Polar Moment of Inertia of Thickened Hollow Welded Shaft Calculator

Formula Used:

\[ J = 2\pi t r^3 \]

Polar Moment of Inertia (J):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Polar Moment of Inertia of Welded Hollow Shaft?

The Polar Moment of Inertia of Welded Hollow Shaft is defined as the Polar moment of inertia of the welded hollow thickened shaft about its Center of Gravity. It represents the shaft's resistance to torsional deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ J = 2\pi t r^3 \]

Where:

\( J \) — Polar Moment of Inertia of Welded Hollow Shaft (m⁴)
\( t \) — Thickness of welded shaft (m)
\( r \) — Radius of welded shaft (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the polar moment of inertia for a hollow welded shaft based on its thickness and radius.

3. Importance of Polar Moment of Inertia Calculation

Details: Accurate calculation of polar moment of inertia is crucial for determining the torsional stiffness of shafts, designing mechanical systems, and ensuring structural integrity under torsional loads.

4. Using the Calculator

Tips: Enter thickness and radius in meters. Both values must be positive numbers. The calculator will compute the polar moment of inertia in meters to the fourth power (m⁴).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of polar moment of inertia in shaft design?
A: Polar moment of inertia determines a shaft's resistance to twisting and is essential for calculating torsional stress and deflection.

Q2: How does thickness affect the polar moment of inertia?
A: The polar moment of inertia increases linearly with thickness - doubling the thickness doubles the polar moment of inertia.

Q3: How does radius affect the polar moment of inertia?
A: The polar moment of inertia increases with the cube of the radius - doubling the radius increases the polar moment of inertia by a factor of eight.

Q4: What are typical units for polar moment of inertia?
A: In the SI system, polar moment of inertia is measured in meters to the fourth power (m⁴).

Q5: When is this formula applicable?
A: This formula is specifically for calculating the polar moment of inertia of thickened hollow welded shafts with uniform thickness.