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formula_5_13n

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_13n

Formula 5.13N from EN 1992-1-1:2004: Chapter 5 Structural Analysis.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_13n.Form5Dot13nSlendernessCriterionIsolatedMembers 

Form5Dot13nSlendernessCriterionIsolatedMembers(
    a: DIMENSIONLESS,
    b: DIMENSIONLESS,
    c: DIMENSIONLESS,
    n_ed: N,
    a_c: MM2,
    f_cd: MPA,
)

Bases: Formula

Class representing formula 5.13N for the calculation of the slenderness limit where second order effects may be ignored.

[\(λ_{lim}\)] Calculation of the slenderness limit, where second order effects may be ignored (dimensionless).

Note: The value of [\(λ_{lim}\)] for use in a Country may be found in its National Annex. The recommended value follows from this equation.

EN 1992-1-1:2004 art.5.8.3.1 (1) - formula (5.13N)

Parameters:

  • a (DIMENSIONLESS) –

    [\(A\)] calculation value, based on the effective creep ratio [\(-\)]. Follows from equation 5.13A. If unknown, A = 0,7. Use your own implementation of this value or use the SubForm5Dot13aCreepRatio class.

  • b (DIMENSIONLESS) –

    [\(B\)] calculation value, based on the mechanical reinforcement ratio [\(-\)]. Follows from equation 5.13B. If unknown, B = 1,1. Use your own implementation of this value or use the SubForm5Dot13bMechanicalReinforcementFactor class.

  • c (DIMENSIONLESS) –

    [\(C\)] calculation value, based on the moment ratio [\(-\)]. Follows from equation 5.13C. If unknown, C = 0,7. Use your own implementation of this value or use the SubForm5Dot13cMomentRatio class.

  • n_ed (N) –

    [\(N_{Ed}\)] is the design value of the axial force [\(N\)].

  • a_c (MM2) –

    [\(A_c\)] is the area of the concrete section [\(mm^2\)].

  • f_cd (MPA) –

    [\(f_{cd}\)] is the design value of concrete compressive strength [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_13n.py 
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def __init__(self, a: DIMENSIONLESS, b: DIMENSIONLESS, c: DIMENSIONLESS, n_ed: N, a_c: MM2, f_cd: MPA) -> None:
    """[$λ_{lim}$] Calculation of the slenderness limit, where second order effects may be ignored (dimensionless).

    Note:
    The value of [$λ_{lim}$] for use in a Country may be found in its National Annex. The recommended value
    follows from this equation.

    EN 1992-1-1:2004 art.5.8.3.1 (1) - formula (5.13N)

    Parameters
    ----------
    a : DIMENSIONLESS
        [$A$] calculation value, based on the effective creep ratio [$-$].
        Follows from equation 5.13A. If unknown, A = 0,7.
        Use your own implementation of this value or use the `SubForm5Dot13aCreepRatio` class.
    b : DIMENSIONLESS
        [$B$] calculation value, based on the mechanical reinforcement ratio [$-$].
        Follows from equation 5.13B. If unknown, B = 1,1.
        Use your own implementation of this value or use the `SubForm5Dot13bMechanicalReinforcementFactor` class.
    c : DIMENSIONLESS
        [$C$] calculation value, based on the moment ratio [$-$].
        Follows from equation 5.13C. If unknown, C = 0,7.
        Use your own implementation of this value or use the `SubForm5Dot13cMomentRatio` class.
    n_ed : N
        [$N_{Ed}$] is the design value of the axial force [$N$].
    a_c : MM2
        [$A_c$] is the area of the concrete section [$mm^2$].
    f_cd :
        [$f_{cd}$] is the design value of concrete compressive strength [$MPa$].
    """
    super().__init__()
    self.a = a
    self.b = b
    self.c = c
    self.n_ed = n_ed
    self.a_c = a_c
    self.f_cd = f_cd

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_13n.Form5Dot13nSlendernessCriterionIsolatedMembers.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.13N.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_13n.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.13N."""
    _equation: str = r"\frac{20 \cdot A \cdot B \cdot C}{\sqrt{N_{Ed} \cdot A_c \cdot f_{cd}}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A_c": f"{self.a_c:.{n}f}",
            r"A": f"{self.a:.{n}f}",
            r"B": f"{self.b:.{n}f}",
            r"C": f"{self.c:.{n}f}",
            r"N_{Ed}": f"{self.n_ed:.{n}f}",
            r"f_{cd}": f"{self.f_cd:.{n}f}",
        },
        True,
    )

    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"A_c": rf"{self.a_c:.{n}f} \ mm^2",
            r"A": f"{self.a:.{n}f}",
            r"B": f"{self.b:.{n}f}",
            r"C": f"{self.c:.{n}f}",
            r"N_{Ed}": rf"{self.n_ed:.{n}f} \ N",
            r"f_{cd}": rf"{self.f_cd:.{n}f} \ MPa",
        },
    )
    return LatexFormula(
        return_symbol=r"\lambda_{lim}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="-",
    )

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_13n.SubForm5Dot13aCreepRatio 

SubForm5Dot13aCreepRatio(phi_ef: DIMENSIONLESS)

Bases: Formula

Class representing sub-formula for [\(A\)] in formula (5.13N).

[\(A\)] Calculation of the factor [\(A\)] in formula (5.13N).

