Add formulas 6.39-6.40 from Eurocode 1993-1-1

blueprints/codes/eurocode/nen_en_1993_1_1_c2_a1_2016/chapter_6_ultimate_limit_state/formula_6_39.py

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+"""Formula 6.39 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, NMM
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class Form6Dot39ReducedBendingMomentResistance(Formula):
+    r"""Class representing formula 6.39 for the calculation of [$M_{N,y,Rd}$]."""
+
+    label = "6.39"
+    source_document = NEN_EN_1993_1_1_C2_A1_2016
+
+    def __init__(
+        self,
+        mpl_y_rd: NMM,
+        n: DIMENSIONLESS,
+        a_w: DIMENSIONLESS,
+    ) -> None:
+        r"""[$M_{N,y,Rd}$] Calculation of the reduced bending moment [$Nmm$].
+
+        NEN-EN 1993-1-1+C2+A1:2016 art.6.2.9.1(5) - Formula (6.39)
+
+        Parameters
+        ----------
+        mpl_y_rd : NMM
+            [$M_{pl,y,Rd}$] Plastic bending moment resistance about the y-axis [$Nmm$].
+        n : DIMENSIONLESS
+            [$n$] Axial force ratio, see equation 6.38n (dimensionless).
+        a_w : DIMENSIONLESS
+            [$a_w$] Reduction factor for the web (dimensionless), see equation 6.39aw.
+        """
+        super().__init__()
+        self.mpl_y_rd = mpl_y_rd
+        self.n = n
+        self.a_w = a_w
+
+    @staticmethod
+    def _evaluate(
+        mpl_y_rd: NMM,
+        n: DIMENSIONLESS,
+        a_w: DIMENSIONLESS,
+    ) -> NMM:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(mpl_y_rd=mpl_y_rd, n=n, a_w=a_w)
+        raise_if_less_or_equal_to_zero(denominator=(1 - 0.5 * a_w))
+
+        return min(mpl_y_rd * (1 - n) / (1 - 0.5 * a_w), mpl_y_rd)
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 6.39."""
+        _equation: str = r"\min \left( M_{pl,y,Rd} \cdot \frac{1 - n}{1 - 0.5 \cdot a_w}, M_{pl,y,Rd} \right)"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"M_{pl,y,Rd}": f"{self.mpl_y_rd:.3f}",
+                r" n": f" {self.n:.3f}",
+                r"a_w": f"{self.a_w:.3f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"M_{pl,y,Rd}": rf"{self.mpl_y_rd:.3f} \ Nmm",
+                r" n": rf" {self.n:.3f}",
+                r"a_w": rf"{self.a_w:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"M_{N,y,Rd}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            numeric_equation_with_units=_numeric_equation_with_units,
+            comparison_operator_label=r"=",
+            unit="Nmm",
+        )

blueprints/codes/eurocode/nen_en_1993_1_1_c2_a1_2016/chapter_6_ultimate_limit_state/formula_6_39aw.py

