Static Equilibium

Page 3
This text is meant to accompany class discussions. It is not everything there is to know about static equilibrium. It is meant as a  prep for class.

Extended Free Body Diagrams

BEAM forces

 

Where beams attach to the wall there exists a pin hinge. The pin hinge exerts a reaction force. This force is broken down into two smaller forces we are calling the vertical force, “V” and a horizontal force “H.” The vertical force, “V,” keep the beam from sliding down the wall. The horizontal force, “H,” keeps the beam from punching through the wall into the building. Identify the reaction force on your free body diagrams and extended free body diagrams two forces.

The weight of the beam is located at the center of mass of the beam. If you were to hold the beam up with one finger, you would lift at the center of mass with a force equal to the weight of the beam. If a beam is described as, "homogeneous," then the center of mass is located in the middle of the beam.

 

An extended free body diagram is used to show forces and distances on the same diagram.

 

This YouTube video can be found at http://goo.gl/4Bj06P

This information shown below is the non-video, abreviated,version of the YouTube video above.

 

This is what a typical problem might look like. It will have some forces that do not all act at the same location.
This is the diagram that shows more than the picture that was given. The cable indictes a tension on the beam. The fact that the beam has mass indicates that is has weight pulling it down. The "R" force is new. It is the reaction force of the wall. This force does two things. If pushes to the right to keep the beam from puncturing the wall and it holds the left end up.

This is the first diagram you write on the paper. Make it large! Notice that is missing all force components.

The body is no longer a dot. It is now a line that shows horizontal distances.

This is the second diagram you write on the paper. Make it large. Use about half the width of the paper. To highlight the differences in the two diagams the components are shown in red.

Click to see an example of what a notebook page looks like with this information.

 

Process for drawing extended freebody diagrams

  1. Draw a line as the body. Draw it the same angle as the body.
  2. Identify all the forces.
  3. Draw the forces at the relative distances along the body.
  4. Label the forces with variables and the distances with numbers and units.
  5. Use trigonometry to break up the forces into components that are parallel and pependicular to the line that was drawn to represent the body. (Makesure the tails of the componenets and the original force are all touching.

 

Practice
  • Question
  • Paper Solution
Draw an extended freebody diagram of the beam for the diagram shown below. The beam is homogeneous and has mass.
Solution

 

 

Practice
  • Question2
  • Paper Solution
Draw an extended freebody diagram of the beam for the diagram shown below. Each mark on beam stands for 1 foot of distance.
Setup image

Here are two possible solutions. There are more... The difference is where the pivot point is placed. The top solution places it on the right. The bottom solution places it on the left. Both solution will work.

The solution below shows the distance as being measured from the other left instead of the right. The distance's starting point can be anywhere.

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by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)