FACULTY OF ENGINEERING AND APPLIED SCIENCE

Engineering: 4312

Mechanics of Solids I

Lab Test #4 – Torsion Test

OBJECTIVES:

To carry out a torsion test to destruction in order to determine for a 1020 carbon steel rod specimen: 1. The modulus of rigidity, 2. The shear stress at the limit of proportionality, 3. The general characteristics of the torque, angle of twist relationship.

REFERENCES:

1. Hibbeler, R. C. "Mechanics of Materials", Prentice-Hall, 7th Edition. 2. Instruction Bulletin of Tecquipment Ltd.

MATERIAL:

Mild Steel rod 6 mm diameter over 3" length (overall length including hexagon ends = 5⅝").

EQUIPMENT:

1. Torsion testing Machine and Torsiometer of Tecquipment Ltd. 2. Steel rule and micrometer.

THEORY:

From the general torsion theory for circular specimen:

T Gθ = J l

where, T = Applied Torque; J = Polar Second Moment of Area; G = Modulus of Rigidity; θ = Angle of Twist (over length l); l = Gauge Length. (Nm) (mm2) (N / mm2) (radians) (mm)

PROCEDURE:

1. Measure the overall length and test diameter of the specimen. 2. Draw a line down the length of the test section of the specimen with a pencil; this serves as a visual aid to the degree of twist being put on the specimen during loading. 3. Mount the specimen firmly in the torsion testing machine as indicated in the operating instructions – see later. (If the Torsiometer is to be used the fixed procedure should be carried as prescribed in the last part the bulletin). For each increment of strain record the following: (a) Angle of twist of the specimen (θ) in degrees. (b) Applied torque (T) (c) Angle of twist over the 50 mm (or 2.0 in) gauge length in radians, as recorded by dial gauge indicator (θ) radians. (d) When the elastic limit has been passed, continue to test destruction with increasing increments of strain, recording for each strain increment, i) ii) Angle of twist in degrees; Applied torque.

MEASUREMENT:

1. Record the following - Initial diameter of specimen. - Final diameter of the specimen. Gauge length of the specimen. - Intial overall length of the specimen. Final overall of specimen. 2. Tabulate the results as follows: Angle of Twist (θ in degrees) Applied Torque T Angle of Twist Over the 50 mm

RESULTS REQUIRED:

a. A graph of applied torque 'T' against angle of twist θ as a base for the elastic region. Use the slope of the graph to determine the value of modulus of rigidity. Also from this graph determine the torque, and then calculate the shear stress at the limit of proportionality. b. A graph of applied torque against angle of twist of the specimen as base, for the complete test destruction. c. Discussions of errors involved in determining the modulus of rigidity using the angle of twist from the machine dial, and compare the result obtained with the value found by using the Torsiometer.

Fig. 1 Typical torsion-test specimens; it is mounted between The two heads of a testing machine and twisted.

Shear Stress

Slope = G= Shear Modulus Shear Strain (Radians)

Fig. 2 The Shear Modulus is the Slope of the Linear Part of the Relationship between the Shear Stress and Shear Strain

OPERATING INSTRUCTIONS FOR THE TORSION TESTING MACHINE AND TORSIOMETER (In Instruction Form)

1. Allow the spring balance to hang free of the torque arm and zero the balance by adjusting the small knurled screw at the top right hand of the balance.

2. Slide the hook of the balance under knife edge on ~ torque arm with the hook. Hanging free its lowest position. 3. Clamp the specimen into the jaws of the Torsion Machine and fit the torsiometer onto the specimen – a full account of this is found in the bulletin under main heading "Use and Operation of Torsiometer". It is essential when using the Torsion Machine to make sure that the whole length of the hexagon ends of the specimen are contained fully within the chuck jaws. Also when the straining head, specimen and Torsiometer...

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