Module 13
Beam deflection
How much a beam moves, why that often governs, and how to picture the shape first.
What this module covers
- Distinguish deflection from rotation
- Relate bending moment to curvature
- Sketch a deflected shape from the supports and loading
- Use standard deflection formulae and check span/deflection limits
- Explain why serviceability often decides the beam size
Lessons
Euler–Bernoulli theory: from exact curvature to EI d²v/dx² = M, and where it fails.
Start lesson →Picture the shape before you calculate the number.
Start lesson →The formulae worth knowing, and why deflection often decides the size.
Start lesson →Every deflection calculation so far has used a theory nobody named, resting on an assumption nobody stated. This lesson states it, drops it, and finds out what changes.
Start lesson →Two ways to get a deflection when the loading is not in any table.
Start lesson →Beams that move sideways, and the deflection that bending theory leaves out.
Start lesson →
Module checkpoint
Check what you have taken in
5 questions
Question 1
A uniformly loaded steel beam has a span-to-depth ratio of 4. Taking the shear share as 2.5(d/L)², what percentage of the bending deflection does shear add?
Question 2
A beam's shear deflection is 4% of its bending deflection. The span is doubled and the depth left alone. What is the shear share now, as a percentage?
Question 3
A simply supported beam of 6.0 m carries a UDL of 10 kN/m. E = 205 000 N/mm² and I = 3.0 × 10⁸ mm⁴. What is the maximum deflection? (Note 10 kN/m = 10 N/mm.)
Question 4
A simply supported beam's span is doubled, with the same UDL intensity. What happens to the maximum deflection?
Question 5
At a simple support, which is zero?