2. Geometry#

concreteproperties uses the pre-processor from sectionproperties to build reinforced concrete cross-sections as CompoundGeometry objects. concreteproperties expects a CompoundGeometry object to contain geometry information describing both the concrete and reinforcement components of the cross-section. The concrete portion of the cross-section can be constructed in many ways:

Primitive Sections Library (e.g. rectangles, circles etc.)
Standards Sections Library (e.g. Concrete Sections Library, Bridge Sections Library)
Geometry from points, facets, holes, and control points
Geometry from .dxf Files and Geometry from Rhino
Combining Geometries Using Set Operations

Next, reinforcing bars can be added to the concrete geometry using the methods in the pre module, and are also included in geometries generated by the Concrete Sections Library.

Alternatively, other sections (such as structural steel sections) can be combined with concrete geometry to create composite sections. This can be done using geometry creation methods similar to that of concrete, except that a different material object will be provided.

Below is a brief overview of the various methods that can be used to create geometries to be used by concreteproperties. A more exhaustive overview can be found in the sectionproperties documentation.

2.1. Axis Conventions#

Concrete cross-sections in concreteproperties are constructed in the x-y plane. A key feature of concreteproperties is that the analyses are not restricted to bending about the x or y axis. All analysis types (where relevant) give the user the option of performing the analysis about a rotated u-v axis, defined by the angle \(\theta\) (in radians).

Results in concreteproperties are labelled with consistent references to the axes. Below are a few examples:

m_x and m_y relate to bending moments about the x and y axes respectively.
m_xy relates to a resultant bending moment, i.e. the positive square root of the sum of the squares of m_x and m_y.
ixx_g and iyy_g relate to the second moments of area about the global x and y axes respectively. The global axis refers to an axis centred at the origin (0, 0).
ixx_c and iyy_c relate to the second moments of area about the centroidal x and y axes respectively. The centroidal axis refers to an axis centred at the elastic centroid (cx, cy).
i11 and i22 relate to the second moments of area about the principal centroidal 11 and 22 axes respectively. The principal centroidal axis refers to an axis centred at the elastic centroid (cx, cy), rotated by the principal bending angle phi.
iuu relates to the second moment of area about the rotated local u axis, defined by the angle theta.

2.2. Primitive Sections#

The primitive sections library contains basic shapes describing common concrete cross-sections, and can also be used as building blocks for more complex geometries.

The following code creates a rectangular concrete cross-section 600 mm deep and 300 mm wide:

from sectionproperties.pre.library.primitive_sections import rectangular_section

concrete = None  # define your concrete material properties here
geom = rectangular_section(d=600, b=300, material=concrete)
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

600 mm deep x 300 mm wide concrete beam#

The following code creates a circular concrete cross-section with a diameter of 600 mm. As concreteproperties constructs a mesh of triangular elements to calculate section properties, circles must be discretised into a finite number of discrete edges. The below example uses 32 points to discretise the circle:

from sectionproperties.pre.library.primitive_sections import circular_section

concrete = None  # define your concrete material properties here
geom = circular_section(d=600, n=32, material=concrete)
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

600 mm diameter concrete cross-section#

By discretising the above circle, the cross-sectional area is slightly lower than a true circle:

>>> import math
>>> from sectionproperties.pre.library.primitive_sections import circular_section
>>> geom = circular_section(d=600, n=32)
>>> print(f"{geom.calculate_area():.2f}")
280930.06
>>> print(f"{math.pi * 600 * 600 / 4:.2f}")
282743.34

This discretisation error can be avoided by using the circular_section_by_area() function, which adjusts the diameter based on the number of discrete points to ensure a circle with the correct area is generated:

import math
from sectionproperties.pre.library.primitive_sections import circular_section_by_area

concrete = None  # define your concrete material properties here
geom = circular_section_by_area(area=math.pi * 600 * 600 / 4, n=32, material=concrete)
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

600 mm diameter concrete cross-section#

>>> import math
>>> from sectionproperties.pre.library.primitive_sections import circular_section_by_area
>>> geom =   geom = circular_section_by_area(area=math.pi * 600 * 600 / 4, n=32)
>>> print(f"{geom.calculate_area():.2f}")
282743.34
>>> print(f"{math.pi * 600 * 600 / 4:.2f}")
282743.34

2.3. Standard Sections#

The concrete and bridge sections library allow common reinforced concrete cross-sections to be quickly generated. The concrete section library also allows for the addition of simple reinforcing bars.

