Shear Stress At Surface Of Shaft Using Shear Stress-induced At Radius 'r' From Center Of Shaft Calculator

Formula Used:

\[ \text{Shear Stress at Radius r} = \frac{\text{Shear Stress in Shaft} \times \text{Radius from Center to Distance r}}{\text{Radius of Shaft}} \] \[ T_r = \frac{\tau \times r}{R} \]

Shear Stress in Shaft (τ):

Pascal

Radius from Center to Distance r (r):

Meter

Radius of Shaft (R):

Meter

Shear Stress at Radius r (T_r):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Shear Stress at Radius r?

Shear Stress at Radius r from shaft is a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. When a shaft is subjected to torque or twisting, shearing stress is produced in the shaft.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_r = \frac{\tau \times r}{R} \]

Where:

\( T_r \) — Shear Stress at Radius r (Pascal)
\( \tau \) — Shear Stress in Shaft (Pascal)
\( r \) — Radius from Center to Distance r (Meter)
\( R \) — Radius of Shaft (Meter)

Explanation: This formula calculates the shear stress at any radial distance r from the center of a shaft based on the maximum shear stress at the surface and the geometry of the shaft.

3. Importance of Shear Stress Calculation

Details: Calculating shear stress distribution in shafts is crucial for mechanical design, structural analysis, and ensuring that materials can withstand applied torques without failure. It helps engineers determine stress concentrations and design shafts with appropriate safety factors.

4. Using the Calculator

Tips: Enter shear stress in Pascal, both radii in meters. All values must be positive numbers. The radius from center to distance r should be less than or equal to the radius of the shaft for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between shear stress and radius in a shaft?
A: Shear stress increases linearly with radius from the center of the shaft. Maximum shear stress occurs at the outer surface of the shaft.

Q2: When is this formula applicable?
A: This formula applies to circular shafts subjected to pure torsion and assumes linear elastic material behavior.

Q3: What are typical units for these measurements?
A: Shear stress is typically measured in Pascals (Pa) or Megapascals (MPa), while radii are measured in meters (m) or millimeters (mm).

Q4: How does shaft material affect shear stress calculations?
A: The formula calculates stress based on geometry and applied torque. Material properties determine whether the shaft will yield or fail under the calculated stress.

Q5: Can this formula be used for hollow shafts?
A: This specific formula is derived for solid circular shafts. Different formulas apply for hollow shafts with annular cross-sections.