Shear Stress in Key Given Torque Transmitted Calculator

Shear Stress in Key Formula:

\[ \text{Shear Stress in Key} = \frac{2 \times \text{Transmitted Torque by Keyed Shaft}}{\text{Width of Key} \times \text{Length of Key} \times \text{Diameter of Shaft using Key}} \]

Transmitted Torque by Keyed Shaft (Mt):

N·m

Width of Key (bk):

Length of Key (l):

Diameter of Shaft using Key (ds):

Shear Stress in Key:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Shear Stress in Key?

Shear Stress in Key is the force per unit area tending to cause deformation of the key by slippage along a plane or planes parallel to the imposed stress. It is a critical parameter in mechanical design to ensure proper torque transmission between shafts and connected components.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

\[ \text{Shear Stress in Key} = \frac{2 \times \text{Transmitted Torque by Keyed Shaft}}{\text{Width of Key} \times \text{Length of Key} \times \text{Diameter of Shaft using Key}} \]

Where:

Transmitted Torque by Keyed Shaft (Mt) - Torque transferred from a shaft using a key (N·m)
Width of Key (bk) - Width of the key fixed between shaft and hub (m)
Length of Key (l) - Length of the key used to prevent rotation (m)
Diameter of Shaft using Key (ds) - External surface diameter of shaft using a key (m)

Explanation: The formula calculates the shear stress distribution in the key based on the transmitted torque and key/shaft dimensions.

3. Importance of Shear Stress Calculation

Details: Accurate shear stress calculation is crucial for ensuring that keys can safely transmit torque without failure. It helps prevent mechanical failures and ensures reliable operation of power transmission systems.

4. Using the Calculator

Tips: Enter transmitted torque in N·m, width of key in meters, length of key in meters, and diameter of shaft in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for shear stress in keys?
A: Shear stress values depend on material properties, but typically range from 20-100 MPa for steel keys in mechanical applications.

Q2: How does key material affect shear stress calculation?
A: Different materials have different shear strength limits. The calculated stress must be compared to the material's allowable shear stress.

Q3: What factors influence key design besides shear stress?
A: Key design also considers crushing stress, keyway dimensions, material compatibility, and manufacturing constraints.

Q4: When should I use this calculation?
A: This calculation is essential when designing or analyzing keyed connections in power transmission systems, machinery, and rotating equipment.

Q5: Are there limitations to this formula?
A: This formula assumes uniform stress distribution and may not account for stress concentrations at keyway corners or dynamic loading conditions.