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formula_5_21

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_21

Formula 5.21 from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

  • Form5Dot21NominalStiffness –

    Class representing formula 5.21 for the calculation of the nominal stiffness of slender compression members

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_21.Form5Dot21NominalStiffness 

Form5Dot21NominalStiffness(
    k_c: DIMENSIONLESS,
    e_cd: MPA,
    i_c: MM4,
    k_s: DIMENSIONLESS,
    e_s: MPA,
    i_s: MM4,
)

Bases: Formula

Class representing formula 5.21 for the calculation of the nominal stiffness of slender compression members with arbitrary cross-section, [\(EI\)] [\(Nmm^2\)].

[\(EI\)] Nominal stiffness of slender compression members with arbitrary cross-section.

EN 1992-1-1:2004 art.5.8.7.2(2) or (3) - Formula (5.21)

Parameters:

  • k_c (DIMENSIONLESS) –

    [\(K_{c}\)] is a factor for effects of cracking, creep etc. see 5.8.7.2 (2) or (3).

  • e_cd (MPA) –

    [\(E_{cd}\)] is the design value of the modulus of elasticity of concrete, see 5.8.6 (3)

  • i_c (MPA) –

    [\(I_{c}\)] is the moment of inertia of concrete cross section.

  • k_s (DIMENSIONLESS) –

    [\(K_{s}\)] is a factor for contribution of reinforcement, see 5.8.7.2 (2) or (3).

  • e_s (MPA) –

    [\(E_{s}\)] is the design value of the modulus of elasticity of reinforcement, 5.8.6 (3).

  • i_s (MPA) –

    [\(I_{s}\)] is the second moment of area of reinforcement, about the centre of area of the concrete.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_21.py 
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def __init__(self, k_c: DIMENSIONLESS, e_cd: MPA, i_c: MM4, k_s: DIMENSIONLESS, e_s: MPA, i_s: MM4) -> None:
    r"""[$EI$] Nominal stiffness of slender compression members with arbitrary cross-section.

    EN 1992-1-1:2004 art.5.8.7.2(2) or (3) - Formula (5.21)

    Parameters
    ----------
    k_c : DIMENSIONLESS
        [$K_{c}$] is a factor for effects of cracking, creep etc. see 5.8.7.2 (2) or (3).
    e_cd : MPA
        [$E_{cd}$] is the design value of the modulus of elasticity of concrete, see 5.8.6 (3)
    i_c : MPA
        [$I_{c}$] is the moment of inertia of concrete cross section.
    k_s : DIMENSIONLESS
        [$K_{s}$] is a factor for contribution of reinforcement, see 5.8.7.2 (2) or (3).
    e_s : MPA
        [$E_{s}$] is the design value of the modulus of elasticity of reinforcement, 5.8.6 (3).
    i_s : MPA
        [$I_{s}$] is the second moment of area of reinforcement, about the centre of area of the concrete.
    """
    super().__init__()
    self.k_c = k_c
    self.e_cd = e_cd
    self.i_c = i_c
    self.k_s = k_s
    self.e_s = e_s
    self.i_s = i_s

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_21.Form5Dot21NominalStiffness.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.21.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_21.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.21."""
    return LatexFormula(
        return_symbol=r"EI",
        result=f"{self:.{n}f}",
        equation=r"K_{c} \cdot E_{cd} \cdot I_{c} + K_{s} \cdot E_{s} \cdot I_{s}",
        numeric_equation=rf"{self.k_c:.{n}f} \cdot {self.e_cd:.{n}f} "
        rf"\cdot {self.i_c:.{n}f} + {self.k_s:.{n}f} \cdot {self.e_s:.{n}f} \cdot {self.i_s:.{n}f}",
        comparison_operator_label="=",
    )