Overview Materials define the physical properties of structural components (elasticity, strength, density), while sections describe the geometric properties of cross-sections (area, moment of inertia). Together, they determine how structural elements behave under load.
Materials Adding a Material Create a material by specifying its elastic properties:
material = model.add_material( name = "Steel" , modulus_elasticity = 200e9 , # Young's modulus (Pa) poisson_ratio = 0.3 , # Poisson's ratio specific_weight = 78500 # Specific weight (N/m³) )
Material Parameters
Modulus of Elasticity (E)
The material’s stiffness, measured in Pascals (Pa). Common values:
Steel: 200 GPa (200e9 Pa)
Concrete: 25-35 GPa
Aluminum: 70 GPa
Ratio of transverse strain to axial strain. Must be between -1 and 0.5:
Steel: 0.30
Concrete: 0.15-0.20
Aluminum: 0.33
Weight per unit volume (N/m³ or kg/m³). Used for self-weight calculations:
Steel: 78,500 N/m³ (7,850 kg/m³)
Concrete: 24,000 N/m³ (2,400 kg/m³)
Aluminum: 27,000 N/m³ (2,700 kg/m³)
Material Properties Once created, materials automatically calculate the shear modulus:
material = model.materials[ "Steel" ] E = material.E # Modulus of elasticity nu = material.v # Poisson's ratio G = material.G # Shear modulus (calculated as E / (2 * (1 + ν))) gamma = material.g # Specific weight
Thermal Expansion Coefficients Materials also support thermal expansion coefficients:
material = model.materials[ "Steel" ] material.alpha = 1.2e-5 # Linear thermal expansion coefficient material.beta = 2.4e-5 # Surface thermal expansion coefficient material.gamma = 3.6e-5 # Volumetric thermal expansion coefficient
The shear modulus G is automatically calculated from Young’s modulus and Poisson’s ratio: G = E / (2 * (1 + ν))
Sections milcapy provides several predefined section types for different geometric configurations.
Rectangular Section The most common section type for beams and columns:
section = model.add_rectangular_section( name = "SEC-30x50" , material_name = "Concrete" , base = 0.30 , # Width (m) height = 0.50 # Depth (m) )
Properties calculated automatically:
Area: A = base × height
Moment of inertia: I = (base × height³) / 12
Shear coefficient: k = 5/6 (Timoshenko) or k = 10(1+ν)/(12+11ν) (Cowper)
Circular Section For circular beams or columns:
section = model.add_circular_section( name = "PIPE-200" , material_name = "Steel" , diameter = 0.20 # Outer diameter (m) )
Properties calculated automatically:
Area: A = π × r²
Moment of inertia: I = π × r⁴ / 4
Shear coefficient: k = 6/7 (Timoshenko)
Generic Section For custom sections with known properties:
section = model.add_generic_section( name = "CUSTOM-1" , material_name = "Steel" , area = 0.0085 , # Cross-sectional area (m²) inertia = 7.2e-5 , # Moment of inertia (m⁴) k_factor = 0.8333 # Shear coefficient )
Use generic sections when you have pre-calculated section properties from tables or CAD software.
Shell Section For membrane and plate elements:
section = model.add_shell_section( name = "WALL-200" , material_name = "Concrete" , thickness = 0.20 # Thickness (m) )
Section Property Modifiers Modify section properties without changing the base geometry:
model.set_property_modifiers( section_name = "SEC-30x50" , axial_area = 1.0 , # Modifier for area (default: 1.0) shear_area = 1.0 , # Modifier for shear area (default: 1.0) moment_inertia = 0.35 , # Reduce stiffness for cracked concrete weight = 1.0 # Modifier for self-weight (default: 1.0) )
Common use cases:
Cracked concrete sections : Reduce moment_inertia to 0.35-0.70Composite sections : Adjust axial_area for effective areaConstruction phases : Modify weight for temporary conditionsShear deformation : Adjust shear_area for refined analysis Shear Coefficient Methods For rectangular and circular sections, you can choose the shear coefficient calculation method:
from milcapy.utils.types import ShearCoefficientMethodType # Timoshenko method (default) section = model.add_rectangular_section( name = "SEC-1" , material_name = "Concrete" , base = 0.30 , height = 0.50 ) # Uses k = 5/6 for rectangular, k = 6/7 for circular # Cowper method (more accurate) # k = 10(1 + ν) / (12 + 11ν)
The shear coefficient affects the shear deformation in Timoshenko beam theory. For Euler-Bernoulli beams, shear deformation is neglected.
Accessing Section Properties Retrieve calculated section properties:
section = model.sections[ "SEC-30x50" ] # Geometric properties A = section.A() # Area I = section.I() # Moment of inertia k = section.k() # Shear coefficient # Material properties (from linked material) E = section.E() # Young's modulus G = section.G() # Shear modulus v = section.v() # Poisson's ratio g = section.g() # Specific weight
Complete Example
Define materials
# Concrete material model.add_material( name = "C30" , modulus_elasticity = 30e9 , poisson_ratio = 0.2 , specific_weight = 24000 ) # Steel material model.add_material( name = "A36" , modulus_elasticity = 200e9 , poisson_ratio = 0.3 , specific_weight = 78500 )
Create sections
# Concrete beam section model.add_rectangular_section( name = "BEAM-40x60" , material_name = "C30" , base = 0.40 , height = 0.60 ) # Steel column section model.add_circular_section( name = "COL-300" , material_name = "A36" , diameter = 0.30 ) # Concrete wall section model.add_shell_section( name = "WALL-250" , material_name = "C30" , thickness = 0.25 )
Apply modifiers (optional)
# Account for concrete cracking model.set_property_modifiers( section_name = "BEAM-40x60" , moment_inertia = 0.5 # 50% effective stiffness )
Best Practices Material Must Exist : Always add materials before creating sections that reference them. The model will raise a ValueError if the material doesn’t exist.
Consistent Units : Use consistent units throughout your model. SI units (meters, Newtons, Pascals) are recommended.
Meaningful Names : Use descriptive names that indicate dimensions or properties:
"C30" for concrete grade"BEAM-40x60" for 40cm × 60cm beam"WALL-250" for 250mm wall thickness
System Model Learn about the main model structure
Elements Use sections to create structural elements
