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MECHANICS - CASE STUDY

    Introduction


Cantilever Beam Used to move
Electronic Parts

 

The boss just reviewed your work for the electronic part assembly system, and he does not think the tip deflection is correct (it was previously calculated using the moment-curvature equation in the previous section and was found to be 0.2120 mm).

Recall, a mechanical assembly system moves sensitive electronic parts from one location to another using a cantilever beam. The beam has two sections as shown in the diagram. The electronic parts will only be located on the extended section of the beam. The deflection of the beam tip is critical in the assembly process.

What is known:

  • A solid steel beam supports electronic parts over half of the beam.
  • The parts have an average weight of 0.04 N/mm2.
  • The steel stiffness, E, is 200 GPa.
  • The two beam parts are rigidly connected.
  • The beam is attached to the delivery mechanism and the connection can be assumed to be fixed.
     
    Question

   

What is the deflection of the beam tip using a method other than the moment-curvature equation?

     
    Approach

   
  • Modify the area load to a linear load.
  • Determine the moment of inertia of both beam sections.
  • Use the load-deflection differential equation to determine the deflection.

         EIv´´´´ = -w(x)

  • Identify the boundary conditions (four for each beam section).
  • Integrate the load-deflection equation to find the deflection equations.
     
   
 
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