Torsion report.pdf

7/29/2019 Torsion report.pdf

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OBJECTIVES

The objectives of this experiment are:

1. To develop the relationship between torque T and shear stress with angle of twist .

2. To determine the modulus of rigidity G of the material.

3. To determine the maximum shear stress at the elastic limit and at failure of the material.

THEORY

1. General

At the limit of the elastic range yielding will first occur in the outermost fibres whilst the

core is still elastic. As the specimen is twisted further into the plastic region a greater

proportion of the cross-section yields until there is a plastic zone through into the centre

of the bar. Work hardening occurs at a gradually decreasing rate as straining proceeds.

However, there is no drop in the curve as necking does not occur.

Torsion is a variation of shear occurring in machine axles, drive shafts and twist drills.

From observation, the angle of twist of the shaft is proportional to the applied torque and

to the shaft length. When subjected to torsion, every cross-section of a circular shaft

remains plane and undistorted, because a circular shaft is axisymmetric. Cross-sections of

noncircular shafts are distorted when subjected to torsion.

2. Stress, Strain and Angle of Twist

Consider a solid circular shaft of radius r and length L subjected to a torque T [Nm] at

one end, the other end being fixed (Figure 1). Under the action of this toque, a radial line

at the free end of the shaft twists through an angle [rad], point A moves to B, and AB

subtends an angle at the fixed end. This is then the angle of distortion of the shaft, i.e.

shear strain.


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Figure 1: Schematic representation of torsional deformation.

Arc AB = r= L

= r/L-----(1)

But = /G, where [N/m] is the shear stress and G [N/m] is the modulus of rigidity.

By substitution and rearranging

/r = G/L-----(2)

The torque can be equated to the sum of the moments of the tangential stresses on the

elements 2rr.

T =(2rdr)r = (G/L)(2rdr)r = (G/L)J-----(3)

Where J [m4] is called the polar second moment of area (=r

4/2).

Combining (2) and (3) produces the so-called simple theory of torsion, and gives the

fundamental relationship between shear stress, torque and geometry.

T/J = /r = G/ L-----(4)

Showing that, for a given torque, the shear stress is proportional to the radius.

The shear stresses which are developed in a shaft subjected to pure torsion are indicated

as

= (G/L)r-----(5)

TA

B

r

L

T


3/31

Now from the definition of the modulus rigidity G, = G. It therefore follows that the

two equations may be combined to relate the shear stress and strain in the shaft to the

angle of twist per unit length, thus

= (G/L)r = G-----(6)

This equation indicates that the shear stress and shear strain vary linearly with radius and

have their maximum value at the outside radius.

SPECIMENS AND EQUIPMENTS

1. Torsion testing machineNorwood 50 Nm

2. Vernier caliper

3. Torsion specimens: steel, brass and aluminium

PROCEDURES

1. The initial length and the initial gauge length diameter of the specimen were measured.

2. The specimen was mounted between the loading device and the torque measurement

unit into the straining hexagon sockets.

3. The hand-wheel was turned as required aligning the specimen.

4. The tailstock unit was slide so that the specimen was fully inserted into the hexagon

sockets.

5. It was made sure that there was no preload on the specimen.

6. The pointer on the zero degree point on the protractor scale was zeroed.

7. The digital torque meter was adjusted to read zero.

8. The hand-wheel was turned clockwise slowly to load the specimen. It was only turned

for a defined angle increment.

9. The torque value was read from the digital torque meter and it was noticed together

with the indicated angle of twist.

10. The process of steps 8 and 9 was continued until fracture occurs.

11. The experiment was repeated for other specimens.


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RESULT

Calculation:

T/J = G/L = /r

Torque (Nm) Shear stress (Nm-2

at radius r)

JPolar moment of area (m4) Angle of twist (radius, over length L)

GShear modulus (MNm-2

) LLength of the bar (m)

r - Radius (m)

From the formula above modulus of rigidity, G can be calculated by

J

LkG

Where k is the gradient of the graph torque, T versus angle of twist,.

For Steel

Dimension Reading 1 Reading 2 Reading 3 Average

reading

Initial gauge length

diameter

6.98 6.92 6.00 6.63

Initial length

74.96 74.66 75.00 74.87

Final gauge length

5.90 5.98 5.90 5.93

Finallength

76.76 75.62 75.32 75.90

k=

Sheer stress,


5/31

Angle of Twist,

Torque,T = Tr/J = r/L

() (rad) (Nm) ( Pa ) (rad)

0 0.00 0.00 0.0 0.0010.00 0.17 15.20 265759493.67 0.0120.00 0.35 19.20 335696202.53 0.0230.00 0.52 20.00 349683544.30 0.0240.00 0.70 20.10 351431962.03 0.0350.00 0.87 20.40 356677215.19 0.0460.00 1.05 20.50 358425632.91 0.0570.00 1.22 20.50 358425632.91 0.0580.00 1.40 20.50 358425632.91 0.0690.00 1.57 20.20 353180379.75 0.07

