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formula_8_36

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_36

Formula 8.36 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_36.Form8Dot36EffectiveDepthPrestressedMembers 

Form8Dot36EffectiveDepthPrestressedMembers(
    d_s: MM, a_s: MM2, d_p: MM, a_p: MM2
)

Bases: Formula

Class representing formula 8.36 for the calculation of the effective depth of prestressed members with bonded tendons.

[\(d\)] Effective depth of prestressed members with bonded tendons [\(mm\)].

FprEN 1992-1-1:2023 (E) art 8.2.2 (6) - Formula (8.36)

The area of prestressed reinforcement [\(A_p\)] may be omitted if including it reduces the shear resistance through the reduced effective depth, provided the longitudinal tension reinforcement [\(A_s\)] is sufficient to carry [\(M_{Ed}\)] and [\(N_{Ed}\)] taking into account the effect of prestressing. Passing [\(A_p = 0\)] returns [\(d_s\)], which is that omission.

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 [\(mm^2\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_36.py 
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def __init__(self, d_s: MM, a_s: MM2, d_p: MM, a_p: MM2) -> None:
    r"""[$d$] Effective depth of prestressed members with bonded tendons [$mm$].

    FprEN 1992-1-1:2023 (E) art 8.2.2 (6) - Formula (8.36)

    The area of prestressed reinforcement [$A_p$] may be omitted if including it reduces the shear
    resistance through the reduced effective depth, provided the longitudinal tension reinforcement
    [$A_s$] is sufficient to carry [$M_{Ed}$] and [$N_{Ed}$] taking into account the effect of
    prestressing. Passing [$A_p = 0$] returns [$d_s$], which is that omission.

    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 [$mm^2$].
    """
    super().__init__()
    self.d_s = d_s
    self.a_s = a_s
    self.d_p = d_p
    self.a_p = a_p

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_36.Form8Dot36EffectiveDepthPrestressedMembers.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.36.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_36.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.36."""
    _equation: str = r"\frac{\left(d_s\right)^2 \cdot A_s + \left(d_p\right)^2 \cdot A_p}{d_s \cdot A_s + d_p \cdot A_p}"
    _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}",
        },
        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",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"d",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="mm",
    )