927 copying steel equations from 2005 to 2025, for those that are the same, batch 4

blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_23.py

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+"""Formula 8.23 from EN 1993-1-1:2022: Chapter 8 - Ultimate Limit State."""
+
+import numpy as np
+
+from blueprints.codes.eurocode.en_1993_1_1_2022 import EN_1993_1_1_2022
+from blueprints.codes.formula import Formula
+from blueprints.codes.latex_formula import LatexFormula, latex_replace_symbols
+from blueprints.type_alias import DIMENSIONLESS, MM2, MPA, N
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class Form8Dot23DesignPlasticShearResistance(Formula):
+    r"""Class representing formula 8.23 for the calculation of [$V_{pl,Rd}$]."""
+
+    label = "8.23"
+    source_document = EN_1993_1_1_2022
+
+    def __init__(
+        self,
+        a_v: MM2,
+        f_y: MPA,
+        gamma_m0: DIMENSIONLESS,
+    ) -> None:
+        r"""[$V_{pl,Rd}$] Calculation of the design plastic shear resistance [$N$].
+
+        EN 1993-1-1:2022 art.8.2.6(2) - Formula (8.23)
+
+        Parameters
+        ----------
+        a_v : MM2
+            [$A_v$] Shear area, to be taken from a subformula from 8.23 [$mm^2$].
+        f_y : MPA
+            [$f_y$] Yield strength of the material [$MPa$].
+        gamma_m0 : DIMENSIONLESS
+            [$\gamma_{M0}$] Partial safety factor for resistance of cross-sections.
+        """
+        super().__init__()
+        self.a_v = a_v
+        self.f_y = f_y
+        self.gamma_m0 = gamma_m0
+
+    @staticmethod
+    def _evaluate(
+        a_v: MM2,
+        f_y: MPA,
+        gamma_m0: DIMENSIONLESS,
+    ) -> N:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(a_v=a_v, f_y=f_y)
+        raise_if_less_or_equal_to_zero(gamma_m0=gamma_m0)
+
+        return (a_v * (f_y / np.sqrt(3))) / gamma_m0
+
+    def latex(self, n: int = 3) -> LatexFormula:
+        """Returns LatexFormula object for formula 8.23."""
+        _equation: str = r"\frac{A_v \cdot (f_y / \sqrt{3})}{\gamma_{M0}}"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"A_v": f"{self.a_v:.{n}f}",
+                r"f_y": f"{self.f_y:.{n}f}",
+                r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"A_v": rf"{self.a_v:.{n}f} \ mm^2",
+                r"f_y": rf"{self.f_y:.{n}f} \ MPa",
+                r"\gamma_{M0}": f"{self.gamma_m0:.{n}f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"V_{pl,Rd}",
+            result=f"{self:.{n}f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            numeric_equation_with_units=_numeric_equation_with_units,
+            comparison_operator_label="=",
+            unit="N",
+        )

blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_25.py

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+"""Formula 8.25 from EN 1993-1-1:2022: Chapter 8 - Ultimate Limit State."""
+
+from blueprints.codes.eurocode.en_1993_1_1_2022 import EN_1993_1_1_2022
+from blueprints.codes.formula import Formula
+from blueprints.codes.latex_formula import LatexFormula, latex_replace_symbols
+from blueprints.type_alias import MM, MM3, MM4, MPA, N
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class Form8Dot25ShearStress(Formula):
+    r"""Class representing formula 8.25 for the calculation of [$\tau_{Ed}$]."""
+
+    label = "8.25"
+    source_document = EN_1993_1_1_2022
+
+    def __init__(
+        self,
+        v_ed: N,
+        s: MM3,
+        i: MM4,
+        t: MM,
+    ) -> None:
+        r"""[$\tau_{Ed}$] Calculation of the design elastic shear stress [$MPa$].
+
+        EN 1993-1-1:2022 art.8.2.6(4) - Formula (8.25)
+
+        Parameters
+        ----------
+        v_ed : N
+            [$V_{Ed}$] Design value of the shear force [$N$].
+        s : MM3
+            [$S$] First moment of area about the centroidal axis of that portion of the cross-section between
+            the point at which the shear is required and the boundary of the cross-section [$mm^3$].
+        i : MM4
+            [$I$] Second moment of area of the whole cross section [$mm^4$].
+        t : MM
+            [$t$] Thickness at the examined point [$mm$].
+        """
+        super().__init__()
+        self.v_ed = v_ed
+        self.s = s
+        self.i = i
+        self.t = t
+
+    @staticmethod
+    def _evaluate(
+        v_ed: N,
+        s: MM3,
+        i: MM4,
+        t: MM,
+    ) -> MPA:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(v_ed=v_ed, s=s)
+        raise_if_less_or_equal_to_zero(i=i, t=t)
+
+        return (v_ed * s) / (i * t)
+
+    def latex(self, n: int = 3) -> LatexFormula:
+        """Returns LatexFormula object for formula 8.25."""
+        _equation: str = r"\frac{V_{Ed} \cdot S}{I \cdot t}"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"V_{Ed}": f"{self.v_ed:.{n}f}",
+                r"S": f"{self.s:.{n}f}",
+                r"I": f"{self.i:.{n}f}",
+                r" t": f" {self.t:.{n}f}",
+            },
+            False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            {
+                r"V_{Ed}": rf"{self.v_ed:.{n}f} \ N",
+                r"S": rf"{self.s:.{n}f} \ mm^3",
+                r"I": rf"{self.i:.{n}f} \ mm^4",
+                r" t": rf" {self.t:.{n}f} \ mm",
+            },
+            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",
+        )

blueprints/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/formula_8_26.py

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+"""Formula 8.26 from EN 1993-1-1:2022: Chapter 8 - Ultimate Limit State."""
+
+from blueprints.codes.eurocode.en_1993_1_1_2022 import EN_1993_1_1_2022
+from blueprints.codes.formula import Formula
+from blueprints.codes.latex_formula import LatexFormula, latex_replace_symbols
+from blueprints.type_alias import MM2, MPA, N
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class Form8Dot26ShearStressIOrHSection(Formula):
+    r"""Class representing formula 8.26 for the calculation of [$\tau_{Ed}$]."""
+
+    label = "8.26"
+    source_document = EN_1993_1_1_2022
+
+    def __init__(
+        self,
+        v_ed: N,
+        a_w: MM2,
+        a_f: MM2,
+    ) -> None:
+        r"""[$\tau_{Ed}$] Calculation of the design elastic shear stress [$MPa$].
+        For I- or H-sections the shear stress in the web may be taken with this equation.
+
+        EN 1993-1-1:2022 art.8.2.6(5) - Formula (8.26)
+
+        Parameters
+        ----------
+        v_ed : N
+            [$V_{Ed}$] Design shear force [$N$].
+        a_w : MM2
+            [$A_w$] Area of the web [$mm^2$].
+        a_f : MM2
+            [$A_f$] Area of one flange [$mm^2$].
+        """
+        super().__init__()
+        self.v_ed = v_ed
+        self.a_w = a_w
+        self.a_f = a_f
+
+    @staticmethod
+    def _evaluate(
+        v_ed: N,
+        a_w: MM2,
+        a_f: MM2,
+    ) -> MPA:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(v_ed=v_ed, a_f=a_f)
+        raise_if_less_or_equal_to_zero(a_w=a_w)
+        if not a_f / a_w >= 0.6:
+            raise ValueError("A_f / A_w must be greater than or equal to 0.6")
+
+        return v_ed / a_w
+
+    def latex(self, n: int = 3) -> LatexFormula:
+        """Returns LatexFormula object for formula 8.26."""
+        _equation: str = r"\frac{V_{Ed}}{A_w} \text{ if } A_f / A_w \ge 0.6"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            replacements={
+                r"V_{Ed}": f"{self.v_ed:.{n}f}",
+                r"A_w": f"{self.a_w:.{n}f}",
+                r"A_f": f"{self.a_f:.{n}f}",
+            },
+            unique_symbol_check=False,
+        )
+        _numeric_equation_with_units: str = latex_replace_symbols(
+            _equation,
+            replacements={
+                r"V_{Ed}": rf"{self.v_ed:.{n}f} \ N",
+                r"A_w": rf"{self.a_w:.{n}f} \ mm^2",
+                r"A_f": rf"{self.a_f:.{n}f} \ mm^2",
+            },
+            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",
+        )

tests/codes/eurocode/en_1993_1_1_2022/chapter_8_ultimate_limit_state/test_formula_8_23.py

