---
title: "Two copper, one steel rod: 5000 kg"
subject: "Strength of Materials"
chapter: 3
key: "semester_3/strength_of_materials:two-copper-one-steel-rods-5000kg"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/two-copper-one-steel-rods-5000kg
site: BCT Engineering
---

# Two copper, one steel rod: 5000 kg

Strength of Materials · Chapter 3: Simple Stress and Strain

- Asked in: 2074 Chaitra, 6 marks
- Video: [[107-108] SIMPLE STRESS / NORMAL STRESS : Composite Bar](https://www.youtube.com/watch?v=Hj6vvPy752o) — Engr Pogs
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/two-copper-one-steel-rods-5000kg
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-3

## Question

Two copper rods and one steel rod is of 3 cm diameter, together support a load of 5000 kg as shown in figure below. Find the stresses in each rod. Take 'E' for steel and copper as $2\times10^6\ \text{kg/cm}^2$ and $10^6\ \text{kg/cm}^2$. [Figure: a rigid plate carrying a 5000 kg load rests on two outer copper rods (3 m long) and a central steel rod standing in a recess 1 m deeper.]

## Short answer

Compatibility gives σ_steel = 1.50 σ_copper. From equilibrium, stress in each copper rod is 202.10 kg/cm² and in the steel rod 303.15 kg/cm² (compressive).

## Answer

The rigid plate rests on three rods, so all rods shorten equally. The steel rod stands in a recess 1 m deeper: copper is 3 m long, steel 4 m.

#### Compatibility
$$
\frac{\sigma_c L_c}{E_c} = \frac{\sigma_s L_s}{E_s}
\Rightarrow \frac{\sigma_c(300)}{10^6} = \frac{\sigma_s(400)}{2\times10^6}
\Rightarrow \sigma_s = 1.50\,\sigma_c
$$

#### Equilibrium
$A = \dfrac{\pi}{4}(3)^2 = 7.069$ cm² for each rod.

$$
5000 = \sigma_cA(2+1.50) \Rightarrow \sigma_c = \frac{5000}{7.069\times3.50} = 202.102\ \text{kg/cm}^2
$$
$$
\sigma_s = 1.50\times202.102 = 303.152\ \text{kg/cm}^2
$$

**Answer: each copper rod 202.10 kg/cm²; steel rod 303.15 kg/cm² (compressive).**

## Check yourself

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

1. What lengths are used for the rods?
   A. Copper 3 m, steel 4 m
   B. Both 3 m
   C. Copper 4 m, steel 3 m
   D. Both 4 m
   Answer: A. The steel rod stands in a recess 1 m deeper. (Key point: Lengths)

2. What stress ratio results?
   A. sigma_s = 0.67 sigma_c
   B. sigma_s = 1.50 sigma_c
   C. sigma_s = 2 sigma_c
   D. sigma_s = 1.33 sigma_c
   Answer: B. sigma_c(300)/1e6 = sigma_s(400)/2e6 gives 1.5. (Key point: Compatibility)

3. How is sigma_c obtained?
   A. 5000 = sigma_c A (2 + 1.5)
   B. 5000 = sigma_c A (1 + 1.5)
   C. 5000 = sigma_c A (2 x 1.5)
   D. 5000 = sigma_c A / 3.5
   Answer: A. Two copper rods plus the steel rod at 1.5 times copper stress. (Key point: Equilibrium)

4. What is the copper stress?
   A. 303.15 kg/cm^2
   B. 141.5 kg/cm^2
   C. 202.10 kg/cm^2
   D. 707 kg/cm^2
   Answer: C. 5000/(7.069 x 3.5) = 202.1 kg/cm^2. (Key point: Result)

## Close variants set in other exams

- [Two copper, one steel rod: 3000 kg](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Atwo-copper-one-steel-rods-3000kg) — Strength of Materials, chapter 3, asked 2×

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