video :https://www.youtube.com/watch?v=DkoOLIPYSuI&list=PLQVMpQ7G7XvHrdHLJgH8SeZQsiy2lQUcV&index=16

• from the previous section here, we had got the global stiffness matrix of the structure
• in the above image we apply the boundary conditions and external forces
  • node 1 is resting on a horizontal roller
    • ⇒ reaction force in y but not x ⇒ $f_{1x}$ = 0 , $f_{1y}$ = ?
    • ⇒ fixed in y but not x ⇒ $d_{1x}$ = ? and $d_{1y}$ = 0
  • node 2 is a free node but an external force in the y
    • ⇒ $f_{2x}$ = 0 , $f_{2y}$ = F = -100
    • ⇒ free in both x and y ⇒ $d_{2x}$ = ? and $d_{2y}$ = ?
  • node 3 is fixed on x and y axis
    • ⇒ $f_{3x}$ and $f_{3y}$ = ?
    • ⇒ fixed in both x and y ⇒ $d_{3x}$ = 0 and $d_{3y}$ = 0

solving the system we get: