mec unit 2

Engineering Mechanics - Statics

Chapter 2: Force Systems

Learning Outcomes

• At the end of this chapter, students should be able to:
  • Define clearly the classification of forces in two- and three-dimensional systems.
  • Apply the principle of moments and free body diagrams to calculate the unknown resultant forces.

Force Systems

• Definition: Forces are vectors with magnitude, direction, and point of application.
• Properties:
  • Forces can be considered fixed vectors.
  • Effects of a force on a body include:
  • External Effect: Applied forces produce reactive forces.
  • Internal Effect: Applied forces lead to internal deformations, relevant in studying the strength of materials.

Principle of Transmissibility

• Statement: A force may be applied at any point along its line of action without changing the resultant effects of the external force on the rigid body.
• Illustration: If a force P is applied at points A or B on a plate, the effect of P remains unchanged:


Classification of Forces

• Types of Forces:
  • Contact Force: Forces that occur when two objects are in contact.
  • Body Force: Forces that act at a distance, such as gravity or magnetic force.
  • Concentrated or Point Force: Forces that act at a single point.
  • Distributed Force: Forces that are spread over an area.

Concurrent Forces

• Definition: Forces are concurrent if their lines of action intersect at a common point.
• Examples:
  • Figures 2/3a to e demonstrate concurrent forces and the principle of transmissibility. Some methods to find resultant forces include:
  • Example 2/3a: Concurrent forces at point A.
  • Example 2/3b: Application of the principle of transmissibility.
  • Example 2/3c: Results are maintained with preserved line of action.
  • Example 2/3d: Distorted resultant due to lost line of action.
  • Example 2/3e: Perpendicular projection of forces.

Rectangular or Coplanar Forces

• Approach: To determine the resultant of multiple forces, resolve each force into its components along specified axes and add them algebraically:
  
• Resolving a Force at an Angle:
  • If a force F is at an angle, its components can be as follows:
  • $F_{1} = F imes ext{sin}(\beta)$
  • $F_{x} = F imes ext{cos}(\beta)$
  • Example: For a force at an angle, resolve using appropriate trigonometric functions.

Moments

• Definition: The moment (M) produced by a force is given by the product of the force and the perpendicular distance from the pivot point:

  • $M = F imes d$
  • Where:
    • F = force
    • d = perpendicular distance

• Illustration: For non-perpendicular distances, the moment can be calculated as:

  • $M_{1} = F imes d = F imes r imes ext{sin}( heta)$

Direction of Moments in 2-D

• Direction is determined by the right-hand rule:
  • Counter Clockwise (CCW): Out of the page.
  • Clockwise (CW): Into the page.

Varignon's Theorem

• Statement: The moment of a force about any point is equal to the sum of the moments of the components of the force about the same point.
• Problem example: Calculate moments using five different methods for a specific force.

Couples

• Definition: A couple is formed by equal, opposite, and non-collinear forces.
• Property: The moment of a couple remains constant regardless of the point from which it is calculated.
• Calculation:
  • Moment due to a couple can be given as:
  • $M = F imes (a + d) - F imes a$
  • Simplified to: $M = F imes d$
  • Coupling can be visual