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be06037 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 | # 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
ops.model('basic', '-ndm', 2, '-ndf', 3) # Define a 2D model with 3 degrees of freedom per node (DOF)
# Column and girder lengths
colL, girL = 4., 6.
# Section properties: cross-sectional area (A) and moment of inertia (Iz)
Acol, Agir = 2.e-3, 6.e-3
IzCol, IzGir = 1.6e-5, 5.4e-5
# Young's modulus (E)
E = 200.e9
# Define the material property dictionary for columns and girders
Ep = {
1: [2e11, 2e-3, 1.6e-5], # Column 1
2: [2e11, 2e-3, 1.6e-5], # Column 2
3: [2e11, 2e-3, 1.6e-5], # Column 3
4: [2e11, 2e-3, 1.6e-5], # Column 4
5: [2e11, 2e-3, 1.6e-5], # Column 5
6: [2e11, 6e-3, 5.4e-5], # Girder 1
7: [2e11, 6e-3, 5.4e-5], # Girder 2
8: [2e11, 6e-3, 5.4e-5] # Girder 3
}
# Define the node coordinates
ops.node(1, 0, 0) # Node 1
ops.node(2, 0, 4) # Node 2
ops.node(3, 6, 0) # Node 3
ops.node(4, 6, 4) # Node 4
ops.node(5, 6, 8) # Node 5
ops.node(6, 12, 0) # Node 6
ops.node(7, 12, 4) # Node 7
ops.node(8, 12, 8) # Node 8
# Define boundary conditions (supports)
ops.fix(1, 1, 1, 1) # Node 1 fixed
ops.fix(3, 1, 1, 1) # Node 3 fixed
ops.fix(6, 1, 1, 1) # Node 6 fixed
# 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)
# Define column and girder elements (elastic beam-column elements)
ops.element('elasticBeamColumn', 1, 1, 2, 2e-3, 2e11, 1.6e-5, 1) # Column 1
ops.element('elasticBeamColumn', 2, 3, 4, 2e-3, 2e11, 1.6e-5, 1) # Column 2
ops.element('elasticBeamColumn', 3, 4, 5, 2e-3, 2e11, 1.6e-5, 1) # Column 3
ops.element('elasticBeamColumn', 4, 6, 7, 2e-3, 2e11, 1.6e-5, 1) # Column 4
ops.element('elasticBeamColumn', 5, 7, 8, 2e-3, 2e11, 1.6e-5, 1) # Column 5
ops.element('elasticBeamColumn', 6, 2, 4, 6e-3, 2e11, 5.4e-5, 1) # Girder 1
ops.element('elasticBeamColumn', 7, 4, 7, 6e-3, 2e11, 5.4e-5, 1) # Girder 2
ops.element('elasticBeamColumn', 8, 5, 8, 6e-3, 2e11, 5.4e-5, 1) # Girder 3
# Define external loads
Px = 2e3 # Horizontal point load
# Create a dictionary to store element loads
Ew = {} # No distributed loads provided
# 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
ops.load(2, Px, 0.0, 0.0) # Point load at node 2
ops.load(5, Px, 0.0, 0.0) # Point load at node 5
# 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') # Apply transformation constraints
ops.numberer('RCM') # Renumber the nodes using Reverse Cuthill-McKee (RCM)
ops.system('BandGeneral') # Define the solution algorithm
ops.test('NormDispIncr', 1.0e-6, 6, 2) # Convergence test criteria
ops.algorithm('Linear') # Use linear algorithm for solving
ops.integrator('LoadControl', 1) # Control load increments
ops.analysis('Static') # Define a static analysis
ops.analyze(1) # Perform the analysis
# 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, # Number of points along each element
sfac=1, # Scale factor for loads
fig_wi_he=(10, 5), # Width and height of the figure
fig_lbrt=(0.1, 0.1, 0.9, 0.9), # Left, bottom, right, top margins
fmt_model_loads={'color': 'red', 'linewidth': 1.5}, # Formatting for load arrows
node_supports=True, # Display node supports
truss_node_offset=0.05, # Offset for truss elements
ax=None) # Matplotlib axis, None to use current axis
# 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 # Scale factors for internal force diagrams
# Plot axial force distribution
opsv.section_force_diagram_2d('N', sfacN)
plt.title('Axial force distribution')
# Plot shear force distribution
opsv.section_force_diagram_2d('T', sfacV)
plt.title('Shear force distribution')
# Plot bending moment distribution
opsv.section_force_diagram_2d('M', sfacM)
plt.title('Bending moment distribution')
# Show all plots
plt.show()
# Exit the program
exit() |