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formula_5_18

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_18

Formula 5.18 from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_18.Form5Dot18ComparisonGeneralSecondOrderEffects 

Form5Dot18ComparisonGeneralSecondOrderEffects(
    f_ved: KN,
    k_1: DIMENSIONLESS,
    n_s: DIMENSIONLESS,
    length: M,
    e_cd: MPA,
    i_c: MM4,
)

Class representing comparison 5.18 for general second-order effects in buildings.

[\(CHECK\)] Criteria met, based on damage accumulation.

EN 1992-1-1:2004 art.5.8.3.3(1) - Formula (5.18)

Parameters:

  • f_ved (KN) –

    [\(F_{v,ed}\)] Total vertical load (on braced and bracing members) [\(kN\)].

  • k_1 (DIMENSIONLESS) –

    [\(k_1\)] The value of k1 for use in a Country may be found in its National Annex. Recommend value is 0.31 [\(-\)].

  • n_s (DIMENSIONLESS) –

    [\(n_s\)] is the total number of storeys [\(-\)].

  • length (M) –

    [\(L\)] is the total height of the building above level of moment restraint. [\(m\)].

  • e_cd (MPa) –

    [\(E_{cd}\)] is the design value of the modulus of elasticity of concrete. [\(MPa\)].

  • i_c (MM4) –

    [\(I_c\)] is the second moment of area (uncracked concrete section) of bracing member(s). [\(mm^4\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_18.py 
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def __init__(self, f_ved: KN, k_1: DIMENSIONLESS, n_s: DIMENSIONLESS, length: M, e_cd: MPA, i_c: MM4) -> None:
    r"""[$CHECK$] Criteria met, based on damage accumulation.

    EN 1992-1-1:2004 art.5.8.3.3(1) - Formula (5.18)

    Parameters
    ----------
    f_ved : KN
        [$F_{v,ed}$] Total vertical load (on braced and bracing members) [$kN$].
    k_1 : DIMENSIONLESS
        [$k_1$] The value of k1 for use in a Country may be found in its National Annex. Recommend value is
        0.31 [$-$].
    n_s : DIMENSIONLESS
        [$n_s$] is the total number of storeys [$-$].
    length : M
        [$L$] is the total height of the building above level of moment restraint. [$m$].
    e_cd : MPa
        [$E_{cd}$] is the design value of the modulus of elasticity of concrete. [$MPa$].
    i_c : MM4
        [$I_c$] is the second moment of area (uncracked concrete section) of bracing member(s). [$mm^4$].
    """
    self.f_ved = f_ved
    self.k_1 = k_1
    self.n_s = n_s
    self.length = length
    self.e_cd = e_cd
    self.i_c = i_c

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_18.Form5Dot18ComparisonGeneralSecondOrderEffects.left_hand_side property 

left_hand_side: KN

Calculate the left hand side of the comparison.

Returns:

  • KN –

    Left hand side of the comparison.

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_18.Form5Dot18ComparisonGeneralSecondOrderEffects.ratio property 

ratio: DIMENSIONLESS

Ratio between left hand side and right hand side of the comparison, commonly referred to as unity check.

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_18.Form5Dot18ComparisonGeneralSecondOrderEffects.right_hand_side property 

right_hand_side: KN

Calculate the right hand side of the comparison.

Returns:

  • KN –

    Right hand side of the comparison.

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_18.Form5Dot18ComparisonGeneralSecondOrderEffects.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.18.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_18.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.18."""
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if self.__bool__() else "\\text{Not OK}",
        equation=r"F_{V,Ed} \leq \frac{n_s}{n_s + 1.6} \cdot \frac{\sum E_{cd} \cdot I_c}{L^2}",
        numeric_equation=(
            rf"{self.left_hand_side:.{n}f}"
            rf"\leq \frac{{{self.n_s}}}{{{self.n_s + 1.6}}} \cdot \frac{{\sum {self.e_cd} \cdot {self.i_c}}}{{{self.length**2}}}"
        ),
        comparison_operator_label=r"\rightarrow",
    )