100.00 1.75 20.00 349683544.30 0.08110.00 1.92 19.90 347935126.58 0.09120.00 2.09 19.80 346186708.86 0.09130.00 2.27 19.90 347935126.58 0.10140.00 2.44 20.00 349683544.30 0.11150.00 2.62 20.00 349683544.30 0.12160.00 2.79 20.00 349683544.30 0.12170.00 2.97 20.10 351431962.03 0.13180.00 3.14 20.10 351431962.03 0.14190.00 3.32 20.10 351431962.03 0.15200.00 3.49 20.10 351431962.03 0.16210.00 3.67 19.90

347935126.58 0.16220.00 3.84 19.90 347935126.58 0.17230.00 4.01 19.90 347935126.58 0.18240.00 4.19 19.90 347935126.58 0.19250.00 4.36 19.90 347935126.58 0.19260.00 4.54 20.00 349683544.30 0.20270.00 4.71 20.00 349683544.30 0.21280.00 4.89 20.00 349683544.30 0.22290.00 5.06 20.00 349683544.30 0.22300.00 5.24 20.00 349683544.30 0.23

310.00 5.41 20.00 349683544.30 0.24320.00 5.59 20.00 349683544.30 0.25330.00 5.76 19.70 344438291.14 0.26340.00 5.93 10.50 183583860.76 0.26


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0.00

5.00

10.00

15.00

20.00

25.00

0.00 2.00 4.00 6.00 8.00

Torque(Nm)

Angle of twist,

Torque,T (Nm) versus angle of twist,

Steel

0.0

50000000.0

100000000.0

150000000.0

200000000.0

250000000.0

300000000.0

350000000.0

400000000.0

450000000.0

0.00 2.00 4.00 6.00 8.00

shear stress

Pa

angle of twist,

Shear stress versus angle of twist,

Steel


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For Brass

Readings for Brass

Determination

1 2 3 Average

Initial gauge length diamater, d0

(mm) 6.00 6.00 6.00 6.00

Initial length, L0 (mm) 75.84 76.04 76.00 75.96

Final gauge length diamater, d

(mm) 5.90 5.92 5.88 5.90

Final length, L (mm) 79.4 79.42 79.32 79.38

0.0

50000000.0

100000000.0

150000000.0

200000000.0

250000000.0

300000000.0

350000000.0

400000000.0

450000000.0

0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000

shear stress

Pa

shear strain

shear stress versus shear strain

Steel

1.Proportional Limit Shear Stress in Torsion 26.58x10 Pa

2.Shear modulus of elasticity 3.35GPa

3.Ultimate Shear Stress 3.58x10Pa


8/31

ForBrass,

J = /32 x D4

= /32 x (6.00 x 10-3

)4

= 1.27 x 10-10

m4

k = (7.7-0) / (0.17-0)

= 45.29Nmrad-1

G = (45.29x 75.96x 10-3

) / 1.27 x 10-10

= 27.04GNm-2

Shear stress, = Gr / L

ForBrass,

G = 27.04 GNm-2

= 0.17 rad

L = 75.96 x 10-3

m

r = 3.000 x 10-3

m

= Gr / L

= (27.04x 109)(0.17)(3.00 x 10

-3) / (75.96 x 10

-3)

= 181.55 MPa


9/31

Brass

Angle of Twist, Torque,

T = Tr/J = r/L

() (rad) (Nm) ( Pa ) (rad)

