Torsional Moment in Screw given Torsional Shear Stress Calculator

Formula Used:

\[ Torsional\ Moment\ on\ Screw = \frac{Torsional\ shear\ stress\ in\ screw \times \pi \times (Core\ diameter\ of\ screw)^3}{16} \] \[ M_{tt} = \frac{\tau \times \pi \times d_c^3}{16} \]

Torsional Moment on Screw (M_tt):

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1. What is Torsional Moment in Screw?

The torsional moment in a screw is the torque applied that generates torsion (twist) within the screw body. It's a crucial parameter in mechanical design that determines the screw's ability to withstand twisting forces without failure.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the maximum torque a screw can withstand based on the material's shear stress limit and the screw's core diameter.

3. Importance of Torsional Moment Calculation

Details: Accurate torsional moment calculation is essential for ensuring screw integrity under twisting loads, preventing mechanical failure, and optimizing screw design for various applications.

4. Using the Calculator

Tips: Enter torsional shear stress in Pascals (Pa) 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 torsional shear stress?
A: Torsional shear stress is the shear stress produced in a material due to twisting forces or torque applied to it.

Q2: Why is core diameter used instead of outer diameter?
A: Core diameter represents the smallest cross-sectional area of the screw, making it the critical section for stress calculations.

Q3: What are typical values for torsional shear stress?
A: Values vary by material, ranging from 50-400 MPa for steel screws to 20-150 MPa for aluminum screws, depending on grade and treatment.

Q4: How does this relate to screw tightening torque?
A: This calculation helps determine the maximum torque that can be applied during tightening without causing shear failure in the screw.

Q5: Are there limitations to this formula?
A: This formula assumes pure torsion and homogeneous material properties. It may need adjustment for complex geometries or combined loading conditions.