Merge pull request #444 from Blueprints-org/443-add-formulas-from-chapter-644-from-nen_en_1992_1_1

443 add formulas from chapter 644 from nen en 1992 1 1

Author: GerjanDorgelo

blueprints/codes/eurocode/nen_en_1992_1_1_c2_2011/chapter_6_ultimate_limit_state/formula_6_47.py

@@ -0,0 +1,106 @@
+"""Formula 6.47 from NEN-EN 1992-1-1+C2:2011: Chapter 6 - Ultimate Limit State."""
+
+from blueprints.codes.eurocode.nen_en_1992_1_1_c2_2011 import NEN_EN_1992_1_1_C2_2011
+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 Form6Dot47PunchingShearResistance(Formula):
+    r"""Class representing formula 6.47 for the calculation of punching shear resistance, $$v_{Rd,c}$$ of slabs and column bases
+    without shear reinforcement.
+    """
+
+    label = "6.47"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(
+        self,
+        c_rd_c: DIMENSIONLESS,
+        k: DIMENSIONLESS,
+        rho_l: DIMENSIONLESS,
+        f_ck: MPA,
+        k_1: DIMENSIONLESS,
+        sigma_cp: MPA,
+        v_min: MPA,
+    ) -> None:
+        r"""$$v_{Rd,c}$$ Calculation of punching shear resistance of slabs and column bases without shear reinforcement.
+
+        NEN-EN 1992-1-1+C2:2011 art.6.4.4(1) - Formula (6.47).
+
+        The values of $$C_{Rd,c}$$, $$v_{min}$$, and $$k_1$$ for use in a country may be found in its national annex.
+        The recommended value for $$C_{Rd,c}$$ is $$0.18 / \gamma_c$$, for $$v_{min}$$ is given by Expression (6.3N),
+        and that for $$k_1$$ is $$0.1$$.
+
+        Parameters
+        ----------
+        c_rd_c : DIMENSIONLESS
+            $$C_{Rd,c}$$ Coefficient for punching shear resistance, recommended value $$0.18 / \gamma_c$$ [-].
+        k : DIMENSIONLESS
+            $$k$$ Size effect factor, see equation SubForm6Dot47FactorK [-].
+        rho_l : DIMENSIONLESS
+            $$\rho_l$$ Longitudinal reinforcement ratio, see equation SubForm6Dot47FactorRhoL [-].
+        f_ck : MPA
+            $$f_{ck}$$ Characteristic compressive strength of concrete [$$MPa$$].
+        k_1 : DIMENSIONLESS
+            $$k_1$$ Coefficient for concrete strength, recommended value 0.1 [-].
+        sigma_cp : MPA
+            $$\sigma_{cp}$$ Stress in the critical section as average of the two perpendicular directions, see
+             equation SubForm6Dot47FactorSigmaCp [$$MPa$$].
+        v_min : MPA
+            $$v_{min}$$ Minimum shear stress capacity concrete, recommended value with Expression (6.3N) [$$MPa$$].
+        """
+        super().__init__()
+        self.c_rd_c = c_rd_c
+        self.k = k
+        self.rho_l = rho_l
+        self.f_ck = f_ck
+        self.k_1 = k_1
+        self.sigma_cp = sigma_cp
+        self.v_min = v_min
+
+    @staticmethod
+    def _evaluate(
+        c_rd_c: DIMENSIONLESS,
+        k: DIMENSIONLESS,
+        rho_l: DIMENSIONLESS,
+        f_ck: MPA,
+        k_1: DIMENSIONLESS,
+        sigma_cp: MPA,
+        v_min: MPA,
+    ) -> MPA:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(c_rd_c=c_rd_c, k=k, rho_l=rho_l, f_ck=f_ck, k_1=k_1, sigma_cp=sigma_cp, v_min=v_min)
+
+        term1 = c_rd_c * k * (100 * rho_l * f_ck) ** (1 / 3) + k_1 * sigma_cp
+        term2 = v_min + k_1 * sigma_cp
+        return max(term1, term2)
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 6.47."""
+        _equation: str = (
+            r"\max \left( C_{Rd,c} \cdot k \cdot (100 \cdot \rho_l \cdot f_{ck})^{1/3} "
+            r"+ k_1 \cdot \sigma_{cp}, v_{min} + k_1 \cdot \sigma_{cp} \right)"
+        )
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"C_{Rd,c}": f"{self.c_rd_c:.3f}",
+                r"\rho_l": f"{self.rho_l:.3f}",
+                r"f_{ck}": f"{self.f_ck:.3f}",
+                r"k_1": f"{self.k_1:.3f}",
+                r"\sigma_{cp}": f"{self.sigma_cp:.3f}",
+                r"v_{min}": f"{self.v_min:.3f}",
+                r"k": f"{self.k:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"v_{Rd,c}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="MPa",
+        )

blueprints/codes/eurocode/nen_en_1992_1_1_c2_2011/chapter_6_ultimate_limit_state/formula_6_47_subs.py

