Uniform Stress on Bar due to Self-Weight Calculator

Uniform Stress Formula:

\[ \sigma_{Uniform} = \frac{L}{(2.303 \times \log_{10}(A1/A2)) / \gamma_{Rod}} \]

Length:

Area 1:

m²

Area 2:

m²

Specific Weight of Rod:

N/m³

Tolerance:

Uniform Stress (Pa):

Stress Range (±5%):

1. What is Uniform Stress on Bar due to Self-Weight?

Definition: This calculator determines the uniform stress distribution in a bar considering its self-weight, accounting for varying cross-sectional areas.

Purpose: It helps engineers analyze stress distribution in structural elements where self-weight is significant.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{Uniform} = \frac{L}{(2.303 \times \log_{10}(A1/A2)) / \gamma_{Rod}} \]

Where:

\( \sigma_{Uniform} \) — Uniform stress (Pascals)
\( L \) — Length of the bar (meters)
\( A1 \) — Cross-sectional area at one end (m²)
\( A2 \) — Cross-sectional area at other end (m²)
\( \gamma_{Rod} \) — Specific weight of rod material (N/m³)

Explanation: The formula calculates stress considering the logarithmic relationship between the varying cross-sections and the material's specific weight.

3. Importance of Uniform Stress Calculation

Details: Accurate stress calculation ensures structural integrity, prevents material failure, and helps in optimal material selection.

4. Using the Calculator

Tips: Enter the bar length, both cross-sectional areas, specific weight of material, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is specific weight?
A: Specific weight is the weight per unit volume of a material (N/m³), different from density which is mass per unit volume.

Q2: Why use logarithmic relationship for areas?
A: The logarithmic relationship accounts for the non-linear stress distribution when cross-sections vary along the length.

Q3: What's a typical specific weight for steel?
A: Steel typically has a specific weight of about 78,500 N/m³ (or 7.85 g/cm³ converted to weight units).

Q4: When would I change the tolerance value?
A: Adjust tolerance based on required precision - lower for critical applications, higher for rough estimates.

Q5: Can this be used for any material?
A: Yes, as long as you have the correct specific weight value for your material.