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formula_9_1n

codes.eurocode.en_1992_1_1_2004.chapter_9_detailling_and_specific_rules.formula_9_1n

Formula 9.1N from EN 1992-1-1:2004: Chapter 9 - Detailing of members and particular rules.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_9_detailling_and_specific_rules.formula_9_1n.Form9Dot1nMinimumTensileReinforcementBeam 

Form9Dot1nMinimumTensileReinforcementBeam(
    f_ctm: MPA, f_yk: MPA, b_t: MM, d: MM
)

Bases: Formula

Class representing the formula 9.1N for the calculation of minimum tensile reinforcement area in longitudinal direction for beams.

[\(A_{s,min}\)] Calculates minimum required tensile reinforcement area in longitudinal direction for beams [\(\text{mm}^2\)].

EN 1992-1-1:2004 art.9.2.1.1(1) - Formula (9.1N)

Notes

[\({A_{s,min}}\)] is no less than [\({0.0013 \cdot b_t \cdot d}\)]

Parameters:

  • f_ctm (MPA) –

    [\({f_{ctm}}\)] Mean axial tensile stress concrete [\(\text{MPa}\)]. Should be determined with respect to the relevant strength class according to Table 3.1

  • f_yk (MPA) –

    [\({f_{yk}}\)] Characteristic yield strength reinforcement steel [\(\text{MPa}\)].

  • b_t (MM) –

    [\({b_t}\)] Mean width of the concrete tension zone, for T-beams with a flange under compression only the width of the web is considered for calculating [\({b_t}\)] [\(\text{mm}\)].

  • d (MM) –

    [\({d}\)] Effective height of the cross-section [\(\text{mm}\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_9_detailling_and_specific_rules/formula_9_1n.py 
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def __init__(
    self,
    f_ctm: MPA,
    f_yk: MPA,
    b_t: MM,
    d: MM,
) -> None:
    r"""[$A_{s,min}$] Calculates minimum required tensile reinforcement area in longitudinal direction for beams [$\text{mm}^2$].

    EN 1992-1-1:2004 art.9.2.1.1(1) - Formula (9.1N)

    Notes
    -----
    [${A_{s,min}}$] is no less than [${0.0013 \cdot b_t \cdot d}$]

    Parameters
    ----------
    f_ctm: MPA
        [${f_{ctm}}$] Mean axial tensile stress concrete [$\text{MPa}$].
        Should be determined with respect to the relevant strength class according to Table 3.1
    f_yk: MPA
        [${f_{yk}}$] Characteristic yield strength reinforcement steel [$\text{MPa}$].
    b_t: MM
        [${b_t}$] Mean width of the concrete tension zone, for T-beams with a flange under compression only the width of the web is
        considered for calculating [${b_t}$] [$\text{mm}$].
    d: MM
        [${d}$] Effective height of the cross-section [$\text{mm}$].
    """
    super().__init__()
    self.f_ctm = f_ctm
    self.f_yk = f_yk
    self.b_t = b_t
    self.d = d

codes.eurocode.en_1992_1_1_2004.chapter_9_detailling_and_specific_rules.formula_9_1n.Form9Dot1nMinimumTensileReinforcementBeam.latex 

latex(n: int = 2) -> LatexFormula

Returns LatexFormula object for formula 9.1N.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_9_detailling_and_specific_rules/formula_9_1n.py 
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def latex(self, n: int = 2) -> LatexFormula:
    """Returns LatexFormula object for formula 9.1N."""
    fraction = latex_fraction(numerator=f"{self.f_ctm:.{n}f}", denominator=f"{self.f_yk:.{n}f}")
    return LatexFormula(
        return_symbol=r"A_{s,min}",
        result=f"{self:.{n}f}",
        equation=latex_max_curly_brackets(
            rf"0.26 \cdot {latex_fraction(numerator=r'f_{ctm}', denominator=r'f_{yk}')} \cdot b_t \cdot d",
            r"0.0013 \cdot b_t \cdot d",
        ),
        numeric_equation=latex_max_curly_brackets(
            rf"0.26 \cdot {fraction} \cdot {self.b_t:.{n}f} \cdot {self.d:.{n}f}",
            rf"0.0013 \cdot {self.b_t:.{n}f} \cdot {self.d:.{n}f}",
        ),
        comparison_operator_label="=",
    )