Length of Rod of Truncated Conical Section Calculator

Length of Tapered Bar Formula:

\[ l = \sqrt{\frac{\delta l}{\frac{\gamma_{Rod} \times (d_1 + d_2)}{6 \times E \times (d_1 - d_2)}}} \]

Elongation:

Specific Weight of Rod:

N/m³

Diameter1:

Diameter2:

Young's Modulus:

Length of Tapered Bar:

1. What is Length of Rod of Truncated Conical Section?

Definition: This calculator determines the length of a tapered rod section based on its elongation, material properties, and diameters at both ends.

Purpose: It helps engineers and designers calculate the appropriate length for tapered rod sections in mechanical and structural applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = \sqrt{\frac{\delta l}{\frac{\gamma_{Rod} \times (d_1 + d_2)}{6 \times E \times (d_1 - d_2)}}} \]

Where:

\( l \) — Length of tapered bar (meters)
\( \delta l \) — Elongation (percentage)
\( \gamma_{Rod} \) — Specific weight of rod (N/m³)
\( d_1 \) — Diameter at one end (meters)
\( d_2 \) — Diameter at other end (meters)
\( E \) — Young's Modulus (Pascals)

Explanation: The formula calculates the length needed to achieve a specific elongation under the given material properties and geometry.

3. Importance of Tapered Rod Length Calculation

Details: Proper calculation ensures structural integrity, predictable deformation behavior, and optimal material usage in tapered components.

4. Using the Calculator

Tips: Enter elongation as percentage, specific weight in N/m³, both diameters in meters (must be different), and Young's Modulus in Pascals.

5. Frequently Asked Questions (FAQ)

Q1: Why is elongation input as percentage?
A: Elongation is typically measured as percentage of original length in material testing.

Q2: What's a typical Young's Modulus for steel?
A: For most steels, it's approximately 200 GPa (200,000,000,000 Pa).

Q3: What if diameters are equal?
A: The formula requires different diameters (d1 ≠ d2) as it's for tapered sections.

Q4: How does specific weight affect the result?
A: Higher specific weight materials require shorter lengths to achieve same elongation.

Q5: Can this be used for compression as well?
A: Yes, but the elongation value would represent compression (negative strain).