Area at Section 2 of Bars of Uniform Strength Calculator

Area at Section 2 Formula:

\[ A_2 = \frac{A_1}{e^{\left(\frac{\gamma \times L}{\sigma}\right)}} \]

Area 1 (A₁):

m²

Specific Weight (γ):

N/m³

Length of Rod (L):

Uniform Stress (σ):

Area 2 (A₂):

+5%:

-5%:

1. What is Area at Section 2 of Bars of Uniform Strength?

Definition: This calculator determines the cross-sectional area at the second end of a bar under uniform stress, based on the initial area, specific weight, length, and stress.

Purpose: It helps engineers design bars or rods that maintain uniform strength throughout their length by calculating the required tapering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A_2 = \frac{A_1}{e^{\left(\frac{\gamma \times L}{\sigma}\right)}} \]

Where:

\( A_2 \) — Cross-sectional area at section 2 (m²)
\( A_1 \) — Cross-sectional area at section 1 (m²)
\( \gamma \) — Specific weight of material (N/m³)
\( L \) — Length of the rod (m)
\( \sigma \) — Uniform stress (Pa)
\( e \) — Napier's constant (~2.71828)

Explanation: The formula accounts for how the area needs to change along the length to maintain uniform stress under the material's own weight.

3. Importance of Uniform Strength Calculation

Details: Proper calculation ensures structural integrity, optimal material usage, and uniform stress distribution in tapered members.

4. Using the Calculator

Tips: Enter the initial area, material specific weight, rod length, and desired uniform stress. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is uniform strength in bars?
A: A bar has uniform strength when the stress is constant throughout its length under self-weight loading.

Q2: When would I use this calculation?
A: When designing tapered columns, suspension bridge cables, or any structure where uniform stress is desired.

Q3: What are typical specific weight values?
A: Steel ~78,500 N/m³, Aluminum ~27,000 N/m³, Concrete ~24,000 N/m³.

Q4: Why include ±5% values?
A: To account for manufacturing tolerances and material property variations.

Q5: Does this consider external loads?
A: No, this only considers the bar's self-weight. External loads require additional analysis.