: Find the nodal forces and moments in element 1.

We will use the element stiffness matrix along with the nodal displacements and rotations that we found earlier, to find the unknown forces and moments in element 1. The FEM equation for element 1, with the values for the nodal displacements and rotations substituted, is shown below.

We will find f₃ by multiplying the 1st row of our element stiffness matrix by the column of nodal displacements and rotations for element 1, as follows:

After matrix multiplication, our solution is:

We already should have known the solution for f₃, would be -340 lb (the same as our applied force F₃), but calculating it again, using our FEM equation, is an easy check of our solution procedure. The other unknown force and moments for element 1 can be calculated, by multiplying the column of known displacements and rotations by the remaining rows of the stiffness matrix. The solution for element 1 is:

: Find the nodal forces and moments in element 2.

The nodal forces and moments for element 2 can be found, in the same manner as we found the nodal forces and moments for element 1. It should be noted that node one appears in the FEM equations for both element 1 and element 2, this ensures compatibility by assuring that each element will have the same displacement and rotation at the shared node 1 and therefore these two functions will be continuous throughout the structure. The FEM equation for element 2 follows:

Using the same procedure as for element 1, the solution for element 2 is:

As a check of our solution procedure we can compare our solution for f₂ and m₂ with our solution of F₂ and M₂ from our reaction forces solution. (The 4 lb difference in f₂ and F₂ is a result of rounding error, since all numbers were rounded to 3 significant figures, in order to fit the matrix equations for the total structure, on your computer screen). FEM solutions should be checked, when ever possible, in order to catch any mistakes that may have been made, before the results are used in any analysis.

: Graphical interpretation.

The forces and moments at the shared node 1 in the above figure, have elemental forces and moments (f₁ and m₁) acting in opposite directions. This is necessary in order to satisfy equilibrium within the elements.