Length of Bar using Elongation due to Self Weight in Prismatic bar Calculator

Length Formula:

\[ L = \sqrt{\frac{\delta l}{\left(\frac{\gamma_{Rod}}{E \times 2}\right)}} \]

Length (m):

1. What is Length of Bar using Elongation due to Self Weight?

Definition: This calculator determines the length of a prismatic bar based on its elongation under self-weight, material properties, and specific weight.

Purpose: It helps engineers and designers calculate the maximum length a bar can have before its own weight causes significant elongation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \sqrt{\frac{\delta l}{\left(\frac{\gamma_{Rod}}{E \times 2}\right)}} \]

Where:

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

Explanation: The formula calculates the length at which a bar's self-weight causes a specified elongation percentage, considering the material's stiffness.

3. Importance of Length Calculation

Details: Proper length estimation ensures structural integrity and prevents excessive deformation in vertical or hanging structural elements.

4. Using the Calculator

Tips: Enter elongation as a percentage, specific weight of the rod material (default 4930960 N/m³ for steel), and Young's Modulus (default 200 GPa for steel). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why does elongation matter in structural design?
A: Excessive elongation can lead to structural instability, misalignment, or failure in load-bearing applications.

Q2: What's a typical elongation limit for structural elements?
A: Most engineering applications limit elongation to 0.1%-0.5% of the original length, depending on the material and application.

Q3: How does Young's Modulus affect the calculation?
A: Higher Young's Modulus (stiffer materials) allow for longer bars before reaching the same elongation percentage.

Q4: Can this be used for non-prismatic bars?
A: No, this formula is specifically for uniform cross-section (prismatic) bars.

Q5: What safety factors should be considered?
A: Always apply appropriate safety factors based on application requirements and material properties.