yield stress of the longitudinal reinforcement [$MPa$].
    t_ed : NMM
        [$T_{Ed}$] Design value of the torsional moment [$Nmm$].
    a_k : MM2
        [$A_k$] Area enclosed by the centre-lines of the connecting walls, including inner hollow areas [$mm^2$].
    theta : DEG
        [$\theta$] Angle of compression struts (see Figure 6.5) [$degrees$].
    """
    super().__init__()
    self.u_k = u_k
    self.f_yd = f_yd
    self.t_ed = t_ed
    self.a_k = a_k
    self.theta = theta

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_28.Form6Dot28RequiredCrossSectionalArea.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.28.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_28.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.28."""
    return LatexFormula(
        return_symbol=r"\Sigma A_{sl}",
        result=f"{self:.{n}f}",
        equation=r"\frac{u_k}{f_{yd}} \cdot \frac{T_{Ed}}{2 \cdot A_k} \cdot \cot(\theta)",
        numeric_equation=rf"\frac{{{self.u_k:.{n}f}}}{{{self.f_yd:.{n}f}}} \cdot \frac{{{self.t_ed:.{n}f}}}"
        rf"{{2 \cdot {self.a_k:.{n}f}}} \cdot \cot({self.theta:.{n}f})",
        comparison_operator_label="=",
        unit="mm^2",
    )