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formula_6_78_79

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_78_79

Formula 6.78 and 6.79 from EN 1992-1-1:2004: Chapter 6 - Ultimate limit state.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_78_79.Form6Dot78And79FatigueResistance 

Form6Dot78And79FatigueResistance(
    v_ed_max: N, v_ed_min: N, v_rd_c: N, f_ck: DIMENSIONLESS
)

Bases: Formula

Class representing formula 6.78 and 6.79 for the calculation of the fatigue resistance.

[\(\sigma_{Rd,max}\)] Fatigue resistance check [\(-\)].

EN 1992-1-1:2004 art.6.8.7(4) - Formula (6.78 and 6.79)

Parameters:

  • v_ed_max (N) –

    [\(V_{Ed,max}\)] Design value of the maximum applied shear force under frequent load combination [\(N\)].

  • v_ed_min (N) –

    [\(V_{Ed,min}\)] Design value of the minimum applied shear force under frequent load combination in the cross-section where [\(V_{Ed,max}\)] occurs [\(N\)].

  • v_rd_c (N) –

    [\(V_{Rd,c}\)] Design value for shear-resistance according to Expression (6.2.a) [\(N\)].

  • f_ck (DIMENSIONLESS) –

    [\(f_{ck}\)] Characteristic compressive strength of concrete [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_78_79.py 
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def __init__(
    self,
    v_ed_max: N,
    v_ed_min: N,
    v_rd_c: N,
    f_ck: DIMENSIONLESS,
) -> None:
    r"""[$\sigma_{Rd,max}$] Fatigue resistance check [$-$].

    EN 1992-1-1:2004 art.6.8.7(4) - Formula (6.78 and 6.79)

    Parameters
    ----------
    v_ed_max : N
        [$V_{Ed,max}$] Design value of the maximum applied shear force under frequent load combination [$N$].
    v_ed_min : N
        [$V_{Ed,min}$] Design value of the minimum applied shear force under frequent load combination
        in the cross-section where [$V_{Ed,max}$] occurs [$N$].
    v_rd_c : N
        [$V_{Rd,c}$] Design value for shear-resistance according to Expression (6.2.a) [$N$].
    f_ck : DIMENSIONLESS
        [$f_{ck}$] Characteristic compressive strength of concrete [$MPa$].
    """
    super().__init__()
    self.v_ed_max = v_ed_max
    self.v_ed_min = v_ed_min
    self.v_rd_c = v_rd_c
    self.f_ck = f_ck

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_78_79.Form6Dot78And79FatigueResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.78/6.79.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_78_79.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.78/6.79."""
    _equation: str = (
        r"\begin{cases} \frac{\left|V_{Ed,max}\right|}{\left|V_{Rd,c}\right|} \leq "
        r"\min\left(0.5 + 0.45 \cdot \frac{\left|V_{Ed,min}\right|}{\left|V_{Rd,c}\right|}, "
        r"\begin{cases} 0.9 & \text{if } f_{ck} \le 50 \\ 0.8 & \text{if } f_{ck} > 50 \end{cases} \right) & \text{if } "
        r"\frac{V_{Ed,min}}{V_{Ed,max}} \geq 0 \\ \frac{\left|V_{Ed,max}\right|}{\left|V_{Rd,c}\right|} \leq 0.5 - "
        r"\frac{\left|V_{Ed,min}\right|}{\left|V_{Rd,c}\right|} & "
        r"\text{if } \frac{V_{Ed,min}}{V_{Ed,max}} < 0 \end{cases}"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            "V_{Ed,max}": f"{self.v_ed_max:.{n}f}",
            "V_{Ed,min}": f"{self.v_ed_min:.{n}f}",
            "V_{Rd,c}": f"{self.v_rd_c:.{n}f}",
            "f_{ck}": f"{self.f_ck:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if self.__bool__() else "\\text{Not OK}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="\\to",
        unit="",
    )