Modulus of Elasticity using Elongation of Circular Tapering Rod Calculator

Young's Modulus Formula:

\[ E = \frac{4 \times W \times L}{\pi \times \delta l \times d1 \times d2} \]

Applied Load:

Length:

Elongation:

Diameter 1:

Diameter 2:

Young's Modulus (Pa):

1. What is Modulus of Elasticity?

Definition: Young's Modulus is a mechanical property of linear elastic solid substances that describes the relationship between longitudinal stress and longitudinal strain.

Purpose: This calculator determines Young's Modulus for a circular tapering rod based on elongation under applied load.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{4 \times W \times L}{\pi \times \delta l \times d1 \times d2} \]

Where:

\( E \) — Young's Modulus (Pascals)
\( W \) — Applied Load (Newtons)
\( L \) — Length of the rod (meters)
\( \delta l \) — Elongation (percentage)
\( d1 \) — Diameter at one end (meters)
\( d2 \) — Diameter at other end (meters)

Explanation: The formula calculates the stiffness of a tapering rod by considering the applied force, dimensional changes, and material deformation.

3. Importance of Young's Modulus

Details: Young's Modulus is crucial for material selection in engineering applications, predicting how materials will deform under stress.

4. Using the Calculator

Tips: Enter all required values in appropriate units. Elongation should be entered as a percentage (e.g., 2 for 2%).

5. Frequently Asked Questions (FAQ)

Q1: Why is elongation input as a percentage?
A: Elongation is typically measured as a percentage of the original length, making it more intuitive for practical applications.

Q2: What's a typical Young's Modulus for steel?
A: Steel typically has a Young's Modulus around 200 GPa (200 × 10⁹ Pa).

Q3: How does tapering affect the calculation?
A: The formula accounts for tapering by using both diameters, unlike simpler formulas for uniform rods.

Q4: Can I use this for non-circular cross-sections?
A: No, this formula is specifically for circular tapering rods.

Q5: What if my rod has uniform diameter?
A: Simply enter the same value for both diameters (d1 and d2).