---
title: "Limit states of strength and serviceability"
subject: "Design of RCC Structure"
chapter: 3
key: "semester_7/design_of_rcc_structure:limit-states-of-strength-and-serviceability"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/limit-states-of-strength-and-serviceability
site: BCT Engineering
---

# Limit states of strength and serviceability

Design of RCC Structure · Chapter 3: Limit State Method of design

- Asked in: 2072 Kartik, 4 marks; 2067 Asar (old course), 5 marks; 2075 Asoj, 6 marks (asked 3 times)
- Video: [5. Limit States Design](https://www.youtube.com/watch?v=QGNxgFQDymo) — Chee Seng Yeap
- 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/limit-states-of-strength-and-serviceability
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-3

## Question

State all the possible safety and serviceability requirements and limit states to be considered in the design by Limit State Method, and define the limit states of strength and serviceability.

## Short answer

Limit state of strength (collapse) checked with factored loads (γf=1.5) and reduced material strengths (γmc=1.5, γms=1.15) for flexure, shear, torsion, compression, overturning, sliding. Limit state of serviceability checked at service loads (γm=1.0) for deflection (span/250 total, span/350 or 20mm after finishes), cracking (0.3mm general, 0.2mm aggressive), durability, vibration, fire.

## Answer

A **limit state** is a state beyond which the structure no longer performs as it was designed to. Limit state design keeps the probability of reaching any limit state acceptably small. IS 456:2000 cl. 35 lists the following.

#### Limit state of strength (collapse)

The structure, or any part of it, must not collapse, buckle, overturn or become unstable under the worst factored loads. It is checked for:

- flexure (bending), compression, shear and torsion (member level);
- overturning, sliding, loss of stability and rupture of critical sections (structure level).

It is checked with design loads ($\gamma_f\times$ characteristic load) and design material strengths ($f_{ck}/1.5$, $f_y/1.15$).

#### Limit state of serviceability

The structure must remain comfortable and usable under service loads. It is checked for:

- **Deflection:** excessive sag spoils the appearance and damages partitions and finishes. Limits: span/250 for the total deflection, and span/350 or 20 mm (whichever is less) after finishes and partitions are built.
- **Cracking:** crack width should generally not exceed 0.3 mm, and 0.2 mm where members are exposed to weather, moisture or aggressive conditions, to protect the appearance and the steel.
- **Durability:** adequate cover, cement content and water-cement ratio for the exposure condition.
- **Vibration**, **fire resistance**, **fatigue** and **impact** where relevant.

#### Other limit states

Fire resistance, special impact or explosion loads, or other limit states as required for the structure.

| Limit state | Loads used | Material factors |
|---|---|---|
| Collapse | Factored ($1.5\times$) | $\gamma_m=1.5, 1.15$ |
| Serviceability | Service (unfactored) | $\gamma_m=1.0$ |

## Check yourself

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

1. What does the limit state of strength (collapse) ensure?
   A. No cracking under service loads
   B. The structure does not collapse, buckle or overturn under worst factored loads
   C. Deflection stays below span/250
   D. Vibrations are small
   Answer: B. The strength limit state guards against collapse and instability under design (factored) loads. (Key point: Limit state of strength)

2. Which loads and material factors are used for the serviceability limit state?
   A. Factored loads with gamma_m = 1.5 and 1.15
   B. Service (unfactored) loads with gamma_m = 1.0
   C. Factored loads with gamma_m = 1.0
   D. Service loads with gamma_m = 1.5
   Answer: B. Serviceability is checked at working loads with no material reduction. (Key point: Loads and factors)

3. Which deflection limits are stated for serviceability?
   A. Total span/250; after finishes span/350 or 20 mm, whichever is less
   B. Total span/350; after finishes span/250
   C. Total span/150 only
   D. 20 mm for all spans
   Answer: A. IS 456 limits total deflection to span/250 and the part after partitions and finishes to span/350 or 20 mm, whichever is smaller. (Key point: Deflection limits)

## Related in Design of RCC Structure

- [Limit state of serviceability, requirements](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Alimit-state-of-serviceability-requirements) — Design of RCC Structure, chapter 3, asked 2×
- [Serviceability limit state and splicing types](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aserviceability-limit-state-and-splicing-types) — Design of RCC Structure, chapter 3
- [Serviceability; short and long-term deflection](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aserviceability-short-and-long-term-deflection) — Design of RCC Structure, chapter 8
- [Design strength and design load in LSM](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-strength-and-design-load-in) — Design of RCC Structure, chapter 3
- [Limit state design of beam, 45 kN/m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Alimit-state-design-of-beam-45) — Design of RCC Structure, chapter 4
- [Earthquake design philosophy, strength and ductility](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aearthquake-design-philosophy-strength-and-ductility) — Design of RCC Structure, chapter 12

## Related in other subjects

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- [Different limit states in steel design](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atypes-of-limit-states) — Design of Steel and Timber Structure, chapter 3
- [Gumbel design flood, factor of safety 1.3, 45-year life](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Agumbel-25yr-life45-fos1-3) — Engineering Hydrology, chapter 6
- [T/F: thermal limit design urban, losses rural](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-thermal-limit-urban-loss-rural) — Transmission and Distribution System Design, chapter 7, asked 3×