Shaft Stiffness calculator online free tool will help you calculate shaft stiffness for multi-cross-sectional shafts as shown in the below drawing. Your CAD model stiffness might show slightly different stiffness values.

## What is Shaft stiffness Formula? How to calculate Shaft Stiffness Manually?

We know the Torsion equation right?

Where

*τ*= Shear stress (MPa)*r*= Radius of the shaft (mm)*T*= Torque (Nm)*J*= Polar moment of inertia*G*= Modulus of rigidity or Shear Modulus(MPa)*θ*= Angle of twist (rad)*l*= Length of the shaft

Let us disregard the middle portion of the above equation and only consider the following

Now we rewrite this equation as

Torque divided by angle of twist is known as the stiffness.

This is the Shaft Stiffness Formula that we have used in the above calculation. where k is represented with the shaft stiffness.

where J is the Polar Moment of Inertia

### How to calculate the shaft stiffness for multiple sections?

Well, let us do it for the 5 sections.

Where assume the total stiffness k

k_{1} is the section 1 stiffness, J_{1} is the Polar moment of inertia of section 1, and *l _{1}* is the length of section 1

k_{2} is the section 2 stiffness, J_{2} is the Polar moment of inertia of section 2, and *l _{1}* is the length of section 2

k_{3} is the section 3 stiffness, J_{3} is the Polar moment of inertia of section 3, and *l _{3}* is the length of section 3

k_{4} is the section 4 stiffness, J_{4} is the Polar moment of inertia of section 4, and *l _{4}* is the length of section 4

k_{5} is the section 5 stiffness, J_{5} is the Polar moment of inertia of section 5, and *l _{5}* is the length of section 5

Calculate the stiffness for each section by using the above shaft stiffness formula with as mentioned above parameters.

Now to sum the shaft stiffness together use the following series.

If you have more sections than 5, you can calculate each section’s stiffness and sum them as per the above mention stiffness formula series.

And be careful with the units of each parameter. The unit of the Shaft Stiffness is Nm/rad. Check out the unit converters it might help.

Want to calculate the inertia the same way? Check it Here!

Do you like this Shaft Stiffness calculator?

There are some more useful Engineering calculators for you.