Create test_w_shear.py

Author: claudioperez

tests/test_w_shear.py

@@ -0,0 +1,121 @@
+import pytest
+from xsection.library import WideFlange, from_aisc
+from xsection.analysis import SaintVenantSectionAnalysis
+import numpy as np
+
+point_poisson = [#-0.9, -0.5, 
+                 0, 0.3, 0.499]
+
+def wide_flange_cowper(shape: WideFlange, nu=0.3):
+    b  = shape.bf
+    tf = shape.tf
+    tw = shape.tw
+    d  = shape.d
+
+    m = 2*b*tf/(d*tw)
+    n = b/d
+
+    D = ((12 + 72*m + 150*m**2 + 90*m**3) + nu*(11+66*m + 135*m**2 + 90*m**3) + 30*n**2*(m + m**2) + 5*nu*n**2*(8*m+9*m**2))
+    return (10*(1+nu)*(1+3*m)**2)/D
+
+
+def single_flange_cowper(shape: WideFlange, nu):
+    r"""
+    $\frac{10(1+\nu)(1+4 m)^2}{\left(12+96 m+276 m^2+192 m^3\right)+\nu\left(11+88 m+248 m^2+216 m^3\right)+30 n^2\left(m+m^2\right)+10 \nu n^2\left(4 m+5 m^2+m^3\right)}$
+    """
+    b  = shape.bf
+    tf = shape.tf
+    tw = shape.tw
+    d  = shape.d
+
+    m = b*tf/(d*tw)
+    n = b/d
+    D = (12 + 96*m + 276*m**2 + 192*m**3) + nu*(11 + 88*m + 248*m**2 + 216*m**3) + 30*n**2*(m+m**2) + 10*nu*n**2*(4*m+5*m**2+m**3)
+    return (10*(1+nu)*(1+4*m)**2)/D
+
+
+def wide_flange_timoshenko(shape: WideFlange, nu=0.3):
+    b  = shape.bf
+    tf = shape.tf
+    tw = shape.tw
+    d  = shape.d
+    A  = shape.area
+    I  = shape.elastic.Iy
+    return float(8*tw*I/(A*(b*d**2 - (b - tw)*(d - 2*tf)**2)))
+
+
+def wide_flange_newlin(shape: WideFlange, nu=0.3):
+    b  = shape.bf
+    tf = shape.tf
+    tw = shape.tw
+    d  = shape.d
+    A  = shape.area
+    I  = shape.elastic.Iy
+    d1 = d - 2*tf
+    aw = A*b/(64*I**2)*(d1**5*(8*tw/(15*b)+b/tw-4/3)-d1**3*d**2*(2*b/tw-4/3)+d1*d**4*(b/tw))
+    af = A*b/(64*I**2)*(-d1**5/5 + 2/3*d1**3*d**2 - d1*d**4 + 8/15*d**5)
+    return float(1/(aw + af))
+
+
+
+
+def test_poisson():
+    for name in [ "W14x48"]: # "W18x40",
+        shape = from_aisc(name, mesh_scale=1/10, fillet=False, mesher="gmsh", mesh_type="T6")
+        for nu in [0, 0.3]:
+            sv = SaintVenantSectionAnalysis(shape, nu=nu)
+            cowper = sv.create_trace(form="geometric").sce()
+            assert cowper[0] > 0
+            assert cowper[1] == pytest.approx(wide_flange_cowper(shape, nu=nu), rel=1e-2)
+
+
+
+def test_single_flange():
+    for name in ["WT18x115.5"]:
+        shape = from_aisc(name, mesh_scale=1/10, fillet=False, mesher="gmsh", mesh_type="T6")
+        shape = shape.translate(-shape.centroid)
+        for nu in [0, 0.3]:
+            sv = SaintVenantSectionAnalysis(shape, nu=nu)
+            cowper = sv.create_trace(form="geometric").sce()
+            assert cowper[0] > 0
+            assert cowper[1] == pytest.approx(single_flange_cowper(shape, nu=nu), rel=5e-2)
+
+
+
+
+# def test_material():
+#     for name in ["W18x40"]:
+#         shape = from_aisc(name, mesh_scale=1/10, fillet=False, mesher="gmsh", mesh_type="T6")
+#         for nu in [0, 0.3]:
+#             sv = SaintVenantSectionAnalysis(shape, nu=nu)
+#             cowper = sv.create_trace(form="geometric").sce()
+#             assert cowper[0] > 0
+#             assert cowper[1] == pytest.approx(wide_flange_cowper(shape, nu=nu), rel=1e-2)
+
+
+
+if __name__ == "__main__":
+    import sys
+    # "W14x48"
+    if len(sys.argv) > 1:
+        name = sys.argv[1]
+    else:
+        name = "W18x40"
+
+    print("Section:", name)
+
+    shape = from_aisc(name, mesh_scale=1/10, fillet=False, mesher="gmsh")
+
+    print("A/(d*tw)",     shape.depth*shape.tw/shape.elastic.A)
+    for nu in 0.3, 0:
+        print(f"nu = {nu}")
+        print(" Cowper\t\t",     wide_flange_cowper(shape, nu=nu))
+        print(" Timoshenko\t",   wide_flange_timoshenko(shape, nu=nu))
+        print(" Newlin\t\t",     wide_flange_newlin(shape, nu=nu))
+
+        shear_model = shape._analysis.shear_model(nu=nu)
+        Xr = shape._analysis.shear_factor_romano(nu=0.0)[0][1]
+        print(" Romano\t\t", Xr)
+        print(" Cowper\t\t", shear_model.correction(form="average"))
+        print("-"*10, "\n")
+