Torsional Shear Stress Of Screw Calculator

Formula Used:

\[ \tau = \frac{16 \times M_{tt}}{\pi \times d_c^3} \]

Torsional Shear Stress in Screw (τ):

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1. What is Torsional Shear Stress in Screw?

Torsional shear stress in screw is the shear stress produced in the screw due to the twisting moment applied. It represents the internal resistance of the screw material to torsional deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \frac{16 \times M_{tt}}{\pi \times d_c^3} \]

Where:

\( \tau \) — Torsional shear stress in screw (Pa)
\( M_{tt} \) — Torsional moment on screw (N·m)
\( d_c \) — Core diameter of screw (m)
\( \pi \) — Archimedes' constant (≈ 3.14159)

Explanation: This formula calculates the maximum shear stress in a circular shaft (screw) subjected to pure torsion, based on the core diameter and applied torsional moment.

3. Importance of Torsional Shear Stress Calculation

Details: Calculating torsional shear stress is crucial for ensuring that screws and fasteners can withstand applied torque without failure. It helps in material selection and determining appropriate safety factors for mechanical designs.

4. Using the Calculator

Tips: Enter torsional moment in Newton-meters (N·m) and core diameter in meters (m). Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the core diameter of a screw?
A: Core diameter of screw is defined as the smallest diameter of the thread of the screw or nut. It is also known as the "minor diameter" in thread terminology.

Q2: How does torsional moment affect screw design?
A: Torsional moment determines the twisting force applied to the screw. Higher torsional moments require larger core diameters or stronger materials to prevent shear failure.

Q3: What are typical units for torsional shear stress?
A: Torsional shear stress is typically measured in Pascals (Pa) or Megapascals (MPa) in the SI system, and pounds per square inch (psi) in the imperial system.

Q4: When is this formula applicable?
A: This formula applies to solid circular shafts (screws) made of homogeneous, isotropic materials that follow Hooke's law and are subjected to pure torsion.

Q5: What safety factors should be considered?
A: Typical safety factors range from 2 to 4 depending on the application, material properties, loading conditions, and consequences of failure.