Free body diagrams

• lets convert these local variables (with the hat) to local (without the hat)

• using continuity (the fact we dont allow the structure to break at node 2) we can say:

  

• using equilibrium:

  

• now we want to try finding each of the $f_{nx}$

• finally we can build the global stiffness matrix:

• apply boundary conditions and forces and solve
  • reaction force at node one ⇒ $f_{1x}$ is unknown
  • no external forces at node 2 ⇒ $f_{2x}$ = 0
  • force applied at node 3 ⇒ $f_{3x}$ = F
  • node 1 is fixed ⇒ $d_{1x}$ = 0