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formula_8_45

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_45

Formula 8.45 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_45.Form8Dot45CheckAxialForceY 

Form8Dot45CheckAxialForceY(n_ed: N, n_pl_rd: N)

Bases: ComparisonFormula

Class representing formula 8.45 for checking axial force about the y-y axis.

For doubly symmetrical I- and H-sections or other flanges sections, allowance need not be made for the effect of the axial force on the plastic resistance moment about the y-y axis when 8.45 and 8.46 are satisfied.

EN 1993-1-1:2022 art.8.2.9.1(4) - Formula (8.45)

Parameters:

  • n_ed (N) –

    [\(N_{Ed}\)] Design axial force [\(N\)].

  • n_pl_rd (N) –

    [\(N_{pl,Rd}\)] Plastic resistance normal force [\(N\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_45.py 
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def __init__(
    self,
    n_ed: N,
    n_pl_rd: N,
) -> None:
    r"""For doubly symmetrical I- and H-sections or other flanges sections,
    allowance need not be made for the effect of the axial force on the
    plastic resistance moment about the y-y axis when 8.45 and 8.46 are satisfied.

    EN 1993-1-1:2022 art.8.2.9.1(4) - Formula (8.45)

    Parameters
    ----------
    n_ed : N
        [$N_{Ed}$] Design axial force [$N$].
    n_pl_rd : N
        [$N_{pl,Rd}$] Plastic resistance normal force [$N$].
    """
    super().__init__()
    self.n_ed = n_ed
    self.n_pl_rd = n_pl_rd

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_45.Form8Dot45CheckAxialForceY.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.45.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_45.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.45."""
    _equation: str = r"N_{Ed} \leq 0.25 \cdot N_{pl,Rd}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        replacements={
            r"N_{Ed}": f"{self.n_ed:.{n}f}",
            r"N_{pl,Rd}": f"{self.n_pl_rd:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        replacements={
            r"N_{Ed}": rf"{self.n_ed:.{n}f} \ N",
            r"N_{pl,Rd}": rf"{self.n_pl_rd:.{n}f} \ N",
        },
        unique_symbol_check=True,
    )
    return LatexFormula(
        return_symbol="CHECK",
        result="OK" if bool(self) else "\\text{Not OK}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="\\to",
        unit="",
    )