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formula_5_45

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_45

Formula 5.45 from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

  • Form5Dot45LossesDueToFriction –

    Class representing formula 5.45 for the calculation of losses due to friction in post-tensioned tendons, [\(\Delta P_{\mu}(x)\)].

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_45.Form5Dot45LossesDueToFriction 

Form5Dot45LossesDueToFriction(
    p_max: KN, mu: DIMENSIONLESS, theta: DIMENSIONLESS, k: ONE_OVER_M, x: M
)

Bases: Formula

Class representing formula 5.45 for the calculation of losses due to friction in post-tensioned tendons, [\(\Delta P_{\mu}(x)\)].

[\(\Delta P_{\mu}(x)\)] Losses due to friction [\(kN\)].

EN 1992-1-1:2004 art.5.10.5.2(1) - Formula (5.45)

Parameters:

  • p_max (KN) –

    [\(P_{max}\)] Force at the active end during tensioning [\(kN\)].

  • mu (DIMENSIONLESS) –

    [\(\mu\)] Coefficient of friction between the tendon and its duct [\(-\)].

  • theta (DIMENSIONLESS) –

    [\(\theta\)] Sum of the angular displacements over a distance x (irrespective of direction or sign) [\(-\)].

  • k (ONE_OVER_M) –

    [\(k\)] Unintentional angular displacement for internal tendons (per unit length) [\(1/m\)].

  • x (M) –

    [\(x\)] Distance along tendon from point where the prestressing force equals Pmax (force at active end during tensioning) [\(m\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_45.py 
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def __init__(
    self,
    p_max: KN,
    mu: DIMENSIONLESS,
    theta: DIMENSIONLESS,
    k: ONE_OVER_M,
    x: M,
) -> None:
    r"""[$\Delta P_{\mu}(x)$] Losses due to friction [$kN$].

    EN 1992-1-1:2004 art.5.10.5.2(1) - Formula (5.45)

    Parameters
    ----------
    p_max : KN
        [$P_{max}$] Force at the active end during tensioning [$kN$].
    mu : DIMENSIONLESS
        [$\mu$] Coefficient of friction between the tendon and its duct [$-$].
    theta : DIMENSIONLESS
        [$\theta$] Sum of the angular displacements over a distance x (irrespective of direction or sign) [$-$].
    k : ONE_OVER_M
        [$k$] Unintentional angular displacement for internal tendons (per unit length) [$1/m$].
    x : M
        [$x$] Distance along tendon from point where the prestressing force equals Pmax (force at active end during tensioning) [$m$].
    """
    super().__init__()
    self.p_max = p_max
    self.mu = mu
    self.theta = theta
    self.k = k
    self.x = x

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_45.Form5Dot45LossesDueToFriction.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.45.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_45.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.45."""
    return LatexFormula(
        return_symbol=r"\Delta P_{\mu}(x)",
        result=f"{self:.{n}f}",
        equation=r"P_{max} \cdot \left( 1 - e^{-\mu \cdot (\theta + k \cdot x)} \right)",
        numeric_equation=rf"{self.p_max:.{n}f} \cdot \left( 1 - e^{{-{self.mu:.{n}f} \cdot ({self.theta:.{n}f} + "
        rf"{self.k:.{n}f} \cdot {self.x:.{n}f})}} \right)",
        comparison_operator_label="=",
        unit="kN",
    )