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formula_6_47_subs

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs

Formula 6.47 from EN 1992-1-1:2004: Chapter 6 - Ultimate Limit State.

Classes:

  • SubForm6Dot47FactorK –

    Class representing the sub-formula which calculates the factor [\(k\)] for formula 6.47 .

  • SubForm6Dot47FactorRhoL –

    Class representing the sub-formula which calculates the factor [\(\rho_l\)] for formula 6.47 .

  • SubForm6Dot47FactorSigmaCp –

    Class representing the sub-formula which calculates the factor [\(\sigma_{cp}\)] for formula 6.47,.

  • SubForm6Dot47FactorSigmaCy –

    Class representing the sub-formula which calculates the factor [\(\sigma_{cy}\)] for formula 6.47.

  • SubForm6Dot47FactorSigmaCz –

    Class representing the sub-formula which calculates the factor [\(\sigma_{cz}\)] for formula 6.47.

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorK 

SubForm6Dot47FactorK(d: MM)

Bases: Formula

Class representing the sub-formula which calculates the factor [\(k\)] for formula 6.47 .

[\(k\)] Calculation of factor k.

EN 1992-1-1:2004 art.6.4.4(1) - Factor k for Formula (6.47)

Parameters:

  • d (MM) –

    [\(d\)] Effective depth [\(mm\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def __init__(self, d: MM) -> None:
    r"""[$k$] Calculation of factor k.

    EN 1992-1-1:2004 art.6.4.4(1) - Factor k for Formula (6.47)

    Parameters
    ----------
    d : MM
        [$d$] Effective depth [$mm$].
    """
    super().__init__()
    self.d = d

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorK.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for sub-formula 6.47 (factor k).

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for sub-formula 6.47 (factor k)."""
    _equation: str = r"\min \left( 1 + \sqrt{\frac{200}{d}}, 2.0 \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"d": f"{self.d:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"k",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorRhoL 

SubForm6Dot47FactorRhoL(rho_ly: DIMENSIONLESS, rho_lz: DIMENSIONLESS)

Bases: Formula

Class representing the sub-formula which calculates the factor [\(\rho_l\)] for formula 6.47 .

[\(\rho_l\)] Calculation of factor [\(\rho_l\)].

EN 1992-1-1:2004 art.6.4.4(1) - Factor rho_l for Formula (6.47)

Parameters:

  • rho_ly (DIMENSIONLESS) –

    [\(\rho_{ly}\)] Related to the bonded tension steel in y- drection. The value \(\rho_ly\) should be calculated as mean values taking into account a slab width equal to the column width plus 3d each side [\(-\)].

  • rho_lz (DIMENSIONLESS) –

    [\(\rho_{lz}\)] Related to the bonded tension steel in z- drection. The value \(\rho_lz\) should be calculated as mean values taking into account a slab width equal to the column width plus 3d each side [\(-\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def __init__(self, rho_ly: DIMENSIONLESS, rho_lz: DIMENSIONLESS) -> None:
    r"""[$\rho_l$] Calculation of factor [$\rho_l$].

    EN 1992-1-1:2004 art.6.4.4(1) - Factor rho_l for Formula (6.47)

    Parameters
    ----------
    rho_ly : DIMENSIONLESS
        [$\rho_{ly}$] Related to the bonded tension steel in y- drection. The value $\rho_ly$ should be calculated as mean values taking
        into account a slab width equal to the column width plus 3d each side [$-$].
    rho_lz : DIMENSIONLESS
        [$\rho_{lz}$] Related to the bonded tension steel in z- drection. The value $\rho_lz$ should be calculated as mean values taking
        into account a slab width equal to the column width plus 3d each side [$-$].
    """
    super().__init__()
    self.rho_ly = rho_ly
    self.rho_lz = rho_lz

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorRhoL.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for sub-formula 6.47 (factor rho_l).

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for sub-formula 6.47 (factor rho_l)."""
    _equation: str = r"\min \left( \sqrt{\rho_{ly} \cdot \rho_{lz}}, 0.02 \right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\rho_{ly}": f"{self.rho_ly:.{n}f}",
            r"\rho_{lz}": f"{self.rho_lz:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\rho_l",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorSigmaCp 

SubForm6Dot47FactorSigmaCp(sigma_cy: MPA, sigma_cz: MPA)

Bases: Formula

Class representing the sub-formula which calculates the factor [\(\sigma_{cp}\)] for formula 6.47,.

[\(\sigma_{cp}\)] Calculation of factor [\(\sigma_{cp}\)].

EN 1992-1-1:2004 art.6.4.4(1) - Factor sigma_cp for Formula (6.47)

Parameters:

  • sigma_cy (MPA) –

    [\(\sigma_{cy}\)] Normal concrete stress in the critical section in the y-direction [\(MPa\)], Positive if compression. See equation SubForm6Dot47FactorSigmaCy.

  • sigma_cz (MPA) –

    [\(\sigma_{cz}\)] Normal concrete stress inm the critical section in the z-direction [\(MPa\)], Positive if compression. See equation SubForm6Dot47FactorSigmaCz.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def __init__(self, sigma_cy: MPA, sigma_cz: MPA) -> None:
    r"""[$\sigma_{cp}$] Calculation of factor [$\sigma_{cp}$].

