Specific Weight of Truncated Conical Rod Calculator

Specific Weight of Truncated Conical Rod using its Elongation due to Self Weight

Specific Weight Formula:

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

Elongation:

Length of Bar:

Diameter 1:

Diameter 2:

Young's Modulus:

Specific Weight: N/m³

1. What is Specific Weight of Truncated Conical Rod?

Definition: This calculator determines the specific weight (weight per unit volume) of a truncated conical rod based on its elongation due to self-weight.

Purpose: It helps engineers analyze the material properties of tapered rods under their own weight.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \gamma \) — Specific weight (N/m³)
\( \delta l \) — Elongation (m)
\( l \) — Length of bar (m)
\( d_1 \) — Diameter at one end (m)
\( d_2 \) — Diameter at other end (m)
\( E \) — Young's Modulus (Pa)

Explanation: The formula relates the rod's elongation under its own weight to its material properties and geometry.

3. Importance of Specific Weight Calculation

Details: Calculating specific weight helps in material selection, structural analysis, and predicting deformation under self-weight.

4. Using the Calculator

Tips: Enter all dimensions in meters. Young's Modulus defaults to 20 GPa for steel. All values must be positive and diameters must be different.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated conical rod?
A: It's a rod with circular cross-section that tapers linearly from one diameter to another.

Q2: Why does the rod elongate under its own weight?
A: The weight of the material itself creates tensile stress that causes elongation.

Q3: What's a typical Young's Modulus for steel?
A: About 200 GPa (200,000,000,000 Pa) for most steels.

Q4: Can I use this for other materials?
A: Yes, as long as you input the correct Young's Modulus for the material.

Q5: What if my diameters are equal?
A: The formula doesn't work for cylindrical rods (equal diameters) - use a different formula for uniform cross-sections.