code/16.py

# Parameters configuration
import openseespy.opensees as ops  # Import OpenSeesPy for structural analysis
import opsvis as opsv  # Import opsvis for visualization
import matplotlib.pyplot as plt  # Import Matplotlib for plotting

ops.wipe()  # Clear any existing model

# Define a 2D model with 3 degrees of freedom per node (DOF)
ops.model('basic', '-ndm', 2, '-ndf', 3)

# Frame dimensions
colH = 4.e0  # Height of the columns (m)
colSpacing = 8.e0  # Spacing between the columns (m)
roofPeak = 3.e0  # Height of the roof peak above the top of columns (m)

# Section properties: cross-sectional area (A) and moment of inertia (Iz)
Acol, Adiag = 2.e-3, 6.e-3
IzCol, IzDiag = 1.6e-5, 5.4e-5

# Material property: Young's Modulus (E)
E = 2.e11  # Elastic modulus (Pa)

# Load configuration
qDiag = 1.e4  # Uniform distributed load on the diagonal members (N/m)
# Define the material property dictionary for columns and girders
Ep = {
    1: [2e11, 2e-3, 1.6e-5],  # Columns
    2: [2e11, 6e-3, 5.4e-5]   # Diagonal members
}

# Define the node coordinates
ops.node(1, 0, 0)         # Bottom-left column node
ops.node(2, 8.0, 0)       # Bottom-right column node
ops.node(3, 0, 4.0)       # Top-left column node
ops.node(4, 8.0, 4.0)     # Top-right column node
ops.node(5, 4.0, 7.0)     # Peak of the roof

# Define boundary conditions (supports)
ops.fix(1, 1, 1, 1)  # Fully fixed support at node 1
ops.fix(2, 1, 1, 1)  # Fully fixed support at node 2

# Plot the model before defining elements
opsv.plot_model()
# Add title
plt.title('plot_model before defining elements')

# Define transformation type for elements (Linear)
ops.geomTransf('Linear', 1)  # Transformation ID 1 for linear transformation

# Define column and diagonal elements (elastic beam-column elements)
ops.element('elasticBeamColumn', 1, 1, 3, 2e-3, 2e11, 1.6e-5, 1)  # Left column
ops.element('elasticBeamColumn', 2, 2, 4, 2e-3, 2e11, 1.6e-5, 1)  # Right column
ops.element('elasticBeamColumn', 3, 3, 5, 6e-3, 2e11, 5.4e-5, 1)  # Left diagonal
ops.element('elasticBeamColumn', 4, 4, 5, 6e-3, 2e11, 5.4e-5, 1)  # Right diagonal

# Define external loads
Wy = -1e4  # Uniform distributed load inward on diagonal members
Wx = 0.0   # No distributed x-direction load

# Create a dictionary to store element loads
Ew = {
    3: ['-beamUniform', Wy, Wx],   # Distributed load on left diagonal
    4: ['-beamUniform', -Wy, Wx]  # Distributed load on right diagonal (reversed coordinate order)
}

# Define time series for constant loads
ops.timeSeries('Constant', 1)

# Define load pattern using the constant time series
ops.pattern('Plain', 1, 1)

# Applying point loads
# No point loads in the system based on the problem statement

# Applying distributed loads
for etag in Ew:
    ops.eleLoad('-ele', etag, '-type', Ew[etag][0], Ew[etag][1], Ew[etag][2])
# Analysis settings
ops.constraints('Transformation')
ops.numberer('RCM')
ops.system('BandGeneral')
ops.test('NormDispIncr', 1.0e-6, 6, 2)
ops.algorithm('Linear')
ops.integrator('LoadControl', 1)
ops.analysis('Static')
ops.analyze(1)

# Print the model data
ops.printModel()

# Plot the model after defining elements
opsv.plot_model()
plt.title('plot_model after defining elements')

# Plot the applied loads on the model in 2D
opsv.plot_loads_2d(nep=10,
                   sfac=1,
                   fig_wi_he=(10, 5),
                   fig_lbrt=(0.1, 0.1, 0.9, 0.9),
                   fmt_model_loads={'color': 'red', 'linewidth': 1.5},
                   node_supports=True,
                   truss_node_offset=0.05,
                   ax=None)

# Plot deformations (scaled) after analysis
opsv.plot_defo()

# Plot internal force diagrams: N (axial), V (shear), M (moment)
sfacN, sfacV, sfacM = 5.e-5, 5.e-5, 5.e-5
opsv.section_force_diagram_2d('N', sfacN)
plt.title('Axial force distribution')
opsv.section_force_diagram_2d('T', sfacV)
plt.title('Shear force distribution')
opsv.section_force_diagram_2d('M', sfacM)
plt.title('Bending moment distribution')

# Show all plots
plt.show()

# Exit the program
exit()