Torque To Shear Stress Calculator

Shear Stress Formula:

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

Shear Stress (τ):

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1. What is Shear Stress?

Shear stress (τ) is the component of stress coplanar with a material cross section that arises from forces applied parallel to the surface. It represents the force per unit area acting parallel to the plane of interest.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

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

Where:

\( \tau \) — Shear stress (Pa)
\( T \) — Torque (Nm)
\( r \) — Radius (m)
\( J \) — Polar moment of inertia (m⁴)

Explanation: This formula calculates the maximum shear stress in a circular shaft subjected to torsion, which occurs at the outer surface of the shaft.

3. Importance of Shear Stress Calculation

Details: Calculating shear stress is crucial in mechanical engineering for designing shafts, beams, and other structural elements to ensure they can withstand applied torsional loads without failure.

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 an object's ability to resist torsion. For a solid circular shaft, J = πd⁴/32, where d is the diameter.

Q2: Where does maximum shear stress occur?
A: In a circular shaft under torsion, maximum shear stress occurs at the outer surface where the radius is greatest.

Q3: What are typical shear stress values for materials?
A: Shear stress limits vary by material. Steel typically has allowable shear stress around 0.4-0.6 times its yield strength, while aluminum is around 0.3-0.5 times its yield strength.

Q4: How does shaft diameter affect shear stress?
A: Shear stress is inversely proportional to the polar moment of inertia, which increases with the fourth power of diameter. Thus, slightly increasing diameter significantly reduces shear stress.

Q5: Can this formula be used for non-circular sections?
A: No, this specific formula applies only to circular cross-sections. Non-circular sections require different formulas to calculate shear stress under torsion.