Elastic Extreme-Fiber Bending Stress
Estimate the maximum bending stress magnitude at a beam section.
Try this formula
Calculate extreme-fiber bending stress magnitude or choose another supported quantity.
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Try this formula
Calculate extreme-fiber bending stress magnitude or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Extreme-fiber bending stress magnitude
Enter the known values to see the result.
Use small strains and a homogeneous, linearly elastic material. Loads are static or slowly applied; remain below the proportional limit. Use elementary beam bending about the appropriate centroidal principal axis. Plane sections remain plane; evaluate away from concentrated-load and support disturbances. The expression gives a magnitude; tension and compression lie on opposite sides of the neutral axis.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
Donney Fan — MECH 360 — Mechanics of MaterialsReference equation: Bending — Normal Stress. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
The bending stress grows linearly with distance from the neutral axis. The extreme fiber is therefore critical, and placing material farther from the neutral axis can increase the area moment efficiently.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Extreme-fiber bending stress magnitude | ||
| Bending moment magnitude | ||
| Extreme-fiber distance from the neutral axis | ||
| Second moment of area about the bending axis |
Real-World Applications
Beam stress
Estimate the largest elastic normal stress from a bending moment.
Section selection
Compare the stress demand on different beam sections.
Worked Example
Problem
A beam section carries 2,000 N·m, with c = 0.05 m and I = 0.000004 m⁴. Find the extreme-fiber stress magnitude.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Bending — Normal Stress. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use small strains and a homogeneous, linearly elastic material.
- • Loads are static or slowly applied; remain below the proportional limit.
- • Use elementary beam bending about the appropriate centroidal principal axis.
- • Plane sections remain plane; evaluate away from concentrated-load and support disturbances.
- • The expression gives a magnitude; tension and compression lie on opposite sides of the neutral axis.
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