How to calculate elastic section modulus
The outermost fibres of a bending section are furthest from its neutral axis. Section modulus combines the area distribution I with this outer-fibre distance.
What the formula is saying
Divide the second moment I by y, the distance from the neutral axis to the extreme fibre. For a symmetric rectangle about its centroid, y is half the depth, not the full depth.
Read the symbols in plain language
- I
- Second moment of aream⁴
- ymax
- Extreme-fibre distancem
Sort out the units first
I in m⁴ divided by y in m gives W in m³. The example takes I = 0.0054 m⁴ and y = 0.3 m from a 0.6 m deep rectangle.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- I · Second moment of area
- 0.0054 m⁴
- ymax · Extreme-fibre distance
- 0.3 m
Locate the extreme fibre
Measure from the relevant neutral axis, not from the bottom edge.
(0.3) = 0.3 mDivide the area property by that distance
m⁴ divided by m leaves m³.
(0.0054) ÷ (0.3) = 0.018 m³
Does this worked answer make sense?
For the worked rectangle, bh²/6 = 0.3 × 0.6² / 6 = 0.018 m³ gives the same result independently.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- I · Second moment of area
- 0.00045 m⁴
- ymax · Extreme-fibre distance
- 0.15 m
Find: elastic section modulus
A hint, not the answer
Divide the second moment I by y, the distance from the neutral axis to the extreme fibre. For a symmetric rectangle about its centroid, y is half the depth, not the full depth.
I in m⁴ divided by y in m gives W in m³. The example takes I = 0.0054 m⁴ and y = 0.3 m from a 0.6 m deep rectangle.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Locate the extreme fibre
Measure from the relevant neutral axis, not from the bottom edge.
(0.15) = 0.15 mDivide the area property by that distance
m⁴ divided by m leaves m³.
(0.00045) ÷ (0.15) = 0.003 m³
Avoid the common trap
Using full depth instead of half depth for a symmetric rectangle halves W incorrectly. Elastic W is not the plastic section modulus.
When this method applies — and when it does not
Elastic section modulus for the stated bending axis. An asymmetric section may have different top and bottom values.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.