Calculating Area Properties¶
This example demonstrates how to create a simple reinforced concrete cross-section and obtain the gross area properties. We start by importing the necessary modules.
[1]:
from sectionproperties.pre.library import concrete_rectangular_section
from concreteproperties import (
Concrete,
ConcreteLinear,
ConcreteSection,
RectangularStressBlock,
SteelBar,
SteelElasticPlastic,
)
Assign Materials¶
The materials used in this example will be 32 MPa concrete and 500 MPa steel, specified in accordance with AS 3600:2018.
[2]:
concrete = Concrete(
name="32 MPa Concrete",
density=2.4e-6,
stress_strain_profile=ConcreteLinear(elastic_modulus=30.1e3),
ultimate_stress_strain_profile=RectangularStressBlock(
compressive_strength=32,
alpha=0.802,
gamma=0.89,
ultimate_strain=0.003,
),
flexural_tensile_strength=3.4,
colour="lightgrey",
)
steel = SteelBar(
name="500 MPa Steel",
density=7.85e-6,
stress_strain_profile=SteelElasticPlastic(
yield_strength=500,
elastic_modulus=200e3,
fracture_strain=0.05,
),
colour="grey",
)
Create Geometry and Concrete Section¶
The section being analysed in this example is a 600D x 400W rectangular beam. The reinforcement detailed is 3N20 top bars and 3N24 bottom bars, with 30 mm of cover. The geometry is generated using the sectionproperties concrete sections library.
[3]:
geom = concrete_rectangular_section(
d=600,
b=400,
dia_top=20,
area_top=310,
n_top=3,
c_top=30,
dia_bot=24,
area_bot=450,
n_bot=3,
c_bot=30,
conc_mat=concrete,
steel_mat=steel,
)
conc_sec = ConcreteSection(geom)
conc_sec.plot_section()
[3]:
<Axes: title={'center': 'Reinforced Concrete Section'}>
Gross Properties¶
Creating a ConcreteSection object automatically calculates the gross area properties of the reinforced concrete cross-section. These can be obtained by using the get_gross_properties() method. The section properties can be printed by calling the print_results() method.
[4]:
gross_props = conc_sec.get_gross_properties()
gross_props.print_results()
Gross Concrete Section Properties ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━┓ ┃ Property ┃ Value ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━┩ │ Total Area │ 240.0 x 10^3 │ │ Concrete Area │ 237.7 x 10^3 │ │ Lumped Reinforcement Area │ 2.280 x 10^3 │ │ Axial Rigidity (EA) │ 7.611 x 10^9 │ │ Mass (per unit length) │ 588.4 x 10^-3 │ │ Perimeter │ 2.000 x 10^3 │ ├───────────────────────────┼────────────────┤ │ E.Qx │ 2.265 x 10^12 │ │ E.Qy │ 1.522 x 10^12 │ │ x-Centroid │ 200.0 │ │ y-Centroid │ 297.6 │ │ x-Centroid (Gross) │ 200.0 │ │ y-Centroid (Gross) │ 300.0 │ ├───────────────────────────┼────────────────┤ │ E.Ixx_g │ 916.8 x 10^12 │ │ E.Iyy_g │ 407.3 x 10^12 │ │ E.Ixy_g │ 453.1 x 10^12 │ │ E.Ixx_c │ 242.6 x 10^12 │ │ E.Iyy_c │ 102.8 x 10^12 │ │ E.Ixy_c │ -187.5 x 10^-3 │ │ E.I11 │ 242.6 x 10^12 │ │ E.I22 │ 102.8 x 10^12 │ │ Principal Axis Angle │ 0.000 rads │ ├───────────────────────────┼────────────────┤ │ E.Zxx+ │ 802.4 x 10^9 │ │ E.Zxx- │ 815.3 x 10^9 │ │ E.Zyy+ │ 514.2 x 10^9 │ │ E.Zyy- │ 514.2 x 10^9 │ │ E.Z11+ │ 802.4 x 10^9 │ │ E.Z11- │ 815.3 x 10^9 │ │ E.Z22+ │ 514.2 x 10^9 │ │ E.Z22- │ 514.2 x 10^9 │ ├───────────────────────────┼────────────────┤ │ Ultimate Concrete Strain │ 3.000 x 10^-3 │ └───────────────────────────┴────────────────┘
Transformed Properties¶
The above section properties are multiplied by the elastic moduli, e.g. axial rigidity (EA) and flexural rigidity (EI). Transformed section properties can be obtained using get_transformed_gross_properties() and providing a reference elastic_modulus.
[5]:
transformed_props = conc_sec.get_transformed_gross_properties(elastic_modulus=30.1e3)
transformed_props.print_results()
Transformed Gross Concrete Section Properties ┏━━━━━━━━━━┳━━━━━━━━━━━━━━━━┓ ┃ Property ┃ Value ┃ ┡━━━━━━━━━━╇━━━━━━━━━━━━━━━━┩ │ E_ref │ 30.10 x 10^3 │ │ Area │ 252.9 x 10^3 │ ├──────────┼────────────────┤ │ Qx │ 75.26 x 10^6 │ │ Qy │ 50.57 x 10^6 │ │ Ixx_g │ 30.46 x 10^9 │ │ Iyy_g │ 13.53 x 10^9 │ │ Ixy_g │ 15.05 x 10^9 │ │ Ixx_c │ 8.061 x 10^9 │ │ Iyy_c │ 3.417 x 10^9 │ │ Ixy_c │ -6.229 x 10^-6 │ │ I11 │ 8.061 x 10^9 │ │ I22 │ 3.417 x 10^9 │ ├──────────┼────────────────┤ │ Zxx+ │ 26.66 x 10^6 │ │ Zxx- │ 27.08 x 10^6 │ │ Zyy+ │ 17.08 x 10^6 │ │ Zyy- │ 17.08 x 10^6 │ │ Z11+ │ 26.66 x 10^6 │ │ Z11- │ 27.08 x 10^6 │ │ Z22+ │ 17.08 x 10^6 │ │ Z22- │ 17.08 x 10^6 │ └──────────┴────────────────┘