Five steps of displacement method:

Step 1: Define a coordinate system for unknown joint displacements with sense, define matrix of

required actions with positive sense.

, .

Step 2: Determine restraining actions (along the coordinates) and required actions due to applied

load cases on fully restrained structure (fixed end actions).

This means find F1, F2, and F3 also find the required actions

, .

Step 3: Turn by turn apply unit displacements along the degrees of freedom and determine actions

along all coordinates. This gives the stiffness matrix . Also find the required actions due to unit

displacements applied turn by turn which gives the matrix of required actions due to unit

displacements .

, .

Step 4: Solve the equilibrium equations.

, where is the matrix of displacements produces on the actual structure

(displacements along the coordinates).

Step 5: Using equation of superposition determine the matrix of required actions .

.