484 feature request add formulas 716-721 from nen en 1992 1 1

blueprints/codes/eurocode/nen_en_1992_1_1_c2_2011/chapter_7_serviceability_limit_state/formula_7_16_ab.py

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+"""Formula 7.16a/b from NEN-EN 1992-1-1+C2:2011: Chapter 7 - Serviceability 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, MPA
+from blueprints.validations import raise_if_less_or_equal_to_zero, raise_if_negative
+
+
+class Form7Dot16abSpanDepthRatio(Formula):
+    r"""Class representing formula 7.16a/b for the calculation of the limit span/depth ratio."""
+
+    label = "7.16a/b"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(
+        self,
+        capital_k: DIMENSIONLESS,
+        f_ck: MPA,
+        rho: DIMENSIONLESS,
+        rho_0: DIMENSIONLESS,
+        rho_prime: DIMENSIONLESS,
+    ) -> None:
+        r"""[$\frac{l}{d}$] Limit span/depth ratio [-].
+
+        NEN-EN 1992-1-1+C2:2011 art.7.4.2(2) - Formula (7.16a and 7.16b)
+
+        Parameters
+        ----------
+        capital_k : DIMENSIONLESS
+            [$K$] Factor to take into account the different structural systems [-].
+        f_ck : MPA
+            [$f_{ck}$] Characteristic compressive strength of concrete [$MPa$].
+        rho : DIMENSIONLESS
+            [$\rho$] Required tension reinforcement ratio at mid-span to resist the moment
+            due to the design loads (at support for cantilevers) [-].
+        rho_0 : DIMENSIONLESS
+            [$\rho_0$] Reference reinforcement ratio [$\sqrt{f_{ck}} \cdot 10^{-3}$] [-].
+        rho_prime : DIMENSIONLESS
+            [$\rho'$] Required compression reinforcement ratio at mid-span to resist the moment
+            due to design loads (at support for cantilevers) [-].
+        """
+        super().__init__()
+        self.capital_k = capital_k
+        self.f_ck = f_ck
+        self.rho = rho
+        self.rho_0 = rho_0
+        self.rho_prime = rho_prime
+
+    @staticmethod
+    def _evaluate(
+        capital_k: DIMENSIONLESS,
+        f_ck: MPA,
+        rho: DIMENSIONLESS,
+        rho_0: DIMENSIONLESS,
+        rho_prime: DIMENSIONLESS,
+    ) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(capital_k=capital_k, f_ck=f_ck, rho=rho, rho_0=rho_0, rho_prime=rho_prime)
+        raise_if_less_or_equal_to_zero(rho=rho)
+
+        if rho <= rho_0:
+            l_over_d = capital_k * (11 + 1.5 * np.sqrt(f_ck) * rho_0 / rho + 3.2 * np.sqrt(f_ck) * (rho_0 / rho - 1) ** 1.5)
+        else:
+            l_over_d = capital_k * (11 + 1.5 * np.sqrt(f_ck) * rho_0 / (rho - rho_prime) + 1 / 12 * np.sqrt(f_ck) * np.sqrt(rho_prime / rho_0))
+
+        return l_over_d
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 7.16a/b."""
+        _equation: str = (
+            r"\begin{cases} K \cdot \left[11 + 1.5 \cdot \sqrt{f_{ck}} \cdot \frac{\rho_0}{\rho} + "
+            r"3.2 \cdot \sqrt{f_{ck}} \cdot \left(\frac{\rho_0}{\rho} - 1\right)^{3/2}\right] & \text{if } \rho \leq \rho_0 \\ "
+            r"K \cdot \left[11 + 1.5 \cdot \sqrt{f_{ck}} \cdot \frac{\rho_0}{\rho - \rho'} + "
+            r"\frac{1}{12} \cdot \sqrt{f_{ck}} \cdot \sqrt{\frac{\rho'}{\rho_0}}\right] & \text{if } \rho > \rho_0 \end{cases}"
+        )
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"K": f"{self.capital_k:.3f}",
+                r"f_{ck}": f"{self.f_ck:.3f}",
+                r"\rho_0": f"{self.rho_0:.4f}",
+                r"\rho'": f"{self.rho_prime:.4f}",
+                r"\rho": f"{self.rho:.4f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\frac{l}{d}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="-",
+        )
+
+
+class Form7Dot16ReferenceReinforcementRatio(Formula):
+    r"""Class representing formula 7.16 for the calculation of [$\rho_0$]."""
+
+    label = "7.16_rho_0"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(
+        self,
+        f_ck: MPA,
+    ) -> None:
+        r"""[$\rho_0$] Reference reinforcement ratio [-].
+
+        NEN-EN 1992-1-1+C2:2011 art.7.4.2(2) - Formula (7.16)
+
+        Parameters
+        ----------
+        f_ck : MPA
+            [$f_{ck}$] Characteristic compressive strength of concrete [$MPa$].
+        """
+        super().__init__()
+        self.f_ck = f_ck
+
+    @staticmethod
+    def _evaluate(
+        f_ck: MPA,
+    ) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(f_ck=f_ck)
+
+        return np.sqrt(f_ck) * 10**-3
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 7.16_rho_0."""
+        _equation: str = r"\sqrt{f_{ck}} \cdot 10^{-3}"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"f_{ck}": f"{self.f_ck:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\rho_0",
+            result=f"{self:.6f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="-",
+        )

