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formula_6_13

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_13

Formula 6.13 from EN 1993-1-1:2005: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_13.Form6Dot13MCRdClass1And2 

Form6Dot13MCRdClass1And2(w_pl: MM3, f_y: MPA, gamma_m0: DIMENSIONLESS)

Bases: Formula

Class representing formula 6.13 for the calculation of [\(M_{c,Rd}\)].

[\(M_{c,Rd}\)] Calculation of the design resistance of the cross-section for bending about one principal axis [\(Nmm\)]. This equation is only valid for cross-sections with class 1, or 2.

EN 1993-1-1:2005 art.6.2.5(2) - Formula (6.13)

Parameters:

  • w_pl (MM3) –

    [\(W_{pl}\)] Plastic section modulus of the cross-section [\(mm^3\)].

  • f_y (MPA) –

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

  • gamma_m0 (DIMENSIONLESS) –

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

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_13.py 
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def __init__(
    self,
    w_pl: MM3,
    f_y: MPA,
    gamma_m0: DIMENSIONLESS,
) -> None:
    r"""[$M_{c,Rd}$] Calculation of the design resistance of the cross-section for bending about one principal axis [$Nmm$].
    This equation is only valid for cross-sections with class 1, or 2.

    EN 1993-1-1:2005 art.6.2.5(2) - Formula (6.13)

    Parameters
    ----------
    w_pl : MM3
        [$W_{pl}$] Plastic section modulus of the cross-section [$mm^3$].
    f_y : MPA
        [$f_y$] Yield strength of the material [$MPa$].
    gamma_m0 : DIMENSIONLESS
        [$\gamma_{M0}$] Partial safety factor for resistance of cross-sections.
    """
    super().__init__()
    self.w_pl = w_pl
    self.f_y = f_y
    self.gamma_m0 = gamma_m0

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_13.Form6Dot13MCRdClass1And2.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.13.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_13.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.13."""
    _equation: str = r"\frac{W_{pl} \cdot f_y}{\gamma_{M0}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"W_{pl}": f"{self.w_pl:.{n}f}",
            r"f_y": f"{self.f_y:.{n}f}",
            r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"M_{c,Rd}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="Nmm",
    )