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formula_8_37

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_37

Formula 8.37 from FprEN 1992-1-1:2023: Chapter 8: Ultimate limit states (ULS).

Classes:

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_37.Form8Dot37ReinforcementRatioPrestressedMembers 

Form8Dot37ReinforcementRatioPrestressedMembers(
    d_s: MM, a_s: MM2, d_p: MM, a_p: MM2, b_w: MM, d: MM
)

Bases: Formula

Class representing formula 8.37 for the calculation of the reinforcement ratio of prestressed members with bonded tendons.

[\(\rho_l\)] Reinforcement ratio of prestressed members with bonded tendons [\(-\)].

FprEN 1992-1-1:2023 (E) art 8.2.2 (6) - Formula (8.37)

The area of prestressed reinforcement [\(A_p\)] may be omitted under the conditions given in 8.2.2(6). With [\(A_p = 0\)] and [\(d = d_s\)] this formula reduces to Formula (8.28).

Parameters:

  • d_s (MM) –

    [\(d_s\)] Effective depth of the longitudinal tension reinforcement [\(mm\)].

  • a_s (MM2) –

    [\(A_s\)] Area of the longitudinal tension reinforcement [\(mm^2\)].

  • d_p (MM) –

    [\(d_p\)] Effective depth of the prestressed reinforcement [\(mm\)].

  • a_p (MM2) –

    [\(A_p\)] Area of the prestressed reinforcement [\(mm^2\)].

  • b_w (MM) –

    [\(b_w\)] Width of the cross-section of linear members [\(mm\)].

  • d (MM) –

    [\(d\)] Effective depth according to Formula (8.36), see Form8Dot36EffectiveDepthPrestressedMembers [\(mm\)]. Within this clause it is not a free value: for the same member it follows from the four reinforcement quantities above. Passing anything else yields a ratio that is silently inconsistent with the section it claims to describe.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_37.py 
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def __init__(self, d_s: MM, a_s: MM2, d_p: MM, a_p: MM2, b_w: MM, d: MM) -> None:
    r"""[$\rho_l$] Reinforcement ratio of prestressed members with bonded tendons [$-$].

    FprEN 1992-1-1:2023 (E) art 8.2.2 (6) - Formula (8.37)

    The area of prestressed reinforcement [$A_p$] may be omitted under the conditions given in 8.2.2(6).
    With [$A_p = 0$] and [$d = d_s$] this formula reduces to Formula (8.28).

    Parameters
    ----------
    d_s : MM
        [$d_s$] Effective depth of the longitudinal tension reinforcement [$mm$].
    a_s : MM2
        [$A_s$] Area of the longitudinal tension reinforcement [$mm^2$].
    d_p : MM
        [$d_p$] Effective depth of the prestressed reinforcement [$mm$].
    a_p : MM2
        [$A_p$] Area of the prestressed reinforcement [$mm^2$].
    b_w : MM
        [$b_w$] Width of the cross-section of linear members [$mm$].
    d : MM
        [$d$] Effective depth according to Formula (8.36), see Form8Dot36EffectiveDepthPrestressedMembers [$mm$].
        Within this clause it is not a free value: for the same member it follows from the four
        reinforcement quantities above. Passing anything else yields a ratio that is silently
        inconsistent with the section it claims to describe.
    """
    super().__init__()
    self.d_s = d_s
    self.a_s = a_s
    self.d_p = d_p
    self.a_p = a_p
    self.b_w = b_w
    self.d = d

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_37.Form8Dot37ReinforcementRatioPrestressedMembers.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.37.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_37.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.37."""
    _equation: str = r"\frac{d_s \cdot A_s + d_p \cdot A_p}{b_w \cdot \left(d\right)^2}"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"d_s": f"{self.d_s:.{n}f}",
            r"A_s": f"{self.a_s:.{n}f}",
            r"d_p": f"{self.d_p:.{n}f}",
            r"A_p": f"{self.a_p:.{n}f}",
            r"b_w": f"{self.b_w:.{n}f}",
            r"\left(d\right)": rf"\left({self.d:.{n}f}\right)",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"d_s": rf"{self.d_s:.{n}f} \ mm",
            r"A_s": rf"{self.a_s:.{n}f} \ mm^2",
            r"d_p": rf"{self.d_p:.{n}f} \ mm",
            r"A_p": rf"{self.a_p:.{n}f} \ mm^2",
            r"b_w": rf"{self.b_w:.{n}f} \ mm",
            r"\left(d\right)": rf"\left({self.d:.{n}f} \ mm\right)",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"\rho_l",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="-",
    )