Elongation due to Self Weight in Prismatic Bar Calculator

Elongation Formula:

\[ \delta l = \frac{\gamma_{Rod} \times L^2}{E \times 2} \]

Elongation (δl):

1. What is Elongation due to Self Weight in Prismatic Bar?

Definition: This calculator computes the elongation of a prismatic bar under its own weight, which is an important consideration in structural engineering.

Purpose: It helps engineers determine how much a vertical bar will stretch due to its own weight, which is crucial for designing tall structures and suspension systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta l = \frac{\gamma_{Rod} \times L^2}{E \times 2} \]

Where:

\( \delta l \) — Elongation (meters)
\( \gamma_{Rod} \) — Specific weight of the rod (N/m³)
\( L \) — Length of the rod (meters)
\( E \) — Young's Modulus (Pascals)

Explanation: The elongation is proportional to the square of the length and the specific weight, and inversely proportional to Young's Modulus.

3. Importance of Elongation Calculation

Details: Proper elongation estimation ensures structural integrity, prevents overstressing of materials, and helps in designing components with appropriate tolerances.

4. Using the Calculator

Tips: Enter the specific weight of the material in N/m³, length in meters, and Young's Modulus in Pascals. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is typical Young's Modulus for steel?
A: For structural steel, Young's Modulus is typically around 200 GPa (200 × 10⁹ Pa).

Q2: How does length affect elongation?
A: Elongation increases with the square of the length, so doubling the length quadruples the elongation.

Q3: What's the specific weight of common materials?
A: Steel: ~78,500 N/m³, Aluminum: ~27,000 N/m³, Concrete: ~24,000 N/m³.

Q4: Is this calculation only for vertical bars?
A: Yes, this formula specifically applies to vertically hanging prismatic bars under their own weight.

Q5: How accurate is this calculation?
A: It provides theoretical values under ideal conditions. Actual elongation may vary ±5% due to material imperfections and environmental factors.