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+"""Formula 6.39aw 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, MM, MM2
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class Form6Dot39awHollowSections(Formula):
+    r"""Class representing formula 6.39aw for [$a_w$] in hollow sections."""
+
+    label = "6.39aw_hollow"
+    source_document = NEN_EN_1993_1_1_C2_A1_2016
+
+    def __init__(
+        self,
+        a: MM2,
+        b: MM,
+        t: MM,
+    ) -> None:
+        r"""[$a_w$] Calculation of the reduction factor for hollow sections (dimensionless).
+
+        NEN-EN 1993-1-1+C2+A1:2016 art.6.2.9.1(5) - Formula (6.39aw)
+
+        Parameters
+        ----------
+        a : MM2
+            [$A$] Total cross-sectional area [$mm^2$].
+        b : MM
+            [$b$] Width of the section [$mm$].
+        t : MM
+            [$t$] Thickness of the section [$mm$].
+        """
+        super().__init__()
+        self.a = a
+        self.b = b
+        self.t = t
+
+    @staticmethod
+    def _evaluate(
+        a: MM2,
+        b: MM,
+        t: MM,
+    ) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(a=a, b=b, t=t)
+        raise_if_less_or_equal_to_zero(denominator=a)
+
+        return min((a - 2 * b * t) / a, 0.5)
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 6.39aw."""
+        _equation: str = r"\min \left( \frac{A - 2 \cdot b \cdot t}{A}, 0.5 \right)"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"A": f"{self.a:.3f}",
+                r"b": f"{self.b:.3f}",
+                r" t": f" {self.t:.3f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"A": rf"{self.a:.3f} \ mm^2",
+                r"b": rf"{self.b:.3f} \ mm",
+                r" t": rf" {self.t:.3f} \ mm",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"a_w",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            numeric_equation_with_units=_numeric_equation_with_units,
+            comparison_operator_label=r"=",
+            unit="-",
+        )
+
+
+class Form6Dot39awWeldedBoxSections(Formula):
+    r"""Class representing formula 6.39aw for [$a_w$] in welded box sections."""
+
+    label = "6.39aw_welded_box"
+    source_document = NEN_EN_1993_1_1_C2_A1_2016
+
+    def __init__(
+        self,
+        a: MM2,
+        b: MM,
+        t_f: MM,
+    ) -> None:
+        r"""[$a_w$] Calculation of the reduction factor for welded box sections (dimensionless).
+
+        NEN-EN 1993-1-1+C2+A1:2016 art.6.2.9.1(5) - Formula (6.39aw)
+
+        Parameters
+        ----------
+        a : MM2
+            [$A$] Total cross-sectional area [$mm^2$].
+        b : MM
+            [$b$] Width of the section [$mm$].
+        t_f : MM
+            [$t_f$] Flange thickness [$mm$].
+        """
+        super().__init__()
+        self.a = a
+        self.b = b
+        self.t_f = t_f
+
+    @staticmethod
+    def _evaluate(
+        a: MM2,
+        b: MM,
+        t_f: MM,
+    ) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(a=a, b=b, t_f=t_f)
+        raise_if_less_or_equal_to_zero(denominator=a)
+
+        return min((a - 2 * b * t_f) / a, 0.5)
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 6.39aw."""
+        _equation: str = r"\min \left( \frac{A - 2 \cdot b \cdot t_f}{A}, 0.5 \right)"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"A": f"{self.a:.3f}",
+                r"b": f"{self.b:.3f}",
+                r"t_f": f"{self.t_f:.3f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"A": rf"{self.a:.3f} \ mm^2",
+                r"b": rf"{self.b:.3f} \ mm",
+                r"t_f": rf"{self.t_f:.3f} \ mm",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"a_w",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            numeric_equation_with_units=_numeric_equation_with_units,
+            comparison_operator_label=r"=",
+            unit="-",
+        )

blueprints/codes/eurocode/nen_en_1993_1_1_c2_a1_2016/chapter_6_ultimate_limit_state/formula_6_40.py

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+"""Formula 6.40 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, NMM
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class Form6Dot40ReducedBendingMomentResistance(Formula):
+    r"""Class representing formula 6.40 for the calculation of [$M_{N,z,Rd}$]."""
+
+    label = "6.40"
+    source_document = NEN_EN_1993_1_1_C2_A1_2016
+
+    def __init__(
+        self,
+        mpl_z_rd: NMM,
+        n: DIMENSIONLESS,
+        a_f: DIMENSIONLESS,
+    ) -> None:
+        r"""[$M_{N,z,Rd}$] Calculation of the reduced bending moment [$Nmm$].
+
+        NEN-EN 1993-1-1+C2+A1:2016 art.6.2.9.1(5) - Formula (6.40)
+
+        Parameters
+        ----------
+        mpl_z_rd : NMM
+            [$M_{pl,z,Rd}$] Plastic bending moment resistance about the z-axis [$Nmm$].
+        n : DIMENSIONLESS
+            [$n$] Axial force ratio, see equation 6.38n (dimensionless).
+        a_f : DIMENSIONLESS
+            [$a_f$] Reduction factor for the flange (dimensionless).
+        """
+        super().__init__()
+        self.mpl_z_rd = mpl_z_rd
+        self.n = n
+        self.a_f = a_f
+
+    @staticmethod
+    def _evaluate(
+        mpl_z_rd: NMM,
+        n: DIMENSIONLESS,
+        a_f: DIMENSIONLESS,
+    ) -> NMM:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(mpl_z_rd=mpl_z_rd, n=n, a_f=a_f)
+        raise_if_less_or_equal_to_zero(denominator=(1 - 0.5 * a_f))
+
+        return min(mpl_z_rd * (1 - n) / (1 - 0.5 * a_f), mpl_z_rd)
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 6.40."""
+        _equation: str = r"\min \left( M_{pl,z,Rd} \cdot \frac{1 - n}{1 - 0.5 \cdot a_f}, M_{pl,z,Rd} \right)"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"M_{pl,z,Rd}": f"{self.mpl_z_rd:.3f}",
+                r" n": f" {self.n:.3f}",
+                r"a_f": f"{self.a_f:.3f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"M_{pl,z,Rd}": rf"{self.mpl_z_rd:.3f} \ Nmm",
+                r" n": rf" {self.n:.3f}",
+                r"a_f": rf"{self.a_f:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"M_{N,z,Rd}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            numeric_equation_with_units=_numeric_equation_with_units,
+            comparison_operator_label=r"=",
+            unit="Nmm",
+        )