Bending Stress for Hollow Circular Section given Diameter Calculator

Formula Used:

\[ \sigma_b = \frac{M}{\left(\frac{\pi}{32 \cdot d_{circle}}\right) \cdot \left((d_{circle}^4) - (d_i^4)\right)} \]

Moment due to eccentric load (M):

N·m

Outer Diameter of Hollow Circular Section (d_circle):

Hollow Circular Section Inner Diameter (d_i):

Bending Stress in Column (σ_b):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Bending Stress in Hollow Circular Section?

Bending Stress in a hollow circular section refers to the internal stress developed due to applied bending moments. It is a critical parameter in structural engineering for designing columns and beams subjected to eccentric loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_b = \frac{M}{\left(\frac{\pi}{32 \cdot d_{circle}}\right) \cdot \left((d_{circle}^4) - (d_i^4)\right)} \]

Where:

\( \sigma_b \) — Bending Stress in Column (Pa)
\( M \) — Moment due to eccentric load (N·m)
\( d_{circle} \) — Outer Diameter of Hollow Circular Section (m)
\( d_i \) — Hollow Circular Section Inner Diameter (m)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: The formula calculates bending stress by considering the moment of inertia of the hollow circular cross-section and the applied bending moment.

3. Importance of Bending Stress Calculation

Details: Accurate bending stress calculation is crucial for structural design, ensuring that components can withstand applied loads without failure, and for determining safety factors in engineering applications.

4. Using the Calculator

Tips: Enter moment in N·m, diameters in meters. Ensure all values are positive and outer diameter is greater than inner diameter for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is bending stress?
A: Bending stress is the internal stress induced in a structural element when an external moment or force is applied, causing it to bend.

Q2: Why use hollow circular sections?
A: Hollow circular sections offer high strength-to-weight ratio, making them efficient for columns and beams where weight reduction is important.

Q3: What are typical applications?
A: This calculation is used in structural engineering for designing columns, poles, and shafts subjected to eccentric loading conditions.

Q4: What are the limitations of this formula?
A: The formula assumes linear elastic material behavior and may not be accurate for materials with non-linear properties or under extreme loading conditions.

Q5: How does inner diameter affect bending stress?
A: Increasing inner diameter (while keeping outer diameter constant) reduces the moment of inertia, which typically increases bending stress for a given moment.