Length Of Shaft With Known Shear Stress Induced At Radius R From Center Of Shaft Calculator

Formula Used:

\[ L_{shaft} = \frac{R \times G_{Torsion} \times \theta_{Torsion}}{\tau} \]

Radius of Shaft (R):

Modulus of Rigidity (G):

Angle of Twist (θ):

rad

Shear Stress in Shaft (τ):

Length of Shaft (L):

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1. What is the Length of Shaft Calculation?

The Length of Shaft with known Shear Stress induced at Radius r from Center of Shaft calculation determines the length of a shaft based on its radius, modulus of rigidity, angle of twist, and shear stress. This is important in mechanical engineering for designing shafts that can withstand torsional loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_{shaft} = \frac{R \times G_{Torsion} \times \theta_{Torsion}}{\tau} \]

Where:

\( L_{shaft} \) — Length of Shaft (m)
\( R \) — Radius of Shaft (m)
\( G_{Torsion} \) — Modulus of Rigidity (Pa)
\( \theta_{Torsion} \) — Angle of Twist (rad)
\( \tau \) — Shear Stress in Shaft (Pa)

Explanation: This formula calculates the required length of a shaft that will experience a specific shear stress when subjected to torsional loading with given material properties and geometric parameters.

3. Importance of Shaft Length Calculation

Details: Accurate shaft length calculation is crucial for designing mechanical systems that transmit torque, ensuring proper stress distribution, and preventing mechanical failure due to excessive torsional stress.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Radius, modulus of rigidity, angle of twist, and shear stress must be positive values greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is Modulus of Rigidity?
A: Modulus of Rigidity (G) is a material property that measures the stiffness of a material when subjected to shear stress. It represents the ratio of shear stress to shear strain.

Q2: How is Angle of Twist measured?
A: Angle of Twist is typically measured in radians and represents the angular displacement between two cross-sections of a shaft when torque is applied.

Q3: What factors affect Shear Stress in a shaft?
A: Shear stress is affected by the applied torque, shaft radius, and material properties. It increases with higher torque and decreases with larger shaft radius.

Q4: When is this calculation most useful?
A: This calculation is particularly useful in mechanical design for determining appropriate shaft dimensions to ensure they can handle specified torsional loads without exceeding material stress limits.

Q5: Are there limitations to this formula?
A: This formula assumes homogeneous, isotropic material properties and applies to circular shafts undergoing elastic deformation. It may not be accurate for non-circular cross-sections or materials with anisotropic properties.