Skip to content

formula_6_52

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_52

Formula 6.52 from EN 1992-1-1:2004: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_52.Form6Dot52PunchingShearResistance 

Form6Dot52PunchingShearResistance(
    v_rd_c: MPA, d: MM, s_r: MM, a_sw: MM2, f_ywd_ef: MPA, u_1: MM, alpha: DEG
)

Bases: Formula

Class representing formula 6.52 for the calculation of punching shear resistance.

EN 1992-1-1:2004 art.6.4.5(1) - Formula (6.52)

Parameters:

  • v_rd_c (MPA) –

    [\(v_{Rd,c}\)] Design shear strength of concrete without shear reinforcement [\(MPa\)].

  • d (MM) –

    [\(d\)] Mean effective depth of the slab [\(mm\)].

  • s_r (MM) –

    [\(s_r\)] Radial spacing of perimeters of shear reinforcement [\(mm\)].

  • a_sw (MM2) –

    [\(A_{sw}\)] Area of one perimeter of shear reinforcement around the column [\(mm^2\)].

  • f_ywd_ef (MPA) –

    [\(f_{ywd,ef}\)] Effective design strength of the punching shear reinforcement [\(MPa\)].

  • u_1 (MM) –

    [\(u_{y1}\)] Perimeter of the critical section [\(mm\)].

  • alpha (DEG) –

    [\(\alpha\)] Angle between the shear reinforcement and the plane of the slab [\(deg\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_52.py 
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
def __init__(
    self,
    v_rd_c: MPA,
    d: MM,
    s_r: MM,
    a_sw: MM2,
    f_ywd_ef: MPA,
    u_1: MM,
    alpha: DEG,
) -> None:
    super().__init__()
    self.v_rd_c = v_rd_c
    self.d = d
    self.s_r = s_r
    self.a_sw = a_sw
    self.f_ywd_ef = f_ywd_ef
    self.u_1 = u_1
    self.alpha = alpha

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_52.Form6Dot52PunchingShearResistance.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.52.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_52.py 
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.52."""
    _equation: str = (
        r"0.75 \cdot v_{Rd,c} + 1.5 \cdot \frac{ d}{s_r} \cdot A_{sw} \cdot f_{ywd,ef} \cdot \frac{1}{u_{1} \cdot d} \cdot \sin(\alpha)"
    )
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"v_{Rd,c}": f"{self.v_rd_c:.{n}f}",
            r"s_r": f"{self.s_r:.{n}f}",
            r"A_{sw}": f"{self.a_sw:.{n}f}",
            r"f_{ywd,ef}": f"{self.f_ywd_ef:.{n}f}",
            r"u_{1}": f"{self.u_1:.{n}f}",
            r"\alpha": f"{self.alpha:.{n}f}",
            r" d": f" {self.d:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"v_{Rd,cs}",
        result=f"{self._evaluate(self.v_rd_c, self.d, self.s_r, self.a_sw, self.f_ywd_ef, self.u_1, self.alpha):.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="MPa",
    )

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_52.Form6Dot52Sub1EffectiveYieldStrength 

Form6Dot52Sub1EffectiveYieldStrength(d: MM, f_ywd: MPA)

Bases: Formula

Class representing formula 6.52sub1 for the calculation of [\(f_{ywd,ef}\)].

[f_{ywd,ef}] Calculation of [\(f_{ywd,ef}\)].

EN 1992-1-1:2004 art.6.4.5(1) - Formula (6.52sub1)

Parameters:

  • d (MM) –

    [\(d\)] Mean effective depth of the slab [\(mm\)].

  • f_ywd (MPA) –

    [\(f_{ywd}\)] Design yield strength of the reinforcement [\(MPa\)].

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_52.py 
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
def __init__(
    self,
    d: MM,
    f_ywd: MPA,
) -> None:
    r"""[f_{ywd,ef}] Calculation of [$f_{ywd,ef}$].

    EN 1992-1-1:2004 art.6.4.5(1) - Formula (6.52sub1)

    Parameters
    ----------
    d : MM
        [$d$] Mean effective depth of the slab [$mm$].
    f_ywd : MPA
        [$f_{ywd}$] Design yield strength of the reinforcement [$MPa$].
    """
    super().__init__()
    self.d = d
    self.f_ywd = f_ywd

codes.eurocode.en_1992_1_1_2004.chapter_6_ultimate_limit_state.formula_6_52.Form6Dot52Sub1EffectiveYieldStrength.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.52sub1.

Source code in blueprints/codes/eurocode/en_1992_1_1_2004/chapter_6_ultimate_limit_state/formula_6_52.py 
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.52sub1."""
    _equation: str = r"\min\left(250 + 0.25 \cdot d, f_{ywd}\right)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"f_{ywd}": f"{self.f_ywd:.{n}f}",
            r" d": f" {self.d:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"f_{ywd,ef}",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="MPa",
    )