    EN 1992-1-1:2004 art.6.4.4(1) - Factor sigma_cp for Formula (6.47)

    Parameters
    ----------
    sigma_cy : MPA
        [$\sigma_{cy}$] Normal concrete stress in the critical section in the y-direction [$MPa$], Positive if compression.
        See equation SubForm6Dot47FactorSigmaCy.
    sigma_cz : MPA
        [$\sigma_{cz}$] Normal concrete stress inm the critical section in the z-direction [$MPa$], Positive if compression.
        See equation SubForm6Dot47FactorSigmaCz.
    """
    super().__init__()
    self.sigma_cy = sigma_cy
    self.sigma_cz = sigma_cz

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorSigmaCp.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for sub-formula 6.47 (sigma_cp).

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for sub-formula 6.47 (sigma_cp)."""
    _equation: str = r"\frac{\sigma_{cy} + \sigma_{cz}}{2}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\sigma_{cy}": f"{self.sigma_cy:.{n}f}",
            r"\sigma_{cz}": f"{self.sigma_cz:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\sigma_{cp}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="MPa",
    )

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorSigmaCy 

SubForm6Dot47FactorSigmaCy(n_ed_y: N, a_cy: MM2)

Bases: Formula

Class representing the sub-formula which calculates the factor [\(\sigma_{cy}\)] for formula 6.47.

[\(\sigma_{cy}\)] Calculation of factor [\(\sigma_{cy}\)].

EN 1992-1-1:2004 art.6.4.4(1) - Factor sigma_cy for Formula (6.47)

Parameters:

  • n_ed_y (N) –

    [\(N_{Ed,y}\)] Longitudinal forces across the full bay for internal columns and the logintudinal force across the control section for edge columns. The force may be from a load or prestressing action [\(N\)].

  • a_cy (MM2) –

    [\(A_{cy}\)] Cross-sectional area in y-direction [\(mm^2\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def __init__(self, n_ed_y: N, a_cy: MM2) -> None:
    r"""[$\sigma_{cy}$] Calculation of factor [$\sigma_{cy}$].

    EN 1992-1-1:2004 art.6.4.4(1) - Factor sigma_cy for Formula (6.47)

    Parameters
    ----------
    n_ed_y : N
        [$N_{Ed,y}$] Longitudinal forces across the full bay for internal columns and the logintudinal force across
        the control section for edge columns. The force may be from a load or prestressing action [$N$].
    a_cy : MM2
        [$A_{cy}$] Cross-sectional area in y-direction [$mm^2$].
    """
    super().__init__()
    self.n_ed_y = n_ed_y
    self.a_cy = a_cy

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorSigmaCy.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for sub-formula 6.47 (sigma_cy).

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for sub-formula 6.47 (sigma_cy)."""
    _equation: str = r"\frac{N_{Ed,y}}{A_{cy}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"N_{Ed,y}": f"{self.n_ed_y:.{n}f}",
            r"A_{cy}": f"{self.a_cy:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\sigma_{cy}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="MPa",
    )

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorSigmaCz 

SubForm6Dot47FactorSigmaCz(n_ed_z: N, a_cz: MM2)

Bases: Formula

Class representing the sub-formula which calculates the factor [\(\sigma_{cz}\)] for formula 6.47.

[\(\sigma_{cz}\)] Calculation of factor [\(\sigma_{cz}\)].

EN 1992-1-1:2004 art.6.4.4(1) - Factor sigma_cz for Formula (6.47)

Parameters:

  • n_ed_z (N) –

    [\(N_{Ed,z}\)] Longitudinal forces across the full bay for internal columns and the logintudinal force across the control section for edge columns. The force may be from a load or prestressing action [\(N\)].

  • a_cz (MM2) –

    [\(A_{cz}\)] Cross-sectional area in z-direction [\(mm^2\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def __init__(self, n_ed_z: N, a_cz: MM2) -> None:
    r"""[$\sigma_{cz}$] Calculation of factor [$\sigma_{cz}$].

    EN 1992-1-1:2004 art.6.4.4(1) - Factor sigma_cz for Formula (6.47)

    Parameters
    ----------
    n_ed_z : N
        [$N_{Ed,z}$] Longitudinal forces across the full bay for internal columns and the logintudinal force across
        the control section for edge columns. The force may be from a load or prestressing action [$N$].
    a_cz : MM2
        [$A_{cz}$] Cross-sectional area in z-direction [$mm^2$].
    """
    super().__init__()
    self.n_ed_z = n_ed_z
    self.a_cz = a_cz

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_47_subs.SubForm6Dot47FactorSigmaCz.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for sub-formula 6.47 sigma_cz.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_47_subs.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for sub-formula 6.47 sigma_cz."""
    _equation: str = r"\frac{N_{Ed,z}}{A_{cz}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"N_{Ed,z}": f"{self.n_ed_z:.{n}f}",
            r"A_{cz}": f"{self.a_cz:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"\sigma_{cz}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="MPa",
    )