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formula_8_7

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_7

Formula 8.7 from EN 1993-1-1:2022: Chapter 8 - Ultimate Limit State.

Classes:

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_7.Form8Dot7AdditionalMoment 

Form8Dot7AdditionalMoment(n_ed: N, e_n: MM)

Bases: Formula

Class representing formula 8.7 for the calculation of additional moment [\(\Delta M_{Ed}\)].

[\(\Delta M_{Ed}\)] Calculation of the additional moment [\(Nmm\)].

EN 1993-1-1:2022 art.8.2.2.5(3) - Formula (8.7)

Notes

Where a class 4 cross-section is subjected to an axial compression force, the method given in EN 1993-1-5 should be used to determine the possible shift [\(e_{N}\)] of the centroid of the effective area [\(A_{eff}\)] relative to the centre of gravity of the gross cross-section and the resulting additional moment according to this formula.

Note: The sign of the additional moment depends on the effect in the combination of internal forces and moments, see 8.2.9.3(2).

Parameters:

  • n_ed (N) –

    [\(N_{Ed}\)] Axial compression force [\(N\)].

  • e_n (MM) –

    [\(e_{N}\)] Shift of the centroid of the effective area relative to the centre of gravity of the gross cross section [\(mm\)]. The method given in EN 1993-1-5 should be used to determine the possible shift [\(e_{N}\)] of the centroid of the effective area [\(A_{eff}\)] relative to the centre of gravity of the gross cross section.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_7.py 
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def __init__(
    self,
    n_ed: N,
    e_n: MM,
) -> None:
    r"""[$\Delta M_{Ed}$] Calculation of the additional moment [$Nmm$].

    EN 1993-1-1:2022 art.8.2.2.5(3) - Formula (8.7)

    Notes
    -----
    Where a class 4 cross-section is subjected to an axial compression force, the method given in EN 1993-1-5 should be used to
    determine the possible shift [$e_{N}$] of the centroid of the effective area [$A_{eff}$] relative to the centre of gravity
    of the gross cross-section and the resulting additional moment according to this formula.

    Note: The sign of the additional moment depends on the effect in the combination of internal forces and moments, see 8.2.9.3(2).

    Parameters
    ----------
    n_ed : N
        [$N_{Ed}$] Axial compression force [$N$].
    e_n : MM
        [$e_{N}$] Shift of the centroid of the effective area relative to the centre of gravity of the gross cross section [$mm$].
        The method given in EN 1993-1-5 should be used to determine the possible shift [$e_{N}$] of the centroid of the effective
        area [$A_{eff}$] relative to the centre of gravity of the gross cross section.
    """
    super().__init__()
    self.n_ed = n_ed
    self.e_n = e_n

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_7.Form8Dot7AdditionalMoment.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.7.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_7.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.7."""
    _equation: str = r"N_{Ed} \cdot e_{N}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"N_{Ed}": f"{self.n_ed:.{n}f}",
            r"e_{N}": f"{self.e_n:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"N_{Ed}": rf"{self.n_ed:.{n}f} \ N",
            r"e_{N}": rf"{self.e_n:.{n}f} \ mm",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\Delta M_{Ed}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="Nmm",
    )