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formula_6_21

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_21

Formula 6.21 from EN 1993-1-1:2005: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_21.Form6Dot21ShearStressIOrHSection 

Form6Dot21ShearStressIOrHSection(v_ed: N, a_w: MM2, a_f: MM2)

Bases: Formula

Class representing formula 6.21 for the calculation of [\(\tau_{Ed}\)].

[\(\tau_{Ed}\)] Calculation of the design elastic shear stress [\(MPa\)]. For I- or H-sections the shear stress in the web may be taken with this equation.

EN 1993-1-1:2005 art.6.2.6(5) - Formula (6.21)

Parameters:

  • v_ed (N) –

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

  • a_w (MM2) –

    [\(A_w\)] Area of the web [\(mm^2\)].

  • a_f (MM2) –

    [\(A_f\)] Area of one flange [\(mm^2\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_21.py 
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def __init__(
    self,
    v_ed: N,
    a_w: MM2,
    a_f: MM2,
) -> None:
    r"""[$\tau_{Ed}$] Calculation of the design elastic shear stress [$MPa$].
    For I- or H-sections the shear stress in the web may be taken with this equation.

    EN 1993-1-1:2005 art.6.2.6(5) - Formula (6.21)

    Parameters
    ----------
    v_ed : N
        [$V_{Ed}$] Design shear force [$N$].
    a_w : MM2
        [$A_w$] Area of the web [$mm^2$].
    a_f : MM2
        [$A_f$] Area of one flange [$mm^2$].
    """
    super().__init__()
    self.v_ed = v_ed
    self.a_w = a_w
    self.a_f = a_f

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_21.Form6Dot21ShearStressIOrHSection.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.21.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_21.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.21."""
    _equation: str = r"\frac{V_{Ed}}{A_w} \text{ if } A_f / A_w \ge 0.6"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"V_{Ed}": f"{self.v_ed:.{n}f}",
            r"A_w": f"{self.a_w:.{n}f}",
            r"A_f": f"{self.a_f:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\tau_{Ed}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="MPa",
    )