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formula_8_25

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_25

Formula 8.25 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_25.Form8Dot25ShearStress 

Form8Dot25ShearStress(v_ed: N, s: MM3, i: MM4, t: MM)

Bases: Formula

Class representing formula 8.25 for the calculation of [\(\tau_{Ed}\)].

[\(\tau_{Ed}\)] Calculation of the design elastic shear stress [\(MPa\)].

EN 1993-1-1:2022 art.8.2.6(4) - Formula (8.25)

Parameters:

  • v_ed (N) –

    [\(V_{Ed}\)] Design value of the shear force [\(N\)].

  • s (MM3) –

    [\(S\)] First moment of area about the centroidal axis of that portion of the cross-section between the point at which the shear is required and the boundary of the cross-section [\(mm^3\)].

  • i (MM4) –

    [\(I\)] Second moment of area of the whole cross section [\(mm^4\)].

  • t (MM) –

    [\(t\)] Thickness at the examined point [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_25.py 
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def __init__(
    self,
    v_ed: N,
    s: MM3,
    i: MM4,
    t: MM,
) -> None:
    r"""[$\tau_{Ed}$] Calculation of the design elastic shear stress [$MPa$].

    EN 1993-1-1:2022 art.8.2.6(4) - Formula (8.25)

    Parameters
    ----------
    v_ed : N
        [$V_{Ed}$] Design value of the shear force [$N$].
    s : MM3
        [$S$] First moment of area about the centroidal axis of that portion of the cross-section between
        the point at which the shear is required and the boundary of the cross-section [$mm^3$].
    i : MM4
        [$I$] Second moment of area of the whole cross section [$mm^4$].
    t : MM
        [$t$] Thickness at the examined point [$mm$].
    """
    super().__init__()
    self.v_ed = v_ed
    self.s = s
    self.i = i
    self.t = t

codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_25.Form8Dot25ShearStress.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.25.

Source code in blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_25.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.25."""
    _equation: str = r"\frac{V_{Ed} \cdot S}{I \cdot t}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"V_{Ed}": f"{self.v_ed:.{n}f}",
            r"S": f"{self.s:.{n}f}",
            r"I": f"{self.i:.{n}f}",
            r" t": f" {self.t:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"V_{Ed}": rf"{self.v_ed:.{n}f} \ N",
            r"S": rf"{self.s:.{n}f} \ mm^3",
            r"I": rf"{self.i:.{n}f} \ mm^4",
            r" t": rf" {self.t:.{n}f} \ mm",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\tau_{Ed}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="MPa",
    )