---
title: "Compound tube: stresses, load share and shortening (750 kN)"
subject: "Strength of Materials"
chapter: 3
key: "semester_3/strength_of_materials:compound-tube-steel-brass-750kn"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/compound-tube-steel-brass-750kn
site: BCT Engineering
---

# Compound tube: stresses, load share and shortening (750 kN)

Strength of Materials · Chapter 3: Simple Stress and Strain

- Asked in: 2066 Jestha (old course), 12 marks
- Video: [COMPOSITE/COMPOUND BARS](https://www.youtube.com/watch?v=eSLLf4fi6fk) — EASY SCIENCE PREP
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/compound-tube-steel-brass-750kn
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-3

## Question

A compound tube consists of steel tube 130mm internal diameter and 10mm thickness and outer brass tube 160mm internal diameter and 10mm thickness. The two tubes are of same length. The combined tube carries a compressive load of 750 kN. Find the stresses and load carried by each of the steel tube and the brass tube and the amount it shortens. Length of each tube is 250mm. $E_{steel} = 2\times10^5\ \text{MPa}$ $E_{brass} = 1\times10^5\ \text{MPa}$.

## Short answer

Equal strain gives σ_s = 2σ_b. With total load 750 kN and areas A_s=4398.2 mm², A_b=5340.7 mm², solving yields σ_s=106.10 MPa, σ_b=53.05 MPa, loads P_s=466.67 kN, P_b=283.33 kN, shortening 0.1326 mm.

## Answer

**Principle:** both tubes have the same length and are loaded together, so they shorten equally: $\varepsilon_s = \varepsilon_b$. The total load is shared: $P_s + P_b = 750$ kN.

#### Areas
Steel: inner $d = 130$ mm, outer $D = 150$ mm. Brass: inner $d = 160$ mm, outer $D = 180$ mm.

$$
A_s = \frac{\pi}{4}(150^2 - 130^2) = 4398.2\ \text{mm}^2, \qquad A_b = \frac{\pi}{4}(180^2 - 160^2) = 5340.7\ \text{mm}^2
$$

#### Stresses
Equal strain gives

$$
\frac{\sigma_s}{E_s} = \frac{\sigma_b}{E_b} \Rightarrow \sigma_s = \frac{E_s}{E_b}\sigma_b = 2\sigma_b
$$

$$
P = \sigma_sA_s + \sigma_bA_b = \sigma_b(2A_s + A_b) \Rightarrow 750\,000 = \sigma_b(2\times4398.2 + 5340.7)
$$

$$
\sigma_b = 53.05\ \text{MPa}, \qquad \sigma_s = 106.10\ \text{MPa}
$$

#### Loads carried
$$
P_s = \sigma_sA_s = 466.67\ \text{kN}, \qquad P_b = \sigma_bA_b = 283.33\ \text{kN}
$$

Check: $466.67 + 283.33 = 750.00$ kN.

#### Shortening
$$
\delta = \frac{\sigma_s L}{E_s} = \frac{106.10\times250}{2\times10^5} = 0.1326\ \text{mm}
$$

(Brass gives the same: $53.05\times250/10^5 = 0.1326$ mm.)

**Answer:** $\sigma_s = 106.10$ MPa, $\sigma_b = 53.05$ MPa; $P_s = 466.67$ kN, $P_b = 283.33$ kN; shortening $= 0.1326$ mm.

## Check yourself

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

1. What condition do the steel and brass tubes satisfy under load?
   A. Equal stress in both tubes
   B. Equal strain (same shortening), with P_s + P_b = 750 kN
   C. Equal load in both tubes
   D. Equal area in both tubes
   Answer: B. Tubes of the same length shorten equally, so strains are equal, while loads add to the total. (Key point: Compatibility condition)

2. How are the stresses related?
   A. sigma_s = sigma_b/2
   B. sigma_s = sigma_b
   C. sigma_s = 4 sigma_b
   D. sigma_s = 2 sigma_b because E_s/E_b = 2
   Answer: D. Equal strain gives sigma_s/E_s = sigma_b/E_b, so sigma_s = (E_s/E_b) sigma_b = 2 sigma_b. (Key point: Stress ratio)

3. Which pair of areas is used?
   A. A_s = 5340.7 mm^2 and A_b = 4398.2 mm^2
   B. A_s = 4398.2 mm^2 and A_b = 5340.7 mm^2
   C. A_s = 6361.7 mm^2 and A_b = 7854 mm^2
   D. A_s = 2199 mm^2 and A_b = 2670 mm^2
   Answer: B. Annular areas pi/4(D^2 - d^2): steel 150 and 130 mm, brass 180 and 160 mm. (Key point: Areas)

4. What load does each tube carry?
   A. Steel 375 kN, brass 375 kN
   B. Steel 283.33 kN, brass 466.67 kN
   C. Steel 500 kN, brass 250 kN
   D. Steel 466.67 kN, brass 283.33 kN
   Answer: D. sigma_b = 53.05 MPa, sigma_s = 106.10 MPa, giving P_s = 466.67 kN and P_b = 283.33 kN. (Key point: Final loads)

## Close variants set in other exams

- [Compound tube: stresses and load share (1000 kN)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Acompound-tube-steel-brass-1000kn) — Strength of Materials, chapter 3, asked 2×

## Related in Strength of Materials

- [Steel rod with two brass rods: stresses](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Asteel-brass-rods-60kn) — Strength of Materials, chapter 3