video : https://www.youtube.com/watch?v=9bnFVE88PaM&list=PLQVMpQ7G7XvHrdHLJgH8SeZQsiy2lQUcV&index=15

• here is the global stiffness matrix for a single truss element
• we will need one with varying $\theta$ values for each element

• A = cross sectional area
• L = length
• E = Youngs modulous
• v = Poisson Ratio

• now we have our three global stiffness matrixs
• since we have 3 nodes each with 2 DOFs, we get:

• for the first stiffness matrix (first element)

  • it corresponds to nodes 1 and 2 and we can see the displacements accordingly

• this means we know which k values it will affect

• for each of the invdividual stiffness matrixes for each element, we need to sum the k values to build the total global stiffness matrix

• $[k]_1$,

• $[k]_2$,

• $[k]_3$

• (we need to make an algo to build the right matrix using node indexs in the structures node list)
• finally we have the global stiffness matrix for the structure