---
title: "Two copper, one steel rod: 3000 kg"
subject: "Strength of Materials"
chapter: 3
key: "semester_3/strength_of_materials:two-copper-one-steel-rods-3000kg"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/two-copper-one-steel-rods-3000kg
site: BCT Engineering
---

# Two copper, one steel rod: 3000 kg

Strength of Materials · Chapter 3: Simple Stress and Strain

- Asked in: 2075 Asoj, 8 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-3000kg
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-3

## Question

Two copper rods and one steel rod are having diameter 4 cm, together support a load 3000 kg as shown in figure below. Determine the stresses in each rod. Take $E_s = 2\times10^6\ \text{kg/cm}^2$, $E_c = 10^6\ \text{kg/cm}^2$. [Figure: a rigid plate carrying a 3000 kg load rests on two outer copper rods and a central steel rod standing on a base; the copper rods are 4 m long and the steel rod stands in a recess 1 m deeper.]

## Short answer

Equal shortening yields σ_steel = 1.60 σ_copper. Equilibrium then gives stress in each copper rod 66.31 kg/cm² and in the steel rod 106.10 kg/cm² (compressive).

## Answer

The load is carried by a rigid plate resting on the three rods, so all rods shorten equally. The steel rod stands in a recess 1 m deeper, so it is 5 m long (copper 4 m).

#### Compatibility
$$
\delta_c = \delta_s \Rightarrow \frac{\sigma_c L_c}{E_c} = \frac{\sigma_s L_s}{E_s}
\Rightarrow \frac{\sigma_c(400)}{10^6} = \frac{\sigma_s(500)}{2\times10^6}
\Rightarrow \sigma_s = 1.60\,\sigma_c
$$

#### Equilibrium
Area of each rod $A = \dfrac{\pi}{4}(4)^2 = 12.566$ cm².

$$
P = 2\sigma_cA + \sigma_sA = \sigma_cA\,(2 + 1.60)
$$
$$
3000 = \sigma_c(12.566)(3.60) \Rightarrow \sigma_c = 66.315\ \text{kg/cm}^2,\quad \sigma_s = 106.103\ \text{kg/cm}^2
$$

Check: $2(833.3) + 1333.3 = 3000.0$ kg.

**Answer: stress in each copper rod = 66.31 kg/cm²; stress in the steel rod = 106.10 kg/cm² (compressive).**

## Check yourself

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

1. Why is the steel rod 5 m long?
   A. It is made longer by design
   B. It stands in a recess 1 m deeper than the copper rods' base
   C. Steel expands more
   D. The load lengthens it
   Answer: B. Copper is 4 m and steel 4 + 1 = 5 m. (Key point: Rod length)

2. What relation follows from equal shortening?
   A. sigma_s = 1.60 sigma_c
   B. sigma_s = 0.625 sigma_c
   C. sigma_s = 2 sigma_c
   D. sigma_s = sigma_c
   Answer: A. sigma_c(400)/1e6 = sigma_s(500)/2e6 gives sigma_s = 1.6 sigma_c. (Key point: Compatibility)

3. Which equation gives the load balance?
   A. P = sigma_c A + 2 sigma_s A
   B. P = 3 sigma_c A
   C. P = 2 sigma_c A + sigma_s A
   D. P = 2 sigma_c A - sigma_s A
   Answer: C. Two copper rods and one steel rod, all with area A. (Key point: Equilibrium)

4. What is the stress in the steel rod?
   A. 106.10 kg/cm^2
   B. 66.31 kg/cm^2
   C. 75 kg/cm^2
   D. 212 kg/cm^2
   Answer: A. sigma_c = 3000/(12.566 x 3.6) = 66.31; steel = 1.6 x 66.31 = 106.10. (Key point: Result)

## Close variants set in other exams

- [Two copper, one steel rod: 5000 kg](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Atwo-copper-one-steel-rods-5000kg) — Strength of Materials, chapter 3, asked 2×

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