4.2 Free Body Diagrams

Free body diagrams are crucial tools in statics, helping visualize all forces acting on an object. They simplify complex systems by isolating a body and showing external forces, making it easier to analyze equilibrium and solve for unknown forces.

Understanding different types of forces and reactions is key to creating accurate free body diagrams. Applied forces, friction, distributed loads, and point loads all play roles in real-world scenarios, while reaction forces from supports maintain equilibrium in structures.

Forces

Types of Forces

Top images from around the web for Types of Forces

• 

  Vector Nature of Forces | Boundless Physics View original

  Is this image relevant?

• 

  Drawing Free-Body Diagrams – University Physics Volume 1 View original

  Is this image relevant?

• 

  HendricksPhysics - • Mechanics & Motion in fields View original

  Is this image relevant?

• 

  Vector Nature of Forces | Boundless Physics View original

  Is this image relevant?

• 

  Drawing Free-Body Diagrams – University Physics Volume 1 View original

  Is this image relevant?

1 of 3

Top images from around the web for Types of Forces

• 

  Vector Nature of Forces | Boundless Physics View original

  Is this image relevant?

• 

  Drawing Free-Body Diagrams – University Physics Volume 1 View original

  Is this image relevant?

• 

  HendricksPhysics - • Mechanics & Motion in fields View original

  Is this image relevant?

• 

  Vector Nature of Forces | Boundless Physics View original

  Is this image relevant?

• 

  Drawing Free-Body Diagrams – University Physics Volume 1 View original

  Is this image relevant?

1 of 3

• Applied forces are external forces that act on a body, causing it to move, deform, or change its state of motion
  • Can be represented as vectors with magnitude and direction (pushing a box, wind load on a building)
• Friction forces resist the relative motion between two surfaces in contact
  • Occur parallel to the surfaces and oppose the direction of motion (sliding a book across a table, tire traction on a road)
• Distributed loads are forces that are spread out over an area or along a line
  • Represented as a force per unit area or force per unit length (snow load on a roof, water pressure on a dam)
• Point loads are concentrated forces that act at a single point on a body
  • Represented as a single vector with magnitude and direction (a person standing on a floor, a cable pulling on a pulley)

Force Characteristics

• Forces are vector quantities, having both magnitude and direction
  • Magnitude represents the intensity of the force, usually measured in units of Newtons (N) or pounds (lbs)
  • Direction indicates the line of action along which the force acts, often specified using angles or coordinate systems
• Forces can be represented graphically using arrows, with the length of the arrow proportional to the magnitude and the arrowhead indicating the direction
• Multiple forces acting on a body can be combined using vector addition to determine the resultant force
  • Concurrent forces act at a single point and can be added directly (forces acting on a joint)
  • Non-concurrent forces act at different points and may cause rotation or bending (forces on a beam)

Reactions

Reaction Forces

• Reaction forces are forces exerted by supports or constraints on a body to maintain equilibrium
  • Occur in response to applied forces and the weight of the body itself
• The magnitude and direction of reaction forces depend on the type of support and the forces acting on the body
  • A pinned support allows rotation but prevents translation, producing a force reaction (a door hinge, a truss joint)
  • A roller support allows translation along a surface but prevents movement perpendicular to the surface, producing a force reaction normal to the surface (a wheel on a track, a sliding drawer)
  • A fixed support prevents both rotation and translation, producing both force and moment reactions (a clamped beam, a bolted connection)

Moment Reactions

• Moment reactions, also known as couple reactions, are forces that occur in pairs to resist rotation
  • Produced by fixed supports or by constraints that prevent rotation
• The magnitude of a moment reaction depends on the distance between the forces and the point of rotation
  • Calculated as the product of the force and the perpendicular distance to the point of rotation, usually measured in units of Newton-meters (N·m) or foot-pounds (ft·lbs)
• The direction of a moment reaction is determined by the right-hand rule
  • Curl the fingers of your right hand in the direction of rotation, and your thumb points in the direction of the moment vector (counterclockwise rotation produces a positive moment, clockwise rotation produces a negative moment)

Diagram Elements

Free Body Diagrams

• A free body diagram (FBD) is a graphical representation of a body or system, showing all the external forces and moments acting on it
  • Used to visualize and analyze the forces acting on a body in equilibrium or in motion
• To create an FBD, the body is isolated from its surroundings, and all the forces and moments are drawn as vectors
  • The body is typically represented as a simplified shape or a point
  • Forces are drawn as arrows, with the tail at the point of application and the head pointing in the direction of the force
  • Moments are drawn as curved arrows, indicating the direction of rotation
• FBDs are essential for solving statics problems, as they help to identify the unknown forces and moments that need to be calculated

Constraints and Supports

• Constraints are conditions that limit the motion or deformation of a body
  • Can be physical, such as supports or connections, or mathematical, such as equations of equilibrium
• Supports are structural elements that provide reaction forces and moments to maintain the equilibrium of a body
  • Common types of supports include pinned, roller, and fixed supports
  • The type of support determines the number and direction of the reaction forces and moments
• In an FBD, supports are typically represented by symbols that indicate the type of support and the direction of the reaction forces and moments
  • A pinned support is shown as a triangle, with a force reaction perpendicular to the surface
  • A roller support is shown as a circle, with a force reaction normal to the surface
  • A fixed support is shown as a triangle with a circle, with both force and moment reactions