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+"""Formula 6.47 from NEN-EN 1992-1-1+C2:2011: Chapter 6 - Ultimate Limit State."""
+
+import numpy as np
+
+from blueprints.codes.eurocode.nen_en_1992_1_1_c2_2011 import NEN_EN_1992_1_1_C2_2011
+from blueprints.codes.formula import Formula
+from blueprints.codes.latex_formula import LatexFormula, latex_replace_symbols
+from blueprints.type_alias import DIMENSIONLESS, MM, MM2, MPA, N
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class SubForm6Dot47FactorK(Formula):
+    r"""Class representing the sub-formula which calculates the factor [$$k$$] for formula 6.47 ."""
+
+    label = "6.47 (factor k)"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(self, d: MM) -> None:
+        r"""[$$k$$] Calculation of factor k.
+
+        NEN-EN 1992-1-1+C2:2011 art.6.4.4(1) - Factor k for Formula (6.47)
+
+        Parameters
+        ----------
+        d : MM
+            [$$d$$] Effective depth [$$mm$$].
+        """
+        super().__init__()
+        self.d = d
+
+    @staticmethod
+    def _evaluate(d: MM) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_less_or_equal_to_zero(d=d)
+        return min(1 + np.sqrt(200 / d), 2.0)
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for sub-formula 6.47 (factor k)."""
+        _equation: str = r"\min \left( 1 + \sqrt{\frac{200}{d}}, 2.0 \right)"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"d": f"{self.d:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"k",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="-",
+        )
+
+
+class SubForm6Dot47FactorRhoL(Formula):
+    r"""Class representing the sub-formula which calculates the factor [$$\rho_l$$] for formula 6.47 ."""
+
+    label = "6.47 (factor rho_l)"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(self, rho_ly: DIMENSIONLESS, rho_lz: DIMENSIONLESS) -> None:
+        r"""[$$\rho_l$$] Calculation of factor [$$\rho_l$$].
+
+        NEN-EN 1992-1-1+C2:2011 art.6.4.4(1) - Factor rho_l for Formula (6.47)
+
+        Parameters
+        ----------
+        rho_ly : DIMENSIONLESS
+            [$$\rho_{ly}$$] Related to the bonded tension steel in y- drection. The value $$\rho_ly$$ should be calculated as mean values taking
+            into account a slab width equal to the column width plus 3d each side [$$-$$].
+        rho_lz : DIMENSIONLESS
+            [$$\rho_{lz}$$] Related to the bonded tension steel in z- drection. The value $$\rho_lz$$ should be calculated as mean values taking
+            into account a slab width equal to the column width plus 3d each side [$$-$$].
+        """
+        super().__init__()
+        self.rho_ly = rho_ly
+        self.rho_lz = rho_lz
+
+    @staticmethod
+    def _evaluate(rho_ly: DIMENSIONLESS, rho_lz: DIMENSIONLESS) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(rho_ly=rho_ly, rho_lz=rho_lz)
+        return min(np.sqrt(rho_ly * rho_lz), 0.02)
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for sub-formula 6.47 (factor rho_l)."""
+        _equation: str = r"\min \left( \sqrt{\rho_{ly} \cdot \rho_{lz}}, 0.02 \right)"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"\rho_{ly}": f"{self.rho_ly:.3f}",
+                r"\rho_{lz}": f"{self.rho_lz:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\rho_l",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="-",
+        )
+
+
+class SubForm6Dot47FactorSigmaCp(Formula):
+    r"""Class representing the sub-formula which calculates the factor [$$\sigma_{cp}$$] for formula 6.47,."""
+
+    label = "6.47 (factor sigma_cp)"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(self, sigma_cy: MPA, sigma_cz: MPA) -> None:
+        r"""[$$\sigma_{cp}$$] Calculation of factor [$$\sigma_{cp}$$].
+
+        NEN-EN 1992-1-1+C2:2011 art.6.4.4(1) - Factor sigma_cp for Formula (6.47)
+
+        Parameters
+        ----------
+        sigma_cy : MPA
+            [$$\sigma_{cy}$$] Normal concrete stress in the critical section in the y-direction [$$MPa$$], Positive if compression.
+            See equation SubForm6Dot47FactorSigmaCy.