The following code generates a 1200 mm deep x 450 mm wide tee-beam with a 1500 mm wide x 200 mm deep flange. Reinforcement is added with 8N24 bars on the top and 4N32 bars on the bottom:

from sectionproperties.pre.library.concrete_sections import concrete_tee_section

concrete = None  # define your concrete material properties here
steel = None  # define your steel material properties here
geom = concrete_tee_section(
  b=450, d=1200, b_f=1500, d_f=200, dia_top=24, n_top=8, dia_bot=32, n_bot=4,
  n_circle=12, cover=30, conc_mat=concrete, steel_mat=steel
)
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

1200 mm deep concrete tee-beam#

The reinforcement generated by the above code suffers from the same problem as the circular_section example, in that the discretisation of the circular reinforcing bars results in a slightly lower reinforcement area. This can be overcome by using the optional area_top and area_bot parameters. Further, as this ensures the desired area, a smaller value for n_circle may be used to speed up the analysis. As the reinforcement area is now independent of n_circle a value of n_circle=4 may be used without any loss of accuracy in the analysis results as the centroid of the bar and area of the bar is all that concreteproperties requires:

from sectionproperties.pre.library.concrete_sections import concrete_tee_section

concrete = None  # define your concrete material properties here
steel = None  # define your steel material properties here
geom = concrete_tee_section(
  b=450, d=1200, b_f=1500, d_f=200, dia_top=24, n_top=8, dia_bot=32, n_bot=4,
  n_circle=4, cover=30, area_top=450, area_bot=800, conc_mat=concrete, steel_mat=steel
)
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

1200 mm deep concrete tee-beam#

The bridge sections library generates typical sections used in bridge construction, such as super tees and I-girders. Reinforcement is not automatically added for sections in this library. The following code creates a T5 Super-T section:

from sectionproperties.pre.library.bridge_sections import super_t_girder_section

concrete = None  # define your concrete material properties here
geom = super_t_girder_section(girder_type=5, material=concrete)
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

T5 Super-T section#

2.4. Arbitrary List of Points#

Concrete geometry can also be created from an arbitrary list of points using the from_points() method. The following example creates a 800 mm deep x 600 mm wide x 100 mm thick hollow box section:

from sectionproperties.pre.geometry import Geometry

concrete = None  # define your concrete material properties here

pts = [
  [0, 0], [600, 0], [600, 800], [0, 800], [100, 100], [500, 100], [500, 700],
  [100, 700]
]
fcts = [[0, 1], [1, 2], [2, 3], [3, 0], [4, 5], [5, 6], [6, 7], [7, 0]]
cps = [[50, 50]]
hls = [[400, 400]]

geom = Geometry.from_points(
  points=pts, facets=fcts, control_points=cps, holes=hls, material=concrete
)
geom.plot_geometry()

(Source code, png, hires.png, pdf)

800 mm deep hollow box section#

2.5. Set Operations and Manipulation#

sectionproperties geometry objects can be manipulated using python’s set operators:

| bitwise or
- bitwise diff
& bitwise and
^ bitwise xor
+ geometry addition

Further geometry manipulation can be performed with the following methods:

align_center() - aligns the centroid of the geometry with the centroid of another Geometry object.
align_to() - aligns an edge of the geometry with the edge of another Geometry object or point.
mirror_section() - mirrors the geometry about the x or y axis.
rotate_section() - rotates the geometry by a certain angle.
shift_section() - translates the geometry by a certain distance in the x and y directions.
split_section() - splits the geometry above and below a line.
offset_perimeter() - dilates or erodes the perimeter of the geometry by a discrete amount.

The following code creates an L-shaped beam:

from sectionproperties.pre.library.primitive_sections import rectangular_section

concrete = None  # define your concrete material properties here
slab = rectangular_section(d=150, b=800, material=concrete)
beam = rectangular_section(
  d=600, b=300, material=concrete
).align_to(other=slab, on="bottom").align_to(other=slab, on="left", inner=True)
geom = slab + beam
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

L-shaped beam#

The following code creates the hollow section geometry example in the Arbitrary List of Points section far more succinctly:

from sectionproperties.pre.library.primitive_sections import rectangular_section

concrete = None  # define your concrete material properties here
outer = rectangular_section(d=800, b=600, material=concrete)
inner = rectangular_section(d=600, b=400).align_center(align_to=outer)
geom = outer - inner
geom.plot_geometry()

(Source code, png, hires.png, pdf)

800 mm deep hollow box section#

The following code adds a 180 mm overlay slab to a T5 Super-T section and demonstrates how different concrete material properties can be assigned to different regions of the geometry. Note how a hole is automatically generated in the closed-off region:

from sectionproperties.pre.library.primitive_sections import rectangular_section
from sectionproperties.pre.library.bridge_sections import super_t_girder_section

conc_precast = None  # define your concrete material properties here
conc_insitu = None  # define your concrete material properties here
beam = super_t_girder_section(girder_type=5, material=conc_precast)
slab = rectangular_section(
  d=180, b=2100, material=conc_insitu
).shift_section(-1050, 75)
geom = beam + slab
geom.plot_geometry()

(Source code, png, hires.png, pdf)

T5 Super-T section with an overlay slab#

The following code creates a 323.9 mm x 12.7 mm circular hollow section filled with concrete and demonstrates how composite sections can be created:

import sectionproperties.pre.library.primitive_sections as sp_ps

conc = None  # define your concrete material properties here
steel = None  # define your steel material properties here
steel_col = sp_ps.circular_section_by_area(
  area=np.pi * 323.9**2 / 4,
  n=64,
  material=steel,
)
inner_conc = sp_ps.circular_section_by_area(
  area=np.pi * (323.9 - 2 * 12.7) ** 2 / 4,
  n=64,
  material=conc,
)
geom = steel_col - inner_conc + inner_conc
geom.plot_geometry()

(Source code, png, hires.png, pdf)

Concrete filled circular hollow section#

2.6. Adding Reinforcing Bars#

Reinforcing bars can be added to any sectionproperties geometry by using the following functions:

add_bar() - adds a single bar to the geometry
add_bar_rectangular_array() - adds a rectangular array of bars to the geometry
add_bar_circular_array() - adds a circular array of bars to the geometry

(Source code)

2.6.1. add_bar()#

add_bar(geometry, area, material, x, y, n=4)[source]

Adds a reinforcing bar to a sectionproperties geometry.

