---
title: "Steel shaft 200 hp: torque, shear, twist"
subject: "Strength of Materials"
chapter: 6
key: "semester_3/strength_of_materials:steel-shaft-200hp-150rpm"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/steel-shaft-200hp-150rpm
site: BCT Engineering
---

# Steel shaft 200 hp: torque, shear, twist

Strength of Materials · Chapter 6: Torsion

- Asked in: 2078 Kartik, 8 marks
- Video: [Torsion in shafts: 07: Numerical problem: allowable twist and shear stress in shaft](https://www.youtube.com/watch?v=vyfiBiX0B_E) — Mech PM
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/steel-shaft-200hp-150rpm
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-6

## Question

A steel shaft transmits 200 horse power at 150 rpm. If the shaft is 110 mm in diameter, find the torque in the shaft and the maximum shear stress developed. Also, determine the angle of twist for the shaft in the length 5 m. Take $G = 90\ \text{GN/m}^2$. (1 hp = 746 watt)

## Short answer

Torque = 9.498 kN·m, maximum shear stress = 36.34 MPa, angle of twist over 5 m = 0.0367 rad (2.10°).

## Answer

**Data:** $P = 200$ hp $= 200\times746 = 149200$ W, $N = 150$ rpm, $d = 110$ mm, $L = 5$ m, $G = 90\ \text{GN/m}^2 = 90\times10^3\ \text{N/mm}^2$.

#### Torque
$$
T = \frac{60P}{2\pi N} = \frac{60(149200)}{2\pi(150)} = 9498.4\ \text{N·m} = 9.4984\times10^{6}\ \text{N·mm}
$$

#### Maximum shear stress
$$
\tau_{max} = \frac{16T}{\pi d^3} = \frac{16(9.4984\times10^{6})}{\pi(110)^3} = 36.34\ \text{N/mm}^2
$$

#### Angle of twist in 5 m
$$
J = \frac{\pi}{32}(110)^4 = 1.4374\times10^{7}\ \text{mm}^4
$$

$$
\varphi = \frac{TL}{GJ} = \frac{(9.4984\times10^{6})(5000)}{(90\times10^3)(1.4374\times10^{7})} = 0.03671\ \text{rad} = 2.103^\circ
$$

**Answer:** $T = 9.498$ kN·m; $\tau_{max} = 36.34$ MPa; $\varphi = 0.0367$ rad $= 2.10^\circ$.

## Check yourself

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

1. What is power in watts?
   A. 200 W
   B. 200 x 746 = 149200 W
   C. 200/746 W
   D. 149.2 W
   Answer: B. 1 hp = 746 W. (Key point: Power)

2. What is the torque?
   A. 94.98 kN.m
   B. 0.95 kN.m
   C. 9.498 kN.m
   D. 1.49 kN.m
   Answer: C. T = 60P/(2 pi N). (Key point: Torque)

3. Which formula?
   A. tau = 32T/(pi d^3)
   B. tau = T/d^3
   C. tau = 16T/(pi d^4)
   D. tau = 16T/(pi d^3) = 36.34 MPa
   Answer: D. Solid shaft. (Key point: Max stress)

4. Which formula for twist?
   A. phi = TL/(GJ) = 0.0367 rad
   B. phi = T/(GJ)
   C. phi = TL/(EJ)
   D. phi = TJ/(GL)
   Answer: A. G is shear modulus, J polar moment. (Key point: Twist)

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