feat: add Eq. M1 according to EUROCODE 1992-3:2006

docs/api/codes/ec2_2004/cracks.md

@@ -104,3 +104,9 @@ The following functions are related to calculating crack widths.
 ```{eval-rst}
 .. autofunction:: structuralcodes.codes.ec2_2004.As_min_2
 ```
+
+## Crack widths due to restraint of imposed deformations
+
+```{eval-rst}
+.. autofunction:: structuralcodes.codes.ec2_2004.eps_sm_eps_cm_restraint_end
+```

structuralcodes/codes/ec2_2004/__init__.py

@@ -45,6 +45,9 @@
     k_sargin,
     n_parabolic_rectangular,
 )
+from ._cracking_restraint_imposed_deformations import (
+    eps_sm_eps_cm_restraint_end,
+)
 from ._reinforcement_material_properties import (
     epsud,
     fyd,
@@ -94,6 +97,7 @@
     'Asw_s_required',
     'alpha_e',
     'eps_sm_eps_cm',
+    'eps_sm_eps_cm_restraint_end',
     'hc_eff',
     'k',
     'k1',

structuralcodes/codes/ec2_2004/_cracking_restraint_imposed_deformations.py

@@ -0,0 +1,41 @@
+"""Collection of functions from EUROCODE 1992-3:2006."""
+
+
+def eps_sm_eps_cm_restraint_end(
+    alpha_e: float,
+    rho_p_eff: float,
+    kc: float,
+    k: float,
+    fct_eff: float,
+    Es: float,
+) -> float:
+    """Returns the strain difference (epsilon_sm - epsilon_cm) needed to
+    compute the crack width for restraint member at its end.
+
+    EN 1992-3:2006, Eq. (M.1).
+
+    Args:
+        alpha_e (float): Is the ratio Es/Ecm.
+        rho_p_eff (float): Effective bond ratio between areas given by Eq.
+            (7.10).
+        kc (float): is a coefficient which takes account of the stress
+            distribution within the section immediately prior to cracking and
+            the change of the lever arm.
+        k (float): is the coefficient which allow for the effect of
+            non-uniform self-equilibrating stresses, which lead to a
+            reduction of restraint forces.
+            k=1 for webs w<=300mm or flanges widths less than 300mm
+            k=0.65 for webs w>=800mm or flanges with widths greater than 800mm
+            Intermediate values may be interpolated.
+        fct_eff (float): Is the mean value of the tensile strength in MPa of
+            the concrete effective at the time when the cracks may first be
+            expected to occur: fct_eff=fctm or fctm(t) if crack is expected
+            earlier than 28 days.
+        Es (float): Steel elastic modulus in MPa.
+
+    Returns:
+        float: The calculated strain difference.
+    """
+    return (
+        0.5 * alpha_e * kc * k * fct_eff * (1 + 1 / (alpha_e * rho_p_eff)) / Es
+    )

tests/test_ec2_2004/test_ec2_2004_cracking_restrained_imposed_deformations.py

@@ -0,0 +1,32 @@
+"""Tests for EUROCODE 1992-3:2006."""
+
+import math
+
+import pytest
+
+from structuralcodes.codes.ec2_2004 import (
+    _cracking_restraint_imposed_deformations,
+)
+
+
+@pytest.mark.parametrize(
+    'alpha_e, rho_p_eff, kc, k, fct_eff, Es, expected',
+    [
+        (5.869, 0.01478, 1, 1, 3.2, 200000, 0.000590),
+        (5.869, 0.009690, 1, 1, 3.2, 200000, 0.000875),
+        (5.512, 0.01478, 1, 1, 3.8, 200000, 0.000694),
+        (5.512, 0.009690, 1, 1, 3.8, 200000, 0.001032),
+    ],
+)
+def test_eps_sm_eps_cm_m1_returns_expected_values(
+    alpha_e, kc, k, fct_eff, rho_p_eff, Es, expected
+):
+    """Test that eps_sm_cm_m1 returns expected values."""
+    # Assert
+    assert math.isclose(
+        _cracking_restraint_imposed_deformations.eps_sm_eps_cm_restraint_end(
+            alpha_e, rho_p_eff, kc, k, fct_eff, Es
+        ),
+        expected,
+        abs_tol=10e-5,
+    )