Add formulas 6.29, 6.29rho, and 6.30 from 1993-1-1

blueprints/codes/eurocode/nen_en_1993_1_1_c2_a1_2016/chapter_6_ultimate_limit_state/formula_6_29.py

@@ -0,0 +1,74 @@
+"""Formula 6.29 from NEN-EN 1993-1-1+A1:2016: Chapter 6 - Ultimate Limit State."""
+
+from blueprints.codes.eurocode.nen_en_1993_1_1_c2_a1_2016 import NEN_EN_1993_1_1_C2_A1_2016
+from blueprints.codes.formula import Formula
+from blueprints.codes.latex_formula import LatexFormula, latex_replace_symbols
+from blueprints.type_alias import DIMENSIONLESS, MPA
+from blueprints.validations import raise_if_negative
+
+
+class Form6Dot29ReducedYieldStrength(Formula):
+    r"""Class representing formula 6.29 for the calculation of reduced yield strength."""
+
+    label = "6.29"
+    source_document = NEN_EN_1993_1_1_C2_A1_2016
+
+    def __init__(
+        self,
+        rho: DIMENSIONLESS,
+        f_y: MPA,
+    ) -> None:
+        r"""[$f_{y,red}$] Calculation of reduced yield strength [$MPa$].
+
+        NEN-EN 1993-1-1+A1:2016 art.6.2.8(3) - Formula (6.29)
+
+        Parameters
+        ----------
+        rho : DIMENSIONLESS
+            [$\rho$] Reduction factor for shear force, see 6.2.8(3) (dimensionless).
+        f_y : MPA
+            [$f_y$] Yield strength of the material [$MPa$].
+        """
+        super().__init__()
+        self.rho = rho
+        self.f_y = f_y
+
+    @staticmethod
+    def _evaluate(
+        rho: DIMENSIONLESS,
+        f_y: MPA,
+    ) -> MPA:
+        """Evaluates the formula, for more information see the __init__ method."""
+        one_minus_rho = 1 - rho
+        raise_if_negative(rho=rho, f_y=f_y, one_minus_rho=one_minus_rho)
+
+        return (1 - rho) * f_y
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 6.29."""
+        _equation: str = r"(1 - \rho) \cdot f_y"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"\rho": f"{self.rho:.3f}",
+                r"f_y": f"{self.f_y:.3f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"\rho": rf"{self.rho:.3f}",
+                r"f_y": rf"{self.f_y:.3f} \ MPa",
+            },
+            True,
+        )
+        return LatexFormula(
+            return_symbol=r"f_{y,red}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            numeric_equation_with_units=_numeric_equation_with_units,
+            comparison_operator_label="=",
+            unit="MPa",
+        )

blueprints/codes/eurocode/nen_en_1993_1_1_c2_a1_2016/chapter_6_ultimate_limit_state/formula_6_29rho.py

