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.