Add more composite plastic tests

Author: robbievanleeuwen

tests/analysis/test_plastic.py

@@ -93,7 +93,7 @@ def test_plastic_centroid():
     # create a Section object
     section = Section(geometry=geometry)
 
-    # perform a geometric, warping and plastic analysis
+    # perform a geometric and plastic analysis
     section.calculate_geometric_properties()
     section.calculate_plastic_properties()
 
@@ -125,3 +125,152 @@ def test_plastic_centroid():
     x_pc, y_pc = nested_sec.get_pc()
     assert x_pc == pytest.approx(37.5)
     assert y_pc == pytest.approx(50)
+
+
+def test_plastic_composite_simple():
+    """Tests the plastic properties of a simple composite section."""
+    mat1 = Material(
+        name="mat1",
+        elastic_modulus=10,
+        poissons_ratio=0.3,
+        density=1,
+        yield_strength=50,
+        color="grey",
+    )
+
+    mat2 = Material(
+        name="mat2",
+        elastic_modulus=20,
+        poissons_ratio=0.3,
+        density=1,
+        yield_strength=80,
+        color="black",
+    )
+
+    rect1 = sections.rectangular_section(d=100, b=50, material=mat1)
+    rect2 = sections.rectangular_section(d=100, b=50, material=mat2).shift_section(
+        x_offset=50
+    )
+    geom = rect1 + rect2
+    geom.create_mesh(mesh_sizes=100)
+
+    sec = Section(geometry=geom)
+    sec.calculate_geometric_properties()
+    sec.calculate_plastic_properties()
+
+    x_pc, y_pc = sec.get_pc()
+    assert y_pc == pytest.approx(50)
+
+    # calculate x_pc
+    f_mat1 = 100 * 50 * 50  # force in mat1
+    x_mat2 = f_mat1 / 80 / 100  # width of mat2 required to equal force in mat1
+    x_left = (50 - x_mat2) / 2  # width of ma2 to left of pc
+    assert x_pc == pytest.approx(x_left + 50)
+
+    mp_xx, mp_yy = sec.get_mp()
+    mp_xx_calc = 50 * 100**2 / 4 * (80 + 50)
+    assert mp_xx == pytest.approx(mp_xx_calc)
+
+    # calculate mp_yy
+    mp_yy_calc = 0
+    mp_yy_calc += f_mat1 * abs(25 - x_pc)  # mat 1 contribution
+    # left mat 2 contribution
+    mp_yy_calc += x_left * 100 * 80 * abs(50 + x_left / 2 - x_pc)
+    # right mat 2 contribution
+    mp_yy_calc += (50 - x_left) * 100 * 80 * abs(100 - (50 - x_left) / 2 - x_pc)
+    assert mp_yy == pytest.approx(mp_yy_calc)
+
+    # check principal calc with rotation 45 deg
+    geom.rotate_section(angle=45)
+    geom.create_mesh(mesh_sizes=100)
+    sec = Section(geometry=geom)
+    sec.calculate_geometric_properties()
+    sec.calculate_plastic_properties()
+
+    mp_11, mp_22 = sec.get_mp_p()
+    assert mp_11 == pytest.approx(mp_xx_calc)
+    assert mp_22 == pytest.approx(mp_yy_calc)
+
+
+def test_plastic_composite_example():
+    """Tests the composite example on the sectionproperties docs, refer issue #460.
+
+    The steel section is simplified to have no root radii to allow hand calculation
+    comparison.
+    """
+    # create the steel material
+    steel = Material(
+        name="Steel",
+        elastic_modulus=200e3,
+        poissons_ratio=0.3,
+        density=7.85e-6,
+        yield_strength=500,
+        color="grey",
+    )
+
+    # create the timber material
+    timber = Material(
+        name="Timber",
+        elastic_modulus=8e3,
+        poissons_ratio=0.35,
+        yield_strength=20,
+        density=0.78e-6,
+        color="burlywood",
+    )
+
+    # universal steel beam
+    ub = steel_sections.i_section(
+        d=304, b=165, t_f=10.2, t_w=6.1, r=0, n_r=2, material=steel
+    )
+
+    # timber floor panel
+    panel = sections.rectangular_section(d=100, b=600, material=timber)
+    panel = panel.align_center(align_to=ub).align_to(other=ub, on="top")
+
+    # combine geometry
+    geom = ub + panel
+
+    geom.create_mesh(mesh_sizes=[50, 500])
+    sec = Section(geometry=geom)
+    sec.calculate_geometric_properties()
+    sec.calculate_plastic_properties()
+
+    # get calculated values
+    x_pc, y_pc = sec.get_pc()
+    mp_xx, mp_yy = sec.get_mp()
+
+    # hand calcs
+    # 1) x-axis bending
+    # calculate y_pc -> assume centroid in top flange
+    f_timber = 600 * 100 * 20
+    f_web = (304 - 2 * 10.2) * 6.1 * 500
+    f_flange = 165 * 10.2 * 500
+
+    # let y = distance from bottom of top flange to y_pc
+    # A) bot = 165 * y * 500
+    # B) top = 165 * (10.2 - y) * 500
+    # C) (A) - (B) = f_timber - f_web - f_flange  = f_diff
+    # 165 * 500 (2y - 10.2) = f_diff
+    # y = (f_diff / (165 * 500) + 10.2) / 2
+    f_diff = f_timber - f_web - f_flange
+    y = (f_diff / (165 * 500) + 10.2) / 2
+    assert y_pc == pytest.approx(304 - 10.2 + y)
+
+    # calculate mp_xx
+    mp_xx_calc = 0
+    mp_xx_calc += f_timber * abs(304 + 50 - y_pc)  # timber contribution
+    mp_xx_calc += (10.2 - y) * 165 * 500 * abs((10.2 - y) / 2)  # top flange p1
+    mp_xx_calc += y * 165 * 500 * abs(y / 2)  # top flange p2
+    mp_xx_calc += f_web * abs(10.2 + (304 - 2 * 10.2) / 2 - y_pc)  # web contribution
+    mp_xx_calc += f_flange * abs(10.2 / 2 - y_pc)  # bot flange contribution
+    assert mp_xx == pytest.approx(mp_xx_calc)
+
+    # 2) y-axis bending
+    assert x_pc == pytest.approx(165 / 2)
+
+    # calculate mp_yy
+    mp_yy_calc = 0
+    mp_yy_calc += 2 * (10.2 * 165**2 / 4) * 500  # 2 flanges
+    mp_yy_calc += (304 - 10.2 * 2) * 6.1**2 / 4 * 500  # web
+    mp_yy_calc += 100 * 600**2 / 4 * 20  # timber
+    assert mp_yy == pytest.approx(mp_yy_calc)