In most mechanical applications, spring combinations are very common. Spring combinations mean that multiple springs are attached to the system or to each other to obtain the required mechanical system.

Springs are generally combined in a serial and parallel manner. And this combination must be considered in the total stiffness value of the spring system.

Here we explain how to calculate the stiffness of the parallel and serial combination springs.

## Stiffness Calculation In Spring Combinations

As we stated above, spring systems are considered serial or parallel. And the calculation of the spring coefficients which are also called stiffness is very simple.

### Parallel Combined Springs

The parallel spring systems are like above as you see in general. If you consider these two springs are combined as parallel, the total stiffness of this parallel spring system is calculated like below;

As you understand from this equation, the stiffness’ of individual springs of a parallel system is summed up directly. This means that if you want to obtain a more stiff spring system in your physical model, you can combined multiple springs as parallel.

### Serial Combined Springs

If the individual springs are combined like above, the total spring system is called serial springs. The total stiffness calculation of the serial spring systems is different from the parallel system.

As you see in the calculation, the reverse of the total stiffness of the serial spring system with respect to multiplication is equal to the summation of the reverse of individual stiffness’ of the springs with respect to multiplication again.

### Complex Spring Combinations

With these two calculation principles, you can easily calculate the total stiffness of complex spring systems. In the calculation of these systems, you must start the calculation from the small system to the bigger system. Select the small system inside the whole system, which is most far away from the load or loads.

## Conclusion

As you see above that dealing with the spring combinations is very simple in mechanics.

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