Statics of Rigid Bodies

STATICS OF RIGID BODIES

Introduction to Engineering Mechanics

• Engineering Mechanics: Study of the conditions of rest or motion of bodies under the action of forces.
  • Divided into three main parts:
  • Mechanics of Rigid Bodies
  • Mechanics of Deformable Bodies
  • Mechanics of Fluids

Mechanics of Rigid Bodies

• Subdivisions:
  • Statics: Focus on bodies at rest.
  • Dynamics: Focus on bodies in motion.
• Assumption: Bodies are considered to be perfectly rigid.

Mechanics of Deformable Bodies

• Consideration: Bodies deform under applied loads.

Mechanics of Fluids

• Subdivisions:
  • Incompressible Fluids (Hydraulics)
  • Compressible Fluids

Fundamental Concepts

• Length: A measure to locate points in space; describes the size of a physical system.
• Time: Measures the succession of events.
• Mass: Property of matter; reflects gravitational attraction, and quantifies matter's resistance to velocity change.
• Force: Action by one body on another. Can be contact-based or at a distance. Characterized by:
  • Point of application
  • Magnitude
  • Direction
• Particle: Idealized point with concentrated mass.
• Rigid Body: Composed of numerous particles, maintaining fixed distances despite load applications.
• Concentrated Force: Effect of load acting at a single point.

Fundamental Principles

1. Parallelogram Law:
   • Two forces on a particle can be replaced by their resultant obtained from the diagonal of the parallelogram formed by the forces.
2. Principle of Transmissibility:
   • Conditions of equilibrium or motion remain unchanged if a force is moved along its line of action, maintaining magnitude and direction.
3. Newton’s First Law:
   • A particle at rest remains at rest or continues in uniform motion if the resultant force is zero.
4. Newton’s Second Law:
   • A particle experiences acceleration proportional to the resultant force acting on it.
   • Formula: F = m * a
5. Newton’s Third Law:
   • For every action, there is an equal and opposite reaction between bodies in contact.
6. Newton’s Law of Gravitation:
   • Two particles attract each other with equal and opposite forces, magnitude defined by:
   • Formula: F = (G * m1 * m2) / r²
   • Where G = universal gravitation constant and r = distance between particles.

Systems of Forces

• Coplanar Forces: Forces whose lines of action lie in the same plane.
• Non-Coplanar Forces: Forces whose lines of action do not lie in the same plane.

Types of Force Systems

• Collinear Force System: Common line of action.
• Parallel Force System: Forces are parallel but do not meet at a point.
• Concurrent Force System: Lines of action intersect at a common point.
• Non-Concurrent Force System: Lines of action do not converge at a point.