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formula_8_54

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_54

Formula 8.54 from FprEN 1992-1-1:2023: Chapter 8: Ultimate limit states (ULS).

Classes:

  • Form8Dot54NominalWebWidth –

    Class representing formula 8.54 for the calculation of the nominal web width of a web containing ducts.

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_54.Form8Dot54NominalWebWidth 

Form8Dot54NominalWebWidth(b_w: MM, k_duct: DIMENSIONLESS, sum_phi_duct: MM)

Bases: Formula

Class representing formula 8.54 for the calculation of the nominal web width of a web containing ducts.

[\(b_{w,nom}\)] Nominal web width to be used where the web contains ducts [\(mm\)].

FprEN 1992-1-1:2023 (E) art 8.2.3 (10) - Formula (8.54)

The standard applies this reduction where the web contains ducts of diameters such that [\(\Sigma\phi_{duct} > b_w/8\)]. That is a condition of application, not a bound on the result, so it is not enforced here: the caller decides whether the clause applies. For a smaller sum of duct diameters the formula still returns a value, it is simply not the one the standard asks for.

Parameters:

  • b_w (MM) –

    [\(b_w\)] Width of the web of the cross-section. For sections with variable width see 8.2.3(9) and Figure 8.10 [\(mm\)].

  • k_duct (DIMENSIONLESS) –

    [\(k_{duct}\)] Coefficient evaluated depending on the material and filling of the duct. The standard gives 0,5 for grouted steel ducts, 0,8 for grouted plastic ducts with a wall thickness [\(\leq \max\{0,035 \cdot \phi_{duct}; 2 mm\}\)], and 1,2 for non-grouted ducts, for grouted plastic ducts with a wall thickness [\(> \max\{0,035 \cdot \phi_{duct}; 2 mm\}\)] or for ducts injected with soft filling material. None of these three carries a formula number, so the classification is made by the caller. Zero and negative values are rejected, since neither is a coefficient the standard offers and zero would leave the web width unreduced. Membership of the three values is not checked, so the choice between them stays with the caller [\(-\)].

  • sum_phi_duct (MM) –

    [\(\Sigma\phi_{duct}\)] Sum of the outer diameters of the ducts, determined for the most unfavourable level. In the case of variable cross-section widths, calculations at different heights can be necessary to determine the decisive nominal value of the web width [\(mm\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_54.py 
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def __init__(self, b_w: MM, k_duct: DIMENSIONLESS, sum_phi_duct: MM) -> None:
    r"""[$b_{w,nom}$] Nominal web width to be used where the web contains ducts [$mm$].

    FprEN 1992-1-1:2023 (E) art 8.2.3 (10) - Formula (8.54)

    The standard applies this reduction where the web contains ducts of diameters such that
    [$\Sigma\phi_{duct} > b_w/8$]. That is a condition of application, not a bound on the result, so it is
    not enforced here: the caller decides whether the clause applies. For a smaller sum of duct diameters
    the formula still returns a value, it is simply not the one the standard asks for.

    Parameters
    ----------
    b_w : MM
        [$b_w$] Width of the web of the cross-section. For sections with variable width see 8.2.3(9) and
        Figure 8.10 [$mm$].
    k_duct : DIMENSIONLESS
        [$k_{duct}$] Coefficient evaluated depending on the material and filling of the duct. The standard
        gives 0,5 for grouted steel ducts, 0,8 for grouted plastic ducts with a wall thickness
        [$\leq \max\{0,035 \cdot \phi_{duct}; 2 mm\}$], and 1,2 for non-grouted ducts, for grouted plastic
        ducts with a wall thickness [$> \max\{0,035 \cdot \phi_{duct}; 2 mm\}$] or for ducts injected with
        soft filling material. None of these three carries a formula number, so the classification is made
        by the caller. Zero and negative values are rejected, since neither is a coefficient the standard
        offers and zero would leave the web width unreduced. Membership of the three values is not checked,
        so the choice between them stays with the caller [$-$].
    sum_phi_duct : MM
        [$\Sigma\phi_{duct}$] Sum of the outer diameters of the ducts, determined for the most unfavourable
        level. In the case of variable cross-section widths, calculations at different heights can be
        necessary to determine the decisive nominal value of the web width [$mm$].
    """
    super().__init__()
    self.b_w = b_w
    self.k_duct = k_duct
    self.sum_phi_duct = sum_phi_duct

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_54.Form8Dot54NominalWebWidth.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.54.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_54.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.54."""
    _equation: str = r"b_w - k_{duct} \cdot \Sigma\phi_{duct}"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"b_w": f"{self.b_w:.{n}f}",
            r"k_{duct}": f"{self.k_duct:.{n}f}",
            r"\Sigma\phi_{duct}": f"{self.sum_phi_duct:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"b_w": rf"{self.b_w:.{n}f} \ mm",
            r"k_{duct}": f"{self.k_duct:.{n}f}",
            r"\Sigma\phi_{duct}": rf"{self.sum_phi_duct:.{n}f} \ mm",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"b_{w,nom}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="mm",
    )