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formula_6_30

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_30

Formula 6.30 from NEN-EN 1993-1-1+A1:2016: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_30.Form6Dot30ReducedPlasticResistanceMoment 

Form6Dot30ReducedPlasticResistanceMoment(
    w_pl_y: MM3,
    rho: DIMENSIONLESS,
    h_w: MM,
    t_w: MM,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
    m_y_c_rd: NMM,
)

Bases: Formula

Class representing formula 6.30 for the calculation of [\(M_{y,V,Rd}\)].

[\(M_{y,V,Rd}\)] Reduced design plastic resistance moment [\(Nmm\)].

NEN-EN 1993-1-1+A1:2016 art.6.2.8(5) - Formula (6.30)

Parameters:

  • w_pl_y (MM3) –

    [\(W_{pl,y}\)] Plastic section modulus about the y-axis [\(mm^3\)].

  • rho (DIMENSIONLESS) –

    [\(\rho\)] Shear force ratio (see 6.2.8 (3) or equation 6.29 (rho)) [-].

  • h_w (MM) –

    [\(h_w\)] Web height [\(mm\)].

  • t_w (MM) –

    [\(t_w\)] Web thickness [\(mm\)].

  • f_y (MPA) –

    [\(f_y\)] Yield strength of the material [\(MPa\)].

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial safety factor for resistance of cross-sections [-].

  • m_y_c_rd (NMM) –

    [\(M_{y,c,Rd}\)] Design resistance moment, obtained from 6.2.5(2) [\(Nmm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_30.py 
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def __init__(
    self,
    w_pl_y: MM3,
    rho: DIMENSIONLESS,
    h_w: MM,
    t_w: MM,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
    m_y_c_rd: NMM,
) -> None:
    r"""[$M_{y,V,Rd}$] Reduced design plastic resistance moment [$Nmm$].

    NEN-EN 1993-1-1+A1:2016 art.6.2.8(5) - Formula (6.30)

    Parameters
    ----------
    w_pl_y : MM3
        [$W_{pl,y}$] Plastic section modulus about the y-axis [$mm^3$].
    rho : DIMENSIONLESS
        [$\rho$] Shear force ratio (see 6.2.8 (3) or equation 6.29 (rho)) [-].
    h_w : MM
        [$h_w$] Web height [$mm$].
    t_w : MM
        [$t_w$] Web thickness [$mm$].
    f_y : MPA
        [$f_y$] Yield strength of the material [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial safety factor for resistance of cross-sections [-].
    m_y_c_rd : NMM
        [$M_{y,c,Rd}$] Design resistance moment, obtained from 6.2.5(2) [$Nmm$].
    """
    super().__init__()
    self.w_pl_y = w_pl_y
    self.rho = rho
    self.h_w = h_w
    self.t_w = t_w
    self.f_y = f_y
    self.gamma_m0 = gamma_m0
    self.m_y_c_rd = m_y_c_rd

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_30.Form6Dot30ReducedPlasticResistanceMoment.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.30.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_30.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.30."""
    _equation: str = (
        r"\min\left(\frac{\left[W_{pl,y} - \frac{\rho \cdot (h_w \cdot t_w)^2}{4 \cdot t_w}\right] \cdot f_y}{\gamma_{M0}}, M_{y,c,Rd}\right)"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"W_{pl,y}": f"{self.w_pl_y:.{n}f}",
            r"\rho": f"{self.rho:.{n}f}",
            r"h_w": f"{self.h_w:.{n}f}",
            r"t_w": f"{self.t_w:.{n}f}",
            r"f_y": f"{self.f_y:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
            r"M_{y,c,Rd}": f"{self.m_y_c_rd:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"W_{pl,y}": rf"{self.w_pl_y:.{n}f} \ mm^3",
            r"\rho": rf"{self.rho:.{n}f}",
            r"h_w": rf"{self.h_w:.{n}f} \ mm",
            r"t_w": rf"{self.t_w:.{n}f} \ mm",
            r"f_y": rf"{self.f_y:.{n}f} \ MPa",
            r"\gamma_{M0}": rf"{self.gamma_m0:.{n}f}",
            r"M_{y,c,Rd}": rf"{self.m_y_c_rd:.{n}f} \ Nmm",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"M_{y,V,Rd}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="Nmm",
    )