Skip to content

formula_8_19

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_19

Formula 8.19 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_19.Form8Dot19AverageShearStressPlanarMembers 

Form8Dot19AverageShearStressPlanarMembers(v_ed: N_MM, z: MM)

Bases: Formula

Class representing formula 8.19 for the calculation of the average shear stress over the cross-section of planar 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 (8.19)

Parameters:

  • v_ed (N_MM) –

    [\(v_{Ed}\)] Design shear force per unit width in planar members [\(N/mm\)]. Note that this is the lower case [\(v_{Ed}\)] of planar members, not the shear force [\(V_{Ed}\)] in [\(N\)] used in Formula (8.18).

  • 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_19.py 
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
def __init__(self, v_ed: N_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 (8.19)

    Parameters
    ----------
    v_ed : N_MM
        [$v_{Ed}$] Design shear force per unit width in planar members [$N/mm$]. Note that this is the lower case
        [$v_{Ed}$] of planar members, not the shear force [$V_{Ed}$] in [$N$] used in Formula (8.18).
    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.z = z

codes.eurocode.fpr_en_1992_1_1_2023.chapter_8_ultimate_limit_states.formula_8_19.Form8Dot19AverageShearStressPlanarMembers.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 8.19.

Source code in blueprints/codes/eurocode/fpr_en_1992_1_1_2023/chapter_8_ultimate_limit_states/formula_8_19.py 
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 8.19."""
    _equation: str = r"\frac{v_{Ed}}{z}"
    _numeric_equation: str = latex_replace_symbols(
        template=_equation,
        replacements={r"v_{Ed}": f"{self.v_ed:.{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/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",
    )