Shaft Length For Given Maximum Permissible Shear Stress And Modulus Of Rigidity Calculator

Formula Used:

\[ L_{shaft} = \frac{G_{Torsion} \times \theta \times R}{\tau_{max}} \]

Modulus of Rigidity (G):

Angle of Twist (θ):

rad

Radius of Shaft (R):

Maximum Shear Stress (τ_max):

Length of Shaft (L_shaft):

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1. What is the Shaft Length Formula?

The shaft length formula calculates the length of a shaft based on the modulus of rigidity, angle of twist, radius of the shaft, and maximum permissible shear stress. This is important in mechanical engineering for designing shafts that can withstand torsional loads without failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_{shaft} = \frac{G_{Torsion} \times \theta \times R}{\tau_{max}} \]

Where:

\( L_{shaft} \) — Length of shaft (m)
\( G_{Torsion} \) — Modulus of rigidity (Pa)
\( \theta \) — Angle of twist (rad)
\( R \) — Radius of shaft (m)
\( \tau_{max} \) — Maximum shear stress (Pa)

Explanation: This formula calculates the required length of a shaft to ensure that the maximum shear stress does not exceed the permissible limit under given torsional conditions.

3. Importance of Shaft Length Calculation

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

4. Using the Calculator

Tips: Enter modulus of rigidity in Pascals, angle of twist in radians, radius in meters, and maximum shear stress in Pascals. All values must be positive.

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 under shear stress, defined as 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 under torsion.

Q3: What factors affect maximum shear stress?
A: Maximum shear stress depends on the material properties, cross-sectional geometry, and applied torque.

Q4: Can this formula be used for hollow shafts?
A: This specific formula is for solid circular shafts. Hollow shafts require a different approach that accounts for the inner and outer diameters.

Q5: What are typical values for modulus of rigidity?
A: For steel, G is approximately 79.3 GPa; for aluminum, about 26 GPa; and for brass, around 40 GPa.