+        sigma_cz : MPA
+            [$$\sigma_{cz}$$] Normal concrete stress inm the critical section in the z-direction [$$MPa$$], Positive if compression.
+            See equation SubForm6Dot47FactorSigmaCz.
+        """
+        super().__init__()
+        self.sigma_cy = sigma_cy
+        self.sigma_cz = sigma_cz
+
+    @staticmethod
+    def _evaluate(sigma_cy: MPA, sigma_cz: MPA) -> MPA:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(sigma_cy=sigma_cy, sigma_cz=sigma_cz)
+        return (sigma_cy + sigma_cz) / 2
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for sub-formula 6.47 (sigma_cp)."""
+        _equation: str = r"\frac{\sigma_{cy} + \sigma_{cz}}{2}"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"\sigma_{cy}": f"{self.sigma_cy:.3f}",
+                r"\sigma_{cz}": f"{self.sigma_cz:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\sigma_{cp}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="MPa",
+        )
+
+
+class SubForm6Dot47FactorSigmaCy(Formula):
+    r"""Class representing the sub-formula which calculates the factor [$$\sigma_{cy}$$] for formula 6.47."""
+
+    label = "6.47 (factor sigma_cy)"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(self, n_ed_y: N, a_cy: MM2) -> None:
+        r"""[$$\sigma_{cy}$$] Calculation of factor [$$\sigma_{cy}$$].
+
+        NEN-EN 1992-1-1+C2:2011 art.6.4.4(1) - Factor sigma_cy for Formula (6.47)
+
+        Parameters
+        ----------
+        n_ed_y : N
+            [$$N_{Ed,y}$$] Longitudinal forces across the full bay for internal columns and the logintudinal force across
+            the control section for edge columns. The force may be from a load or prestressing action [$$N$$].
+        a_cy : MM2
+            [$$A_{cy}$$] Cross-sectional area in y-direction [$$mm^2$$].
+        """
+        super().__init__()
+        self.n_ed_y = n_ed_y
+        self.a_cy = a_cy
+
+    @staticmethod
+    def _evaluate(n_ed_y: N, a_cy: MM2) -> MPA:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_less_or_equal_to_zero(a_cy=a_cy)
+        raise_if_negative(n_ed_y=n_ed_y)
+        return n_ed_y / a_cy
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for sub-formula 6.47 (sigma_cy)."""
+        _equation: str = r"\frac{N_{Ed,y}}{A_{cy}}"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"N_{Ed,y}": f"{self.n_ed_y:.3f}",
+                r"A_{cy}": f"{self.a_cy:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\sigma_{cy}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="MPa",
+        )
+
+
+class SubForm6Dot47FactorSigmaCz(Formula):
+    r"""Class representing the sub-formula which calculates the factor [$$\sigma_{cz}$$] for formula 6.47."""
+
+    label = "6.47 (factor sigma_cz)"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(self, n_ed_z: N, a_cz: MM2) -> None:
+        r"""[$$\sigma_{cz}$$] Calculation of factor [$$\sigma_{cz}$$].
+
+        NEN-EN 1992-1-1+C2:2011 art.6.4.4(1) - Factor sigma_cz for Formula (6.47)
+
+        Parameters
+        ----------
+        n_ed_z : N
+            [$$N_{Ed,z}$$] Longitudinal forces across the full bay for internal columns and the logintudinal force across
+            the control section for edge columns. The force may be from a load or prestressing action [$$N$$].
+        a_cz : MM2
+            [$$A_{cz}$$] Cross-sectional area in z-direction [$$mm^2$$].
+        """
+        super().__init__()
+        self.n_ed_z = n_ed_z
+        self.a_cz = a_cz
+
+    @staticmethod
+    def _evaluate(n_ed_z: N, a_cz: MM2) -> MPA:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_less_or_equal_to_zero(a_cz=a_cz)
+        raise_if_negative(n_ed_z=n_ed_z)
+        return n_ed_z / a_cz
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for sub-formula 6.47 sigma_cz."""
+        _equation: str = r"\frac{N_{Ed,z}}{A_{cz}}"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"N_{Ed,z}": f"{self.n_ed_z:.3f}",
+                r"A_{cz}": f"{self.a_cz:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\sigma_{cz}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="MPa",
+        )