blueprints/codes/eurocode/nen_en_1992_1_1_c2_2011/chapter_7_serviceability_limit_state/formula_7_17.py

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+"""Formula 7.17 from NEN-EN 1992-1-1+C2:2011: Chapter 7 - Serviceability limit state (SLS)."""
+
+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, MM2, N
+from blueprints.validations import raise_if_less_or_equal_to_zero
+
+
+class Form7Dot1MultiplicationFactorLimitSlenderness(Formula):
+    r"""Class representing formula 7.17 for the calculation of the stress multiplication factor for the limit span to depth ratio."""
+
+    label = "7.17"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(
+        self,
+        f_yk: N,
+        a_s_req: MM2,
+        a_s_prov: MM2,
+    ) -> None:
+        r"""[$\frac{310}{\sigma_s}$] Calculation of the multiplication factor [$-$].
+
+        NEN-EN 1992-1-1+C2:2011 art.7.4.2(2) - Formula (7.17)
+
+        Parameters
+        ----------
+        f_yk : MPa
+            [$f_{yk}$] Characteristic yield strength of the steel [$MPa$].
+        a_s_req : MM2
+            [$A_{s,req}$] Area of steel required at this section for ultimate limit state [$mm^2$].
+        a_s_prov : MM2
+            [$A_{s,prov}$] Area of steel provided at this section [$mm^2$].
+        """
+        super().__init__()
+        self.f_yk = f_yk
+        self.a_s_req = a_s_req
+        self.a_s_prov = a_s_prov
+
+    @staticmethod
+    def _evaluate(
+        f_yk: N,
+        a_s_req: MM2,
+        a_s_prov: MM2,
+    ) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_less_or_equal_to_zero(f_yk=f_yk, a_s_req=a_s_req, a_s_prov=a_s_prov)
+
+        return 500 / (f_yk * a_s_req / a_s_prov)
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 7.17."""
+        _equation: str = r"\frac{500}{f_{yk} \cdot \frac{A_{s,req}}{A_{s,prov}}}"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"f_{yk}": f"{self.f_yk:.3f}",
+                r"A_{s,req}": f"{self.a_s_req:.3f}",
+                r"A_{s,prov}": f"{self.a_s_prov:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\frac{310}{\sigma_s}",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="-",
+        )

blueprints/codes/eurocode/nen_en_1992_1_1_c2_2011/chapter_7_serviceability_limit_state/formula_7_18.py

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+"""Formula 7.18 from NEN-EN 1992-1-1+C2:2011: Chapter 7 - Serviceability 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
+from blueprints.validations import raise_if_negative
+
+
+class Form7Dot18DeformationParameter(Formula):
+    r"""Class representing formula 7.18 for the calculation of [$\alpha$]."""
+
+    label = "7.18"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(
+        self,
+        zeta: DIMENSIONLESS,
+        alpha_l: DIMENSIONLESS,
+        alpha_ll: DIMENSIONLESS,
+    ) -> None:
+        r"""[$\alpha$] Calculation of the deformation parameter [$\alpha$].
+
+        NEN-EN 1992-1-1+C2:2011 art.7.4.3(3) - Formula (7.18)
+
+        Parameters
+        ----------
+        zeta : DIMENSIONLESS
+            [$\zeta$] Distribution coefficient allowing for tension stiffening at a section, calculated with Expression (7.19).
+        alpha_l : DIMENSIONLESS
+            [$\alpha_{I}$] Value of the parameter calculated for the uncracked condition
+        alpha_ll : DIMENSIONLESS
+            [$\alpha_{II}$] Value of the parameter calculated for the fully cracked condition.
+        .
+        """
+        super().__init__()
+        self.zeta = zeta
+        self.alpha_l = alpha_l
+        self.alpha_ll = alpha_ll
+
+    @staticmethod
+    def _evaluate(
+        zeta: DIMENSIONLESS,
+        alpha_l: DIMENSIONLESS,
+        alpha_ll: DIMENSIONLESS,
+    ) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(alpha_ll=alpha_ll, alpha_l=alpha_l, zeta=zeta)
+
+        return zeta * alpha_ll + (1 - zeta) * alpha_l
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 7.18."""
+        _equation: str = r"\zeta \cdot \alpha_{II} + (1 - \zeta) \cdot \alpha_{I}"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"\zeta": f"{self.zeta:.3f}",
+                r"\alpha_{II}": f"{self.alpha_ll:.3f}",
+                r"\alpha_{I}": f"{self.alpha_l:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\alpha",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="-",
+        )

