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formula_8_18

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_18

Formula 8.18 from FprEN 1992-1-1:2023: Chapter 8: Ultimate limit states (ULS).

Classes:

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_18.Form8Dot18AverageShearStress 

Form8Dot18AverageShearStress(v_ed: N, b_w: MM, z: MM)

Bases: Formula

Class representing formula 8.18 for the calculation of the average shear stress over the cross-section of linear members in regions without geometric discontinuities.

[\(\tau_{Ed}\)] Average shear stress over the cross-section area in regions of members without geometric discontinuities [\(MPa\)].

FprEN 1992-1-1:2023 (E) art 8.2.1 (3) - Formula (8.18)

Parameters:

  • v_ed (N) –

    [\(V_{Ed}\)] Design shear force at the control section in linear members [\(N\)]. Note that this is the upper case [\(V_{Ed}\)] of linear members, not the shear force per unit width [\(v_{Ed}\)] in [\(N/mm\)] used in Formula (8.19).

  • b_w (MM) –

    [\(b_w\)] Width of the cross-section of linear members. The width [\(b_w\)] for cross-sections with variable width and for circular cross-sections is defined in 8.2.3(9) [\(mm\)].

  • z (MM) –

    [\(z\)] Lever arm for the shear stress calculation defined as [\(z = 0.9 \cdot d\)], where [\(d\)] refers to the centroid of tensile reinforcement [\(mm\)].

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_18.py 
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def __init__(self, v_ed: N, b_w: MM, z: MM) -> None:
    r"""[$\tau_{Ed}$] Average shear stress over the cross-section area in regions of members without geometric discontinuities [$MPa$].

    FprEN 1992-1-1:2023 (E) art 8.2.1 (3) - Formula (8.18)

    Parameters
    ----------
    v_ed : N
        [$V_{Ed}$] Design shear force at the control section in linear members [$N$]. Note that this is the upper case
        [$V_{Ed}$] of linear members, not the shear force per unit width [$v_{Ed}$] in [$N/mm$] used in Formula (8.19).
    b_w : MM
        [$b_w$] Width of the cross-section of linear members. The width [$b_w$] for cross-sections with variable width
        and for circular cross-sections is defined in 8.2.3(9) [$mm$].
    z : MM
        [$z$] Lever arm for the shear stress calculation defined as [$z = 0.9 \cdot d$], where [$d$] refers to the
        centroid of tensile reinforcement [$mm$].
    """
    super().__init__()
    self.v_ed = v_ed
    self.b_w = b_w
    self.z = z

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_18.Form8Dot18AverageShearStress.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.18.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_18.py 
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def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.18."""
    _equation: str = r"\frac{V_{Ed}}{b_w \cdot z}"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={r"V_{Ed}": f"{self.v_ed:.{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"V_{Ed}": rf"{self.v_ed:.{n}f} \ N",
            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"\tau_{Ed}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        numeric_equation_with_units=_numeric_equation_with_units,
        comparison_operator_label="=",
        unit="MPa",
    )