In this part we consider adding a parallel flanged channel (PFC) or I-Section to the flange of an I-Section.
This configuration is used quite often for crane rails (for adding a channel) to deal with lateral thrusts from a runway crane of for simply strengthening a beam for flexure and getting a little more bang for your buck than simply adding a plate to one flange. For the case of adding an I-Section, this comes up quite often in buildings to form composite columns or even to increase the bending capacity of beams.
Like outlined in the earlier posts in this series, be mindful of creating sections in intimate contact and of whether or not you have intermittent welding which might invalidate some of the properties. Read previous posts essentially and engage brain and decide what might apply to your situation.
The code…
PFC and I-Section
import copy
import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection
# -------------------------------------------------------------
# Inputs
# -------------------------------------------------------------
top_flg = True # apply PFC to top or bottom flg
d = 612 # I-section depth
b_f = 229 # I-section flange width
t_f = 19.6 # I-section flange thickness
t_w = 11.9 # I-section web thickness
r_1 = 14 # I-section root radii
d_1 = 380 # strengthening PFC depth
b_f1 = 100 # strengthening PFC width
t_f1 = 17.5 # strenghtening PFC flange thickness
t_w1 = 10 # strengthening PFC web thickness
r_2 = 14 # strengthening PFC root radii
gap = 0.3 # gap between I-Section and PFC
weld_size = 10 # weld size
n_r = 50 # number of points considered around root radii
mesh_area = 10 # max mesh size
# -------------------------------------------------------------
# Calculations
# -------------------------------------------------------------
# create constituent geometry
# weld base geometry
weld = sections.CustomSection(
points=[[0, 0], [weld_size, 0], [0, weld_size]], facets=[[0, 1], [1, 2], [2, 0]], holes=[], control_points=[[weld_size / 3, weld_size / 3]]
)
if d_1 > b_f and not gap == 0:
weld_vert_move = -gap
else:
weld_vert_move = 0
# I-Section beam
geometry1 = sections.ISection(d=d, b=b_f, t_f=t_f, t_w=t_w, r=r_1, n_r=n_r, shift=[-b_f / 2, -d / 2])
# strengthening PFC
geometry2 = sections.PfcSection(d=d_1, b=b_f1, t_f=t_f1, t_w=t_w1, r=r_2, n_r=n_r, shift=[0, -d / 2 - d_1 / 2 - gap])
if top_flg:
geometry2 = sections.PfcSection(d=d_1, b=b_f1, t_f=t_f1, t_w=t_w1, r=r_2, n_r=n_r, shift=[0, d / 2 - d_1 / 2 + gap + t_w1])
geometry2.rotate_section(angle=-90, rot_point=[0, d / 2 + gap + t_w1])
else:
geometry2 = sections.PfcSection(d=d_1, b=b_f1, t_f=t_f1, t_w=t_w1, r=r_2, n_r=n_r, shift=[0, -d / 2 - d_1 / 2 - gap])
geometry2.rotate_section(angle=-90, rot_point=[0, -d / 2 - gap])
# weld 1 & 2
geometry3 = copy.deepcopy(weld)
if b_f > d_1:
geometry3.mirror_section(axis='x', mirror_point=[0, 0])
geometry3.shift = [min(d_1 / 2, b_f / 2), -d / 2 + weld_vert_move]
geometry3.shift_section()
geometry4 = copy.deepcopy(geometry3)
geometry4.mirror_section(axis='y', mirror_point=[0, 0])
if top_flg:
geometry3.mirror_section(axis='x', mirror_point=[0, 0])
geometry4.mirror_section(axis='x', mirror_point=[0, 0])
# total number of individual geometry elements
geo_number = 4
# assemble geometry list
geo_list = [globals()[f'geometry{i}'] for i in range(1, geo_number + 1)]
# create merged section
geometry = sections.MergedSection(geo_list)
# add holes for gaps between I-Section and strengthening tee
if not gap == 0:
if top_flg:
geometry.add_hole([0, d / 2 + gap / 2])
else:
geometry.add_hole([0, -d / 2 - gap / 2])
# clean geometry
geometry.clean_geometry(verbose=True)
# create mesh
mesh = geometry.create_mesh(mesh_sizes=[mesh_area] * geo_number)
# create section
section = CrossSection(geometry, mesh)
# calculate results
section.calculate_geometric_properties()
section.calculate_plastic_properties()
section.calculate_warping_properties()
# -------------------------------------------------------------
# Display results
# -------------------------------------------------------------
# plot results
section.plot_mesh()
section.plot_centroids()
# display all results
# check https://sectionproperties.readthedocs.io/en/latest/rst/post.html for definitions
section.display_results(fmt='.3f')
You can add a PFC to the top or bottom flange depending on your use case.
