---
title: "Define load factor"
subject: "Theory of Structures II"
chapter: 5
key: "semester_5/theory_of_structures_ii:define-load-factor"
source: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/define-load-factor
site: BCT Engineering
---

# Define load factor

Theory of Structures II · Chapter 5: Introduction to plastic analysis

- Asked in: 2070 Chaitra (old course), 2 marks; 2069 Asar, 1 marks (asked 2 times)
- Video: [Intro to Structural Analysis - Loads and LRFD](https://www.youtube.com/watch?v=vh8JmHjhECk) — Structures with Prof. H
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/define-load-factor
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-5

## Question

Define load factor.

## Short answer

Load factor is the ratio of collapse load to working load. In plastic design, working loads are multiplied by this factor (specified by codes for load combinations) and the structure is sized to just collapse under factored loads.

## Answer

**Load factor** $\lambda$ is the ratio of the collapse load (the load that produces a plastic collapse mechanism) to the working (service) load:
$$
\lambda = \frac{W_c}{W_w}
$$
In plastic design the working loads are multiplied by this factor (specified by the code, which gives different values for dead, live and wind combinations) and the structure is designed to just collapse under the factored loads. For a section it is related to the shape factor: $\lambda = S\times F$, where $F$ is the factor of safety against first yield (when moments are proportional to the loads).

## Check yourself

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

1. Load factor is the ratio of:
   A. working load to collapse load
   B. collapse load to working load
   C. yield moment to plastic moment
   D. yield stress to working stress
   Answer: B. lambda = W_c / W_w. (Key point: Definition)

2. In plastic design the structure is designed to:
   A. remain elastic under factored loads
   B. never yield under working loads
   C. just collapse under the factored loads
   D. collapse at working loads
   Answer: C. Working loads are multiplied by the load factor and the structure is designed to just collapse under them. (Key point: Use in design)

3. How is the load factor related to the shape factor S and factor of safety F against first yield?
   A. lambda = S / F
   B. lambda = S x F
   C. lambda = S + F
   D. lambda = F / S
   Answer: B. When moments are proportional to loads, lambda = S x F. (Key point: Relation)

## Related in Theory of Structures II

- [Collapse moment of portal frame, load factor 1.75](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Acollapse-moment-portal-load-factor-1) — Theory of Structures II, chapter 5

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