---
title: "Factor of safety and partial safety factor"
subject: "Design of Steel and Timber Structure"
chapter: 3
key: "semester_6/design_of_steel_and_timber_structure:factor-safety-partial-safety"
source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/factor-safety-partial-safety
site: BCT Engineering
---

# Factor of safety and partial safety factor

Design of Steel and Timber Structure · Chapter 3: Limit State Design Method

- Asked in: 2071 Bhadra, 5 marks; 2070 Bhadra (asked 2 times)
- Video: [What is Partial Safety Factor :Types](https://www.youtube.com/watch?v=-7pLbFOKkp4) — Civil Center
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/factor-safety-partial-safety
- Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-3

## Question

Write about (differentiate between) factor of safety and partial safety factor used in steel structures.

## Short answer

Factor of safety in WSM is a single number (e.g., 1.67) applied to material strength to get permissible stress, covering all uncertainties. Partial safety factors in LSM are separate factors for loads (γ_f) and material (γ_m), statistically derived for uniform reliability.

## Answer

| Point | Factor of safety | Partial safety factor |
|---|---|---|
| Used in | Working stress method | Limit state method |
| Definition | $f_y/\sigma_{perm}$ (ratio of failure stress to permissible stress) | Separate factors on loads ($\gamma_f$) and on material ($\gamma_m$) |
| Number | One factor for all uncertainties | Several, each for a particular uncertainty |
| Applied to | Material strength only | Loads and strengths separately |
| Typical value | About 1.67 ($\sigma=0.6f_y$) | $\gamma_f=1.5$, $\gamma_{m0}=1.10$, $\gamma_{m1}=1.25$, bolts 1.25, welds 1.25/1.5 |
| Basis | Experience / judgement | Statistical, reliability-based |
| Result | Non-uniform reliability | More uniform reliability |

Example: for a beam under working load, WSM limits the stress to $0.66f_y$. In LSM the load is multiplied by 1.5 and the design strength is $f_y/1.10$.

## Check yourself

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

1. Where is the factor of safety used?
   A. Limit state method
   B. Plastic method only
   C. Working stress method
   D. Probabilistic method
   Answer: C. Factor of safety is the single factor of WSM, while partial safety factors belong to LSM. (Key point: Where used)

2. How do the numbers of factors differ?
   A. FOS has several, PSF only one
   B. FOS is one for all uncertainties, PSF are several for particular uncertainties
   C. Both are one
   D. Both are several
   Answer: B. A single FOS covers all uncertainties; partial factors are separate for loads and materials. (Key point: Number of factors)

3. For a beam, what happens in WSM and in LSM?
   A. WSM limits stress to 0.66fy; LSM multiplies load by 1.5 and design strength is fy/1.10
   B. WSM multiplies load by 1.5; LSM limits stress to 0.66fy
   C. Both limit stress to 0.66fy
   D. LSM divides load by 1.5
   Answer: A. WSM keeps stress below 0.66fy, whereas LSM uses factored load 1.5 x and design strength fy/1.10. (Key point: Beam example)

## Related in Design of Steel and Timber Structure

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