Self Weight of Prismatic Bar with known Elongation Calculator

Formula:

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

Elongation (δl):

Length (L):

Young's Modulus (E):

Tolerance:

Specific Weight (γ):

1. What is Self Weight of Prismatic Bar with known Elongation?

Definition: This calculator determines the specific weight (weight per unit volume) of a prismatic bar based on its elongation under its own weight.

Purpose: It helps engineers and designers calculate the material properties needed to achieve specific deformation characteristics.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \gamma \) — Specific Weight (N/m³)
\( \delta l \) — Elongation (m)
\( L \) — Length of the bar (m)
\( E \) — Young's Modulus (Pa)

Explanation: The formula relates the bar's elongation due to its own weight to its material properties and dimensions.

3. Importance of This Calculation

Details: Understanding how a bar elongates under its own weight is crucial for structural design, especially for tall or long structures where self-weight effects become significant.

4. Using the Calculator

Tips:

Enter elongation in meters (typically small values for most materials)
Length should be the full length of the prismatic bar
Young's Modulus is typically in GPa (1 GPa = 1,000,000,000 Pa)
Tolerance is optional (default ±5%)

5. Frequently Asked Questions (FAQ)

Q1: What is a prismatic bar?
A: A prismatic bar has constant cross-section along its length and is made of homogeneous material.

Q2: Why include tolerance?
A: Tolerance accounts for material variations and measurement uncertainties in real-world applications.

Q3: What are typical Young's Modulus values?
A: Steel ≈ 200 GPa, Aluminum ≈ 70 GPa, Concrete ≈ 30 GPa, Wood ≈ 10 GPa.

Q4: How does length affect the result?
A: Elongation increases with the square of the length, so longer bars show more pronounced effects.

Q5: Can this be used for non-prismatic bars?
A: No, this formula is specifically for prismatic bars with uniform cross-sections.