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This example demonstrates how to create a simple portal frame structure using milcapy. You’ll learn how to define materials, sections, nodes, members, restraints, and loads to perform a complete structural analysis.

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Overview

The portal frame consists of:
  • Two inclined columns (walls) at the base
  • Beam members forming the frame structure
  • Truss elements for diagonal bracing
  • Various advanced features including local axis definitions, elastic supports, end offsets, and member releases

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Complete Example

1

Import the library

Start by importing the necessary modules from milcapy:
from milcapy import SystemModel, BeamTheoriesType, model_viewer
2

Create the model and define materials

Initialize the structural model and define the concrete material:
model = SystemModel()

model.add_material(
    name="concreto", 
    modulus_elasticity=2.1e6, 
    poisson_ratio=0.2
)
The material properties are defined in units of tonf/m².
3

Define cross-sections

Create rectangular sections for the different structural members:
model.add_rectangular_section(
    name="vigas", 
    material_name="concreto", 
    base=0.3, 
    height=0.5
)

model.add_rectangular_section(
    name="muros", 
    material_name="concreto", 
    base=0.3, 
    height=2.0
)
  • vigas: Beam sections (0.3m × 0.5m)
  • muros: Column/wall sections (0.3m × 2.0m)
4

Define the geometry

Add nodes to define the structure’s geometry:
model.add_node(1, 0, 0)      # Base left
model.add_node(2, 0, 5)      # Column top left
model.add_node(3, 7, 8.5)    # Ridge apex
model.add_node(4, 14, 5)     # Column top right
model.add_node(5, 14, 0)     # Base right
model.add_node(6, 7, 5)      # Interior node
This creates a portal frame with a peaked roof configuration.
5

Add structural members

Define frame members and trusses connecting the nodes:
# Columns (using Timoshenko beam theory)
model.add_member(1, 1, 2, "muros", BeamTheoriesType.TIMOSHENKO)
model.add_member(4, 4, 5, "muros", BeamTheoriesType.TIMOSHENKO)

# Beams (using Euler-Bernoulli beam theory)
model.add_member(2, 2, 3, "vigas", BeamTheoriesType.EULER_BERNOULLI)
model.add_member(3, 3, 4, "vigas", BeamTheoriesType.EULER_BERNOULLI)
model.add_member(5, 2, 6, "vigas", BeamTheoriesType.EULER_BERNOULLI)
model.add_member(6, 6, 4, "vigas", BeamTheoriesType.EULER_BERNOULLI)

# Truss elements (axial load only)
model.add_truss(7, 1, 6, "vigas")
model.add_truss(8, 6, 5, "vigas")
Beam Theory Selection:
  • Timoshenko: Accounts for shear deformation, suitable for stocky members
  • Euler-Bernoulli: Classical beam theory, suitable for slender members
  • Truss: Axial-only elements with no bending stiffness
6

Apply boundary conditions

Define restraints at the base nodes:
model.add_restraint(1, *(False, True, True))  # Roller in x-direction
model.add_restraint(5, *(False, True, True))  # Roller in x-direction
The tuple represents (x, y, rotation) restraints. True means fixed, False means free.
7

Add local coordinate systems

Define inclined local axes for the base nodes to simulate inclined supports:
import math

model.add_local_axis_for_node(1, -37 * math.pi/180)  # -37 degrees
model.add_local_axis_for_node(5, +37 * math.pi/180)  # +37 degrees
This allows the roller supports to be oriented at an angle.
8

Add advanced features

Incorporate elastic supports, end offsets, and member releases:
lengthOffset = 1

# Elastic support at apex
model.add_elastic_support(3, ky=10)

# End length offsets for rigid end zones
model.add_end_length_offset(2, la=lengthOffset)
model.add_end_length_offset(3, lb=lengthOffset)

# Moment releases (pinned connections)
model.add_releases(5, mi=True)
model.add_releases(6, mj=True)
  • Elastic support: Spring support with stiffness ky=10 tonf/m
  • End offset: Rigid end zones of 1m length
  • Releases: Create pinned connections at member ends (mi = start, mj = end)
9

Define loads

Create a load pattern and apply various load types:
model.add_load_pattern("Live Load")

# Point load at apex
model.add_point_load(3, "Live Load", 0, -50, 0)

# Distributed loads on beams
model.add_distributed_load(2, "Live Load", -10, -5)  # Varying load
model.add_distributed_load(3, "Live Load", -5, -10)  # Varying load
model.add_distributed_load(5, "Live Load", -5, -5)   # Uniform load
model.add_distributed_load(6, "Live Load", -5, -5)   # Uniform load

