Structural Analysis Fundamentals / Bending of beams
Why bending causes stress
Curvature, the neutral axis, and the linear stress distribution.
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Read the lesson register and outstanding review notesWhy this matters
Bending produces longitudinal strain across a beam section. Relating that strain to stress explains the role of the neutral axis and section geometry.
By the end of this lesson you should be able to
- Explain the strain distribution in a bent beam
- Locate the neutral axis
- Describe the stress distribution
In a homogeneous beam under pure sagging bending, lower fibres extend and upper fibres shorten. The surface with zero longitudinal strain intersects the section at the neutral axis. For homogeneous linear elastic bending without axial force, that axis passes through the centroid; section symmetry is not required.
If plane sections remain plane, longitudinal strain varies linearly across the section. For a homogeneous linear elastic material, bending stress also varies linearly. Cracking, different material moduli and yielding can change the stress distribution even where the strain remains linear.
Predict first
What is the bending stress at the neutral axis of a beam carrying a bending moment?
Practice
A homogeneous symmetric beam 400 mm deep is in pure bending about its horizontal principal axis. Its top-face strain magnitude is 500 microstrain. What is the strain magnitude 100 mm above the neutral axis, in microstrain?
Practice
At a point 150 mm from the neutral axis the bending strain is 300 microstrain. If E = 205 000 N/mm², what is the bending stress there?
Practice
A symmetric beam section is 500 mm deep and carries a bending moment. What is the bending stress exactly at mid-depth?
Summary
- Bending stretches one face and shortens the other
- The neutral axis has zero strain and zero bending stress
- Plane sections remaining plane gives a linear stress distribution