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 previouslyattached 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 aForce 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)
FixedSupports
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 composedsolelyoftwo-forcemembers
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 twononcollinear members form a truss joint and noexternalloadorsupport reaction is applied to the joint, the two members are bothzero-force members
Case 2: If threemembers form a truss joint for which two of the members are collinear, the thirdmember is a zero-force member provided that, there is noapplied external force or support reaction on that joint
Special Case of Case 2: If twomembers form a truss joint in which one of them iscollinear to an externalforce 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 amember when the pin is disconnected or dismembered. If the pin is reconnected, these action-reaction forces will disappear since they will cancel each other.