Retrieving Section Properties

This example demonstrates how to retrieve cross-section properties in sectionproperties. It is suggested that you are familiar with How Material Properties Affect Results before reading this example.

Geometric-only Properties

This section retrieves the frame properties for a 150 x 100 x 8 UA stiffened by a 125 x 12 plate at its base.

from sectionproperties.analysis import Section
from sectionproperties.pre.library import angle_section, rectangular_section


angle = angle_section(d=150, b=100, t=8, r_r=12, r_t=5, n_r=8)
plate = rectangular_section(d=12, b=125)
geom = angle + plate.shift_section(x_offset=-12.5, y_offset=-12)
geom.create_mesh(mesh_sizes=[10, 25])
sec = Section(geometry=geom)
sec.plot_mesh(materials=False)

<Axes: title={'center': 'Finite Element Mesh'}>

We can perform a frame analysis and use the various get methods to retrieve the cross-section properties required for a frame analysis.

sec.calculate_frame_properties()
area = sec.get_area()
ixx_c, iyy_c, ixy_c = sec.get_ic()
phi = sec.get_phi()
j = sec.get_j()

print(f"Area = {area:.1f} mm2")
print(f"Ixx = {ixx_c:.3e} mm4")
print(f"Iyy = {iyy_c:.3e} mm4")
print(f"Ixy = {ixy_c:.3e} mm4")
print(f"Principal axis angle = {phi:.1f} deg")
print(f"Torsion constant = {j:.3e} mm4")

Area = 3456.8 mm2
Ixx = 6.955e+06 mm4
Iyy = 4.226e+06 mm4
Ixy = -2.816e+06 mm4
Principal axis angle = -147.9 deg
Torsion constant = 2.926e+05 mm4

Composite Properties

To demonstrate how to retrieve cross-section properties from a composite analysis, a reinforced concrete beam will be modelled.

First we create our concrete and steel material properties.

from sectionproperties.pre import Material


concrete = Material(
    name="Concrete",
    elastic_modulus=30.1e3,
    poissons_ratio=0.2,
    yield_strength=32,
    density=2.4e-6,
    color="lightgrey",
)
steel = Material(
    name="Steel",
    elastic_modulus=200e3,
    poissons_ratio=0.3,
    yield_strength=500,
    density=7.85e-6,
    color="grey",
)

Next we define our reinforced concrete geometry, generate a mesh and a Section object.

from sectionproperties.pre.library import concrete_rectangular_section


geom = concrete_rectangular_section(
    d=600,
    b=300,
    dia_top=16,
    area_top=200,
    n_top=3,
    c_top=20,
    dia_bot=20,
    area_bot=310,
    n_bot=3,
    c_bot=30,
    n_circle=8,
    conc_mat=concrete,
    steel_mat=steel,
)

geom.create_mesh(mesh_sizes=2500)
sec = Section(geometry=geom)
sec.plot_mesh()

<Axes: title={'center': 'Finite Element Mesh'}>

In this case, we are interested in obtaining the uncracked axial rigidity, flexural rigidity and torsional rigidity. We will therefore conduct a frame analysis.

props = sec.calculate_frame_properties()

Note that we cannot retrieve the geometric second moments of area as in the previous example because we have conducted a composite analysis (i.e. provided material properties).

sec.get_ic()

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
Cell In[7], line 1
----> 1 sec.get_ic()

File ~/checkouts/readthedocs.org/user_builds/sectionproperties/envs/latest/lib/python3.10/site-packages/sectionproperties/analysis/section.py:2081, in Section.get_ic(self)
   2079     msg = "Attempting to get a geometric only property for a composite analysis"
   2080     msg += " (material properties have been applied). Consider using get_eic()."
-> 2081     raise RuntimeError(msg)
   2083 try:
   2084     assert self.section_props.ixx_c is not None

RuntimeError: Attempting to get a geometric only property for a composite analysis (material properties have been applied). Consider using get_eic().

The above error message is helpful, informing us that we should instead use get_eic().

# get relevant modulus weighted properties
eixx, _, _ = sec.get_eic()
ea = sec.get_ea()
ej = sec.get_ej()

# print results
print(f"Axial rigidity (E.A): {ea:.3e} N")
print(f"Flexural rigidity (E.I): {eixx:.3e} N.mm2")

# note we are usually interested in G.J not E.J
# geometric analysis required for effective material properties
sec.calculate_geometric_properties()
gj = sec.get_g_eff() / sec.get_e_eff() * ej
print(f"Torsional rigidity (G.J): {gj:.3e} N.mm2")

Axial rigidity (E.A): 5.678e+09 N
Flexural rigidity (E.I): 1.807e+14 N.mm2
Torsional rigidity (G.J): 4.671e+13 N.mm2

Note that transformed cross-section properties are often required for design purposes. We can use the e_ref argument to provide either a material of elastic modulus to obtain transformed properties in sectionproperties.

print(f"E.I = {eixx:.3e} N.mm2")
print(f"I = {sec.get_eic(e_ref=concrete)[0]:.3e} mm4")
print(f"I = {sec.get_eic(e_ref=30.1e3)[0]:.3e} mm4")

E.I = 1.807e+14 N.mm2
I = 6.005e+09 mm4
I = 6.005e+09 mm4

Note that the transformed second moment of area includes the contribution of the steel and is therefore larger than that of a 600D x 300W rectangle.

print(f"I_rect = {300 * 600**3 / 12:.3e} mm4")

I_rect = 5.400e+09 mm4