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MECHANICS - EXAMPLE

    Example


Two Member Structure
 

What is the internal moment at section a-a?

   
    Solution


Reaction Forces
 

Before a member can be cut, the reaction loads at the supports need to be determined. Since both members AB and CB are two force members, the direction of the reaction force at A and C are known. Considering the full structure, summation of forces at C gives

     ΣMC = 0
     -15(10) + FAB cos45 = 0
     FAB = 212.1 N

     


Member Cut at a-a

 

Member AB can now be cut member at a-a. At the cut, both the shear and moment internal forces are unknowns. The vertical and horizontal components of the force FAB are

     FAB-x = FAB-y = FAB / cos45 = 150 N

Vertical and horizontal distances are shown on diagram. Summing moments at the cut gives,

     ΣMcut = 0
     M + 150(10)(1-cos25) - 150(10)(sin25) = 0

     M = 493.4 N

     
   
 
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