JohnsonFormulaCalculator

Introduction

The JohnsonFormulaCalculator is designed to calculate the diameter of a shaft based on the Johnson formula, which is commonly used in mechanical engineering to determine the size of shafts required to support axial loads while maintaining specific deflection constraints.

How to Use

1. Enter the axial load (P) in Newtons (N).
2. Enter the Young's Modulus (E) of the material in Pascals (Pa).
3. Enter the Shear Modulus (G) of the material in Pascals (Pa). Note: Shear Modulus is not used in the current calculation but may be needed for more advanced applications.
4. Enter the maximum allowable deflection (δ) in meters (m).
5. Enter the length of the shaft (L) in meters (m).
6. Click the "Calculate" button to compute the required diameter.
7. The result will be displayed in meters (m).

Johnson Formula Explanation

The Johnson formula used in this calculator is:

d = √(32 * P * L / (π * E * δ))

Where:

• d = Diameter of the shaft (m)
• P = Axial load (N)
• L = Length of the shaft (m)
• E = Young's Modulus (Pa)
• δ = Maximum deflection (m)

Applications

This calculator is useful in various engineering applications including:

• Design of mechanical shafts in vehicles and machinery
• Structural analysis in construction
• Manufacturing processes where shaft dimensions are critical