Rotational Stiffness Calculator

The rotational stiffness calculator determines a body's rotational stiffness using the angle of rotation and the applied momentum. The rotational stiffness is important to study to assess an object's ability to deform under loading conditions. The application of the concept can be found in different studies involving turbines, vibrations, and springs. Read on to understand the rotational stiffness formula and how to calculate rotational stiffness.

Before explaining rotational stiffness, let's take a look at stiffness. The stiffness is a property of a body that is defined as the resistance to deformation under loads. The stiffness of a body $k$ can be written as the ratio of force applied $F$ to the displacement $\delta$ produced due to the force as:

Similarly, the rotational stiffness is defined as the property of a body to resist rotation or the ratio of applied momentum $M$ to the angle of rotation $\Theta$. Mathematically, the rotational stiffness equation can be written as:

Follow the steps below to calculate the rotational stiffness of a body, using this calculator:

• Step 1: Enter the value of applied momentum.
• Step 2: Insert the value of rotation angle in radians.
• Step 3: The calculator will now return the value of rotational stiffness.

Find the rotational stiffness of an object rotated to an angle of $0.7$ radians, having applied momentum of $16\ \mathrm{N\cdot m}$.

• Step 1: Enter the value of applied momentum, $M =16\ \mathrm{N\cdot m}$.
• Step 2: Insert the value of rotation angle in radians, $\Theta = 0.7$ radians.
• Step 3: The calculator will now use the rotational stiffness equation:

Therefore, to deform the object, it would take $22.857\ \mathrm{N\cdot m}$ of momentum per every radian of rotation.

Did you know?

• Rotational stiffness is used in foundations and construction work. The rotational stiffness formula is used to estimate the stiffness of a circular foundation subjected to rocking motion.
• Rotational stiffness is also significant in building construction, to calculate the rigidity of individual structural elements, beams, columns, arches.
• The parameter is also associated with mechanical components such as wings of an aircraft, and building and construction components as chimneys, where crossflow winds can induce vibrations.
• The design and construction of offshore wind turbine platforms also takes rotational stiffness into account to design for maximum stability whilst it floats in the ocean among different intensities of water waves.

The stiffness is a property of a body to resist deforming under loads. Mathematically, stiffness is the ratio of force applied to displacement.

Rotational stiffness is defined as ratio of the applied momentum to the angle of rotation. In other words, the amount of applied momentum required per radian of rotation.

Rotational stiffness is measured in kiloNewton meter per radian (kN · m/rad) or kiloNewton meter per degree Nmº.

To calculate rotational stiffness: Divide the applied momentum by the angle of rotation.