Elongation of Truncated Conical Rod due to Self Weight Calculator

Elongation Formula:

\[ \delta l = \frac{(\gamma_{Rod} \times l^2) \times (d1 + d2)}{6 \times E \times (d1 - d2)} \]

Specific Weight of Rod:

N/m³

Length of Tapered Bar:

Diameter1:

Diameter2:

Young's Modulus:

Elongation (m):

Elongation (%):

1. What is Elongation of Truncated Conical Rod?

Definition: This calculator computes the elongation of a tapered rod due to its own weight, considering the variation in diameter along its length.

Purpose: It helps mechanical engineers and designers understand how much a conical rod will stretch under its own weight.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta l = \frac{(\gamma_{Rod} \times l^2) \times (d1 + d2)}{6 \times E \times (d1 - d2)} \]

Where:

\( \delta l \) — Elongation (meters)
\( \gamma_{Rod} \) — Specific weight of rod material (N/m³)
\( l \) — Length of tapered bar (meters)
\( d1 \) — Diameter at one end (meters)
\( d2 \) — Diameter at other end (meters)
\( E \) — Young's Modulus of material (Pascals)

Explanation: The formula accounts for the varying cross-sectional area along the length of the conical rod.

3. Importance of Elongation Calculation

Details: Understanding elongation helps in designing structures where self-weight deformation must be minimized or accounted for in the design.

4. Using the Calculator

Tips: Enter all required parameters in consistent units. Ensure diameter1 and diameter2 are different values.

5. Frequently Asked Questions (FAQ)

Q1: What happens if diameters are equal?
A: The formula becomes undefined (division by zero). The rod would be cylindrical, not conical.

Q2: What are typical Young's Modulus values?
A: Steel: ~200 GPa, Aluminum: ~70 GPa, Concrete: ~30 GPa.

Q3: How does elongation vary with length?
A: Elongation increases with the square of the length (l² term in formula).

Q4: What's the practical significance of this calculation?
A: Critical for tall structures, suspension systems, and any application where self-weight deformation affects performance.

Q5: Does this include external loads?
A: No, this calculates only the elongation due to self-weight. External loads would require additional calculations.