EN 1992-1-1:2004 art.5.8.3.1 (1) - formula (5.13N)

Parameters:

  • phi_ef (DIMENSIONLESS) –

    [\(\phi_{ef}\)] Effective creep ratio; see 5.8.4 (If [\(\phi_{ef}\)] is not known, A = 0.7)

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_13n.py 
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def __init__(
    self,
    phi_ef: DIMENSIONLESS,
) -> None:
    r"""[$A$] Calculation of the factor [$A$] in formula (5.13N).

    EN 1992-1-1:2004 art.5.8.3.1 (1) - formula (5.13N)

    Parameters
    ----------
    phi_ef : DIMENSIONLESS
        [$\phi_{ef}$] Effective creep ratio; see 5.8.4 (If [$\phi_{ef}$] is not known, A = 0.7)
    """
    super().__init__()
    self.phi_ef = phi_ef

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_13n.SubForm5Dot13aCreepRatio.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.13a.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_13n.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.13a."""
    _equation: str = r"\frac{1}{(1 + 0.2 \cdot \phi_{ef})}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"\phi_{ef}": f"{self.phi_ef:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"A",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="-",
    )

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_13n.SubForm5Dot13bMechanicalReinforcementFactor 

SubForm5Dot13bMechanicalReinforcementFactor(
    a_s: MM2, f_yd: MPA, a_c: MM2, f_cd: MPA
)

Bases: Formula

Class representing sub-formula for [\(B\)] in formula (5.13N).

[\(B\)] Calculation of the factor [\(B\)] in formula (5.13N).

EN 1992-1-1:2004 art.5.8.3.1 (1) - formula (5.13N)

Parameters:

  • a_s (MM2) –

    [\(A_s\)] is the total area of longitudinal reinforcement [\(mm^2\)].

  • f_yd (MPA) –

    [\(f_{yd}\)] is the design yield stress of the reinforcement [\(MPa\)].

  • a_c (MM2) –

    [\(A_c\)] is the area of concrete section [\(mm^2\)].

  • f_cd (MPA) –

    [\(f_{cd}\)] is the design value of concrete compressive strength [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_13n.py 
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def __init__(
    self,
    a_s: MM2,
    f_yd: MPA,
    a_c: MM2,
    f_cd: MPA,
) -> None:
    r"""[$B$] Calculation of the factor [$B$] in formula (5.13N).

    EN 1992-1-1:2004 art.5.8.3.1 (1) - formula (5.13N)

    Parameters
    ----------
    a_s : MM2
        [$A_s$] is the total area of longitudinal reinforcement [$mm^2$].
    f_yd : MPA
        [$f_{yd}$] is the design yield stress of the reinforcement [$MPa$].
    a_c : MM2
        [$A_c$] is the area of concrete section [$mm^2$].
    f_cd : MPA
        [$f_{cd}$] is the design value of concrete compressive strength [$MPa$].
    """
    super().__init__()
    self.a_s = a_s
    self.f_yd = f_yd
    self.a_c = a_c
    self.f_cd = f_cd

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_13n.SubForm5Dot13bMechanicalReinforcementFactor.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.13b.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_13n.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.13b."""
    _equation: str = r"\sqrt{1 + 2 \cdot \frac{A_s \cdot f_{yd}}{A_c \cdot f_{cd}}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A_s": f"{self.a_s:.{n}f}",
            r"f_{yd}": f"{self.f_yd:.{n}f}",
            r"A_c": f"{self.a_c:.{n}f}",
            r"f_{cd}": f"{self.f_cd:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"A_s": rf"{self.a_s:.{n}f} \ mm^2",
            r"f_{yd}": rf"{self.f_yd:.{n}f} \ MPa",
            r"A_c": rf"{self.a_c:.{n}f} \ mm^2",
            r"f_{cd}": rf"{self.f_cd:.{n}f} \ MPa",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"B",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="-",
    )

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_13n.SubForm5Dot13cMomentRatio 

SubForm5Dot13cMomentRatio(m_01: KNM, m_02: KNM)

Bases: Formula

Class representing sub-formula for [\(C\)] in formula (5.13N).

[\(C\)] Calculation of the factor [\(C\)] in formula (5.13N).

EN 1992-1-1:2004 art.5.8.3.1 (1) - formula (5.13)

Parameters:

  • m_01 (KNM) –

    [\(M_{01}\)] is one of the first order end moments [\(kNm\)].

  • m_02 (KNM) –

    [\(M_{02}\)] is one of the first order end moments [\(kNm\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_13n.py 
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def __init__(
    self,
    m_01: KNM,
    m_02: KNM,
) -> None:
    r"""[$C$] Calculation of the factor [$C$] in formula (5.13N).

    EN 1992-1-1:2004 art.5.8.3.1 (1) - formula (5.13)

    Parameters
    ----------
    m_01 : KNM
        [$M_{01}$] is one of the first order end moments [$kNm$].
    m_02 : KNM
        [$M_{02}$] is one of the first order end moments [$kNm$].
    """
    super().__init__()
    self.m_01 = m_01
    self.m_02 = m_02

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_13n.SubForm5Dot13cMomentRatio.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.13b.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_13n.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.13b."""
    _equation: str = r"1.7 - \frac{M_{01}}{M_{02}}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"M_{01}": f"{self.m_01:.{n}f}",
            r"M_{02}": f"{self.m_02:.{n}f}",
        },
        False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        _equation,
        {
            r"M_{01}": rf"{self.m_01:.{n}f} \ kNm",
            r"M_{02}": rf"{self.m_02:.{n}f} \ kNm",
        },
    )
    return LatexFormula(
        return_symbol=r"C",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="-",
    )