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formula_8_30

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_30

Formula 8.30 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_30.Form8Dot30EffectiveShearSpan 

Form8Dot30EffectiveShearSpan(m_ed: NMM, v_ed: N, d: MM)

Bases: Formula

Class representing formula 8.30 for the calculation of the effective shear span with respect to the control section, for reinforced concrete members.

[\(a_{cs}\)] Effective shear span with respect to the control section [\(mm\)].

FprEN 1992-1-1:2023 (E) art 8.2.2 (3) - Formula (8.30)

The standard prints this as a ratio in absolute value bars, bounded from below by [\(d\)], which is implemented as the maximum of the two. Because of the absolute value, the signs of [\(M_{Ed}\)] and [\(V_{Ed}\)] do not affect the result, so both may be passed signed.

Parameters:

  • m_ed (NMM) –

    [\(M_{Ed}\)] Design bending moment at the control section, including the effects of prestressing according to 8.2.1(8) [\(Nmm\)].

  • v_ed (N) –

    [\(V_{Ed}\)] Design shear force at the control section, including the effects of prestressing according to 8.2.1(8) [\(N\)].

  • d (MM) –

    [\(d\)] Effective depth [\(mm\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_30.py 
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def __init__(self, m_ed: NMM, v_ed: N, d: MM) -> None:
    r"""[$a_{cs}$] Effective shear span with respect to the control section [$mm$].

    FprEN 1992-1-1:2023 (E) art 8.2.2 (3) - Formula (8.30)

    The standard prints this as a ratio in absolute value bars, bounded from below by [$d$], which is
    implemented as the maximum of the two. Because of the absolute value, the signs of [$M_{Ed}$] and
    [$V_{Ed}$] do not affect the result, so both may be passed signed.

    Parameters
    ----------
    m_ed : NMM
        [$M_{Ed}$] Design bending moment at the control section, including the effects of prestressing
        according to 8.2.1(8) [$Nmm$].
    v_ed : N
        [$V_{Ed}$] Design shear force at the control section, including the effects of prestressing
        according to 8.2.1(8) [$N$].
    d : MM
        [$d$] Effective depth [$mm$].
    """
    super().__init__()
    self.m_ed = m_ed
    self.v_ed = v_ed
    self.d = d

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_30.Form8Dot30EffectiveShearSpan.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.30.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_30.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.30."""
    _equation: str = r"\max\left(\left|\frac{M_{Ed}}{V_{Ed}}\right|, d\right)"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"M_{Ed}": f"{self.m_ed:.{n}f}",
            r"V_{Ed}": f"{self.v_ed:.{n}f}",
            r", d": f", {self.d:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"M_{Ed}": rf"{self.m_ed:.{n}f} \ Nmm",
            r"V_{Ed}": rf"{self.v_ed:.{n}f} \ N",
            r", d": rf", {self.d:.{n}f} \ mm",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"a_{cs}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="mm",
    )