In this bending stress calculator, we will show you how to calculate bending stress in just a few steps.
We will also help you understand the bending stress definition and the bending stress formula while we’re at it.
What is bending stress?
Why does it occur in beams and structural members?
How do engineers calculate bending stress in real life?
You will find all the answers here, along with examples, applications, and solved problems. Let’s get started and make bending stress simple to understand!
Bending Stress Calculator
Using the Flexure Formula: σ = (M × y) / I
Flexure Formula Explanation
The primary formula for bending stress in beams is known as the Flexure Formula:
σ = (M × y) / I
- σ = Bending stress (Pa or kPa)
- M = Internal bending moment (N·m)
- y = Distance from neutral axis (m)
- I = Moment of inertia of the cross-section (m⁴)
Real-World Applications
1. Bridges
The formula is used to calculate stress in bridge beams to ensure they can carry traffic loads safely.
2. Buildings
Helps in analyzing beams in multi-story buildings to avoid structural failure.
3. Aircraft Wings
Used in designing airplane wings where bending stress due to aerodynamic loads must be minimized.
4. Railway Tracks
Applied in rail track beams to resist the bending caused by train wheel loads.
Sample Problem with Solution
Problem Statement: A simply supported beam carries a bending moment of 1200 N·m. The distance from the neutral axis (y) is 0.05 m and the moment of inertia (I) is 8 × 10-6 m⁴. Find the bending stress in kPa.
Step-by-Step Solution
Step 1: Given Data
- M = 1200 N·m
- y = 0.05 m
- I = 8 × 10⁻⁶ m⁴
Step 2: Apply Flexure Formula
σ = (M × y) / I
Step 3: Substitute Values
σ = (1200 × 0.05) / (8 × 10⁻⁶)
Step 4: Calculate Stress in Pa
σ = 7.5 × 10⁶ Pa
Step 5: Convert to kPa
σ = (7.5 × 10⁶) / 1000 = 7500 kPa
Reference Table: Typical Bending Stress Values
| Material | Allowable Bending Stress (kPa) | Remarks |
|---|---|---|
| Structural Steel | 250,000 – 350,000 | Commonly used in bridges & buildings |
| Reinforced Concrete | 3,000 – 7,000 | Stress mainly resisted by steel reinforcement |
| Aluminum | 70,000 – 100,000 | Lightweight applications (aircraft, transport) |
| Timber (Structural Grade) | 5,000 – 12,000 | Depends on species, moisture, and defects |
| Cast Iron | 100,000 – 160,000 | Good in compression, weaker in tension |
📌 Values are approximate and depend on material grade, design codes, and safety factors.
FAQs
What is bending stress?
In this bending stress calculator, we will show you how bending stress is the internal force that develops when a beam or material bends under load.
Why is bending stress important?
What makes bending stress so important is that it helps engineers design safe bridges, buildings, and machines without the risk of breaking.
How do you calculate bending stress quickly?
How to calculate bending stress in seconds? Just put your values of M, y, and I into the formula, or use our bending stress calculator to get the result instantly.