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formula_8_20

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_20

Formula 8.20 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_20.Form8Dot20MinimumShearStressResistance 

Form8Dot20MinimumShearStressResistance(
    gamma_v: DIMENSIONLESS, f_ck: MPA, f_yd: MPA, d_dg: MM, d: MM
)

Bases: Formula

Class representing formula 8.20 for the calculation of the minimum shear stress resistance.

[\(\tau_{Rdc,min}\)] Minimum shear stress resistance [\(MPa\)].

FprEN 1992-1-1:2023 (E) art 8.2.1 (4) - Formula (8.20)

Parameters:

  • gamma_v (DIMENSIONLESS) –

    [\(\gamma_V\)] Partial factor for shear design according to Table 4.3 (NDP) or Tables A.1 (NDP) and A.2 (NDP) [\(-\)].

  • f_ck (MPA) –

    [\(f_{ck}\)] Characteristic compressive strength of concrete [\(MPa\)].

  • f_yd (MPA) –

    [\(f_{yd}\)] Design value of the yield strength which has been used to design the flexural reinforcement. In case of prestressed members without ordinary reinforcement it may be replaced by [\(f_{pd} - \sigma_{pm,\infty}\)], where [\(\sigma_{pm,\infty}\)] is the prestress in the tendons after losses [\(MPa\)].

  • d_dg (MM) –

    [\(d_{dg}\)] Size parameter describing the failure zone roughness, which depends on the concrete type and its aggregate properties. The standard gives it as [\(16 + D_{lower} \leq 40\)] for concrete with [\(f_{ck} \leq 60\)] MPa, and as [\(16 + D_{lower} \cdot \left(60/f_{ck}\right)^2 \leq 40\)] for concrete with [\(f_{ck} > 60\)] MPa, both in millimetres. [\(D_{lower}\)] is the smallest value of the upper sieve size [\(D\)] in an aggregate for the coarsest fraction of aggregates in the concrete permitted by the specification of concrete according to EN 206; where [\(D_{max}\)] is known it may replace [\(D_{lower}\)], see the NOTE 2 to 8.2.1(4) [\(mm\)].

  • d (MM) –

    [\(d\)] Effective depth of the flexural reinforcement. For prestressed members see 8.2.2(6) [\(mm\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_20.py 
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def __init__(self, gamma_v: DIMENSIONLESS, f_ck: MPA, f_yd: MPA, d_dg: MM, d: MM) -> None:
    r"""[$\tau_{Rdc,min}$] Minimum shear stress resistance [$MPa$].

    FprEN 1992-1-1:2023 (E) art 8.2.1 (4) - Formula (8.20)

    Parameters
    ----------
    gamma_v : DIMENSIONLESS
        [$\gamma_V$] Partial factor for shear design according to Table 4.3 (NDP) or Tables A.1 (NDP)
        and A.2 (NDP) [$-$].
    f_ck : MPA
        [$f_{ck}$] Characteristic compressive strength of concrete [$MPa$].
    f_yd : MPA
        [$f_{yd}$] Design value of the yield strength which has been used to design the flexural
        reinforcement. In case of prestressed members without ordinary reinforcement it may be replaced by
        [$f_{pd} - \sigma_{pm,\infty}$], where [$\sigma_{pm,\infty}$] is the prestress in the tendons after
        losses [$MPa$].
    d_dg : MM
        [$d_{dg}$] Size parameter describing the failure zone roughness, which depends on the concrete type
        and its aggregate properties. The standard gives it as [$16 + D_{lower} \leq 40$] for concrete with
        [$f_{ck} \leq 60$] MPa, and as [$16 + D_{lower} \cdot \left(60/f_{ck}\right)^2 \leq 40$] for concrete
        with [$f_{ck} > 60$] MPa, both in millimetres. [$D_{lower}$] is the smallest value of the upper sieve
        size [$D$] in an aggregate for the coarsest fraction of aggregates in the concrete permitted by the
        specification of concrete according to EN 206; where [$D_{max}$] is known it may replace
        [$D_{lower}$], see the NOTE 2 to 8.2.1(4) [$mm$].
    d : MM
        [$d$] Effective depth of the flexural reinforcement. For prestressed members see 8.2.2(6) [$mm$].
    """
    super().__init__()
    self.gamma_v = gamma_v
    self.f_ck = f_ck
    self.f_yd = f_yd
    self.d_dg = d_dg
    self.d = d

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_20.Form8Dot20MinimumShearStressResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.20.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_20.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.20."""
    _equation: str = r"\frac{11}{\gamma_V} \cdot \sqrt{\frac{f_{ck}}{f_{yd}} \cdot \frac{d_{dg}}{d}}"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"\gamma_V": f"{self.gamma_v:.{n}f}",
            r"f_{ck}": f"{self.f_ck:.{n}f}",
            r"f_{yd}": f"{self.f_yd:.{n}f}",
            r"d_{dg}": f"{self.d_dg:.{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"\gamma_V": f"{self.gamma_v:.{n}f}",
            r"f_{ck}": rf"{self.f_ck:.{n}f} \ MPa",
            r"f_{yd}": rf"{self.f_yd:.{n}f} \ MPa",
            r"d_{dg}": rf"{self.d_dg:.{n}f} \ mm",
            r"{d}": "{" + rf"{self.d:.{n}f} \ mm" + "}",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"\tau_{Rdc,min}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="MPa",
    )