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formula_5_5

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_5

Formula 5.5 from EN 1993-5:2007 Chapter 5 - Ultimate limit states.

Classes:

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_5.Form5Dot5PlasticShearResistance 

Form5Dot5PlasticShearResistance(a_v: MM2, f_y: MPA, gamma_m_0: DIMENSIONLESS)

Bases: Formula

Class representing formula 5.5 for the design plastic shear resistance for each web.

([\(V_{pl,Rd}\)]) Calculate design plastic shear resistance for each web in [\(kN\)].

EN 1993-5:2007(E) art.5.2.2(4) - Formula (5.5)

Parameters:

  • a_v (MM2) –

    ([\(A_{v}\)]) Projected shear area for each web, acting in the same direction as VEd in [\(mm^2\)].

  • f_y (MPA) –

    ([\(f_{y}\)]) Yield strength in [\(MPa\)].

  • gamma_m_0 (DIMENSIONLESS) –

    ([\(\gamma_{M0}\)]) Partial factor for material properties in [\(-\)].

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_5.py 
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def __init__(
    self,
    a_v: MM2,
    f_y: MPA,
    gamma_m_0: DIMENSIONLESS,
) -> None:
    r"""([$V_{pl,Rd}$]) Calculate design plastic shear resistance for each web in [$kN$].

    EN 1993-5:2007(E) art.5.2.2(4) - Formula (5.5)

    Parameters
    ----------
    a_v : MM2
        ([$A_{v}$]) Projected shear area for each web, acting in the same direction as VEd in [$mm^2$].
    f_y : MPA
        ([$f_{y}$]) Yield strength in [$MPa$].
    gamma_m_0 : DIMENSIONLESS
        ([$\gamma_{M0}$]) Partial factor for material properties in [$-$].
    """
    super().__init__()
    self.a_v: float = a_v
    self.f_y: float = f_y
    self.gamma_m_0: DIMENSIONLESS = gamma_m_0

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_5.Form5Dot5PlasticShearResistance.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 5.5.

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_5.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 5.5."""
    return LatexFormula(
        return_symbol=r"V_{pl,Rd}",
        result=f"{self:.{n}f}",
        equation=latex_fraction(
            numerator="A_v f_y",
            denominator=r"\sqrt{3} \gamma_{M0}",
        ),
        numeric_equation=latex_fraction(
            numerator=rf"{self.a_v} \cdot {self.f_y}",
            denominator=rf"\sqrt{{3}} \cdot {self.gamma_m_0}",
        ),
        comparison_operator_label="=",
    )