@@ -0,0 +1,159 @@
+"""Formula 6.29rho from NEN-EN 1993-1-1+C2+A1:2016: Chapter 6 - Ultimate Limit State."""
+
+from blueprints.codes.eurocode.nen_en_1993_1_1_c2_a1_2016 import NEN_EN_1993_1_1_C2_A1_2016
+from blueprints.codes.formula import Formula
+from blueprints.codes.latex_formula import LatexFormula, latex_replace_symbols
+from blueprints.type_alias import DIMENSIONLESS, N
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class Form6Dot29Rho(Formula):
+    r"""Class representing formula 6.29rho for the calculation of [$\rho$]."""
+
+    label = "6.29rho"
+    source_document = NEN_EN_1993_1_1_C2_A1_2016
+
+    def __init__(
+        self,
+        v_ed: N,
+        v_pl_rd: N,
+    ) -> None:
+        r"""[$\rho$] Calculation of the reduction factor [$\text{dimensionless}$].
+
+        NEN-EN 1993-1-1+C2+A1:2016 art.6.2.10(3) - Formula (6.29rho)
+
+        Parameters
+        ----------
+        v_ed : N
+            [$V_{Ed}$] Design shear force [$N$].
+        v_pl_rd : N
+            [$V_{pl,Rd}$] Plastic shear resistance, obtained from 6.2.6(2) [$N$].
+
+        Note, see also 6.2.10(3)
+        """
+        super().__init__()
+        self.v_ed = v_ed
+        self.v_pl_rd = v_pl_rd
+
+    @staticmethod
+    def _evaluate(
+        v_ed: N,
+        v_pl_rd: N,
+    ) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_less_or_equal_to_zero(v_pl_rd=v_pl_rd)
+        raise_if_negative(v_ed=v_ed)
+
+        if v_ed <= 0.5 * v_pl_rd:
+            return 0
+        return ((2 * v_ed / v_pl_rd) - 1) ** 2
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 6.29rho."""
+        _equation: str = (
+            r"\begin{cases} "
+            r"0 & \text{if } V_{Ed} \leq 0.5 \cdot V_{pl,Rd} \\ "
+            r"\left( \frac{2 \cdot V_{Ed}}{V_{pl,Rd}} - 1 \right)^2 & \text{if } V_{Ed} > 0.5 \cdot V_{pl,Rd} "
+            r"\end{cases}"
+        )
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"V_{Ed}": f"{self.v_ed:.3f}",
+                r"V_{pl,Rd}": f"{self.v_pl_rd:.3f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"V_{Ed}": rf"{self.v_ed:.3f} \ N",
+                r"V_{pl,Rd}": rf"{self.v_pl_rd:.3f} \ N",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\rho",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            numeric_equation_with_units=_numeric_equation_with_units,
+            comparison_operator_label="=",
+            unit="-",
+        )
+
+
+class Form6Dot29RhoWithTorsion(Formula):
+    r"""Class representing formula 6.29rho with torsion for the calculation of [$\rho$]."""
+
+    label = "6.29rho_with_torsion"
+    source_document = NEN_EN_1993_1_1_C2_A1_2016
+
+    def __init__(
+        self,
+        v_ed: N,
+        v_pl_t_rd: N,
+    ) -> None:
+        r"""[$\rho$] Calculation of the reduction factor with torsion [$\text{dimensionless}$].
+
+        NEN-EN 1993-1-1+C2+A1:2016 art.6.2.7(4) - Formula (6.29rho with torsion)
+
+        Parameters
+        ----------
+        v_ed : N
+            [$V_{Ed}$] Design shear force [$N$].
+        v_pl_t_rd : N
+            [$V_{pl,T,Rd}$] Plastic shear resistance with torsion [$N$].
+
+        Note, see also 6.2.7
+        """
+        super().__init__()
+        self.v_ed = v_ed
+        self.v_pl_t_rd = v_pl_t_rd
+
+    @staticmethod
+    def _evaluate(
+        v_ed: N,
+        v_pl_t_rd: N,
+    ) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_less_or_equal_to_zero(v_pl_t_rd=v_pl_t_rd)
+        raise_if_negative(v_ed=v_ed)
+
+        if v_ed <= 0.5 * v_pl_t_rd:
+            return 0
+        return ((2 * v_ed / v_pl_t_rd) - 1) ** 2
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 6.29rho with torsion."""
+        _equation: str = (
+            r"\begin{cases} "
+            r"0 & \text{if } V_{Ed} \leq 0.5 \cdot V_{pl,T,Rd} \\ "
+            r"\left( \frac{2 \cdot V_{Ed}}{V_{pl,T,Rd}} - 1 \right)^2 & \text{if } V_{Ed} > 0.5 \cdot V_{pl,T,Rd} "
+            r"\end{cases}"
+        )
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"V_{Ed}": f"{self.v_ed:.3f}",
+                r"V_{pl,T,Rd}": f"{self.v_pl_t_rd:.3f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"V_{Ed}": rf"{self.v_ed:.3f} \ N",
+                r"V_{pl,T,Rd}": rf"{self.v_pl_t_rd:.3f} \ N",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\rho",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            numeric_equation_with_units=_numeric_equation_with_units,
+            comparison_operator_label="=",
+            unit="-",
+        )

blueprints/codes/eurocode/nen_en_1993_1_1_c2_a1_2016/chapter_6_ultimate_limit_state/formula_6_30.py

