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formula_8_47

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_47

Formula 8.47 from FprEN-1992-1-1:2023: Chapter 8: Ultimate limit states (ULS).

Classes:

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_47.Form8Dot47StrainTensionChord 

Form8Dot47StrainTensionChord(f_td: N, a_st: MM2, e_s: MPA)

Bases: Formula

Class representing formula 8.47 for the calculation of [\(\epsilon_{xt}\)].

Strain of the tension chord where the following may be assumed unless more refined methods are used. [\(\epsilon_{xt} = \frac{F_{td}}{A_{st} \cdot E_{s}}\)]

Strain of the tension chord (dimensionless).

FprEN 1992-1-1:2023 art. 8.2.3 (7) - Formula (8.47)

Parameters:

  • f_td (N) –

    [\(F_{td}\)] Design value of the axial force in the tension chord [\(N\)].

  • a_st (MM2) –

    [\(A_{st}\)] Area of the longitudinal reinforcement in the tension chord [\(mm^2\)].

  • e_s (MPA) –

    [\(E_s\)] Modulus of elasticity of reinforcement steel [\(MPa\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_47.py 
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def __init__(
    self,
    f_td: N,
    a_st: MM2,
    e_s: MPA,
) -> None:
    r"""Strain of the tension chord (dimensionless).

    FprEN 1992-1-1:2023 art. 8.2.3 (7) - Formula (8.47)

    Parameters
    ----------
    f_td : N
        [$F_{td}$] Design value of the axial force in the tension chord [$N$].
    a_st : MM2
        [$A_{st}$] Area of the longitudinal reinforcement in the tension chord [$mm^2$].
    e_s : MPA
        [$E_s$] Modulus of elasticity of reinforcement steel [$MPa$].
    """
    super().__init__()
    self.f_td = f_td
    self.a_st = a_st
    self.e_s = e_s

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_47.Form8Dot47StrainTensionChord.latex 

latex(n: int = 4) -> LatexFormula

Returns LatexFormula object for formula 8.47.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_47.py 
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def latex(self, n: int = 4) -> LatexFormula:
    """Returns LatexFormula object for formula 8.47."""
    _equation: str = r"\frac{F_{td}}{A_{st} \cdot E_s}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"F_{td}": f"{self.f_td:.{n}f}",
            r"A_{st}": f"{self.a_st:.{n}f}",
            r"E_s": f"{self.e_s:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"F_{td}": rf"{self.f_td:.{n}f} \ N",
            r"A_{st}": rf"{self.a_st:.{n}f} \ mm^2",
            r"E_s": rf"{self.e_s:.{n}f} \ MPa",
        },
        True,
    )

    return LatexFormula(
        return_symbol=r"\epsilon_{xt}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="",
    )