ENSC 11 Chapter 2

Cards (23)

  • Free Body Diagram of Rigid Bodies

    Diagram of a "free" body with all the known and unknown external forces (represented by arrows and their corresponding point) acting on the body while maintaining the shape and dimension of the body
  • External Forces
    • Applied Forces
    • Support Reactions
    • Weight
    • Reactions of other bodies previously attached to the body in consideration
  • Reactions/Constraining Forces
    • Oppose a possible motion of the body and constrain a body to remain in the same position
    • Exerted at points where the body is supported by or connected to other bodies
  • Reactions at Supports and Connections for a 2D Structure

    • Reactions equivalent to a Force with a known Line of Action
    • Reactions equivalent to a force of unknown direction and magnitude (sometimes expressed as Rx and Ry)
    • Reactions equivalent to a force and a couple
  • Reactions equivalent to a Force with a known Line of Action

    • Prevent motion of a body in one direction only
    • Rollers, Rockers, Frictionless Surfaces
    • Short Links and Cables
    • Collars on Frictionless Rods and Frictionless Pin in slots
  • Reactions equivalent to a force of unknown direction and magnitude

    • Prevent motion in all directions (movements along x- and y- axes) of a body but not rotational motion
    • Pins/Smooth Pins/Frictionless Pins in Fitted Holes
    • Hinges, Rough Surfaces
  • Reactions equivalent to a force and a couple
    • Prevent all types of motion in all directions of a body (full constraint)
    • Fixed Supports
  • Equilibrium of Rigid Body in 2D
    No net translational ( 𝐹𝑥 = 0 ; 𝐹𝑦 = 0) and rotational motion ( 𝑀 = 0)
  • Two-Force Body

    • A body in equilibrium in which all forces are acting on only two points in the body with no couple moments
    • These forces can be summarized/simplified as Tension or Compressive Forces since these forces will cancel each other out to maintain the body's equilibrium
    • In the two points of application, the resultant forces should be equal in magnitude but opposite in direction
  • Three-Force Body
    • A body in equilibrium in which all forces are acting on only three points in the body with no couple moments
    • Condition for Moment Equilibrium: The three forces are concurrent OR The three forces are parallel
    • If the three forces are parallel, the location of the point of intersection of the forces will approach infinity
  • Truss
    • Frameworks composed of members connected at their ends to form a rigid structure and are composed solely of two-force members
    • Ends of truss members are welded, riveted, or connected by bolts/pins resulting to a pattern of triangles
    • Plane Truss – truss in 2D | Space Truss – truss in 3D
    • Built to support loads and are usually stationary
  • Assumptions of Plane Truss Analysis
    • Analysis is two-dimensional
    • All external loads are applied at the points of connection (joints)
    • Weights of the members are negligible
    • All members are two-force members subjected to tensile or compressive forces
  • Truss Joints
    Points of connections of a truss formed by bolting or welding the ends of the members to a common plate
  • Zero-Force Member

    • A truss member which does not experience internal force or has zero-member force
    • Case 1: If only two noncollinear members form a truss joint and no external load or support reaction is applied to the joint, the two members are both zero-force members
    • Case 2: If three members form a truss joint for which two of the members are collinear, the third member is a zero-force member provided that, there is no applied external force or support reaction on that joint
    • Special Case of Case 2: If two members form a truss joint in which one of them is collinear to an external force applied to the joint, then the other member is a zero-force member
  • Method of Joints
    • Truss Analysis is done joint by joint
    • Each truss joint is treated as a particle
    • Only summations of forces can be used in each FBD (no summations of Moment)
  • Method of Sections
    • Truss Analysis is done section by section
    • Each section is treated as a rigid body
    • Summations of forces and moments can be used in each FBD
    • Cutting plane passes through a member only once
    • Commonly used when we need to find the force in only a few members of the truss
  • Frame
    • Composed of at least one multi-force member unlike trusses
    • Built to support loads and are normally fixed
  • Assumptions of Frame Analysis
    • The joints that connect the members of a frame are not necessarily located at the ends of the members (unlike Truss)
    • The members are joined together by smooth pins
  • There is a corresponding set of action-reaction forces in a point of connection where a frame member is dismembered or disconnected. These forces will not appear unless the member is dismembered from the point/s of connections.
  • Machine
    • Like Frames, it is composed of at least one multi-force member
    • Built to transmit and multiply input forces
    • May or may not be stationary and will always contain moving parts
    • Have irregularly shaped members
  • Procedure on Machine Analysis is the same as Frame Analysis
  • Pin
    • Type of connector in structures that can resist translation but not rotation
    • If a pin connects two or more bodies, it is recommended to treat the pin as a separate body or consider it to be part of a specifically identified body
  • There is a corresponding set of action-reaction forces between a pin and a member when the pin is disconnected or dismembered. If the pin is reconnected, these action-reaction forces will disappear since they will cancel each other.