Elongation due to Self Weight in Prismatic Bar using Applied Load Calculator

Elongation Formula:

\[ \delta l = \frac{W_{Load} \times L}{2 \times A \times E} \]

Applied Load (W_Load):

Length (L):

Cross-Section Area (A):

m²

Young's Modulus (E):

Elongation (δl):

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

Definition: This calculator computes the elongation (δl) of a prismatic bar under its own weight using the applied load formula.

Purpose: It helps engineers and designers determine how much a bar will stretch under its own weight, which is crucial for structural integrity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta l = \frac{W_{Load} \times L}{2 \times A \times E} \]

Where:

\( \delta l \) — Elongation (meters)
\( W_{Load} \) — Applied load (Newtons)
\( L \) — Length of the bar (meters)
\( A \) — Cross-sectional area (square meters)
\( E \) — Young's Modulus (Pascals)

Explanation: The formula calculates the extension of a bar under its own weight by considering the material properties and dimensions.

3. Importance of Elongation Calculation

Details: Proper elongation estimation ensures structural components won't deform excessively under their own weight, preventing failure.

4. Using the Calculator

Tips: Enter the applied load in Newtons, length in meters, cross-sectional area in m², and Young's Modulus in Pascals. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is Young's Modulus?
A: Young's Modulus is a measure of the stiffness of a material, defined as the ratio of stress to strain.

Q2: Why is the factor of 2 in the denominator?
A: The factor accounts for the triangular distribution of stress in a prismatic bar under self-weight.

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

Q4: How does cross-sectional area affect elongation?
A: Larger cross-sections reduce elongation as the load is distributed over more material.

Q5: What if my bar isn't prismatic?
A: This formula is specifically for prismatic (uniform cross-section) bars. Different formulas apply for tapered bars.