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formula_5_20

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_20

Formula 5.20 from EN 1993-5:2007: Chapter 5 - Ultimate Limit States.

Classes:

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_20.Form5Dot20ReducedMomentResistanceClass2ZProfiles 

Form5Dot20ReducedMomentResistanceClass2ZProfiles(
    m_c_rd: KNM, n_ed: KN, n_pl_rd: KN
)

Bases: Formula

Class representing formula 5.20 for the calculation of [\(M_N,Rd\)] for Class 2 Z-profiles.

[\(M_N,Rd\)] Calculation of the reduced design moment resistance allowing for the axial force[\(kNm\)].

EN 1993-5:2007 art. 5.2.3 (11) - Formula (5.20)

Parameters:

  • m_c_rd (KNM) –

    [\(M_c,Rd\)] Design moment resistance of the cross-section [\(kNm\)].

  • n_ed (KN) –

    [\(N_Ed\)] Design value of the axial force [\(kN\)].

  • n_pl_rd (KN) –

    [\(N_pl,Rd\)] Design plastic resistance of the cross-section [\(kN\)].

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_20.py 
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def __init__(
    self,
    m_c_rd: KNM,
    n_ed: KN,
    n_pl_rd: KN,
) -> None:
    r"""[$M_N,Rd$] Calculation of the reduced design moment resistance allowing for the axial force[$kNm$].

    EN 1993-5:2007 art. 5.2.3 (11) - Formula (5.20)

    Parameters
    ----------
    m_c_rd : KNM
        [$M_c,Rd$] Design moment resistance of the cross-section [$kNm$].
    n_ed : KN
        [$N_Ed$] Design value of the axial force [$kN$].
    n_pl_rd : KN
        [$N_pl,Rd$] Design plastic resistance of the cross-section [$kN$].
    """
    super().__init__()
    self.m_c_rd = m_c_rd
    self.n_ed = n_ed
    self.n_pl_rd = n_pl_rd

codes.eurocode.en_1993_5_2007.chapter_5_ultimate_limit_states.formula_5_20.Form5Dot20ReducedMomentResistanceClass2ZProfiles.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.20.

Source code in blueprints/codes/eurocode/en_1993_5_2007/chapter_5_ultimate_limit_states/formula_5_20.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.20."""
    _equation: str = r"1.11 \cdot M_{c,Rd} \cdot \left(1 - \frac{N_{Ed}}{N_{pl,Rd}}\right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"M_{c,Rd}": f"{self.m_c_rd:.{n}f}",
            r"N_{Ed}": f"{self.n_ed:.{n}f}",
            r"N_{pl,Rd}": f"{self.n_pl_rd:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"M_{N,Rd}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="kNm",
    )