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formula_8_53

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_53

Formula 8.53 from FprEN 1992-1-1:2023: Chapter 8 - Ultimate Limit State.

Classes:

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_53.Form8Dot53TensileChordLimitForIntermediateSupportOrConcentratedLoads 

Form8Dot53TensileChordLimitForIntermediateSupportOrConcentratedLoads(
    m_ed_max: NMM, z: MM, n_ed: N
)

Bases: Formula

Class representing formula 8.53 for the calculation of the tensile chord limit in case of direct intermediate support or in the region of concentrated loads.

[\(F_{td,max}\)] Calculation of the chord force [\(N\)] in case of direct intermediate support or concentrated loads.

FprEN 1992-1-1:2023 art.8.5(8) - Formula (8.53)

Parameters:

  • m_ed_max (NMM) –

    [\(M_{Ed,max}\)] Maximum design moment along the member [\(Nmm\)].

  • z (MM) –

    [\(z\)] Internal lever arm [\(mm\)].

  • n_ed (N) –

    [\(N_{Ed}\)] Design value of normal force in the section [\(N\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_53.py 
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def __init__(
    self,
    m_ed_max: NMM,
    z: MM,
    n_ed: N,
) -> None:
    r"""[$F_{td,max}$] Calculation of the chord force [$N$] in case of direct intermediate support or
    concentrated loads.

    FprEN 1992-1-1:2023 art.8.5(8) - Formula (8.53)

    Parameters
    ----------
    m_ed_max : NMM
        [$M_{Ed,max}$] Maximum design moment along the member [$Nmm$].
    z : MM
        [$z$] Internal lever arm [$mm$].
    n_ed : N
        [$N_{Ed}$] Design value of normal force in the section [$N$].
    """
    super().__init__()
    self.m_ed_max = m_ed_max
    self.z = z
    self.n_ed = n_ed

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_53.Form8Dot53TensileChordLimitForIntermediateSupportOrConcentratedLoads.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.53.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_53.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.53."""
    _equation: str = r"\frac{M_{Ed,max}}{z} + \frac{N_{Ed}}{2}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"M_{Ed,max}": f"{self.m_ed_max:.{n}f}",
            r"z": f"{self.z:.{n}f}",
            r"N_{Ed}": f"{self.n_ed:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"M_{Ed,max}": rf"{self.m_ed_max:.{n}f} \ Nmm",
            r"z": rf"{self.z:.{n}f} \ mm",
            r"N_{Ed}": rf"{self.n_ed:.{n}f} \ N",
        },
        True,
    )
    return LatexFormula(
        return_symbol=r"F_{td,max}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="N",
    )