I-Section and I-Section
import copy
import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection
# -------------------------------------------------------------
# Inputs
# -------------------------------------------------------------
top_flg = True
d = 612 # I-section depth
b_f = 229 # I-section flange width
t_f = 19.6 # I-section flange thickness
t_w = 11.9 # I-section web thickness
r_1 = 14 # I-section root radii
d_1 = 612 # strengthening I-Section depth
b_f1 = 229 # strengthening I-Section flange width
t_f1 = 19.6 # strenghtening I-Section flange thickness
t_w1 = 11.9 # strengthening I-Section web thickness
r_2 = 14 # strengthening I-Section root radii
gap = 0.3 # gap between I-Sections
weld_size = 10 # weld size
n_r = 20 # number of points considered around root radii
mesh_area = 10 # max mesh size
# -------------------------------------------------------------
# Calculations
# -------------------------------------------------------------
# create constituent geometry
# weld base geometry
weld = sections.CustomSection(
points=[[0, 0], [weld_size, 0], [0, weld_size]], facets=[[0, 1], [1, 2], [2, 0]], holes=[], control_points=[[weld_size / 3, weld_size / 3]]
)
if d_1 > b_f and not gap == 0:
weld_vert_move = -gap
else:
weld_vert_move = 0
# I-Section beam
geometry1 = sections.ISection(d=d, b=b_f, t_f=t_f, t_w=t_w, r=r_1, n_r=n_r, shift=[-b_f / 2, -d / 2])
# strengthening I-Section
if top_flg:
geometry2 = sections.ISection(d=d_1, b=b_f1, t_f=t_f1, t_w=t_w1, r=r_2, n_r=n_r, shift=[-b_f1 / 2, d / 2 - d_1 / 2 + gap + t_w1 / 2])
geometry2.rotate_section(angle=-90, rot_point=[0, d / 2 + gap + t_w1 / 2])
else:
geometry2 = sections.ISection(d=d_1, b=b_f1, t_f=t_f1, t_w=t_w1, r=r_2, n_r=n_r, shift=[-b_f1 / 2, -d / 2 - d_1 / 2 - gap - t_w1 / 2])
geometry2.rotate_section(angle=-90, rot_point=[0, -d / 2 - gap - t_w1 / 2])
# weld 1 & 2
geometry3 = copy.deepcopy(weld)
if b_f > d_1:
geometry3.mirror_section(axis='x', mirror_point=[0, 0])
geometry3.shift = [min(d_1 / 2, b_f / 2), -d / 2 + weld_vert_move]
geometry3.shift_section()
geometry4 = copy.deepcopy(geometry3)
geometry4.mirror_section(axis='y', mirror_point=[0, 0])
if top_flg:
geometry3.mirror_section(axis='x', mirror_point=[0, 0])
geometry4.mirror_section(axis='x', mirror_point=[0, 0])
# total number of individual geometry elements
geo_number = 4
# assemble geometry list
geo_list = [globals()[f'geometry{i}'] for i in range(1, geo_number + 1)]
# create merged section
geometry = sections.MergedSection(geo_list)
# add holes for gaps between I-Section and strengthening tee
if not gap == 0:
if top_flg:
geometry.add_hole([0, d / 2 + gap / 2])
else:
geometry.add_hole([0, -d / 2 - gap / 2])
# clean geometry
geometry.clean_geometry(verbose=True)
# create mesh
mesh = geometry.create_mesh(mesh_sizes=[mesh_area] * geo_number)
# create section
section = CrossSection(geometry, mesh)
# calculate results
section.calculate_geometric_properties()
section.calculate_plastic_properties()
section.calculate_warping_properties()
# -------------------------------------------------------------
# Display results
# -------------------------------------------------------------
# plot results
section.plot_mesh()
section.plot_centroids()
# display all results
# check https://sectionproperties.readthedocs.io/en/latest/rst/post.html for definitions
section.display_results(fmt='.3f')
Like the PFC version, you can add the new I-Section at the top or bottom flange.
Until Part 6, go forth and make funny tee shaped members from funny I shaped members and/or funny C shaped members.