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formula_5_9

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_9

Formula 5.9 from EN 1992-1-1:2004: Chapter 5 - Structural Analysis.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_9.Form5Dot9DesignSupportMomentReduction 

Form5Dot9DesignSupportMomentReduction(f_ed_sup: KN, t: M)

Bases: Formula

Class representing formula 5.9 for the calculation of the design support moment reduction, [\(ΔM_{Ed}\)]. See Figure 5.4 b.

[\(ΔM_{Ed}\)] Design support moment reduction [\(kN\)].

Note: Regardless of the method of analysis used, where a beam or slab is continuous over a support which may be considered to provide no restraint to rotation (e.g. over walls), the design support moment, calculated on the basis of a span equal to the centre-to-centre distance between supports, may be reduced by an amount [\(ΔM_{Ed}\)].

EN 1992-1-1:2004 art.5.3.2.2(4) - Formula (5.9)

Parameters:

  • f_ed_sup (KN) –

    [\(F_{Ed,sup}\)] Design support reaction [\(kN\)].

  • t (M) –

    [\(t\)] breadth of the support (see Figure 5.4 b) [\(m\)].

    Note: Where support bearings are used [\(t\)] should be taken as the bearing width.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_9.py 
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def __init__(
    self,
    f_ed_sup: KN,
    t: M,
) -> None:
    r"""[$ΔM_{Ed}$] Design support moment reduction [$kN$].

    Note: Regardless of the method of analysis used, where a beam or slab is continuous over a
    support which may be considered to provide no restraint to rotation (e.g. over walls), the design
    support moment, calculated on the basis of a span equal to the centre-to-centre distance
    between supports, may be reduced by an amount [$ΔM_{Ed}$].

    EN 1992-1-1:2004 art.5.3.2.2(4) - Formula (5.9)

    Parameters
    ----------
    f_ed_sup : KN
        [$F_{Ed,sup}$] Design support reaction [$kN$].
    t : M
        [$t$] breadth of the support (see Figure 5.4 b) [$m$].

        Note:  Where support bearings are used [$t$] should be taken as the bearing width.
    """
    super().__init__()
    self.f_ed_sup = f_ed_sup
    self.t = t

codes.eurocode.en_1992_1_1_2004.chapter_5_structural_analysis.formula_5_9.Form5Dot9DesignSupportMomentReduction.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 5.9.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_5_structural_analysis/formula_5_9.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 5.9."""
    return LatexFormula(
        return_symbol=r"ΔM_{Ed}",
        result=f"{self:.{n}f}",
        equation=r"\frac{F_{Ed,sup} \cdot t}{8}",
        numeric_equation=rf"\frac{{{self.f_ed_sup} \cdot {self.t}}}{{8}}",
        comparison_operator_label="=",
    )