blueprints/codes/eurocode/nen_en_1992_1_1_c2_2011/chapter_7_serviceability_limit_state/formula_7_19.py

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+"""Formula 7.19 from NEN-EN 1992-1-1+C2:2011: Chapter 7 - Serviceability 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_less_or_equal_to_zero, raise_if_negative
+
+
+class Form7Dot19DistributionCoefficient(Formula):
+    r"""Class representing formula 7.19 for the calculation of [$\zeta$]."""
+
+    label = "7.19"
+    source_document = NEN_EN_1992_1_1_C2_2011
+
+    def __init__(
+        self,
+        beta: DIMENSIONLESS,
+        sigma_sr: MPA,
+        sigma_s: MPA,
+    ) -> None:
+        r"""[$\zeta$] Calculation of the distribution coefficient, 0 for uncracked sections [$\zeta$].
+
+        Note: $\sigma_{sr} / \sigma_{s}$ may be replaced by $M_{cr} / M$ for flexure or $N_{cr} / N$ for pure tension,
+        where $M_{cr}$ is the cracking moment and $N_{cr}$ is the cracking force.
+
+        NEN-EN 1992-1-1+C2:2011 art.7.4.3(3) - Formula (7.19)
+
+        Parameters
+        ----------
+        beta : DIMENSIONLESS
+            [$\beta$] Coefficient taking account of the influence of the duration of the loading or of
+            repeated loading on the average strain. For short-term loading, [$\beta$] = 1.0. For sustained loads or
+            many cycles of repeated loading [$\beta$] = 0.5 [$-$].
+        sigma_sr : MPA
+            [$\sigma_{sr}$] Stress in the tension reinforcement calculated on the basis of a
+            cracked section under the loading conditions causing first cracking [$MPa$].
+        sigma_s : MPA
+            [$\sigma_{s}$] Stress in the tension reinforcement calculated on the basis of a cracked section under
+            loading conditions causing first cracking [$MPa$].
+        """
+        super().__init__()
+        self.beta = beta
+        self.sigma_sr = sigma_sr
+        self.sigma_s = sigma_s
+
+    @staticmethod
+    def _evaluate(
+        beta: DIMENSIONLESS,
+        sigma_sr: MPA,
+        sigma_s: MPA,
+    ) -> DIMENSIONLESS:
+        """Evaluates the formula, for more information see the __init__ method."""
+        raise_if_negative(beta=beta, sigma_sr=sigma_sr, sigma_s=sigma_s)
+        raise_if_less_or_equal_to_zero(sigma_s=sigma_s)
+
+        return 1 - beta * (sigma_sr / sigma_s) ** 2
+
+    def latex(self) -> LatexFormula:
+        """Returns LatexFormula object for formula 7.19."""
+        _equation: str = r"1 - \beta \left(\frac{\sigma_{sr}}{\sigma_{s}}\right)^2"
+        _numeric_equation: str = latex_replace_symbols(
+            _equation,
+            {
+                r"\beta": f"{self.beta:.3f}",
+                r"\sigma_{sr}": f"{self.sigma_sr:.3f}",
+                r"\sigma_{s}": f"{self.sigma_s:.3f}",
+            },
+            False,
+        )
+        return LatexFormula(
+            return_symbol=r"\zeta",
+            result=f"{self:.3f}",
+            equation=_equation,
+            numeric_equation=_numeric_equation,
+            comparison_operator_label="=",
+            unit="-",
+        )