---
title: "True stress and engineering stress"
subject: "Civil Engineering Materials"
chapter: 1
key: "semester_3/civil_engineering_materials:true-engineering-stress"
source: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/true-engineering-stress
site: BCT Engineering
---

# True stress and engineering stress

Civil Engineering Materials · Chapter 1: Introduction to Civil Engineering Material

- Asked in: 2070 Chaitra (old course), 4 marks
- Video: [Understanding True Stress and True Strain](https://www.youtube.com/watch?v=AkX6JqlWRqc) — The Efficient Engineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/true-engineering-stress
- Whole chapter: https://www.bctengineer.com/md/semester_3/civil_engineering_materials/chapter-1

## Question

Define true stress and engineering stress.

## Short answer

Engineering stress is load over original area; true stress is load over instantaneous area. Up to necking, true stress = engineering stress × (1 + engineering strain), and true strain = ln(1 + engineering strain). Engineering values are used for design, true values for research.

## Answer

#### Engineering stress
Engineering (nominal) stress is the applied load divided by the **original** cross-sectional area:

$$
\sigma_e = \frac{P}{A_0}
$$

Engineering strain is $\varepsilon_e = (L-L_0)/L_0$. It is used in design because $A_0$ is known.

#### True stress
True stress is the load divided by the **instantaneous** cross-sectional area at that moment:

$$
\sigma_t = \frac{P}{A_i} = \sigma_e\,(1+\varepsilon_e)
$$

True strain is $\varepsilon_t = \ln(1+\varepsilon_e)$. These conversions assume constant volume and hold up to the start of necking.

| Basis | Engineering | True |
|---|---|---|
| Area used | Original $A_0$ | Instantaneous $A_i$ |
| After necking | Falls | Keeps rising |
| Value | Lower | Higher (in tension) |
| Use | Design | Material research |

## Check yourself

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

1. Engineering stress uses
   A. instantaneous area
   B. final area
   C. original area A0
   D. neck area
   Answer: C. P/A0. (Key point: Engineering stress)

2. True stress equals
   A. engineering stress / (1 + strain)
   B. engineering stress - strain
   C. strain / stress
   D. engineering stress x (1 + engineering strain)
   Answer: D. Formula given. (Key point: Relation)

3. Engineering stress is used in design because
   A. A0 is known
   B. it is always larger
   C. it equals true stress
   D. it rises after necking
   Answer: A. Stated. (Key point: Use)

## Related in Civil Engineering Materials

- [True stress; stress-strain curve of steel](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Atrue-stress-strain-curve-steel) — Civil Engineering Materials, chapter 1
- [Yield, strain hardening, stress-strain diagram](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Ayield-strain-hardening-stress-strain) — Civil Engineering Materials, chapter 1, asked 2×
- [Stress-strain curve of ductile material](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Astress-strain-curve-ductile) — Civil Engineering Materials, chapter 1
- [Stress, strain, elongation of steel rod](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Anumerical-steel-rod-stress-strain) — Civil Engineering Materials, chapter 1

## Related in other subjects

- [True stress and true strain relations](https://www.bctengineer.com/question.md?key=semester_3%2Fmaterial_science%3Atrue-stress-strain-relations) — Material Science, chapter 3
- [Strain-hardening exponent and true stress](https://www.bctengineer.com/question.md?key=semester_3%2Fmaterial_science%3Astrain-hardening-exponent-numerical) — Material Science, chapter 3
- [Tensile test engineering and true values](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Atensile-test-true-stress-strain-numerical) — Manufacturing and Production Processes, chapter 2
- [Limestone true thickness: A 600 m N28E, C 400 m S10W](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-limestone-true-thickness-a600) — Engineering Geology II, chapter 6, asked 2×