---
title: "Offset method in stress-strain relationship"
subject: "Strength of Materials"
chapter: 3
key: "semester_3/strength_of_materials:offset-method-stress-strain"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/offset-method-stress-strain
site: BCT Engineering
---

# Offset method in stress-strain relationship

Strength of Materials · Chapter 3: Simple Stress and Strain

- Asked in: 2069 Chaitra, 2 marks
- Video: [Mechanics of Materials: Lesson 10 - .2% Offset Rule Explained, Yield Point](https://www.youtube.com/watch?v=yxve9ZzpPrg) — Jeff Hanson
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/offset-method-stress-strain
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-3

## Question

How is offset method defined in drawing stress-strain relationship? Where is it required?

## Short answer

The offset method draws a line parallel to the initial elastic portion from a strain offset (usually 0.2%). The stress where it intersects the curve is the proof stress. It is required for materials without a definite yield point to define a practical yield strength.

## Answer

**Offset method:** many materials (aluminium, high-strength steel, copper, cast iron) show no clear yield point, so their stress–strain curve bends gradually. In the offset method, a straight line is drawn parallel to the initial straight (elastic) part of the curve, starting from a chosen permanent strain on the strain axis (usually a **0.2% offset**, i.e. $\varepsilon = 0.002$). The stress at which this line cuts the curve is taken as the **proof stress (offset yield strength)**.

```text
 stress
   |            ___------  curve
   |        _--'
   |      ,'  .  <- yield (proof) point
   |    ,' . /
   |   / . /   offset line, parallel to the
   |  / /      initial straight part
   | //
   |/_/____________________ strain
   O  0.002
```

**Where it is required:** for materials without a definite yield point, to define a practical yield strength for design (permissible stress = proof stress divided by the factor of safety).

## Check yourself

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

1. Why is the offset method used?
   A. To define yield strength for materials without a clear yield point
   B. To find Young's modulus
   C. To find ultimate strength
   D. To measure hardness
   Answer: A. Aluminium, copper and cast iron bend gradually. (Key point: Purpose)

2. How is the offset line drawn?
   A. Horizontal from the origin
   B. Parallel to the initial elastic line, starting at 0.002 strain
   C. Perpendicular to the elastic line
   D. From the fracture point
   Answer: B. The intersection with the curve gives the proof stress. (Key point: Procedure)

3. How is proof stress used in design?
   A. Permissible stress = proof stress / factor of safety
   B. Permissible stress = ultimate stress
   C. Permissible stress = proof stress x factor of safety
   D. It is not used
   Answer: A. It serves as practical yield strength. (Key point: Use)

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