0 0.00 0.00 0.0 0.000010 0.17 7.70 181889763.8 0.0069

20 0.35 9.00 212598425.2 0.0138

30 0.52 9.50 224409448.8 0.0207

40 0.70 9.90 233858267.7 0.0276

50 0.87 10.20 240944881.9 0.0345

60 1.05 10.40 245669291.3 0.0414

70 1.22 10.60 250393700.8 0.0483

80 1.40 10.80 255118110.2 0.0551

90 1.57 10.90 257480315.0 0.0620

100 1.75 11.10 262204724.4 0.0689110 1.92 11.30 266929133.9 0.0758

120 2.09 11.40 269291338.6 0.0827

130 2.27 11.50 271653543.3 0.0896

140 2.44 11.70 276377952.8 0.0965

150 2.62 11.80 278740157.5 0.1034

160 2.79 11.90 281102362.2 0.1103

170 2.97 12.00 283464566.9 0.1172

180 3.14 12.20 288188976.4 0.1241

190 3.32 12.30 290551181.1 0.1310

200 3.49 12.40 292913385.8 0.1379210 3.67 12.50 295275590.6 0.1448

220 3.84 12.60 297637795.3 0.1516

230 4.01 12.70 300000000.0 0.1585

240 4.19 12.80 302362204.7 0.1654

250 4.36 12.90 304724409.4 0.1723

260 4.54 13.00 307086614.2 0.1792

270 4.71 13.10 309448818.9 0.1861

280 4.89 13.20 311811023.6 0.1930

290 5.06 13.30 314173228.3 0.1999

300 5.24 13.40 316535433.1 0.2068310 5.41 13.50 318897637.8 0.2137

320 5.59 13.60 321259842.5 0.2206

330 5.76 13.60 321259842.5 0.2275

340 5.93 13.80 325984252.0 0.2344

350 6.11 13.80 325984252.0 0.2413

360 6.28 13.90 328346456.7 0.2482


10/31

370 6.46 14.00 330708661.4 0.2550

380 6.63 14.10 333070866.1 0.2619

390 6.81 14.20 335433070.9 0.2688

400 6.98 14.20 335433070.9 0.2757

410 7.16 14.30 337795275.6 0.2826

420 7.33 14.40 340157480.3 0.2895

430 7.50 14.50 342519685.0 0.2964

440 7.68 14.50 342519685.0 0.3033

450 7.85 14.60 344881889.8 0.3102

460 8.03 14.70 347244094.5 0.3171

470 8.20 14.70 347244094.5 0.3240

480 8.38 14.70 347244094.5 0.3309

490 8.55 14.90 351968503.9 0.3378

500 8.73 14.90 351968503.9 0.3447

510 8.90 15.00 354330708.7 0.3515

520 9.08 15.10 356692913.4 0.3584

530 9.25 15.20 359055118.1 0.3653

540 9.42 15.20 359055118.1 0.3722

550 9.60 15.30 361417322.8 0.3791

560 9.77 15.40 363779527.6 0.3860

570 9.95 15.40 363779527.6 0.3929

580 10.12 15.40 363779527.6 0.3998

590 10.30 15.50 366141732.3 0.4067

600 10.47 15.60 368503937.0 0.4136

610 10.65 15.60 368503937.0 0.4205620 10.82 15.70 370866141.7 0.4274

630 11.00 15.70 370866141.7 0.4343

640 11.17 15.80 373228346.5 0.4412

650 11.34 15.80 373228346.5 0.4481

660 11.52 15.90 375590551.2 0.4549

670 11.69 15.90 375590551.2 0.4618

680 11.87 16.00 377952755.9 0.4687

690 12.04 16.10 380314960.6 0.4756

700 12.22 16.10 380314960.6 0.4825

710 12.39 16.20 382677165.4 0.4894720 12.57 16.20 382677165.4 0.4963

730 12.74 16.20 382677165.4 0.5032

740 12.92 16.30 385039370.1 0.5101

750 13.09 16.40 387401574.8 0.5170

760 13.26 16.40 387401574.8 0.5239

770 13.44 16.40 387401574.8 0.5308


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780 13.61 16.50 389763779.5 0.5377

790 13.79 16.50 389763779.5 0.5446

800 13.96 16.60 392125984.3 0.5514

810 14.14 16.60 392125984.3 0.5583

820 14.31 16.60 392125984.3 0.5652

830 14.49 16.70 394488189.0 0.5721

840 14.66 16.70 394488189.0 0.5790

850 14.84 16.80 396850393.7 0.5859

860 15.01 16.80 396850393.7 0.5928

870 15.18 16.90 399212598.4 0.5997

880 15.36 16.90 399212598.4 0.6066

890 15.53 -0.22 -5196850.4 0.6135

-5.00

0.00

5.00

10.00

15.00

20.00

0.00 5.00 10.00 15.00 20.00

Torque(Nm)

Angle of twist,

Torque,T (Nm) versus angle of twist,

Brass


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-50000000.0

0.0

50000000.0

100000000.0

150000000.0

200000000.0

250000000.0

300000000.0

350000000.0

400000000.0

450000000.0

0.00 5.00 10.00 15.00 20.00

shear stress

Pa

angle of twist,

Shear stress versus angle of twist,

Brass

-50000000.0

0.0

50000000.0

100000000.0

150000000.0

200000000.0

250000000.0

300000000.0

350000000.0

400000000.0

450000000.0

0.0000 0.2000 0.4000 0.6000 0.8000

shear stressPa

shear strain

shear stress versus shear strain

Brass


2.Shear modulus of elasticity 26.36 GPa

3.Ultimate Shear Stress 3.99 x10Pa


13/31

For aluminium

For aluminium,

J = /32 x D4

= /32 x (6.03 x 10-3

)4

= 1.30 x 10-10

rad.m4

k = (4.3-0) / (0.175-0)

