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formula_8_28

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_28

Formula 8.28 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_28.Form8Dot28LongitudinalReinforcementRatio 

Form8Dot28LongitudinalReinforcementRatio(a_sl: MM2, b_w: MM, d: MM)

Bases: Formula

Class representing formula 8.28 for the calculation of the longitudinal tensile reinforcement ratio.

Which effective depth belongs here is not settled by the standard. The "where" list is shared between Formulas (8.27) and (8.28) and says that [\(d\)] may be refined according to 8.2.2(3) and 8.2.2(4), while both of those paragraphs name Formula (8.27) alone: (3) replaces [\(d\)] in Formula (8.27) by the mechanical shear span [\(a_v\)], and (4) multiplies [\(d\)] in Formula (8.27) or [\(a_v\)] in Formula (8.29) by [\(k_{vp}\)]. Neither mentions (8.28).

This class therefore takes the unrefined effective depth. A caller who reads the shared list the other way can pass the refined value instead, and should be aware that it then also enters (8.27) through [\(\rho_l\)].

[\(\rho_l\)] Longitudinal tensile reinforcement ratio [\(-\)].

FprEN 1992-1-1:2023 (E) art 8.2.2 (2) - Formula (8.28)

Parameters:

  • a_sl (MM2) –

    [\(A_{sl}\)] Effective area of tensile reinforcement at the distance [\(d\)] beyond the section considered, see Figure 8.7 [\(mm^2\)].

  • b_w (MM) –

    [\(b_w\)] Width of the cross-section of linear members. The width [\(b_w\)] for cross-sections with variable width and for circular cross-sections is defined in 8.2.3(9) [\(mm\)].

  • d (MM) –

    [\(d\)] Effective depth [\(d_{nom}\)]. The value [\(d\)] may be refined according to 8.2.2(3) and 8.2.2(4) for non-slender members and members with axial force [\(mm\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_28.py 
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def __init__(self, a_sl: MM2, b_w: MM, d: MM) -> None:
    r"""[$\rho_l$] Longitudinal tensile reinforcement ratio [$-$].

    FprEN 1992-1-1:2023 (E) art 8.2.2 (2) - Formula (8.28)

    Parameters
    ----------
    a_sl : MM2
        [$A_{sl}$] Effective area of tensile reinforcement at the distance [$d$] beyond the section considered,
        see Figure 8.7 [$mm^2$].
    b_w : MM
        [$b_w$] Width of the cross-section of linear members. The width [$b_w$] for cross-sections with variable width
        and for circular cross-sections is defined in 8.2.3(9) [$mm$].
    d : MM
        [$d$] Effective depth [$d_{nom}$]. The value [$d$] may be refined according to 8.2.2(3) and 8.2.2(4) for
        non-slender members and members with axial force [$mm$].
    """
    super().__init__()
    self.a_sl = a_sl
    self.b_w = b_w
    self.d = d

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_28.Form8Dot28LongitudinalReinforcementRatio.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.28.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_28.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.28."""
    _equation: str = r"\frac{A_{sl}}{b_w \cdot d}"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"A_{sl}": f"{self.a_sl:.{n}f}",
            r"b_w": f"{self.b_w:.{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_{sl}": rf"{self.a_sl:.{n}f} \ mm^2",
            r"b_w": rf"{self.b_w:.{n}f} \ mm",
            r"\cdot d": rf"\cdot {self.d:.{n}f} \ mm",
        },
        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="-",
    )