---
title: "Factor of safety: WSM and LSM"
subject: "Design of RCC Structure"
chapter: 1
key: "semester_7/design_of_rcc_structure:factor-of-safety-wsm-and-lsm"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/factor-of-safety-wsm-and-lsm
site: BCT Engineering
---

# Factor of safety: WSM and LSM

Design of RCC Structure · Chapter 1: Concrete Structures and Design Methods

- Asked in: 2067 Asar (old course), 4 marks
- Video: [Factor of Safety Explained | WSM vs LSM vs LRFD | Civil Engineering by Arsalan](https://www.youtube.com/watch?v=Uj9wUKw_5RM) — Civil Engineering by Arsalan 
- 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/factor-of-safety-wsm-and-lsm
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-1

## Question

Compare the factor of safety used in Working Stress Method and the partial safety factor used in Limit State Method for concrete and steel.

## Short answer

WSM applies one factor to material strength: about 3 for concrete and 1.8 for steel. LSM uses partial safety factors: 1.5 on concrete, 1.15 on steel, and 1.5 on loads, giving design strengths 0.446fck and 0.87fy.

## Answer

In WSM, safety is given by one **factor of safety** applied to the material strength to get a permissible stress. In LSM, safety is split into **partial safety factors**, one for material strength ($\gamma_m$) and one for loads ($\gamma_f$).

#### Working stress method

- Concrete: $\sigma_{cbc} = \dfrac{f_{ck}}{\text{F.O.S.}}$. For M20, $\sigma_{cbc} = 7$ N/mm$^2$, so the factor of safety is about $20/7 \approx 2.86$ (nearly 3 on cube strength).
- Steel: $\sigma_{st} = \dfrac{f_y}{\text{F.O.S.}}$. For Fe415, $\sigma_{st} = 230$ N/mm$^2$, giving $415/230 \approx 1.8$; for mild steel, $\sigma_{st} = 140$ N/mm$^2$, so $250/140 \approx 1.8$.
- Loads are taken at their working values with no factor.

#### Limit state method (IS 456:2000, cl. 36.4)

| Item | Partial safety factor |
|---|---|
| Concrete, $\gamma_{mc}$ | 1.5 |
| Steel, $\gamma_{ms}$ | 1.15 |
| Load (DL + LL), $\gamma_f$ | 1.5 |

Design strengths: concrete $0.67f_{ck}/1.5 = 0.446f_{ck}$ in the stress block; steel $0.87f_y$ (i.e. $f_y/1.15$).

#### Comparison

| Point | WSM | LSM |
|---|---|---|
| Factor | One factor on material | Separate factors on material and load |
| Concrete | About 3 | 1.5 (material) |
| Steel | About 1.8 | 1.15 (material) |
| Load | 1.0 | 1.5 |
| Overall margin | Not known | Known: about $1.5\times1.5 = 2.25$ on concrete and $1.5\times1.15 = 1.73$ on steel |

A lower material factor is acceptable in LSM because the uncertainty in loads is accounted for separately by $\gamma_f$.

## Check yourself

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

1. For M20, sigma_cbc = 7 N/mm2. What is the approximate factor of safety on cube strength in WSM?
   A. About 1.5
   B. About 1.8
   C. About 2.86 (nearly 3)
   D. About 1.15
   Answer: C. 20/7 is about 2.86, nearly 3. (Key point: WSM factor of safety on concrete)

2. For Fe415 with sigma_st = 230 N/mm2, the factor of safety on steel in WSM is about:
   A. 1.8
   B. 3.0
   C. 1.15
   D. 2.25
   Answer: A. 415/230 is about 1.8. (Key point: WSM factor on steel)

3. Which set gives the LSM partial safety factors for concrete, steel and load (DL+LL)?
   A. 1.15, 1.5, 1.5
   B. 1.5, 1.15, 1.5
   C. 1.5, 1.5, 1.15
   D. 3.0, 1.8, 1.0
   Answer: B. gamma_mc = 1.5, gamma_ms = 1.15, gamma_f = 1.5. (Key point: LSM partial factors)

4. Why can LSM use lower material factors than WSM?
   A. Because loads are not considered
   B. Because uncertainty in loads is accounted separately by gamma_f
   C. Because steel is stronger in LSM
   D. Because LSM ignores serviceability
   Answer: B. Load uncertainty is covered by gamma_f, so the material factor need not carry all the safety. (Key point: Why lower material factors)

## Related in Design of RCC Structure

- [WSM beam safety check, 350x650](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Awsm-beam-safety-check-350x650) — Design of RCC Structure, chapter 2
- [WSM vs LSM advantages, section comparison](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Awsm-vs-lsm-advantages-section-comparison) — Design of RCC Structure, chapter 1
- [Working stress vs limit state method](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aworking-stress-vs-limit-state-method) — Design of RCC Structure, chapter 1, asked 6×
- [WSM steel area and resistance, M15](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Awsm-steel-area-and-resistance-m15) — Design of RCC Structure, chapter 2
- [WSM tensile steel for 230x425 beam](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Awsm-tensile-steel-for-230x425-beam) — Design of RCC Structure, chapter 2
- [Beam steel at midspan, limit state](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Abeam-steel-at-midspan-limit-state) — Design of RCC Structure, chapter 4

## Related in other subjects

- [Factor of safety and partial safety factor](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Afactor-safety-partial-safety) — Design of Steel and Timber Structure, chapter 3, asked 2×
- [Normal, shear, bearing stress and factor of safety](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Astress-types-factor-of-safety) — Strength of Materials, chapter 1
- [Bending stress and safety factor of a spur pinion](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aagma-bending-stress-safety-factor) — Machine Design I, chapter 9
- [Merits of limit state over working stress](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Awhy-lsm-better-wsm) — Design of Steel and Timber Structure, chapter 3, asked 3×