= 24.57Nmrad-1

G =

= 14.43GNm-2

Shear stress, = Gr / L

ForAluminium,

G = 14.43GNm-2

= 0.175 rad

L0 = 76.30 x 10-3

m

Readings for Aluminium

Determination number

Average

1 2 3

Initial gauge length diameterd0 (mm)

6.04 6.00 6.06 6.03

Initial lengthL0 (mm)

76.40 76.18 76.24 76.30

Final gauge length diameter

d (mm)5.94 5.98 6.00 5.97

Final lengthL (mm)

80.00 79.76 80.00 79.92


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r = 3.015 x 10-3

m

= Gr / L

= (14.43GNm-2

)( 0.175 rad)( 3.015 x 10-3

m) / (76.30 x 10-3

m)

= 99.79 MPa

Aluminium

Angle of Twist, Torque, TT

= Tr/J =

r/L

[] [rad] [Nm] [ Pa ] [rad]

0 0.000 0 0 0

10 0.175 4.3 99726923.08 0.007

20 0.349 4.5 104365384.6 0.01430 0.524 4.6 106684615.4 0.021

40 0.698 4.7 109003846.2 0.028

50 0.873 4.8 111323076.9 0.034

60 1.047 4.9 113642307.7 0.041

70 1.222 5 115961538.5 0.048

80 1.396 5.1 118280769.2 0.055

90 1.571 5.2 120600000 0.062

100 1.745 5.2 120600000 0.069

110 1.920 5.3 122919230.8 0.076

120 2.094 5.4 125238461.5 0.083

130 2.269 5.4 125238461.5 0.090

140 2.443 5.5 127557692.3 0.097

150 2.618 5.6 129876923.1 0.103

160 2.793 5.6 129876923.1 0.110

170 2.967 5.6 129876923.1 0.117

180 3.142 5.7 132196153.8 0.124

190 3.316 5.7 132196153.8 0.131

200 3.491 5.8 134515384.6 0.138

210 3.665 5.8 134515384.6 0.145220 3.840 5.8 134515384.6 0.152

230 4.014 5.9 136834615.4 0.159

240 4.189 5.9 136834615.4 0.166

250 4.363 5.9 136834615.4 0.172

260 4.538 5.9 136834615.4 0.179

270 4.712 6 139153846.2 0.186


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280 4.887 6 139153846.2 0.193

290 5.061 6 139153846.2 0.200

300 5.236 6 139153846.2 0.207

310 5.411 6.1 141473076.9 0.214

320 5.585 6.1 141473076.9 0.221

330 5.760 6.1 141473076.9 0.228

340 5.934 6.1 141473076.9 0.234

350 6.109 6.1 141473076.9 0.241

360 6.283 6.1 141473076.9 0.248

370 6.458 6.2 143792307.7 0.255

380 6.632 6.2 143792307.7 0.262

390 6.807 6.2 143792307.7 0.269

400 6.981 6.2 143792307.7 0.276

410 7.156 6.2 143792307.7 0.283

420 7.330 6.2 143792307.7 0.290430 7.505 6.3 146111538.5 0.297

440 7.679 6.3 146111538.5 0.303

450 7.854 6.3 146111538.5 0.310

460 8.029 6.3 146111538.5 0.317

470 8.203 6.3 146111538.5 0.324

480 8.378 6.3 146111538.5 0.331

490 8.552 6.3 146111538.5 0.338

500 8.727 6.3 146111538.5 0.345

510 8.901 6.4 148430769.2 0.352520 9.076 6.4 148430769.2 0.359

530 9.250 6.4 148430769.2 0.366

540 9.425 6.4 148430769.2 0.372

550 9.599 6.4 148430769.2 0.379

560 9.774 6.4 148430769.2 0.386

570 9.948 6.4 148430769.2 0.393

580 10.123 6.5 150750000 0.400

590 10.297 6.5 150750000 0.407

600 10.472 6.5 150750000 0.414

610 10.647 6.5 150750000 0.421

620 10.821 6.5 150750000 0.428

630 10.996 6.5 150750000 0.434

640 11.170 6.5 150750000 0.441

650 11.345 6.5 150750000 0.448

660 11.519 6.5 150750000 0.455


16/31

670 11.694 6.5 150750000 0.462

680 11.868 6.5 150750000 0.469

690 12.043 6.5 150750000 0.476

700 12.217 6.6 153069230.8 0.483

710 12.392 6.6 153069230.8 0.490

720 12.566 6.6 153069230.8 0.497

730 12.741 6.6 153069230.8 0.503

740 12.915 6.6 153069230.8 0.510

750 13.090 6.6 153069230.8 0.517

760 13.265 6.6 153069230.8 0.524

770 13.439 6.6 153069230.8 0.531

780 13.614 6.6 153069230.8 0.538

790 13.788 6.6 153069230.8 0.545

800 13.963 6.6 153069230.8 0.552

810 14.137 6.7 155388461.5 0.559820 14.312 6.7 155388461.5 0.566

830 14.486 6.7 155388461.5 0.572

840 14.661 6.7 155388461.5 0.579

850 14.835 6.7 155388461.5 0.586

860 15.010 6.7 155388461.5 0.593

870 15.184 6.7 155388461.5 0.600

880 15.359 6.7 155388461.5 0.607

890 15.533 6.7 155388461.5 0.614

900 15.708 6.7 155388461.5 0.621910 15.882 6.7 155388461.5 0.628

920 16.057 6.7 155388461.5 0.634

930 16.232 6.7 155388461.5 0.641

940 16.406 6.7 155388461.5 0.648

950 16.581 6.7 155388461.5 0.655

960 16.755 6.7 155388461.5 0.662

970 16.930 6.8 157707692.3 0.669

980 17.104 6.8 157707692.3 0.676

990 17.279 6.8 157707692.3 0.683

1000 17.453 6.8 157707692.3 0.690

1010 17.628 6.8 157707692.3 0.697

1020 17.802 6.8 157707692.3 0.703

1030 17.977 6.8 157707692.3 0.710

1040 18.151 6.8 157707692.3 0.717

1050 18.326 6.8 157707692.3 0.724


17/31

1060 18.500 6.8 157707692.3 0.731

1070 18.675 6.8 157707692.3 0.738

1080 18.850 6.8 157707692.3 0.745

1090 19.024 6.8 157707692.3 0.752

1100 19.199 6.8 157707692.3 0.759

1110 19.373 6.8 157707692.3 0.766

1120 19.548 6.8 157707692.3 0.772

1130 19.722 6.8 157707692.3 0.779

1140 19.897 6.8 157707692.3 0.786

1150 20.071 6.8 157707692.3 0.793

1160 20.246 6.8 157707692.3 0.800

1170 20.420 6.8 157707692.3 0.807

1180 20.595 6.8 157707692.3 0.814

1190 20.769 6.8 157707692.3 0.821

1200 20.944 6.8 157707692.3 0.8281210 21.118 6.8 157707692.3 0.834

1220 21.293 6.8 157707692.3 0.841

1230 21.468 6.8 157707692.3 0.848

1240 21.642 6.8 157707692.3 0.855

1250 21.817 6.8 157707692.3 0.862

1260 21.991 6.8 157707692.3 0.869

1270 22.166 6.9 160026923.1 0.876

1280 22.340 6.9 160026923.1 0.883

1290 22.515 6.9 160026923.1 0.8901300 22.689 6.9 160026923.1 0.897

1310 22.864 6.9 160026923.1 0.903

1320 23.038 6.9 160026923.1 0.910

1330 23.213 6.9 160026923.1 0.917

1340 23.387 6.9 160026923.1 0.924

1350 23.562 6.9 160026923.1 0.931

1360 23.736 6.9 160026923.1 0.938

1370 23.911 6.9 160026923.1 0.945

1380 24.086 6.9 160026923.1 0.952

1390 24.260 6.9 160026923.1 0.959

1400 24.435 6.9 160026923.1 0.966

1410 24.609 6.9 160026923.1 0.972

1420 24.784 6.9 160026923.1 0.979

1430 24.958 6.9 160026923.1 0.986

1440 25.133 6.9 160026923.1 0.993


18/31

1450 25.307 6.9 160026923.1 1.000

1460 25.482 6.9 160026923.1 1.007

1470 25.656 6.9 160026923.1 1.014

1480 25.831 6.9 160026923.1 1.021

1490 26.005 6.9 160026923.1 1.028

1500 26.180 6.9 160026923.1 1.035

1510 26.354 6.9 160026923.1 1.041

1520 26.529 6.9 160026923.1 1.048

1530 26.704 6.9 160026923.1 1.055

1540 26.878 6.9 160026923.1 1.062

1550 27.053 6.9 160026923.1 1.069

1560 27.227 6.9 160026923.1 1.076

1570 27.402 6.9 160026923.1 1.083

1580 27.576 6.9 160026923.1 1.090

1590 27.751 6.9 160026923.1 1.0971600 27.925 6.9 160026923.1 1.103

1610 28.100 6.9 160026923.1 1.110

1620 28.274 6.9 160026923.1 1.117

1630 28.449 6.9 160026923.1 1.124

1640 28.623 6.9 160026923.1 1.131

1650 28.798 6.9 160026923.1 1.138

1660 28.972 6.9 160026923.1 1.145

1670 29.147 6.9 160026923.1 1.152

1680 29.322 6.9 160026923.1 1.1591690 29.496 6.9 160026923.1 1.166

1700 29.671 6.9 160026923.1 1.172

1710 29.845 6.9 160026923.1 1.179

1720 30.020 6.9 160026923.1 1.186

1730 30.194 6.9 160026923.1 1.193

1740 30.369 6.9 160026923.1 1.200

1750 30.543 7 162346153.8 1.207

1760 30.718 7 162346153.8 1.214

1770 30.892 7 162346153.8 1.221

1780 31.067 7 162346153.8 1.228

1790 31.241 7 162346153.8 1.235

1800 31.416 7 162346153.8 1.241

1810 31.590 7 162346153.8 1.248

1820 31.765 7 162346153.8 1.255

1830 31.940 7 162346153.8 1.262


19/31

1840 32.114 7 162346153.8 1.269

1850 32.289 7 162346153.8 1.276

1860 32.463 7 162346153.8 1.283

1870 32.638 7 162346153.8 1.290

1880 32.812 7 162346153.8 1.297

1890 32.987 7 162346153.8 1.303

1900 33.161 7 162346153.8 1.310

1910 33.336 7 162346153.8 1.317

1920 33.510 7 162346153.8 1.324

1930 33.685 7 162346153.8 1.331

1940 33.859 7 162346153.8 1.338

1950 34.034 7 162346153.8 1.345

1960 34.208 7 162346153.8 1.352

1970 34.383 7 162346153.8 1.359

1980 34.558 7 162346153.8 1.3661990 34.732 7 162346153.8 1.372

2000 34.907 7 162346153.8 1.379

2010 35.081 7 162346153.8 1.386

2020 35.256 7 162346153.8 1.393

2030 35.430 7 162346153.8 1.400

2040 35.605 7 162346153.8 1.407

2050 35.779 7 162346153.8 1.414

2060 35.954 7 162346153.8 1.421

2070 36.128 7 162346153.8 1.4282080 36.303 7 162346153.8 1.435

2090 36.477 7 162346153.8 1.441

2100 36.652 7 162346153.8 1.448

2110 36.826 7 162346153.8 1.455

2120 37.001 7.1 164665384.6 1.462

2130 37.176 7.1 164665384.6 1.469

2140 37.350 7.1 164665384.6 1.476

2150 37.525 7.1 164665384.6 1.483

2160 37.699 7.1 164665384.6 1.490

2170 37.874 7.1 164665384.6 1.497

2180 38.048 7.1 164665384.6 1.503

2190 38.223 7.1 164665384.6 1.510

2200 38.397 7.1 164665384.6 1.517

2210 38.572 7.1 164665384.6 1.524

2220 38.746 7.1 164665384.6 1.531


20/31

2230 38.921 7.1 164665384.6 1.538

2240 39.095 7.1 164665384.6 1.545

2250 39.270 7.1 164665384.6 1.552

2260 39.444 7.1 164665384.6 1.559

2270 39.619 7.1 164665384.6 1.566

2280 39.794 7.1 164665384.6 1.572

2290 39.968 7.1 164665384.6 1.579

2300 40.143 7.1 164665384.6 1.586

2310 40.317 7.1 164665384.6 1.593

2320 40.492 7.1 164665384.6 1.600

2330 40.666 7.1 164665384.6 1.607

2340 40.841 7.1 164665384.6 1.614

2350 41.015 7.1 164665384.6 1.621

2360 41.190 7.1 164665384.6 1.628

2370 41.364 7.1 164665384.6 1.6352380 41.539 7.1 164665384.6 1.641

2390 41.713 7.2 166984615.4 1.648

2400 41.888 7.2 166984615.4 1.655

2410 42.062 7.2 166984615.4 1.662

2420 42.237 7.2 166984615.4 1.669

2430 42.412 7.2 166984615.4 1.676

2440 42.586 7.2 166984615.4 1.683

2450 42.761 7.2 166984615.4 1.690

2460 42.935 7.2 166984615.4 1.6972470 43.110 7.2 166984615.4 1.703

2480 43.284 7.2 166984615.4 1.710

2490 43.459 7.2 166984615.4 1.717

2500 43.633 7.2 166984615.4 1.724

2510 43.808 7.2 166984615.4 1.731

2520 43.982 7.2 166984615.4 1.738

2530 44.157 7.2 166984615.4 1.745

2540 44.331 7.2 166984615.4 1.752

2550 44.506 7.2 166984615.4 1.759

2560 44.680 7.2 166984615.4 1.766

2570 44.855 7.2 166984615.4 1.772

2580 45.029 7.2 166984615.4 1.779

2590 45.204 7.2 166984615.4 1.786

2600 45.379 7.2 166984615.4 1.793

2610 45.553 7.2 166984615.4 1.800


21/31

2620 45.728 7.2 166984615.4 1.807

2630 45.902 7.2 166984615.4 1.814

2640 46.077 7.2 166984615.4 1.821

2650 46.251 7.2 166984615.4 1.828

2660 46.426 7.2 166984615.4 1.835

2670 46.600 7.2 166984615.4 1.841

2680 46.775 7.2 166984615.4 1.848

2690 46.949 7.2 166984615.4 1.855

2700 47.124 7.2 166984615.4 1.862

2710 47.298 7.2 166984615.4 1.869

2720 47.473 7.2 166984615.4 1.876

2730 47.647 7.2 166984615.4 1.883

2740 47.822 7.2 166984615.4 1.890

2750 47.997 7.2 166984615.4 1.897

2760 48.171 7.2 166984615.4 1.9032770 48.346 7.2 166984615.4 1.910

2780 48.520 7.2 166984615.4 1.917

2790 48.695 7.2 166984615.4 1.924

2800 48.869 7.2 166984615.4 1.931

2810 49.044 7.3 169303846.2 1.938

2820 49.218 7.3 169303846.2 1.945

2830 49.393 7.3 169303846.2 1.952

2840 49.567 7.3 169303846.2 1.959

2850 49.742 7.3 169303846.2 1.9662860 49.916 7.3 169303846.2 1.972

2870 50.091 7.3 169303846.2 1.979

2880 50.265 7.3 169303846.2 1.986

2890 50.440 7.3 169303846.2 1.993

2900 50.615 7.3 169303846.2 2.000

2910 50.789 7.3 169303846.2 2.007

2920 50.964 7.3 169303846.2 2.014

2930 51.138 7.3 169303846.2 2.021

2940 51.313 7.3 169303846.2 2.028

2950 51.487 7.3 169303846.2 2.035

2960 51.662 7.3 169303846.2 2.041

2970 51.836 7.3 169303846.2 2.048

2980 52.011 7.3 169303846.2 2.055

2990 52.185 7.3 169303846.2 2.062

3000 52.360 7.3 169303846.2 2.069


22/31

3010 52.534 7.3 169303846.2 2.076

3020 52.709 7.3 169303846.2 2.083

3030 52.883 7.3 169303846.2 2.090

3040 53.058 7.3 169303846.2 2.097

3050 53.233 7.3 169303846.2 2.103

3060 53.407 7.3 169303846.2 2.110

3070 53.582 7.4 171623076.9 2.117

3080 53.756 7.4 171623076.9 2.124

3090 53.931 7.4 171623076.9 2.131

3100 54.105 7.4 171623076.9 2.138

3110 54.280 7.4 171623076.9 2.145

3120 54.454 7.4 171623076.9 2.152

3130 54.629 7.4 171623076.9 2.159

3140 54.803 7.4 171623076.9 2.166

3150 54.978 7.4 171623076.9 2.1723160 55.152 7.4 171623076.9 2.179

3170 55.327 7.4 171623076.9 2.186

3180 55.501 7.4 171623076.9 2.193

3190 55.676 7.4 171623076.9 2.200

3200 55.851 7.4 171623076.9 2.207

3210 56.025 7.4 171623076.9 2.214

3220 56.200 7.4 171623076.9 2.221

3230 56.374 7.4 171623076.9 2.228

3240 56.549 7.4 171623076.9 2.2353250 56.723 7.4 171623076.9 2.241

3260 56.898 7.4 171623076.9 2.248

3270 57.072 7.4 171623076.9 2.255

3280 57.247 7.4 171623076.9 2.262

3290 57.421 7.4 171623076.9 2.269

3300 57.596 7.4 171623076.9 2.276

3310 57.770 7.4 171623076.9 2.283

3320 57.945 7.4 171623076.9 2.290

3330 58.119 7.4 171623076.9 2.297

3340 58.294 7.4 171623076.9 2.303

3350 58.469 7.4 171623076.9 2.310

3360 58.643 7.4 171623076.9 2.317

3370 58.818 7.4 171623076.9 2.324

3380 58.992 7.4 171623076.9 2.331

3390 59.167 7.5 173942307.7 2.338


23/31

3400 59.341 7.5 173942307.7 2.345

3410 59.516 7.5 173942307.7 2.352

3420 59.690 7.5 173942307.7 2.359

3430 59.865 7.5 173942307.7 2.366

3440 60.039 7.5 173942307.7 2.372

