Modulus of Elasticity of Bar with known elongation of Truncated Conical Rod due to Self Weight Calculator

Young's Modulus Formula:

\[ E = \frac{(γ_{Rod} \times l^2) \times (d_1 + d_2)}{6 \times \delta l \times (d_1 - d_2)} \]

Specific Weight of Rod:

N/m³

Length of Tapered Bar:

Diameter1:

Diameter2:

Elongation:

Young's Modulus (Pa):

1. What is Young's Modulus Calculator for Tapered Rod?

Definition: This calculator determines the modulus of elasticity (Young's Modulus) of a tapered rod based on its elongation under self-weight.

Purpose: It helps engineers and material scientists calculate the elastic properties of conical rods under gravitational loading.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{(γ_{Rod} \times l^2) \times (d_1 + d_2)}{6 \times \delta l \times (d_1 - d_2)} \]

Where:

\( E \) — Young's Modulus (Pa)
\( γ_{Rod} \) — Specific weight of the rod material (N/m³)
\( l \) — Length of the tapered bar (m)
\( d_1 \) — Diameter at one end (m)
\( d_2 \) — Diameter at other end (m)
\( \delta l \) — Elongation (%)

Explanation: The formula relates the elastic deformation of a conical rod to its material properties and geometry.

3. Importance of Young's Modulus Calculation

Details: Young's Modulus is crucial for understanding material stiffness and predicting deformation under load.

4. Using the Calculator

Tips: Enter all dimensions in consistent units. Elongation should be entered as a percentage value.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of typical Young's Modulus values?
A: For metals, it ranges from 45-400 GPa. Rubber might be 0.01-0.1 GPa, while diamond is about 1200 GPa.

Q2: Why does the formula include both diameters?
A: The tapered geometry means the cross-sectional area varies along the length, affecting the stress distribution.

Q3: How accurate is this calculation?
A: It provides theoretical values assuming perfect elasticity and uniform tapering. Real-world factors may affect actual measurements.

Q4: Can I use this for non-tapered rods?
A: No, for uniform rods use the simpler formula \( E = \frac{FL}{A\delta L} \).

Q5: What if my elongation is very small?
A: Ensure precise measurement as small errors in elongation measurement can significantly affect the calculated modulus.