Apprendre Free Body Diagrams with Python | Statics and Engineering Calculations

Understanding free body diagrams (FBDs) is fundamental in mechanical engineering. An FBD is a graphical representation that isolates a body and shows all external forces and moments acting on it. These diagrams help you visualize the forces at play, making it easier to set up equilibrium equations and solve for unknowns. Traditionally, FBDs are drawn by hand, but Python—especially with the matplotlib library—enables you to automate and standardize the creation of these diagrams. This not only saves time but also reduces errors and enhances clarity when communicating engineering solutions.


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import matplotlib.pyplot as plt

# Create a simple beam as a horizontal line
fig, ax = plt.subplots(figsize=(8, 2))
ax.plot([0, 6], [0, 0], color='black', linewidth=4)

# Draw a downward force at 2 meters
ax.arrow(2, 0.2, 0, -0.7, head_width=0.15, head_length=0.15, fc='red', ec='red', linewidth=2)
ax.text(2, 0.3, 'F = 10 kN', ha='center', color='red')

# Draw a support at the left end
ax.plot(0, 0, marker='^', markersize=15, color='blue')
ax.text(0, -0.4, 'Pin Support', ha='center', color='blue')

# Formatting
ax.set_xlim(-1, 7)
ax.set_ylim(-1, 1)
ax.axis('off')
plt.title('Free Body Diagram: Simple Beam with Applied Force')
plt.show()

This code uses matplotlib to plot a simple free body diagram of a beam. The beam is represented by a thick horizontal line, and a downward force is shown as a red arrow using the ax.arrow function. The arrow points downward at the location where the force is applied, and a label indicates the magnitude of the force. The support at the left end is depicted with a blue triangle marker, labeled as a pin support. In engineering diagrams, arrows represent forces, and clear labels are used to identify both the type and magnitude of each force or support. By following these conventions in Python, you can create clear, professional diagrams suitable for reports or presentations.


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import matplotlib.pyplot as plt

# Create the beam
fig, ax = plt.subplots(figsize=(10, 2))
ax.plot([0, 8], [0, 0], color='black', linewidth=4)

# Applied forces
# Downward force at 2 m
ax.arrow(2, 0.2, 0, -0.7, head_width=0.15, head_length=0.15, fc='red', ec='red', linewidth=2)
ax.text(2, 0.35, 'F1 = 8 kN', ha='center', color='red')
# Upward force at 5 m
ax.arrow(5, -0.2, 0, 0.7, head_width=0.15, head_length=0.15, fc='green', ec='green', linewidth=2)
ax.text(5, -0.45, 'F2 = 5 kN', ha='center', color='green')

# Support reactions
# Pin support at left (A)
ax.plot(0, 0, marker='^', markersize=15, color='blue')
ax.arrow(0, -0.2, 0, 0.7, head_width=0.15, head_length=0.15, fc='blue', ec='blue', linewidth=2)
ax.text(0, 0.6, 'R_A', ha='center', color='blue')

# Roller support at right (B)
ax.plot(8, 0, marker='o', markersize=10, color='purple')
ax.arrow(8, -0.2, 0, 0.7, head_width=0.15, head_length=0.15, fc='purple', ec='purple', linewidth=2)
ax.text(8, 0.6, 'R_B', ha='center', color='purple')

# Formatting
ax.set_xlim(-1, 9)
ax.set_ylim(-1, 1)
ax.axis('off')
plt.title('Free Body Diagram: Beam with Multiple Forces and Supports')
plt.show()

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              1234567891011121314151617181920
            
import matplotlib.pyplot as plt

# Create a simple beam as a horizontal line
fig, ax = plt.subplots(figsize=(8, 2))
ax.plot([0, 6], [0, 0], color='black', linewidth=4)

# Draw a downward force at 2 meters
ax.arrow(2, 0.2, 0, -0.7, head_width=0.15, head_length=0.15, fc='red', ec='red', linewidth=2)
ax.text(2, 0.3, 'F = 10 kN', ha='center', color='red')

# Draw a support at the left end
ax.plot(0, 0, marker='^', markersize=15, color='blue')
ax.text(0, -0.4, 'Pin Support', ha='center', color='blue')

# Formatting
ax.set_xlim(-1, 7)
ax.set_ylim(-1, 1)
ax.axis('off')
plt.title('Free Body Diagram: Simple Beam with Applied Force')
plt.show()


              12345678910111213141516171819202122232425262728293031
            
import matplotlib.pyplot as plt

# Create the beam
fig, ax = plt.subplots(figsize=(10, 2))
ax.plot([0, 8], [0, 0], color='black', linewidth=4)

# Applied forces
# Downward force at 2 m
ax.arrow(2, 0.2, 0, -0.7, head_width=0.15, head_length=0.15, fc='red', ec='red', linewidth=2)
ax.text(2, 0.35, 'F1 = 8 kN', ha='center', color='red')
# Upward force at 5 m
ax.arrow(5, -0.2, 0, 0.7, head_width=0.15, head_length=0.15, fc='green', ec='green', linewidth=2)
ax.text(5, -0.45, 'F2 = 5 kN', ha='center', color='green')

# Support reactions
# Pin support at left (A)
ax.plot(0, 0, marker='^', markersize=15, color='blue')
ax.arrow(0, -0.2, 0, 0.7, head_width=0.15, head_length=0.15, fc='blue', ec='blue', linewidth=2)
ax.text(0, 0.6, 'R_A', ha='center', color='blue')

# Roller support at right (B)
ax.plot(8, 0, marker='o', markersize=10, color='purple')
ax.arrow(8, -0.2, 0, 0.7, head_width=0.15, head_length=0.15, fc='purple', ec='purple', linewidth=2)
ax.text(8, 0.6, 'R_B', ha='center', color='purple')

# Formatting
ax.set_xlim(-1, 9)
ax.set_ylim(-1, 1)
ax.axis('off')
plt.title('Free Body Diagram: Beam with Multiple Forces and Supports')
plt.show()

Tout était clair ?

Merci pour vos commentaires !

Section 1. Chapitre 6

Free Body Diagrams with Python

1. Why are free body diagrams essential in mechanical engineering?

2. Which matplotlib function is used to draw arrows representing forces?

3. How can automating FBDs with Python improve engineering workflows?

Free Body Diagrams with Python

1. Why are free body diagrams essential in mechanical engineering?

2. Which matplotlib function is used to draw arrows representing forces?

3. How can automating FBDs with Python improve engineering workflows?