1. What is the Deflection Calculator?

Definition: The Deflection Calculator determines the deflection (\(\delta\)) of a tensile bar using the formula \(\delta = \frac{P \cdot L}{A \cdot E}\), converting the result to millimeters (mm), inches (in), feet (ft), and meters (m).

Purpose: Assists engineers in analyzing material deformation under load.

Reference:Applied Strength of Materials for Engineering Technology

http://www.etcs.pfw.edu/~dupenb/ET_200/Applied%20Str%20of%20Mat%20for%20ET%20v14%20July%202018.pdf

2. How Does the Calculator Work?

Formula:

Where:

• \(\delta\): Deflection (mm, in, ft, m)
• \(P\): Load (N)
• \(L\): Length (m)
• \(A\): Cross-sectional area (m², calculated as \(\frac{\pi d^2}{4}\))
• \(E\): Young's Modulus (Pa)

Steps:

• Step 1: Input Load. Enter the load value (e.g., 30 kN, 6744 lb).
• Step 2: Input Length. Enter the length (e.g., 80 cm, 31.5 in, 2.62 ft).
• Step 3: Input Diameter. Enter the diameter (e.g., 6 mm, 0.236 in).
• Step 4: Input Young's Modulus. Enter the modulus (e.g., 207 GPa, 30e6 psi).
• Step 5: Calculate. The calculator converts units and computes deflection in multiple units.

3. Importance of Deflection Calculation

Calculating deflection is crucial for:

• Material Deformation: Ensures materials stretch within safe limits.
• Design Safety: Prevents excessive deformation or failure.
• Unit Consistency: Supports conversions from kN/lb, cm/in/ft/m, mm/cm/in, and GPa/psi/Pa.

4. Using the Calculator

Example (SI): Load = 30 kN, Length = 80 cm, Diameter = 6 mm, Young's Modulus = 207 GPa:

• Step 1: \( P = 30,000 \, \text{N} \).
• Step 2: \( L = 0.8 \, \text{m} \).
• Step 3: \( d = 0.006 \, \text{m}, A \approx 2.83 \times 10^{-5} \, \text{m}^2 \).
• Step 4: \( E = 207 \times 10^9 \, \text{Pa} \).
• Step 5: \(\delta \approx 4.1 \, \text{mm}, 0.16 \, \text{in}, 0.013 \, \text{ft}, 0.0041 \, \text{m}\).

Example (Imperial): Load = 6744 lb, Length = 2.62 ft, Diameter = 0.236 in, Young's Modulus = 30e6 psi:

• Step 1: \( P = 30,000 \, \text{N} \).
• Step 2: \( L = 0.8 \, \text{m} \).
• Step 3: \( d = 0.006 \, \text{m}, A \approx 2.83 \times 10^{-5} \, \text{m}^2 \).
• Step 4: \( E = 207 \times 10^9 \, \text{Pa} \).
• Step 5: \(\delta \approx 4.1 \, \text{mm}, 0.16 \, \text{in}, 0.013 \, \text{ft}, 0.0041 \, \text{m}\).

5. Frequently Asked Questions (FAQ)

Q: What is deflection?
A: Deflection is the amount a material stretches under load.

Q: Why convert units?
A: The calculator ensures consistent SI units (N, m, Pa) for accurate results and provides multiple output units.

Q: Is this accurate for all materials?
A: Yes, if the load, length, diameter, and modulus are correctly measured.