Spring Assemblies in Series/Parallel: Two Springs in Series

Based on Figure 1, we get:

where:

In matrix form, the above can be re-written as:

Example

 Calculate k₁, δ₂, and f₃.

Solution

Based on Figure 2, we have:

and

The system stiffness matrix is:

Therefore, the problem becomes:

Which in turn results in the 3×3 system of equations:

Finally, we get: