# e4-torsion test - Portal

Mechanics

Oct 30, 2013 (4 years and 7 months ago)

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Solid Mechanics

Laboratory Module

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EXPERIMENT
4

TORSION
TEST

1.
OBJECTIVE
S
:

1.1

To understand the concept of mechanical properties of solid materials

1.2

To construct the
shear
stress
-
strain di
agram based on Torsion Testing

Machine
data

1.3

To understand the
mat
erial behavior under torsion

mode

1.4

To

understand how to determine:

(a)

Shear
Modulus

(b)

Proportional limit

(c)

U
ltimate stress

(d)

Maximum elastic displacement

(e)

Maximum shear stress

2. INTRODUCTION

Many products and components are subjected to torsional forces during their

operation.
Products such as
sh
aft
, switches, fasteners, and

automotive steering columns are just a few
devices subject to such torsional

stresses. By testing these products in torsion,
manufacturers are able to simulate

real life service conditions, check product quality, verify
design
s, and ensure proper

manufacturing techniques.

A torsion test can be conducted on most

materials to determine the torsional

properties of
the material. These properties

are m
odulus of elasticity in shear
, y
ield shear strength
,
u
ltimate shear strength
,
and
m
odulus of rupture in shear

and d
uctility

The torsion test generates t
he "torque versus angle" diagram
that
looks

very similar to a
"stress versus strain" curve
in

a tensile

test.

T
hey a
re not the same however
they are
analogous to properties that can be

d
etermined during a tensile test

3.
EQUIPMENT & MATERIAL
S

3.1

Equipment

Torsion Tester

Machine

3.2

Material
s

Aluminum & Mild Steel

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Fig. 1
Torsion test machine

3.

TORSION TEST

The most notable test that demonstrates the effects of shearing forces and res
ulting
stresses is the torsion test of a solid circular bar or rod. As a matter of fact, this test
generates a state of pure shear stress in the torsional loaded rod. Such a test is used to
ascertain all the major shear properties of metal materials, i.e
., the ultimate shear stress, the
yield shear stress and the modulus of rigidity or shear modulus.

Figure 1

The applied torque (
T
)
as
shown in
Figure 1
,
to the specimen and resulting deformation
(angle of twist,

) are measured during the torsion test. These
results

are converted to shear
stress (

) and shear strain(

) by the following respective equations:

(1)

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(2)

where
c

is the radius of the solid circular rod,
L
o

is the length over which the relative angle of
twist is measured (
this angle must be in radians
) and
J

is the polar moment of inertia defined
as follows:

(3)

The shear modulus of elasticity is defined as the linear slope, of the shear stress
-
shear
strain relation, between zero shear stress and the proportional limit shear stress (defined
below), i.e.,

(4)

This equation clearly states that the shear modulus, like Young’s modulus, is only valid for
the linear elastic range of the material

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4.
PROCEDURE

The setup procedure is given as follow:

4.1

Loosen the four screws on the movable steel plate. Mo
ve the movable steel plate
to behind.

4.2

Select the desired test specimen and identify
the material. Record it into a T
able

1
.

4.3

Measure
diameter of the test specimen using appropriate tools. Repeat the
measurement few times and take the average reading.

4.4

Draw,

with a pencil

or marker
, a line

on the straight section o
f the specimen so
that the line

is

9
0 mm
. This will be the gage length,
Lo
.

4.5

Fix the hexagonal sockets to both
sides

of the torque shafts.

4.6

Insert the test specimen to the one of the hexagonal socket
instruction given
by Teaching Engineer
.

4.7

Push the movable steel plate so that the test specimen can be inserted into the
second hexagonal socket. If the test specimen could not fit into the second
socket, slowly turn the motor shaft adjustor un
til the specimen is inserted to the
socket.

4.8

Tighten the four screws provided.

4.9

Switch ON the MCB/ELCB and the ON/OFF switch on the control box.

4.10

Tare the torque meter and the counter to zero reading. Make sure the maximum
is tare

as well.

4.11

Press the ‘RUN’ soft button on the frequency inverter. Slowly increase the
frequency and keep an eye on the torque reading.

4.12

For

every 0.5
Nm of torque increment,
record downs

the value on dial indicator.
Repeat this step until maximum torque re
ached (where the torque
value no
longer increases
).

4.13

Once the maximum torque reached or plastic region reached, press the stop soft
button on the frequency inverter.

4.14

Repeat procedure for each specimen.

4.15

Turn main switch ‘OFF’.

5
.
ANALYSIS

5.1.

Make a table gi
ving the specimen, the original dimensions and the final
dimension
s.
This will be Table
1
.

5.2.

Construct a
shear
stress
-
shear strain

curve from the
torque
-
angle
curve

i.

First,
make copies of

your
torque
-
angle
curve

data and insert it on
Table 2.

ii.

Next,
construct

the
torque
-
angle
curves

software and name it as Fig. 1.
The

torque

is on the y
-
axis and
angle

is on the x
-
axis.
The unit of torque and angle

are
N.m

and
deg
,

respectively.

iii.

For each point, compute the
shear
str
ess

and
angle.
Use
ian

(
)
as the unit for
shear strain

and
M
Pa

as the unit for
shear
stress.
Insert
the result on Table 3

iv.

Plot the data points of
shear
stress vs
.

shear strain

and dr
aw a
smooth curve through them and name it as Fig. 2

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5.3.

Using the
Fig. 2

make the following

c
alculations (and on the graphs, show how

i.

The
shear
modulus.

ii.

Proportional limit

iii.

Ultimate stress

iv.

Maximum elastic displacement (in elastic region)

v.

Maximum shear stress (in elastic region)

5.4.

Make another table

that is
Table
4

and in
sert the results properly.

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Name

:

______________________________
Date

: ______________

Matrix No

:

______________________________

5.
DATA &
RESULT
S
:

TABLE 1

Material Name

Original
Diameter

Original Gage
Length

Final Gage
Length

TABLE
2

No

Torque

(
N.m
)

Angle

(
deg
)

1

2

3

end

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Name

:

______________________________
Date

: ______________

Matrix No

:

______________________________

Fig. 1

Fig. 1
Torque

vs.
A
ngle

TABLE
3

No

Torque

(
N.m

)

Angle

(
deg

)

Shear
Stress

( MPa )

Shear Strain

(
)

1

2

3

end

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Name

:

______________________________
Date

: ______________

Matrix No

:

______________________________

Fig. 2

Fig. 2(a)
Shear
Stress

vs.
Shear Strain

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Name

:

______________________________
Date

: ______________

Matrix No

:

______________________________

TABLE
4

Parameters

Results

The
shear
modulus

Proportional limit

U
ltimate stress

Maximum elastic
displacement

Ma
ximum shear
stress

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Name

:

______________________________
Date

: ______________

Matrix No

:

______________________________

6. QUESTIONS

Torsion?

6.2. Give three example
s

where torsion are applied?

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Name

:

______________________________
Date

: ______________

Matrix No

:

______________________________

7.
DISCUSSION

(
Include a discussion on the result noting trends in measured data, and comparing measurements with theoretical predictions wh
en
possible.

Include the physical interpretation of the results and graphs, the reasons on deviations of your findings from expected resul
ts, your
)

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Name

:

______________________________
Date

: ______________

Matrix No

:

______________________________

8.
CONCLUSION

(
Based on data and discussion, make your overall conclusion by referring to experiment objective
)
.

The conclusion fo
r this lab is…

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REFERENCES

R.C. Hibbeler. (2005).

SI 2
th
.
e
d
.

Mechanics of Materials
.
Prentice Hall

James M. Gere
. (200
4
).

6
th

ed.
Mechanics of Materials.
Thomson
.

David W. A. Rees
.(
2000
)
.
Mechanics of Solids and Struc
tures

Imperial College Press
.

Instron Homepage, www.instron.com

APPENDIX

Shear Modulus of Elasticity

Tangent or secant modulus of elasticity of a material subjected to shear loading.
Alternate terms are modulus of rigidity and modulus of elasticity
in shear. Also, shear
modulus of elasticity usually is equal to

Torsional Modulus of Elasticity.
A method for
determining shear modulus of elasticity of structural materials by means of a twisting test
is given in ASTM E
-
143. A method for determining shear

modulus of structural
adhesives is given in ASTM E
-
229.

Torsional Modulus of Elasticity

Modulus of

Elasticity