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formula_7_1

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_1

Formula 7.1 from EN 1992-1-1:2004: Chapter 7 - Serviceability Limit State.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_1.Form7Dot1MinReinforcingSteel 

Form7Dot1MinReinforcingSteel(
    k_c: DIMENSIONLESS, k: DIMENSIONLESS, f_ct_eff: MPA, a_ct: MM2, sigma_s: MPA
)

Bases: Formula

Class representing formula 7.1 for the calculation of [\(A_{s,min}\)].

[\(A_{s,min}\)] Calculation of minimum area of reinforcing steel within the tensile zone.

EN 1992-1-1:2004 art.7.3.2(2) - Formula (7.1)

Parameters:

  • k_c (DIMENSIONLESS) –

    [\(k_c\)] Coefficient which takes account of the stress distribution within the section immediately prior to cracking and of the change of the lever arm. For pure tension use 1.0, else use equation 7.2 or 7.3 [\(-\)].

  • k (DIMENSIONLESS) –

    [\(k\)] Coefficient which allows for the effect of non-uniform self-equilibrating stresses, which lead to a reduction of restraint forces [\(-\)].

  • f_ct_eff (MPA) –

    [\(f_{ct,eff}\)] Mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur [\(MPa\)].

  • a_ct (MM2) –

    [\(A_{ct}\)] Area of concrete within the tensile zone [\(mm^2\)].

  • sigma_s (MPA) –

    [\(\sigma_s\)] Absolute value of the maximum stress permitted in the reinforcement immediately after formation of the crack [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_1.py 
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def __init__(
    self,
    k_c: DIMENSIONLESS,
    k: DIMENSIONLESS,
    f_ct_eff: MPA,
    a_ct: MM2,
    sigma_s: MPA,
) -> None:
    r"""[$A_{s,min}$] Calculation of minimum area of reinforcing steel within the tensile zone.

    EN 1992-1-1:2004 art.7.3.2(2) - Formula (7.1)

    Parameters
    ----------
    k_c : DIMENSIONLESS
        [$k_c$] Coefficient which takes account of the stress distribution within the section immediately
        prior to cracking and of the change of the lever arm. For pure tension use 1.0, else use equation 7.2 or 7.3 [$-$].
    k : DIMENSIONLESS
        [$k$] Coefficient which allows for the effect of non-uniform self-equilibrating stresses, which lead to a
        reduction of restraint forces [$-$].
    f_ct_eff : MPA
        [$f_{ct,eff}$] Mean value of the tensile strength of the concrete effective at the time when the cracks may
        first be expected to occur [$MPa$].
    a_ct : MM2
        [$A_{ct}$] Area of concrete within the tensile zone [$mm^2$].
    sigma_s : MPA
        [$\sigma_s$] Absolute value of the maximum stress permitted in the reinforcement immediately after formation
        of the crack [$MPa$].
    """
    super().__init__()
    self.k_c = k_c
    self.k = k
    self.f_ct_eff = f_ct_eff
    self.a_ct = a_ct
    self.sigma_s = sigma_s

codes.eurocode.en_1992_1_1_2004.chapter_7_serviceability_limit_state.formula_7_1.Form7Dot1MinReinforcingSteel.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 7.1.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_7_serviceability_limit_state/formula_7_1.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 7.1."""
    _equation: str = r"\frac{k_c \cdot k \cdot f_{ct,eff} \cdot A_{ct}}{\sigma_s}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"k_c": f"{self.k_c:.{n}f}",
            r"k": f"{self.k:.{n}f}",
            r"f_{ct,eff}": f"{self.f_ct_eff:.{n}f}",
            r"A_{ct}": f"{self.a_ct:.{n}f}",
            r"\sigma_s": f"{self.sigma_s:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"A_{s,min}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )