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formula_5_16

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_16

Formula 5.16 from EN 1993-5:2007 Chapter 5 - Ultimate limit state.

Classes:

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_16.Form5Dot16PlasticDesignResistance 

Form5Dot16PlasticDesignResistance(a: MM2, f_y: MPA, gamma_m0: DIMENSIONLESS)

Bases: Formula

Class representing formula 5.16 for the calculation of the plastic design resistance of the cross-section, [\(N_{pl,Rd}\)].

[\(N_{pl,Rd}\)] Plastic design resistance of the cross-section [\(N\)].

EN 1993-5:2007 art.5.2.3 (9) - Formula (5.16)

Parameters:

  • a (MM2) –

    [\(A\)] Area of the cross-section [\(mm^2\)].

  • f_y (MPA) –

    [\(f_y\)] Yield strength [\(MPa\)].

  • gamma_m0 (DIMENSIONLESS) –

    [\(\gamma_{M0}\)] Partial factor according to 5.1.1 (4) [\(-\)].

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_16.py 
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def __init__(
    self,
    a: MM2,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
) -> None:
    r"""[$N_{pl,Rd}$] Plastic design resistance of the cross-section [$N$].

    EN 1993-5:2007 art.5.2.3 (9) - Formula (5.16)

    Parameters
    ----------
    a : MM2
        [$A$] Area of the cross-section [$mm^2$].
    f_y : MPA
        [$f_y$] Yield strength [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial factor according to 5.1.1 (4) [$-$].
    """
    super().__init__()
    self.a = a
    self.f_y = f_y
    self.gamma_m0 = gamma_m0

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_16.Form5Dot16PlasticDesignResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.16.

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_16.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.16."""
    return LatexFormula(
        return_symbol=r"N_{pl,Rd}",
        result=f"{self:.{n}f}",
        equation=r"\frac{A \cdot f_y}{\gamma_{M0}}",
        numeric_equation=rf"\frac{{{self.a:.{n}f} \cdot {self.f_y:.{n}f}}}{{{self.gamma_m0:.{n}f}}}",
        comparison_operator_label="=",
        unit="N",
    )