---
title: "Balanced, under, over sections with strain diagrams"
subject: "Design of RCC Structure"
chapter: 4
key: "semester_7/design_of_rcc_structure:balanced-under-over-sections-with-strain"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/balanced-under-over-sections-with-strain
site: BCT Engineering
---

# Balanced, under, over sections with strain diagrams

Design of RCC Structure · Chapter 4: Design of beams: Behavior in Flexure

- Asked in: 2067 Asar (old course), 8 marks
- Video: [Balanced | Under Reinforced | Over reinforced | RCC Sections](https://www.youtube.com/watch?v=81geJkd6vsY) — All About Structural Analysis and Design
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/balanced-under-over-sections-with-strain
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-4

## Question

Differentiate among the balanced, under reinforced and over reinforced section in a rectangular reinforced concrete section in limit state method with corresponding strain diagram.

## Short answer

Balanced: x_u = x_u,max, concrete strain 0.0035 and steel at yield strain, simultaneous failure. Under-reinforced: x_u < x_u,max, steel strain exceeds yield, ductile failure. Over-reinforced: x_u > x_u,max, steel strain below yield, concrete crushes suddenly. Only under-reinforced or balanced sections are permitted in design.

## Answer

| Point | Balanced | Under-reinforced | Over-reinforced |
|---|---|---|---|
| Neutral axis | $x_u=x_{u,max}$ | $x_u<x_{u,max}$ | $x_u>x_{u,max}$ |
| Steel area | $A_{st}=A_{st,lim}$ | $A_{st}<A_{st,lim}$ | $A_{st}>A_{st,lim}$ |
| Concrete strain | 0.0035 | 0.0035 | 0.0035 |
| Steel strain | $\varepsilon_y=\dfrac{0.87f_y}{E_s}+0.002$ | $>\varepsilon_y$ | $<\varepsilon_y$ |
| Steel stress | $0.87f_y$ | $0.87f_y$ | $<0.87f_y$ |
| First to fail | Both together | Steel yields | Concrete crushes |
| Failure | Simultaneous | Ductile, with warning | Sudden, brittle |
| Moment | $0.36f_{ck}bx_{u,max}(d-0.42x_{u,max})$ | $0.87f_yA_{st}d(1-\dfrac{A_{st}f_y}{bdf_{ck}})$ | Limited to $M_{u,lim}$ |

**Strain diagrams** (all with concrete strain 0.0035 at the top):

```text
 Under-reinforced   Balanced        Over-reinforced
 0.0035             0.0035          0.0035
 |\                 |\              |\
 | \                | \             |  \
 |  \ xu<xumax      |  \ xu=xumax   |    \ xu>xumax
 +----  NA          +----  NA      +-------  NA
 |   \              |   \           |      \
 |    \ es>ey       |    \ es=ey    |       \ es<ey
```

The depth of the neutral axis is found from the strain diagram: $\dfrac{x_{u,max}}{d}=\dfrac{0.0035}{0.0035+\varepsilon_y}$, which gives 0.53, 0.48 and 0.46 for Fe250, Fe415 and Fe500. Only under-reinforced (or balanced) sections are accepted in design.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the concrete strain at the top fibre at failure in all three types?
   A. 0.002
   B. 0.0035
   C. Depends on type
   D. 0.0045
   Answer: B. All are drawn with ultimate concrete strain 0.0035. (Key point: Concrete strain)

2. How does steel strain compare with yield strain in an over-reinforced section?
   A. Greater
   B. Equal
   C. Less
   D. Zero
   Answer: C. Steel has not yielded, so its strain is below the yield strain and stress is below 0.87 fy. (Key point: Steel strain)

3. Which formula gives xu,max/d from the strain diagram?
   A. 0.0035 / (0.0035 + ey)
   B. ey / 0.0035
   C. 0.0035 / ey
   D. 0.002 / (0.002 + ey)
   Answer: A. By similar triangles with concrete strain 0.0035 and steel strain ey, this gives 0.48 for Fe415. (Key point: Xu,max from strain)

4. What is the steel stress in an under-reinforced section at failure?
   A. Less than 0.87 fy
   B. 0.87 fy
   C. 1.5 fy
   D. 0.446 fck
   Answer: B. Steel has yielded so its design stress is 0.87 fy. (Key point: Steel stress)

## Related in Design of RCC Structure

- [Define balanced, under, over-reinforced sections](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adefine-balanced-under-over-reinforced-sections) — Design of RCC Structure, chapter 4
- [Under, over and balanced sections](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aunder-over-and-balanced-sections) — Design of RCC Structure, chapter 4, asked 6×
- [Significance of under and over-reinforced sections](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Asignificance-of-under-and-over-reinforced) — Design of RCC Structure, chapter 4
- [Sections with stress distribution, moment expressions](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Asections-with-stress-distribution-moment-expressions) — Design of RCC Structure, chapter 4