Bars are discretised by four points by default.

Parameters

geometry (Union[Geometry, CompoundGeometry]) – Reinforced concrete geometry to which the new bar will be added
area (float) – Bar cross-sectional area
material (Union[SteelBar, SteelStrand]) – Material object for the bar
x (float) – x-position of the bar
y (float) – y-position of the bar
n (int, default: 4) – Number of points to discretise the bar circle

Returns

CompoundGeometry – Reinforced concrete geometry with added bar

The following code adds an 80 mm bar to a T5 Super-T section:

from concreteproperties.pre import add_bar

from sectionproperties.pre.library.bridge_sections import super_t_girder_section

concrete = None  # define your concrete material properties here
steel = None  # define your steel material properties here
beam = super_t_girder_section(girder_type=5, material=concrete)
geom = add_bar(geometry=beam, area=5000, material=steel, x=0, y=-1550)
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

T5 Super-T with an 80 mm bar#

2.6.2. add_bar_rectangular_array()#

add_bar_rectangular_array(geometry, area, material, n_x, x_s, n_y=1, y_s=0, anchor=(0, 0), exterior_only=False, n=4)[source]

Adds a rectangular array of reinforcing bars to a sectionproperties geometry.

Bars are discretised by four points by default.

Parameters

geometry (Union[Geometry, CompoundGeometry]) – Reinforced concrete geometry to which the new bar will be added
area (float) – Bar cross-sectional area
material (Union[SteelBar, SteelStrand]) – Material object for the bar
n_x (int) – Number of bars in the x-direction
x_s (float) – Spacing in the x-direction
n_y (int, default: 1) – Number of bars in the y-direction
y_s (float, default: 0) – Spacing in the y-direction
anchor (Tuple[float, float], default: (0, 0)) – Coordinates of the bottom left hand bar in the rectangular array
exterior_only (bool, default: False) – If set to True, only returns bars on the external perimeter
n (int, default: 4) – Number of points to discretise the bar circle

Returns

CompoundGeometry – Reinforced concrete geometry with added bar

The following code adds top and bottom reinforcement to a rectangular beam:

from concreteproperties.pre import add_bar_rectangular_array

from sectionproperties.pre.library.primitive_sections import rectangular_section

concrete = None  # define your concrete material properties here
steel = None  # define your steel material properties here
beam = rectangular_section(d=500, b=300, material=concrete)
geom = add_bar_rectangular_array(
  geometry=beam, area=310, material=steel, n_x=3, x_s=110, n_y=2, y_s=420,
  anchor=(40, 40)
)
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

Rectangular beam with top and bottom reinforcement#

2.6.3. add_bar_circular_array()#

add_bar_circular_array(geometry, area, material, n_bar, r_array, theta_0=0, ctr=(0, 0), n=4)[source]

Adds a circular array of reinforcing bars to a sectionproperties geometry.

Bars are discretised by four points by default.

Parameters

geometry (Union[Geometry, CompoundGeometry]) – Reinforced concrete geometry to which the news bar will be added
area (float) – Bar cross-sectional area
material (Union[SteelBar, SteelStrand]) – Material object for the bar
n_bar (int) – Number of bars in the array
r_array (float) – Radius of the circular array
theta_0 (float, default: 0) – Initial angle (in radians) that the first bar makes with the horizontal axis in the circular array
ctr (Tuple[float, float], default: (0, 0)) – Centre of the circular array
n (int, default: 4) – Number of points to discretise the bar circle

Returns

CompoundGeometry – Reinforced concrete geometry with added bar

The following code adds a circular array of bars to a concrete column:

from concreteproperties.pre import add_bar_circular_array

from sectionproperties.pre.library.primitive_sections import circular_section_by_area

concrete = None  # define your concrete material properties here
steel = None  # define your steel material properties here
circle = circular_section_by_area(area=282.74e3, n=32, material=concrete)
geom = add_bar_circular_array(
  geometry=circle, area=310, material=steel, n_bar=7, r_array=250
)
geom.plot_geometry(labels=[], cp=False, legend=False)

(Source code, png, hires.png, pdf)

Concrete column with circular bar array#

2.6.4. Overlapping Geometry#

Care should be taken when combing multiple geometries to avoid overlapping of regions. If this occurs, the area in these overlapping regions will be double counted and result in erroneous results. The add bar methods in the pre module avoid overlapping geometries by first creating a hole in the concrete at the bar locations and only then adding the bar geometry:

geometry = (geometry - bar) + bar

Warning

A warning will be provided if overlapping geometries are supplied to concreteproperties.