@@ -0,0 +1,113 @@
+"""Formula 6.30 from NEN-EN 1993-1-1+A1:2016: Chapter 6 - Ultimate Limit State."""
+
+from blueprints.codes.eurocode.nen_en_1993_1_1_c2_a1_2016 import NEN_EN_1993_1_1_C2_A1_2016
+from blueprints.codes.formula import Formula
+from blueprints.codes.latex_formula import LatexFormula, latex_replace_symbols
+from blueprints.type_alias import DIMENSIONLESS, MM, MM3, MPA, NMM
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class Form6Dot30ReducedPlasticResistanceMoment(Formula):
+    r"""Class representing formula 6.30 for the calculation of [$M_{y,v,Rd}$]."""
+
+    label = "6.30"
+    source_document = NEN_EN_1993_1_1_C2_A1_2016
+
+    def __init__(
+        self,
+        w_pl_y: MM3,
+        rho: DIMENSIONLESS,
+        h_w: MM,
+        t_w: MM,
+        f_y: MPA,
+        gamma_m0: DIMENSIONLESS,
+        m_y_c_rd: NMM,
+    ) -> None:
+        r"""[$M_{y,v,Rd}$] Reduced design plastic resistance moment [$Nmm$].
+
+        NEN-EN 1993-1-1+A1:2016 art.6.2.8(5) - Formula (6.30)
+
+        Parameters
+        ----------
+        w_pl_y : MM3
+            [$W_{pl,y}$] Plastic section modulus about the y axis [$mm^3$].
+        rho : DIMENSIONLESS
+            [$\rho$] Shear force ratio (see 6.2.8 (3) or (4)) [-].
+        h_w : MM
+            [$h_w$] Web height [$mm$].
+        t_w : MM
+            [$t_w$] Web thickness [$mm$].
+        f_y : MPA
+            [$f_y$] Yield strength of the material [$MPa$].
+        gamma_m0 : DIMENSIONLESS
+            [$\gamma_{M0}$] Partial safety factor for resistance of cross-sections [-].
+        m_y_c_rd : NMM
+            [$M_{y,c,Rd}$] Design resistance moment, obtained from 6.2.5(2) [$Nmm$].
+        """
+        super().__init__()
+        self.w_pl_y = w_pl_y
+        self.rho = rho
+        self.h_w = h_w
+        self.t_w = t_w
+        self.f_y = f_y
+        self.gamma_m0 = gamma_m0
+        self.m_y_c_rd = m_y_c_rd
+
+    @staticmethod
+    def _evaluate(
+        w_pl_y: MM3,
+        rho: DIMENSIONLESS,
+        h_w: MM,
+        t_w: MM,
+        f_y: MPA,
+        gamma_m0: DIMENSIONLESS,
+        m_y_c_rd: NMM,
+    ) -> NMM:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(w_pl_y=w_pl_y, rho=rho, h_w=h_w, f_y=f_y, m_y_c_rd=m_y_c_rd)
+        raise_if_less_or_equal_to_zero(gamma_m0=gamma_m0, t_w=t_w)
+
+        a_w = h_w * t_w
+        m_y_v_rd = (w_pl_y - (rho * a_w**2) / (4 * t_w)) * f_y / gamma_m0
+        return min(m_y_v_rd, m_y_c_rd)
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 6.30."""
+        _equation: str = (
+            r"\min\left(\frac{\left[W_{pl,y} - \frac{\rho \cdot (h_w \cdot t_w)^2}{4 \cdot t_w}\right] \cdot f_y}{\gamma_{M0}}, M_{y,c,Rd}\right)"
+        )
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"W_{pl,y}": f"{self.w_pl_y:.3f}",
+                r"\rho": f"{self.rho:.3f}",
+                r"h_w": f"{self.h_w:.3f}",
+                r"t_w": f"{self.t_w:.3f}",
+                r"f_y": f"{self.f_y:.3f}",
+                r"\gamma_{M0}": f"{self.gamma_m0:.3f}",
+                r"M_{y,c,Rd}": f"{self.m_y_c_rd:.3f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"W_{pl,y}": rf"{self.w_pl_y:.3f} \ mm^3",
+                r"\rho": rf"{self.rho:.3f}",
+                r"h_w": rf"{self.h_w:.3f} \ mm",
+                r"t_w": rf"{self.t_w:.3f} \ mm",
+                r"f_y": rf"{self.f_y:.3f} \ MPa",
+                r"\gamma_{M0}": rf"{self.gamma_m0:.3f}",
+                r"M_{y,c,Rd}": rf"{self.m_y_c_rd:.3f} \ Nmm",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"M_{y,v,Rd}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            numeric_equation_with_units=_numeric_equation_with_units,
+            comparison_operator_label="=",
+            unit="Nmm",
+        )

docs/objects_overview/eurocode/ec3_1993_1_1_2016/formulas.md

@@ -53,8 +53,9 @@ Total of 108 formulas present.
 | 6.26           | :x:  |         |             |
 | 6.27           | :x:  |         |             |
 | 6.28           | :x:  |         |             |
-| 6.29           | :x:  |         |             |
-| 6.30           | :x:  |         |             |
+| 6.29           | :heavy_check_mark:  |         | Form6Dot29ReducedYieldStrength            |
+| 6.29 (rho)     | :heavy_check_mark:  |         | Form6Dot29Rho and Form6Dot29RhoWithTorsion            |
+| 6.30           | :heavy_check_mark:  |         | Form6Dot30ReducedPlasticResistanceMoment            |
 | 6.31           | :x:  |         |             |
 | 6.32           | :x:  |         |             |
 | 6.33           | :x:  |         |             |