# Prescribed displacements (support settlements)
model.add_prescribed_dof(1, "Live Load", uy=-0.01, CSys="LOCAL")
model.add_prescribed_dof(5, "Live Load", uy=-0.01, CSys="LOCAL")

# Gravity load on column
model.add_distributed_load(1, "Live Load", 10, 10, 'GLOBAL', 'GRAVITY')
10

Configure and solve

Set analysis options and solve the model:
# Set number of points for results visualization
model.postprocessing_options.n = 100

# Solve the structural system
model.solve()
11

Visualize results

Configure plotting options and display the model:
# Configure visualization options
model.plotter_options.mod_scale_dist_qload = 0.7
model.plotter_options.element_line_width = 0.8
model.plotter_options.truss_color = "brown"
model.plotter_options.deformation_line_width = 0.8
model.plotter_options.elastic_support_label = False
model.plotter_options.internal_forces_label = True

# Plot the model with loads
model.plot_model('Live Load')

# Or use the interactive viewer
# model_viewer(model)

​
Full Code

from milcapy import SystemModel, BeamTheoriesType, model_viewer
import math

model = SystemModel()

# Define material
model.add_material(name="concreto", modulus_elasticity=2.1e6, poisson_ratio=0.2)

# Define sections
model.add_rectangular_section(name="vigas", material_name="concreto", base=0.3, height=0.5)
model.add_rectangular_section(name="muros", material_name="concreto", base=0.3, height=2.0)

# Add nodes
model.add_node(1, 0, 0)
model.add_node(2, 0, 5)
model.add_node(3, 7, 8.5)
model.add_node(4, 14, 5)
model.add_node(5, 14, 0)
model.add_node(6, 7, 5)

# Add members
model.add_member(1, 1, 2, "muros", BeamTheoriesType.TIMOSHENKO)
model.add_member(2, 2, 3, "vigas", BeamTheoriesType.EULER_BERNOULLI)
model.add_member(3, 3, 4, "vigas", BeamTheoriesType.EULER_BERNOULLI)
model.add_member(4, 4, 5, "muros", BeamTheoriesType.TIMOSHENKO)
model.add_member(5, 2, 6, "vigas", BeamTheoriesType.EULER_BERNOULLI)
model.add_member(6, 6, 4, "vigas", BeamTheoriesType.EULER_BERNOULLI)

# Add trusses
model.add_truss(7, 1, 6, "vigas")
model.add_truss(8, 6, 5, "vigas")

# Add restraints
model.add_restraint(1, *(False, True, True))
model.add_restraint(5, *(False, True, True))

# Add local axes for inclined supports
model.add_local_axis_for_node(1, -37*math.pi/180)
model.add_local_axis_for_node(5, +37*math.pi/180)

# Advanced features
lengthOffset = 1
model.add_elastic_support(3, ky=10)
model.add_end_length_offset(2, la=lengthOffset)
model.add_end_length_offset(3, lb=lengthOffset)
model.add_releases(5, mi=True)
model.add_releases(6, mj=True)

# Define loads
model.add_load_pattern("Live Load")
model.add_point_load(3, "Live Load", 0, -50, 0)
model.add_distributed_load(2, "Live Load", -10, -5)
model.add_distributed_load(3, "Live Load", -5, -10)
model.add_distributed_load(5, "Live Load", -5, -5)
model.add_distributed_load(6, "Live Load", -5, -5)
model.add_prescribed_dof(1, "Live Load", uy=-0.01, CSys="LOCAL")
model.add_prescribed_dof(5, "Live Load", uy=-0.01, CSys="LOCAL")
model.add_distributed_load(1, "Live Load", 10, 10, 'GLOBAL', 'GRAVITY')

# Configure and solve
model.postprocessing_options.n = 100
model.solve()

# Visualize
model.plotter_options.mod_scale_dist_qload = 0.7
model.plotter_options.element_line_width = 0.8
model.plotter_options.truss_color = "brown"
model.plotter_options.internal_forces_label = True

model.plot_model('Live Load')

​
Key Concepts

Multiple Beam Theories

Combine different beam formulations in a single model based on member characteristics

Local Coordinate Systems

Define inclined supports and local reference frames for nodes

Elastic Supports

Model flexible supports with specified spring stiffness

Member Releases

Create pinned connections and control moment transfer at member ends

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Next Steps

Truss Analysis

Learn how to model and analyze truss structures

Membrane Analysis

Explore 2D membrane element modeling

API Reference

View complete API documentation

Advanced Features

Explore advanced modeling capabilities

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