Lecture on Equilibrium of Rigid Bodies

Introduction to Equilibrium

• Equilibrium of a Rigid Body: Achieved when the sum of all forces and moments acting on the body are zero.
  • Object is not moving; is stationary.
• Example: A flower pot held by a rope.
  • Forces:
    • Weight of the pot (acting downwards).
    • Tension in the rope (acting upwards).
  • Equilibrium maintained by equal and opposite forces.

Equations of Equilibrium

• Net Force = 0:
  • Sum of forces in the x-direction: ( \Sigma F_x = 0 )
  • Sum of forces in the y-direction: ( \Sigma F_y = 0 )
• Net Moment = 0:
  • Sum of all moments: ( \Sigma M = 0 )
• Focus on two-dimensional problems (x-y plane).

Support Reactions

• Types of Supports:
  • Roller: Provides vertical support, allows horizontal movement.
  • Pin: Provides support in x and y directions, allows rotation.
  • Fixed Support: Prevents movement in x, y directions, and rotation.
• Example:
  • A bar with roller and pin supports.

Solving Equilibrium Problems

1. Free Body Diagram (FBD):
   • Identify forces, moments, and support reactions.
2. Equations of Equilibrium:
   • Sum forces in x and y directions.
   • Use a moment equation about a strategic point.
   • Usually requires three equations to solve for unknowns.

Example Problems

Problem 1

• Objective: Find reactions at pin A and tension in rope.
• Steps:
  1. Draw FBD.
  2. Identify forces and break into components.
  3. Write and solve equations:
     • ( \Sigma F_x = 0 )
     • ( \Sigma F_y = 0 )
     • ( \Sigma M = 0 ) about a strategic point.

Problem 2

• Objective: Find reactions at roller A and pin B.
• Steps:
  1. Draw FBD and represent distributed load as a resultant force.
  2. Write equations of equilibrium.
  3. Solve system of equations for unknowns.

Problem 3

• Objective: Determine reactions at A and B (smooth collar and contacting surface).
• Steps:
  1. Draw FBD considering perpendicular forces and moments.
  2. Write equations of equilibrium.
  3. Solve for force components and moments.

Problem 4

• Objective: Find angle in a system with a weight, pinned rod, and spring.
• Steps:
  1. Draw FBD.
  2. Use Hooke's Law for spring force.
  3. Simplify moment equation about point A to solve for angle.

Key Concepts

• Importance of correctly identifying support reactions and breaking forces into components.
• Need for strategic selection of points about which to calculate moments.
• Remember: An object in equilibrium has net forces and moments equal to zero.

Conclusion

• Practice with problems and review support types in textbooks.
• Focus on understanding force components and moment calculations.
• Share learning with peers.

• Advice: Use resources like textbooks and descriptions for additional examples and explanations.
• Call to Action: Consider sharing knowledge with classmates to aid their understanding.

End of Lecture