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formula_6_4

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_4

Formula 6.4 from EN 1992-1-1:2004: Chapter 6 - Ultimate Limit State.

Classes:

  • Form6Dot4ShearResistance –

    Class representing formula 6.4 for the calculation of the shear resistance in regions uncracked in bending, [\(V_{Rd,c}\)].

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_4.Form6Dot4ShearResistance 

Form6Dot4ShearResistance(
    i: MM4, b_w: MM, s: MM3, f_ctd: MPA, alpha_l: DIMENSIONLESS, sigma_cp: MPA
)

Bases: Formula

Class representing formula 6.4 for the calculation of the shear resistance in regions uncracked in bending, [\(V_{Rd,c}\)].

[\(V_{Rd,c}\)] Shear resistance in regions uncracked in bending [\(kN\)].

EN 1992-1-1:2004 art.6.2.2(2) - Formula (6.4)

Parameters:

  • i (MM4) –

    [\(I\)] Second moment of area [\(mm^4\)].

  • b_w (MM) –

    [\(b_w\)] Width of the cross-section at the centroidal axis, see equation 6.16 and 6.17 [\(mm\)].

  • s (MM3) –

    [\(S\)] First moment of area above and about the centroidal axis [\(mm^3\)].

  • f_ctd (MPA) –

    [\(f_{ctd}\)] Design tensile strength of concrete [\(MPa\)].

  • alpha_l (DIMENSIONLESS) –

    [\(\alpha_l\)] [\(l_x / l_{pt2} \leq 1.0\)] for pretensioned tendons, [\(1.0\)] for other types of prestressing [\(-\)].

  • sigma_cp (MPA) –

    [\(\sigma_{cp}\)] Concrete compressive stress at the centroidal axis due to axial loading and/or prestressing [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_4.py 
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def __init__(
    self,
    i: MM4,
    b_w: MM,
    s: MM3,
    f_ctd: MPA,
    alpha_l: DIMENSIONLESS,
    sigma_cp: MPA,
) -> None:
    r"""[$V_{Rd,c}$] Shear resistance in regions uncracked in bending [$kN$].

    EN 1992-1-1:2004 art.6.2.2(2) - Formula (6.4)

    Parameters
    ----------
    i : MM4
        [$I$] Second moment of area [$mm^4$].
    b_w : MM
        [$b_w$] Width of the cross-section at the centroidal axis, see equation 6.16 and 6.17 [$mm$].
    s : MM3
        [$S$] First moment of area above and about the centroidal axis [$mm^3$].
    f_ctd : MPA
        [$f_{ctd}$] Design tensile strength of concrete [$MPa$].
    alpha_l : DIMENSIONLESS
        [$\alpha_l$] [$l_x / l_{pt2} \leq 1.0$] for pretensioned tendons, [$1.0$] for other types of prestressing [$-$].
    sigma_cp : MPA
        [$\sigma_{cp}$] Concrete compressive stress at the centroidal axis due to axial loading and/or prestressing [$MPa$].
    """
    super().__init__()
    self.i = i
    self.b_w = b_w
    self.s = s
    self.f_ctd = f_ctd
    self.alpha_l = alpha_l
    self.sigma_cp = sigma_cp

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_4.Form6Dot4ShearResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.4.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_4.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.4."""
    return LatexFormula(
        return_symbol=r"V_{Rd,c}",
        result=f"{self:.{n}f}",
        equation=r"\frac{I \cdot b_w}{S} \cdot \sqrt{(f_{ctd})^2 + \alpha_l \cdot \sigma_{cp} \cdot f_{ctd}}",
        numeric_equation=rf"\frac{{{self.i:.{n}f} \cdot {self.b_w:.{n}f}}}{{{self.s:.{n}f}}} \cdot "
        rf"\sqrt{{({self.f_ctd:.{n}f})^2 + {self.alpha_l:.{n}f} \cdot {self.sigma_cp:.{n}f} \cdot {self.f_ctd:.{n}f}}}",
        comparison_operator_label="=",
        unit="N",
    )