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formula_8_29

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_29

Formula 8.29 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_29.Form8Dot29MechanicalShearSpan 

Form8Dot29MechanicalShearSpan(a_cs: MM, d: MM)

Bases: Formula

Class representing formula 8.29 for the calculation of the mechanical shear span, which may replace the effective depth in Formula (8.27).

[\(a_v\)] Mechanical shear span [\(mm\)].

FprEN 1992-1-1:2023 (E) art 8.2.2 (3) - Formula (8.29)

The value of [\(d\)] in Formula (8.27) may be replaced by [\(a_v\)], for members with an effective shear span [\(a_{cs}\)] shorter than [\(4 \cdot d\)]. That condition is a matter of applicability rather than a branch of the formula, so it is left to the caller and not enforced here.

Parameters:

  • a_cs (MM) –

    [\(a_{cs}\)] Effective shear span with respect to the control section according to Formula (8.30), see Form8Dot30EffectiveShearSpan [\(mm\)].

  • 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_29.py 
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def __init__(self, a_cs: MM, d: MM) -> None:
    r"""[$a_v$] Mechanical shear span [$mm$].

    FprEN 1992-1-1:2023 (E) art 8.2.2 (3) - Formula (8.29)

    The value of [$d$] in Formula (8.27) may be replaced by [$a_v$], for members with an effective shear
    span [$a_{cs}$] shorter than [$4 \cdot d$]. That condition is a matter of applicability rather than a
    branch of the formula, so it is left to the caller and not enforced here.

    Parameters
    ----------
    a_cs : MM
        [$a_{cs}$] Effective shear span with respect to the control section according to Formula (8.30),
        see Form8Dot30EffectiveShearSpan [$mm$].
    d : MM
        [$d$] Effective depth [$mm$].
    """
    super().__init__()
    self.a_cs = a_cs
    self.d = d

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_29.Form8Dot29MechanicalShearSpan.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.29.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_29.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.29."""
    _equation: str = r"\sqrt{\frac{a_{cs}}{4} \cdot d}"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"a_{cs}": f"{self.a_cs:.{n}f}",
            r"\cdot d": rf"\cdot {self.d:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"a_{cs}": rf"{self.a_cs:.{n}f} \ mm",
            r"\cdot d": rf"\cdot {self.d:.{n}f} \ mm",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"a_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="mm",
    )