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formula_5_10a

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_10a

Formula 5.10a from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_10a.Form5Dot10aRedistributionOfMomentsLowerFck 

Form5Dot10aRedistributionOfMomentsLowerFck(
    delta: DIMENSIONLESS, k1: DIMENSIONLESS, k2: DIMENSIONLESS, xu: M, d: M
)

Class representing formula 5.10a for the redistribution of moments in continuous beams or slabs when [\(f_{ck} \leq 50 MPa\)].

[\(\delta\)] Redistribution of moments in continuous beams or slabs when [\(f_{ck} \leq 50 MPa\)].

EN 1992-1-1:2004 art.5.5(4) - Formula (5.10a)

Parameters:

  • delta (DIMENSIONLESS) –

    [\(\delta\)] is the ratio of the redistributed moment to the elastic moment.

  • k1 (DIMENSIONLESS) –

    [\(k_1\)] is a coefficient for redistribution.

  • k2 (DIMENSIONLESS) –

    [\(k_2\)] is a coefficient for redistribution.

  • xu (M) –

    [\(x_u\)] is the depth of the compression zone in the ultimate limit state after redistribution.

  • d (M) –

    [\(d\)] is the effective depth of the section.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_10a.py 
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def __init__(self, delta: DIMENSIONLESS, k1: DIMENSIONLESS, k2: DIMENSIONLESS, xu: M, d: M) -> None:
    r"""[$\delta$] Redistribution of moments in continuous beams or slabs when [$f_{ck} \leq 50 MPa$].

    EN 1992-1-1:2004 art.5.5(4) - Formula (5.10a)

    Parameters
    ----------
    delta : DIMENSIONLESS
        [$\delta$] is the ratio of the redistributed moment to the elastic moment.
    k1 : DIMENSIONLESS
        [$k_1$] is a coefficient for redistribution.
    k2 : DIMENSIONLESS
        [$k_2$] is a coefficient for redistribution.
    xu : M
        [$x_u$] is the depth of the compression zone in the ultimate limit state after redistribution.
    d : M
        [$d$] is the effective depth of the section.
    """
    super().__init__()
    self.delta = delta
    self.k1 = k1
    self.k2 = k2
    self.xu = xu
    self.d = d
    raise_if_less_or_equal_to_zero(delta=delta, k1=k1, k2=k2, xu=xu, d=d)

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_10a.Form5Dot10aRedistributionOfMomentsLowerFck.left_hand_side property 

left_hand_side: DIMENSIONLESS

Calculate the left hand side of the comparison.

Returns:

  • DIMENSIONLESS –

    Left hand side of the comparison.

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_10a.Form5Dot10aRedistributionOfMomentsLowerFck.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_10a.Form5Dot10aRedistributionOfMomentsLowerFck.right_hand_side property 

right_hand_side: DIMENSIONLESS

Calculate the right hand side of the comparison.

Returns:

  • DIMENSIONLESS –

    Right hand side of the comparison.

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_10a.Form5Dot10aRedistributionOfMomentsLowerFck.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.10a.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_10a.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.10a."""
    return LatexFormula(
        return_symbol=r"CHECK",
        result="OK" if self.__bool__() else "\\text{Not OK}",
        equation=r"\delta \geq k_1 + k_2 \frac{x_u}{d}",
        numeric_equation=rf"{self.left_hand_side:.{n}f} \geq {self.k1} + {self.k2} \frac{{{self.xu}}}{{{self.d}}}",
        comparison_operator_label=r"\rightarrow",
    )