Torsion Stress Calculator

Torsion Stress Formula:

\[ \tau = \frac{T \cdot r}{J} \]

Torsional Shear Stress (τ):

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1. What is Torsional Shear Stress?

Torsional shear stress (τ) is the shear stress produced in a material when it is subjected to twisting forces or torque. It occurs in shafts, beams, and other structural elements that experience rotational forces.

2. How Does the Calculator Work?

The calculator uses the torsion stress formula:

\[ \tau = \frac{T \cdot r}{J} \]

Where:

\( \tau \) — Torsional shear stress (Pa)
\( T \) — Applied torque (Nm)
\( r \) — Radius from center to point of interest (m)
\( J \) — Polar moment of inertia (m⁴)

Explanation: The formula calculates the shear stress at a specific point in a circular shaft subjected to torsion, where stress is proportional to torque and radius, and inversely proportional to polar moment of inertia.

3. Importance of Torsion Stress Calculation

Details: Accurate torsion stress calculation is crucial for designing shafts, axles, and other rotating components to ensure they can withstand applied torques without failure or excessive deformation.

4. Using the Calculator

Tips: Enter torque in Newton-meters (Nm), radius in meters (m), and polar moment of inertia in meters to the fourth power (m⁴). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is polar moment of inertia?
A: Polar moment of inertia (J) is a measure of a shaft's resistance to torsion. For solid circular shafts, J = πd⁴/32, where d is the diameter.

Q2: How does radius affect torsion stress?
A: Torsion stress increases linearly with radius. Maximum stress occurs at the outer surface of the shaft.

Q3: What are typical units for torsion stress?
A: Torsion stress is typically measured in Pascals (Pa) or Megapascals (MPa) in the SI system, and psi or ksi in the imperial system.

Q4: Does this formula work for non-circular sections?
A: No, this formula is specifically for circular cross-sections. Non-circular sections require different formulas for torsion stress calculation.

Q5: What is the maximum shear stress theory?
A: Also known as Tresca's theory, it states that yielding occurs when the maximum shear stress in a material reaches the shear yield strength.