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formula_8_5

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_5

Formula 8.5 from EN 1992-1-1:2004: Chapter 8: Detailing of reinforcement and prestressing tendons.

Classes:

  • Form8Dot5ProductAlphas235 –

    Class representing formula 8.5 for the calculating the product of [\(\alpha_{2}\)], [\(\alpha_{3}\)] [\(\alpha_{5}\)] [\(-\)].

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_5.Form8Dot5ProductAlphas235 

Form8Dot5ProductAlphas235(alpha_2: RATIO, alpha_3: RATIO, alpha_5: RATIO)

Bases: Formula

Class representing formula 8.5 for the calculating the product of [\(\alpha_{2}\)], [\(\alpha_{3}\)] [\(\alpha_{5}\)] [\(-\)].

Calculate the product of [\(\alpha_{2}\)], [\(\alpha_{3}\)] and [\(\alpha_{5}\)] [\(-\)].

EN 1992-1-1:2004 art.8.4.4(1) - Formula (8.5) prescribes that [\((\alpha_{2} \cdot \alpha_{3} \cdot \alpha_{5}) \ge 0.7\)]. Used by EN 1992-1-1:2004 art.8.4.4(1) - Formula (8.4)

Parameters:

  • alpha_2 (RATIO) –

    [\(\alpha_{2}\)] Coefficient for the effect of minimum concrete cover (see figure 8.3) [\(-\)].

    [\(= 1.0\)] for bars in compression.

    [\(= 1 - 0.15 \cdot (c_{d} - \varnothing) / \varnothing \le 1\)] with a minimum of [\(0.7\)] for straight bars in tension.

    [\(= 1 - 0.15 \cdot (c_{d} - 3 \cdot \varnothing) / \varnothing \le 1\)] with a minimum of [\(0.7\)] for bars other than straight in tension (see figure 8.1 (b), (c) and (d)).

    Note: see figure 8.3 for values of [\(c_{d}\)].

  • alpha_3 (RATIO) –

    [\(\alpha_{3}\)] Coefficient for the effect of confinement by transverse reinforcement [\(-\)].

    [\(= 1.0\)] for bars in compression.

    [\(= 1 - K \cdot \lambda \le 1\)] with a minimum of [\(0.7\)] for bars in tension.

    Where: [\(\lambda = (\Sigma A_{st} - \Sigma A_{st,min}) / A_{s}\)].

    Where: [\(\Sigma A_{st,min}\)] = cross-sectional area of the minimum transverse reinforcement [\(= 0.25 \cdot A_{s}\)] for beams and [\(0\)] for slabs.

    Note: see figure 8.4 for values of [\(K, A_{s}\)] and [\(A_{st}\)].

  • alpha_5 (RATIO) –

    [\(\alpha_{5}\)] Coefficient for the effect of the pressure transverse to the plane of splitting along the design anchorage length [\(l_{bd}\)] (see 8.6) [\(-\)].

    [\(= 1 - 0.04 \cdot p \le 1\)] with a minimum of [\(0.7\)] for all types of anchorage in compression.

    Where: [\(p\)] = transverse pressure at ultimate limit state along [\(l_{bd}\)] [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_5.py 
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def __init__(
    self,
    alpha_2: RATIO,
    alpha_3: RATIO,
    alpha_5: RATIO,
) -> None:
    r"""Calculate the product of [$\alpha_{2}$], [$\alpha_{3}$] and [$\alpha_{5}$] [$-$].

    EN 1992-1-1:2004 art.8.4.4(1) - Formula (8.5) prescribes that [$(\alpha_{2} \cdot \alpha_{3} \cdot \alpha_{5}) \ge 0.7$].
    Used by EN 1992-1-1:2004 art.8.4.4(1) - Formula (8.4)

    Parameters
    ----------
    alpha_2 : RATIO
        [$\alpha_{2}$] Coefficient for the effect of minimum concrete cover (see figure 8.3) [$-$].

        [$= 1.0$] for bars in compression.

        [$= 1 - 0.15 \cdot (c_{d} - \varnothing) / \varnothing \le 1$] with a minimum of [$0.7$] for straight bars in tension.

        [$= 1 - 0.15 \cdot (c_{d} - 3 \cdot \varnothing) / \varnothing \le 1$] with a minimum of [$0.7$] for bars other than
        straight in tension (see figure 8.1 (b), (c) and (d)).

        Note: see figure 8.3 for values of [$c_{d}$].
    alpha_3 : RATIO
        [$\alpha_{3}$] Coefficient for the effect of confinement by transverse reinforcement [$-$].

        [$= 1.0$] for bars in compression.

        [$= 1 - K \cdot \lambda \le 1$] with a minimum of [$0.7$] for bars in tension.

        Where: [$\lambda = (\Sigma A_{st} - \Sigma A_{st,min}) / A_{s}$].

        Where: [$\Sigma A_{st,min}$] = cross-sectional area of the minimum transverse
        reinforcement [$= 0.25 \cdot A_{s}$] for beams and [$0$] for slabs.

        Note: see figure 8.4 for values of [$K, A_{s}$] and [$A_{st}$].

    alpha_5 : RATIO
        [$\alpha_{5}$] Coefficient for the effect of the pressure transverse to the plane of splitting
        along the design anchorage length [$l_{bd}$] (see 8.6) [$-$].

        [$= 1 - 0.04 \cdot p \le 1$] with a minimum of [$0.7$] for all types of anchorage in compression.

        Where: [$p$] = transverse pressure at ultimate limit state along [$l_{bd}$] [$MPa$].
    """
    super().__init__()
    self.alpha_2 = alpha_2
    self.alpha_3 = alpha_3
    self.alpha_5 = alpha_5

codes.eurocode.en_1992_1_1_2004.chapter_8_detailing_of_reinforcement_and_prestressing_tendons.formula_8_5.Form8Dot5ProductAlphas235.latex 

latex(n: int = 2) -> LatexFormula

Returns a LatexFormula representation of the formula.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_8_detailing_of_reinforcement_and_prestressing_tendons/formula_8_5.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns a LatexFormula representation of the formula."""
    return LatexFormula(
        return_symbol=r"\alpha_2 \alpha_3 \alpha_5",
        result=f"{self:.{n}f}",
        equation=r"\alpha_2 \cdot \alpha_3 \cdot \alpha_5 \ge 0.7",
        numeric_equation=rf"{self.alpha_2} \cdot {self.alpha_3} \cdot {self.alpha_5} \ge 0.7",
        comparison_operator_label="\\to",
    )