---
title: "Deflection, crack width control, crack formula"
subject: "Design of RCC Structure"
chapter: 8
key: "semester_7/design_of_rcc_structure:deflection-crack-width-control-crack-formula"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/deflection-crack-width-control-crack-formula
site: BCT Engineering
---

# Deflection, crack width control, crack formula

Design of RCC Structure · Chapter 8: Limit States of Serviceability: Deflection and Cracking

- Asked in: 2076 Asoj, 3+2 marks
- Video: [Reinforced Concrete Design Series: RC Beam Part 3 (Deflection and Crack Check)](https://www.youtube.com/watch?v=cys9hRAa11g) — Oh Chai Lian
- 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/deflection-crack-width-control-crack-formula
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-8

## Question

Describe methods of controlling deflection and crack width in RCC structures. Describe the empirical formula for calculating the design surface crack width.

## Short answer

Deflection controlled by span/depth ratio method with modification factors. Crack width controlled by limiting bar spacing, using small bars, adequate cover, side-face reinforcement, low steel stress, and crack width ≤0.3mm (0.2mm in aggressive environments). Design surface crack width formula per IS 456 Annex F: wcr = 3·acr·εm / [1 + 2(acr - cmin)/(h - x)], where acr = distance to nearest bar, cmin = min cover, h = overall depth, x = neutral axis depth, εm = average strain.

## Answer

#### Methods of controlling deflection
- Keep the span/effective-depth ratio within the permitted value $= (l/d)_{basic} \times k_t \times k_c \times k_f$ (basic 7, 20 and 26 for cantilever, simply supported and continuous members; IS 456 cl. 23.2.1).
- Increase the depth or the amount of tension steel, add compression steel, and use good-quality concrete with proper curing.
- Limit the total deflection to span/250 and the part after finishes to span/350 or 20 mm.

#### Methods of controlling crack width
- Limit the **spacing** of bars (Table 15 and cl. 26.3.3: in slabs, main bars at not more than $3d$ or 300 mm, whichever is less) and use small-diameter bars well distributed over the tension zone.
- Provide adequate cover and **side-face reinforcement** of 0.1% of the web area in beams whose web depth exceeds 750 mm.
- Keep the steel stress low, provide the minimum steel, and cure properly.
- The surface crack width should not exceed **0.3 mm** (0.2 mm where the member is exposed to moisture or an aggressive environment), cl. 35.3.2.

#### Design surface crack width (IS 456 Annex F)
$$
w_{cr} = \frac{3\, a_{cr}\, \varepsilon_m}{1 + \dfrac{2\,(a_{cr} - c_{min})}{h - x}}
$$

where
- $a_{cr}$ = distance from the point considered (on the surface) to the surface of the nearest longitudinal bar,
- $c_{min}$ = minimum clear cover to the longitudinal bar,
- $h$ = overall depth, $x$ = depth of the neutral axis,
- $\varepsilon_m$ = average strain at the level considered:

$$
\varepsilon_m = \varepsilon_1 - \frac{b_t\,(h - x)(a' - x)}{3\,E_s A_s\,(d - x)}
$$

$\varepsilon_1$ is the strain at the level considered (calculated ignoring the stiffening of the concrete in the tension zone), $b_t$ is the width of the section at the centroid of the tension steel, $a'$ is the distance from the compression face to the point considered, and $E_s$ and $A_s$ are the modulus and area of the tension steel.

## Check yourself

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

1. In w = 3 acr εm / [1 + 2(acr - cmin)/(h - x)], what is acr?
   A. Distance from the point considered on the surface to the nearest longitudinal bar surface
   B. Depth of the neutral axis
   C. Clear cover only
   D. Overall depth
   Answer: A. acr is measured from the considered point to the surface of the nearest bar. (Key point: Crack formula)

2. Surface crack width limit in an aggressive environment is
   A. 0.2 mm
   B. 0.3 mm
   C. 0.5 mm
   D. 1 mm
   Answer: A. IS 456 limits crack width to 0.3 mm generally and 0.2 mm in aggressive environments. (Key point: Crack limit)

3. Side-face reinforcement is provided in beams deeper than 750 mm with area
   A. 0.1% of the web area
   B. 0.01% of the web area
   C. 1% of the web area
   D. 5% of the web area
   Answer: A. It controls cracks on the sides of deep beams. (Key point: Side-face steel)

4. Main-bar spacing in slabs is limited to
   A. Greater of 3d and 300 mm
   B. The lesser of 3d and 300 mm
   C. Exactly 500 mm
   D. d/2
   Answer: B. Limiting spacing limits crack widths. (Key point: Bar spacing)

## Related in Design of RCC Structure

- [Crack control methods as per IS 456](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Acrack-control-methods-as-per-is) — Design of RCC Structure, chapter 8
- [Controlling deflection and cracking](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Acontrolling-deflection-and-cracking) — Design of RCC Structure, chapter 8
- [Deflection control, sufficient stiffness method](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adeflection-control-sufficient-stiffness-method) — Design of RCC Structure, chapter 8, asked 3×
- [Earthquake loads in RCC design](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aearthquake-loads-in-rcc-design) — Design of RCC Structure, chapter 12
- [Beam design with deflection, 5.5 m span](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Abeam-design-with-deflection-5-5) — Design of RCC Structure, chapter 4
- [Intermediate beam design for BM and deflection](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aintermediate-beam-design-for-bm-and) — Design of RCC Structure, chapter 4

## Related in other subjects

- [Empirical formula; voltage for 150 MW over 100 km](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Aempirical-formula-150mw-100km) — Transmission and Distribution System Design, chapter 2
- [Horizontal crack below RCC slab](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Ahorizontal-crack-below-slab) — Building Technology, chapter 10
- [Empirical flood formula, 100 sq km catchment](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aempirical-flood-100sqkm) — Engineering Hydrology, chapter 6
- [Evaluation vs controlling; elements of control](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aevaluation-vs-controlling-elements) — Project Engineering, chapter 4