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+"""Testing formula 8.23 from EN 1993-1-1:2022, chapter 8, ultimate limit state."""
+
+import pytest
+
+from blueprints.codes.eurocode.en_1993_1_1_2022.chapter_8_ultimate_limit_state.formula_8_23 import Form8Dot23DesignPlasticShearResistance
+from blueprints.validations import LessOrEqualToZeroError, NegativeValueError
+
+
+class TestForm8Dot23DesignPlasticShearResistance:
+    """Validation for formula 8.23 from EN 1993-1-1:2022, chapter 8, ultimate limit state."""
+
+    def test_evaluation(self) -> None:
+        """Tests the evaluation of the result."""
+        # Example values
+        a_v = 2000.0
+        f_y = 355.0
+        gamma_m0 = 1.0
+
+        # Object to test
+        formula = Form8Dot23DesignPlasticShearResistance(a_v=a_v, f_y=f_y, gamma_m0=gamma_m0)
+
+        # Expected result, manually calculated
+        manually_calculated_result = 409918.6911246343  # N
+
+        assert formula == pytest.approx(expected=manually_calculated_result, rel=1e-4)
+
+    @pytest.mark.parametrize(
+        ("a_v", "f_y", "gamma_m0"),
+        [
+            (-2000.0, 355.0, 1.0),  # a_v is negative
+            (2000.0, -355.0, 1.0),  # f_y is negative
+            (2000.0, 355.0, -1.0),  # gamma_m0 is negative
+        ],
+    )
+    def test_raise_error_when_invalid_values_are_given(self, a_v: float, f_y: float, gamma_m0: float) -> None:
+        """Test invalid values."""
+        with pytest.raises((NegativeValueError, LessOrEqualToZeroError)):
+            Form8Dot23DesignPlasticShearResistance(a_v=a_v, f_y=f_y, gamma_m0=gamma_m0)
+
+    @pytest.mark.parametrize(
+        ("a_v", "f_y", "gamma_m0"),
+        [
+            (2000.0, 355.0, 0.0),  # gamma_m0 is zero
+            (2000.0, 355.0, -1.0),  # gamma_m0 is negative
+        ],
+    )
+    def test_raise_error_when_gamma_m0_is_invalid(self, a_v: float, f_y: float, gamma_m0: float) -> None:
+        """Test invalid gamma_m0 values."""
+        with pytest.raises(LessOrEqualToZeroError):
+            Form8Dot23DesignPlasticShearResistance(a_v=a_v, f_y=f_y, gamma_m0=gamma_m0)
+
+    @pytest.mark.parametrize(
+        ("representation", "expected"),
+        [
+            (
+                "complete",
+                r"V_{pl,Rd} = \frac{A_v \cdot (f_y / \sqrt{3})}{\gamma_{M0}} = "
+                r"\frac{2000.000 \cdot (355.000 / \sqrt{3})}{1.000} = 409918.691 \ N",
+            ),
+            ("short", r"V_{pl,Rd} = 409918.691 \ N"),
+            (
+                "complete_with_units",
+                r"V_{pl,Rd} = \frac{A_v \cdot (f_y / \sqrt{3})}{\gamma_{M0}} = "
+                r"\frac{2000.000 \ mm^2 \cdot (355.000 \ MPa / \sqrt{3})}{1.000} = 409918.691 \ N",
+            ),
+        ],
+    )
+    def test_latex(self, representation: str, expected: str) -> None:
+        """Test the latex representation of the formula."""
+        # Example values
+        a_v = 2000.0
+        f_y = 355.0
+        gamma_m0 = 1.0
+
+        # Object to test
+        latex = Form8Dot23DesignPlasticShearResistance(a_v=a_v, f_y=f_y, gamma_m0=gamma_m0).latex()
+
+        actual = {
+            "complete": latex.complete,
+            "short": latex.short,
+            "complete_with_units": latex.complete_with_units,
+        }
+
+        assert expected == actual[representation], f"{representation} representation failed."