---
title: "Stress, strain, elongation of steel rod"
subject: "Civil Engineering Materials"
chapter: 1
key: "semester_3/civil_engineering_materials:numerical-steel-rod-stress-strain"
source: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/numerical-steel-rod-stress-strain
site: BCT Engineering
---

# Stress, strain, elongation of steel rod

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

- Asked in: 2059 Poush (old course), 4 marks
- Video: [Total elongation/ change length of steel bar/ Simple stress and strain / strength of Material](https://www.youtube.com/watch?v=b87GH5PXUAQ) — Prof.Dr.Pravin Patil
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/numerical-steel-rod-stress-strain
- Whole chapter: https://www.bctengineer.com/md/semester_3/civil_engineering_materials/chapter-1

## Question

A mild steel rod 3 m long having a cross-sectional area of 4 cm$^2$ is subjected to an axial pull of 1500 kg. If $E$ for steel is $2.1\times10^{6}$ kg/cm$^2$, find stress, strain and elongation of the rod.

## Short answer

Stress σ = P/A = 1500/4 = 375 kg/cm² (≈ 36.8 N/mm²). Strain ε = σ/E = 375/(2.1×10⁶) = 1.786×10⁻⁴. Elongation δ = ε·L = 1.786×10⁻⁴ × 300 cm = 0.0536 cm (0.536 mm).

## Answer

**Given:** $L = 3$ m $= 300$ cm, $A = 4\ \text{cm}^2$, $P = 1500$ kg, $E = 2.1\times10^6\ \text{kg/cm}^2$.

$$
\begin{aligned}
\text{Stress } \sigma &= \frac{P}{A} = \frac{1500}{4} = 375\ \text{kg/cm}^2\\
\text{Strain } \varepsilon &= \frac{\sigma}{E} = \frac{375}{2.1\times10^{6}} = 1.786\times10^{-4}\\
\text{Elongation } \delta &= \varepsilon L = 1.786\times10^{-4}\times300 = 0.0536\ \text{cm}
\end{aligned}
$$

**Answer: Stress = 375 kg/cm² (about 36.8 N/mm²); strain = 1.786 × 10⁻⁴; elongation = 0.0536 cm = 0.536 mm.**

## Check yourself

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

1. Stress is
   A. 1500 kg/cm^2
   B. 6000 kg/cm^2
   C. 375 kg/cm^2
   D. 93.75 kg/cm^2
   Answer: C. 1500/4. (Key point: Stress)

2. Strain is
   A. 1.786 x 10^-2
   B. 5.6 x 10^3
   C. 375
   D. 1.786 x 10^-4
   Answer: D. 375 / 2.1e6. (Key point: Strain)

3. Elongation is
   A. 0.0536 cm
   B. 0.536 cm
   C. 0.0179 cm
   D. 5.36 cm
   Answer: A. 1.786e-4 x 300 cm. (Key point: Elongation)

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