Shear Stress On Cylinder Given Torque Exerted On Inner Cylinder Calculator

Formula Used:

\[ \text{Shear Stress} = \frac{T}{2\pi r_1^2 h} \]

Shear Stress (τ):

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1. What is Shear Stress on Cylinder?

Shear stress on a cylinder refers to the tangential force per unit area acting on the surface of the cylinder. In the context of torque transmission, it represents the stress that causes the material to deform by sliding along planes parallel to the applied torque.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \frac{T}{2\pi r_1^2 h} \]

Where:

\( \tau \) — Shear stress (Pa)
\( T \) — Torque on inner cylinder (N·m)
\( r_1 \) — Radius of inner cylinder (m)
\( h \) — Height of cylinder (m)
\( \pi \) — Mathematical constant (approximately 3.14159)

Explanation: This formula calculates the shear stress on the surface of an inner cylinder when torque is applied, considering the geometry of the cylinder.

3. Importance of Shear Stress Calculation

Details: Calculating shear stress is crucial for designing mechanical components, analyzing material strength, and ensuring structural integrity in rotating systems and fluid mechanics applications.

4. Using the Calculator

Tips: Enter torque in Newton-meters, radius and height in meters. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for input values?
A: Use Newton-meters (N·m) for torque, and meters (m) for both radius and height measurements.

Q2: Why is the radius squared in the denominator?
A: The radius is squared because the torque distribution and resulting shear stress depend on the cross-sectional area moment, which involves the square of the radius.

Q3: Can this formula be used for hollow cylinders?
A: This specific formula is designed for solid inner cylinders. For hollow cylinders, additional factors need to be considered in the calculation.

Q4: What is the typical range of shear stress values?
A: Shear stress values vary widely depending on the material and application, ranging from a few Pascals for fluids to megapascals for structural materials.

Q5: How does cylinder height affect shear stress?
A: Shear stress is inversely proportional to cylinder height - longer cylinders experience lower shear stress for the same applied torque.