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STATICS - THEORY

     
   

Frames and machines are structures similar to trusses except that they have at least one member that is a multi-force member. A multi-force member is an independent piece of the system that has three or more forces acting on it.

Frames are designed to support loads and are generally stationary. Machines contain moving parts that transmit or alter applied forces.

     

  Equilibrium

 

Begin by isolating each segment of the frame and labeling the known and unknown forces. This is usually done by choosing free-body diagrams that provide the simplest path to a solution. These diagrams may consist of single members, sections, or entire structures.

Next, identify two-force members and represent the forces with two equal and opposite vectors that act along the line of action.

Determine which forces are shared by more than one member. It is important that the forces are represented correctly on each member. This means that the forces represented on one member will be opposite in direction on another.

Verify that the number of unknowns does not exceed the equilibrium equations. There are three equilibrium equations that can be used per member for 2D frames,

     ΣFx = 0     ΣFy = 0     ΣMz = 0

Finally, use the equations of equilibrium to solve the problem.

     
   
 
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