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formula_6_51

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_51

Formula 6.51 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_51.Form6Dot51AppliedPunchingShearStressEccentricLoading 

Form6Dot51AppliedPunchingShearStressEccentricLoading(
    v_ed_red: N, u: MM, d: MM, k: DIMENSIONLESS, m_ed: NMM, w: MM2
)

Bases: Formula

Class representing formula 6.51 for the calculation of punching shear stress for eccentric loading [\(v_{Ed}\)] of slabs and column bases without shear reinforcement.

[\(v_{Ed}\)] Calculation of punching shear stress for eccentric loading of slabs and column bases without shear reinforcement.

EN 1992-1-1:2004 art.6.4.4(2) - Formula (6.51)

Parameters:

  • v_ed_red (N) –

    [\(V_{Ed,red}\)] Net applied punching force [\(N\)].

  • u (MM) –

    [\(u\)] Perimeter of the critical section [\(mm\)].

  • d (MM) –

    [\(d\)] Mean effective depth of the slab [\(mm\)].

  • k (DIMENSIONLESS) –

    [\(k\)] Coefficient dependent on the ratio between the column dimensions as defined in 6.4.3(3) or 6.4.3(4) [\(-\)].

  • m_ed (NMM) –

    [\(M_{Ed}\)] Design bending moment [\(Nmm\)].

  • w (MM2) –

    [\(W\)] Similar to [\(W_1\)] as defined in 6.4.3(3) and 6.4.3.(4) but for perimeter [\(u\)] [\(mm^2\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_51.py 
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def __init__(
    self,
    v_ed_red: N,
    u: MM,
    d: MM,
    k: DIMENSIONLESS,
    m_ed: NMM,
    w: MM2,
) -> None:
    r"""[$v_{Ed}$] Calculation of punching shear stress for eccentric loading of slabs and column bases without shear reinforcement.

    EN 1992-1-1:2004 art.6.4.4(2) - Formula (6.51)

    Parameters
    ----------
    v_ed_red : N
        [$V_{Ed,red}$] Net applied punching force [$N$].
    u : MM
        [$u$] Perimeter of the critical section [$mm$].
    d : MM
        [$d$] Mean effective depth of the slab [$mm$].
    k : DIMENSIONLESS
        [$k$] Coefficient dependent on the ratio between the column dimensions as defined in 6.4.3(3) or 6.4.3(4) [$-$].
    m_ed : NMM
        [$M_{Ed}$] Design bending moment [$Nmm$].
    w : MM2
        [$W$] Similar to [$W_1$] as defined in 6.4.3(3) and 6.4.3.(4) but for perimeter [$u$] [$mm^2$].
    """
    super().__init__()
    self.v_ed_red = v_ed_red
    self.u = u
    self.d = d
    self.k = k
    self.m_ed = m_ed
    self.w = w

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_51.Form6Dot51AppliedPunchingShearStressEccentricLoading.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.51.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_51.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.51."""
    _equation: str = r"\frac{V_{Ed,red}}{u \cdot d} \cdot \left(1 + k \cdot \frac{M_{Ed} \cdot u}{V_{Ed,red} \cdot W}\right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"V_{Ed,red}": f"{self.v_ed_red:.{n}f}",
            r"u": f"{self.u:.{n}f}",
            r" d": f" {self.d:.{n}f}",
            r"k": f"{self.k:.{n}f}",
            r"M_{Ed}": f"{self.m_ed:.{n}f}",
            r"W": f"{self.w:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"v_{Ed}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="MPa",
    )