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formula_5_44

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_44

Formula 5.44 from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

  • Form5Dot44PrestressLoss –

    Class representing formula 5.44 for the calculation of the prestress losses, [\(\Delta P_{el}\)].

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_44.Form5Dot44PrestressLoss 

Form5Dot44PrestressLoss(
    a_p: MM2,
    e_p: MPA,
    j: list[AMOUNT],
    delta_sigma_c_t: list[MPA],
    e_cm_t: list[MPA],
)

Bases: Formula

Class representing formula 5.44 for the calculation of the prestress losses, [\(\Delta P_{el}\)].

[\(\Delta P_{el}\)] Prestress loss [\(N\)].

EN 1992-1-1:2004 art.5.10.5.1(2) - Formula (5.44)

Parameters:

  • a_p (MM2) –

    [\(A_{p}\)] Cross-sectional area of the tendon [\(mm^2\)].

  • e_p (MPA) –

    [\(E_{p}\)] Modulus of elasticity of the tendon [\(MPa\)].

  • j (list[AMOUNT]) –

    [\(j\)] (n-1)/2n, with n the number of identical tendons successively prestressed [\(list[-]\)].

  • delta_sigma_c_t (list[MPA]) –

    [\(\Delta \sigma_{c}(t)\)] variation of stress at the centre of gravity of the tendons applied at time t [\(list[MPa]\)].

  • e_cm_t (list[MPA]) –

    [\(E_{cm}(t)\)] 0.1% proof stress of prestressing steel [\(list[MPa]\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_44.py 
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def __init__(
    self,
    a_p: MM2,
    e_p: MPA,
    j: list[AMOUNT],
    delta_sigma_c_t: list[MPA],
    e_cm_t: list[MPA],
) -> None:
    r"""[$\Delta P_{el}$] Prestress loss [$N$].

    EN 1992-1-1:2004 art.5.10.5.1(2) - Formula (5.44)

    Parameters
    ----------
    a_p : MM2
        [$A_{p}$] Cross-sectional area of the tendon [$mm^2$].
    e_p : MPA
        [$E_{p}$] Modulus of elasticity of the tendon [$MPa$].
    j : list[AMOUNT]
        [$j$] (n-1)/2n, with n the number of identical tendons successively prestressed [$list[-]$].
    delta_sigma_c_t : list[MPA]
        [$\Delta \sigma_{c}(t)$] variation of stress at the centre of gravity of the tendons applied at time t [$list[MPa]$].
    e_cm_t: list[MPA]
        [$E_{cm}(t)$] 0.1% proof stress of prestressing steel [$list[MPa]$].
    """
    super().__init__()
    self.a_p: MM2 = a_p
    self.e_p: MPA = e_p
    self.j: list[AMOUNT] = j
    self.delta_sigma_c_t: list[MPA] = delta_sigma_c_t
    self.e_cm_t: list[MPA] = e_cm_t

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_44.Form5Dot44PrestressLoss.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.43.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_44.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.43."""
    numeric_equation = rf"{self.a_p:.{n}f} \cdot {self.e_p:.{n}f} \cdot \left( "
    for i in range(len(self.j)):
        numeric_equation += rf"\frac{{{self.j[i]} \cdot {self.delta_sigma_c_t[i]:.{n}f}}}{{{self.e_cm_t[i]:.{n}f}}}"
        if i < len(self.j) - 1:
            numeric_equation += " + "
    numeric_equation += r" \right)"

    return LatexFormula(
        return_symbol=r"\Delta P_{el}",
        result=f"{self:.{n}f}",
        equation=r"A_{p} \cdot E_{p} \cdot \sum_{i=1}^{n} \frac{j_{i} \cdot \Delta \sigma_{c,i}(t)}{E_{cm,i}(t)}",
        numeric_equation=numeric_equation,
        comparison_operator_label="=",
        unit="N",
    )