What is Stiffness of Springs in Parallel and Series? Explained in 1-Minute

Springs in Parallel

Springs in parallel can be considered to work together. The equivalent stiffness of the springs is the sum of all the springs in parallel. We can consider the following example:

In the above case, the equivalent stiffness will be:

Equivalent stiffness,

Springs in Series

For springs in series, they do not work directly together compared to those in parallel.

For the case above, the equivalent stiffness can be calculated as follows:

Equivalent stiffness,

Applications in Structural Analysis

Let's consider the building frame below...

The columns in the first floor can be considered as have their lateral stiffness in parallel. Similarly for the second floor. The floor slabs can be considered as assembled masses. Therefore we can idealise the building as being made of equivalent "lumped" springs, as follows:

Where...

1F equivalent lateral stiffness:
2F equivalent lateral stiffness:

With this new lumped-mass model, we can find the independent deflection of each floor, or we can perform modal analysis to find the natural frequencies of vibration.

By the way, in order to do such an analysis (by hand), you need to calculate the lateral stiffness of each individual element. Read more about it at the following link:

※ What is Lateral Stiffness? Examples and Formulas