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formula_8_34

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_34

Formula 8.34 from FprEN 1992-1-1:2023: Chapter 8: Ultimate limit states (ULS).

Classes:

  • Form8Dot34FactorK1 –

    Class representing formula 8.34 for the calculation of the factor accounting for the effect of

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_34.Form8Dot34FactorK1 

Form8Dot34FactorK1(a_cs_0: MM, e_p: MM, d: MM, a_c: MM2, b_w: MM, z: MM)

Bases: Formula

Class representing formula 8.34 for the calculation of the factor accounting for the effect of compressive normal forces.

[\(k_1\)] Factor accounting for the effect of compressive normal forces [\(-\)].

FprEN 1992-1-1:2023 (E) art 8.2.2 (5) - Formula (8.34)

The standard offers this factor unless the National Annex gives another value. The printed upper bound is implemented as a minimum.

Parameters:

  • a_cs_0 (MM) –

    [\(a_{cs,0}\)] Effective shear span determined according to Formula (8.30), without considering in [\(M_{Ed}\)] and [\(V_{Ed}\)] the effect of prestressing or external load that produces the compressive axial force [\(mm\)].

  • e_p (MM) –

    [\(e_p\)] Eccentricity of the prestressing force or of the external load that produces the compressive axial force, with respect to the centre of gravity of the cross-section, considered as positive towards the tensile side. A negative value is therefore valid. For statically indeterminate members, the effect of hyperstatic moments due to prestressing should be considered by modifying the tendons eccentricity accordingly [\(mm\)].

  • d (MM) –

    [\(d\)] Effective depth [\(mm\)].

  • a_c (MM2) –

    [\(A_c\)] Area of concrete cross-section [\(mm^2\)].

  • b_w (MM) –

    [\(b_w\)] Width of the cross-section of linear members [\(mm\)].

  • z (MM) –

    [\(z\)] Lever arm for the shear stress calculation [\(mm\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_34.py 
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def __init__(self, a_cs_0: MM, e_p: MM, d: MM, a_c: MM2, b_w: MM, z: MM) -> None:
    r"""[$k_1$] Factor accounting for the effect of compressive normal forces [$-$].

    FprEN 1992-1-1:2023 (E) art 8.2.2 (5) - Formula (8.34)

    The standard offers this factor unless the National Annex gives another value. The printed upper
    bound is implemented as a minimum.

    Parameters
    ----------
    a_cs_0 : MM
        [$a_{cs,0}$] Effective shear span determined according to Formula (8.30), without considering in
        [$M_{Ed}$] and [$V_{Ed}$] the effect of prestressing or external load that produces the compressive
        axial force [$mm$].
    e_p : MM
        [$e_p$] Eccentricity of the prestressing force or of the external load that produces the compressive
        axial force, with respect to the centre of gravity of the cross-section, considered as positive
        towards the tensile side. A negative value is therefore valid. For statically indeterminate members,
        the effect of hyperstatic moments due to prestressing should be considered by modifying the tendons
        eccentricity accordingly [$mm$].
    d : MM
        [$d$] Effective depth [$mm$].
    a_c : MM2
        [$A_c$] Area of concrete cross-section [$mm^2$].
    b_w : MM
        [$b_w$] Width of the cross-section of linear members [$mm$].
    z : MM
        [$z$] Lever arm for the shear stress calculation [$mm$].
    """
    super().__init__()
    self.a_cs_0 = a_cs_0
    self.e_p = e_p
    self.d = d
    self.a_c = a_c
    self.b_w = b_w
    self.z = z

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_34.Form8Dot34FactorK1.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.34.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_34.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.34."""
    _equation: str = (
        r"\min\left(\frac{0.5}{a_{cs,0}} \cdot \left(e_p + \frac{d}{3}\right) \cdot "
        r"\frac{A_c}{b_w \cdot z}, 0.18 \cdot \frac{A_c}{b_w \cdot z}\right)"
    )
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"a_{cs,0}": f"{self.a_cs_0:.{n}f}",
            r"e_p": f"{self.e_p:.{n}f}",
            r"{d}": "{" + f"{self.d:.{n}f}" + "}",
            r"A_c": f"{self.a_c:.{n}f}",
            r"b_w": f"{self.b_w:.{n}f}",
            r"z": f"{self.z:.{n}f}",
        },
        unique_symbol_check=False,
    )
    _numeric_equation_with_units: str = latex_replace_symbols(
        template=_equation,
        replacements={
            r"a_{cs,0}": rf"{self.a_cs_0:.{n}f} \ mm",
            r"e_p": rf"{self.e_p:.{n}f} \ mm",
            r"{d}": "{" + rf"{self.d:.{n}f} \ mm" + "}",
            r"A_c": rf"{self.a_c:.{n}f} \ mm^2",
            r"b_w": rf"{self.b_w:.{n}f} \ mm",
            r"z": rf"{self.z:.{n}f} \ mm",
        },
        unique_symbol_check=False,
    )
    return LatexFormula(
        return_symbol=r"k_1",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="-",
    )