UNIVERSITY OF MAURITIUSFACULTY OF ENGINEERING

MECHANICAL AND PRODUCTION ENGINEERING DEPARTMENT

E443 – Beng(Hons.) Mechanical Engineering (Minor: Energy Systems)

MECH 2012YMechanics of Materials II

Experiment L1: Torsion Machine

GROUP 8

1. BADULLA Muhammad Twaaha (1311150)2. LOREKANG Mokgwabone Funny (1300246)3. NUNHUCK Mohammad Shah Wasil (1313122)

-Date of Experiment: 27 March 2015

- Date Submitted: 5 April 2015

TABLE OF CONTENTS

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1. INTRODUCTION 3

2. OBJECTIVES 3

3. APPARATUS USED 3

4. PROCEDURES 4

5. THEORY 5

6. RESULTS 7

7. ANALYSIS 8

8. CONCLUSION 16

9. REFERENCES 17

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TORSION MACHINE: Modulus of rigidity

1. INTRODUCTION

Torsion is an essential type of loading that allows the formation of critical stresses in engineering applications. Shear stresses are formed when a component is under torsion. The Modulus of Rigidity is defined as the stiffness of a component which is under shear stress. The Modulus of Rigidity is also known as the Shear Modulus. The following analysis plots the correct system for determining the shear modulus for a material. Amid this activity, mild steel and aluminium were both utilized as samples to show how materials carry on during testing conditions. By measuring the connected torque with respect to the point of turn, the shear modulus, shear stress at the limit of proportionality, and failure conditions can be found.

2. OBJECTIVES

A torsion test was carried so as to find out the following:

1. To verify the general characteristics of the torque and angle of twist relationship.

2. The Modulus of Rigidity, G of the two given specimens, Specimen ‘A’ and Specimen ‘B’.

3. APPARATUS USEDThe following equipments were used to carry out the experiment:

1. A torsion testing machine

Figure 1 - Torsion machine with all parts labelled.

3

Newton-Meter

360° Dial Indicator with gearbox ratio 60:1

Grips to clamp the specimen

Hand wheel

Lever Arm

2. Vernier caliper3. A measuring tape4. Two specimens with modulus of rigidity known

Figure 2 - Specimens used to carry out the experiment

4. PROCEDURES

1. The length, L and diameter, D for the two given specimens are measured and recorded using the vernier caliper and the measuring tape.

Figure 3: Dimensions for specimen

2. Specimen ‘A’ is clamped between the grips of the torsion machine with both ends locked in tightly into the rectangular sockets. One of the grips being fixed into the torsion machine and the other grip being fitted into the torque shaft.

3. Initially the dial indicator is set to 0° and it is made sure that the newton meter is reading 0N.

4. The hand wheel is rotated in a clockwise direction by 30° which corresponds to an angle of twist of 0.5°(gearbox ratio 60:1) and the load displayed on the newton meter is noted.

5. The torque is then calculated and noted down.

4

Specimen ‘A’Specimen ‘B’

Length, L

Diameter, D

Total length of specimen

6. Step 4 is repeated by increasing the dial reading by an increment of 30° till it reads 180° with the angle of twist being at a maximum of 3°.

7. Steps 4 and 5 are repeated for specimen ‘B’.

5. THEORY

In solid mechanics, torsion is define as the stress and deformation caused when one end of an object is twisted in one direction and the end is held fixed or is twisted in the opposite direction.Torsion for a circular specimen is calculated using the following equation:

Figure 4: Torsion in a circular rod (civil.njit.edu, n.d.)

TJ=G×∅

L= τ

r (1)

Where: T: Applied torque J: Polar moment of area G: Modulus of rigidity L: Length of specimen r: Radius of specimen τ : Shear stress at radius ‘r’ ∅: Angle of twistThe polar moment of area is obtained using the following equation:

J=π

32D 4

(2)

Where D is the diameter of the specimen (refer to Figure 3)

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Torque is defined as a twisting force that causes rotation the axis of rotation is the point where the object rotates. In this particular experiment torque for the two given specimens are calculated using the following equation:

T=F × Larm (3)

Where: T: Torque applied F: Force Larm: Length of arm which is 400mm (refer to Figure 5)Lever arm (400mm)

Figure 5: Side view of the torsion machine showing the lever arm

Modulus of rigidityThe modulus of rigidity is a measure of the capacity of a material to oppose transverse disfigurements and is a legitimate record of elastic behavior just for little distortions, after which the material has the capacity come back to its unique design. Huge shearing strengths lead to flow and changeless deformity or break. It can be obtained experimentally from a stress-strain graph obtained after conducting several tests on a given specimen.

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6. RESULTS7. ANALYSIS

8. CONCLUSION9. REFERENCES

NJIT: Civil and Environmental Engineering: Lab 3 - Torsion . 2015. NJIT: Civil and Environmental Engineering: Lab 3 - Torsion . [ONLINE] [Accessed 03 April 2015].

shear modulus | physics | Encyclopedia Britannica. 2015. shear modulus | physics | Encyclopedia Britannica. [ONLINE [Accessed 03 April 2015].

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