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formula_6_11abcn

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_11abcn

Formula 6.11a/b/cN 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_11abcn.Form6Dot11abcnCompressionChordCoefficient 

Form6Dot11abcnCompressionChordCoefficient(sigma_cp: MPA, f_cd: MPA)

Bases: Formula

Class representing formula 6.11a/b/cn for the calculation of the coefficient taking account of the state of the stress in the compression chord.

[\(\alpha_{cw}\)] Coefficient taking account of the state of the stress in the compression chord [\(-\)].

EN 1992-1-1:2004 art.6.2.3(3) - Formula (6.11.aN, 6.11.bN, and 6.11.cN)

Parameters:

  • sigma_cp (MPA) –

    [\(\sigma_{cp}\)] Mean compressive stress, measured positive, due to the design axial force [\(MPa\)].

  • f_cd (MPA) –

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

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_11abcn.py 
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def __init__(
    self,
    sigma_cp: MPA,
    f_cd: MPA,
) -> None:
    r"""[$\alpha_{cw}$] Coefficient taking account of the state of the stress in the compression chord [$-$].

    EN 1992-1-1:2004 art.6.2.3(3) - Formula (6.11.aN, 6.11.bN, and 6.11.cN)

    Parameters
    ----------
    sigma_cp : MPA
        [$\sigma_{cp}$] Mean compressive stress, measured positive, due to the design axial force [$MPa$].
    f_cd : MPA
        [$f_{cd}$] Design value of concrete compressive strength [$MPa$].
    """
    super().__init__()
    self.sigma_cp = sigma_cp
    self.f_cd = f_cd

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_11abcn.Form6Dot11abcnCompressionChordCoefficient.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.11a/b/cN.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_11abcn.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.11a/b/cN."""
    return LatexFormula(
        return_symbol=r"\alpha_{cw}",
        result=f"{self:.{n}f}",
        equation=r"\begin{cases} 1 + \frac{\sigma_{cp}}{f_{cd}} & \text{if } 0 \lt \sigma_{cp} \leq 0.25 f_{cd} \\ "
        r"1.25 & \text{if } 0.25 f_{cd} \lt \sigma_{cp} \leq 0.5 f_{cd} \\ "
        r"2.5 \left(1 - \frac{\sigma_{cp}}{f_{cd}}\right) & \text{if } \sigma_{cp} \gt 0.5 f_{cd} \end{cases}",
        numeric_equation=rf"\begin{{cases}} 1 + \frac{{{self.sigma_cp:.{n}f}}}{{{self.f_cd:.{n}f}}} & \text{{if }} 0 \lt {self.sigma_cp:.{n}f} "
        rf"\leq 0.25 \cdot {self.f_cd:.{n}f} \\ 1.250 & \text{{if }} 0.25 \cdot {self.f_cd:.{n}f} \lt {self.sigma_cp:.{n}f} \leq "
        rf"0.5 \cdot {self.f_cd:.{n}f} \\ 2.5 \left(1 - \frac{{{self.sigma_cp:.{n}f}}}{{{self.f_cd:.{n}f}}}\right) & "
        rf"\text{{if }} {self.sigma_cp:.{n}f} \gt 0.5 \cdot {self.f_cd:.3f} \end{{cases}}",
        comparison_operator_label="=",
        unit="-",
    )