Modulus Of Rigidity Given Angle Of Twist Calculator

Formula Used:

\[ G = \frac{584 \times M_{tshaft} \times L}{\theta \times d_{torl}^4} \]

Torsional Moment in Shaft (M_tshaft):

N·m

Length of Shaft from Torsional Rigidity (L):

Angle of Twist in Shaft (θ):

rad

Diameter of Shaft from Torsional Rigidity (d_torl):

Modulus of Rigidity of Shaft (G):

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1. What is Modulus of Rigidity?

The Modulus of Rigidity (also known as shear modulus) is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a shaft is under torsional loading.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G = \frac{584 \times M_{tshaft} \times L}{\theta \times d_{torl}^4} \]

Where:

\( G \) — Modulus of Rigidity of Shaft (Pa)
\( M_{tshaft} \) — Torsional Moment in Shaft (N·m)
\( L \) — Length of Shaft from Torsional Rigidity (m)
\( \theta \) — Angle of Twist in Shaft (rad)
\( d_{torl} \) — Diameter of Shaft from Torsional Rigidity (m)

Explanation: This formula calculates the modulus of rigidity based on the torsional properties of a shaft, relating the applied torque to the resulting angle of twist.

3. Importance of Modulus of Rigidity Calculation

Details: Calculating the modulus of rigidity is crucial for designing shafts and other structural elements that experience torsional loading. It helps engineers ensure that components can withstand applied torques without excessive deformation.

4. Using the Calculator

Tips: Enter all values in the specified units. Torsional moment should be in Newton-meters, length and diameter in meters, and angle of twist in radians. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the constant 584 in the formula?
A: The constant 584 is derived from unit conversions and mathematical simplification of the fundamental torsion formula to make calculations more convenient.

Q2: How does shaft diameter affect the modulus of rigidity?
A: The modulus of rigidity is inversely proportional to the fourth power of the diameter, meaning small changes in diameter significantly affect the calculated modulus.

Q3: What are typical values of modulus of rigidity for common materials?
A: For steel, it's typically around 79.3 GPa; for aluminum, about 26 GPa; and for copper, approximately 44 GPa.

Q4: Why is the angle of twist measured in radians?
A: Radians are used because they are the natural unit for angular measurements in mathematical calculations involving circular functions.

Q5: Can this formula be used for non-circular shafts?
A: No, this specific formula is derived for circular shafts. Different formulas apply to shafts with other cross-sectional shapes.