3450 60.214 7.5 173942307.7 2.379

3460 60.388 7.5 173942307.7 2.386

3470 60.563 7.5 173942307.7 2.393

3480 60.737 7.5 173942307.7 2.400

3490 60.912 7.5 173942307.7 2.407

3500 61.087 7.5 173942307.7 2.414

3510 61.261 7.5 173942307.7 2.421

3520 61.436 7.5 173942307.7 2.428

3530 61.610 7.5 173942307.7 2.435

3540 61.785 7.5 173942307.7 2.4413550 61.959 7.5 173942307.7 2.448

3560 62.134 7.5 173942307.7 2.455

3570 62.308 7.5 173942307.7 2.462

3580 62.483 7.5 173942307.7 2.469

3590 62.657 7.5 173942307.7 2.476

3600 62.832 7.5 173942307.7 2.483

3610 63.006 7.5 173942307.7 2.490

3620 63.181 7.5 173942307.7 2.497

3630 63.355 7.5 173942307.7 2.5033640 63.530 7.5 173942307.7 2.510

3650 63.705 7.5 173942307.7 2.517

3660 63.879 7.5 173942307.7 2.524

3670 64.054 7.5 173942307.7 2.531

3680 64.228 7.5 173942307.7 2.538

3690 64.403 7.5 173942307.7 2.545

3700 64.577 7.5 173942307.7 2.552

3710 64.752 7.5 173942307.7 2.559

3720 64.926 7.5 173942307.7 2.566

3730 65.101 7.5 173942307.7 2.572

3740 65.275 7.5 173942307.7 2.579

3750 65.450 7.5 173942307.7 2.586

3760 65.624 7.5 173942307.7 2.593

3770 65.799 7.5 173942307.7 2.600

3780 65.973 7.5 173942307.7 2.607


24/31

3790 66.148 7.5 173942307.7 2.614

3800 66.323 7.5 173942307.7 2.621

3810 66.497 7.5 173942307.7 2.628

3820 66.672 7.5 173942307.7 2.635

3830 66.846 7.5 173942307.7 2.641

3840 67.021 7.6 176261538.5 2.648

3850 67.195 7.6 176261538.5 2.655

3860 67.370 7.6 176261538.5 2.662

3870 67.544 7.6 176261538.5 2.669

3880 67.719 7.6 176261538.5 2.676

3890 67.893 7.6 176261538.5 2.683

3900 68.068 7.6 176261538.5 2.690

3910 68.242 7.6 176261538.5 2.697

3920 68.417 7.6 176261538.5 2.703

3930 68.591 7.6 176261538.5 2.7103940 68.766 7.6 176261538.5 2.717

3950 68.941 7.6 176261538.5 2.724

3960 69.115 7.6 176261538.5 2.731

3970 69.290 7.6 176261538.5 2.738

3980 69.464 7.6 176261538.5 2.745

3990 69.639 7.6 176261538.5 2.752

4000 69.813 7.6 176261538.5 2.759

4010 69.988 7.6 176261538.5 2.766

4020 70.162 7.7 178580769.2 2.7724030 70.337 7.7 178580769.2 2.779

4040 70.511 7.7 178580769.2 2.786

4050 70.686 7.7 178580769.2 2.793

4060 70.860 7.7 178580769.2 2.800

4070 71.035 7.7 178580769.2 2.807

4080 71.209 7.7 178580769.2 2.814

4090 71.384 7.7 178580769.2 2.821

4100 71.558 7.7 178580769.2 2.828

4110 71.733 7.7 178580769.2 2.835

4120 71.908 7.7 178580769.2 2.841

4130 72.082 7.7 178580769.2 2.848

4140 72.257 7.7 178580769.2 2.855

4150 72.431 7.7 178580769.2 2.862

4160 72.606 7.7 178580769.2 2.869

4170 72.780 7.7 178580769.2 2.876


25/31

4180 72.955 7.7 178580769.2 2.883

4190 73.129 7.7 178580769.2 2.890

4200 73.304 7.7 178580769.2 2.897

4210 73.478 7.7 178580769.2 2.904

4220 73.653 7.7 178580769.2 2.910

4230 73.827 7.7 178580769.2 2.917

4240 74.002 7.7 178580769.2 2.924

4250 74.176 7.7 178580769.2 2.931

4260 74.351 7.7 178580769.2 2.938

4270 74.526 7.7 178580769.2 2.945

4280 74.700 7.7 178580769.2 2.952

4290 74.875 7.7 178580769.2 2.959

4300 75.049 7.7 178580769.2 2.966

4310 75.224 7.7 178580769.2 2.972

4320 75.398 7.7 178580769.2 2.9794330 75.573 7.7 178580769.2 2.986

4340 75.747 7.7 178580769.2 2.993

4350 75.922 7.7 178580769.2 3.000

4360 76.096 7.7 178580769.2 3.007

4370 76.271 7.8 180900000 3.014

4380 76.445 7.8 180900000 3.021

4390 76.620 7.8 180900000 3.028

4400 76.794 7.8 180900000 3.035

4410 76.969 7.8 180900000 3.0414420 77.144 7.8 180900000 3.048

4430 77.318 7.8 180900000 3.055

4440 77.493 7.8 180900000 3.062

4450 77.667 7.8 180900000 3.069

4460 77.842 7.8 180900000 3.076

4470 78.016 7.8 180900000 3.083

4480 78.191 7.8 180900000 3.090

4490 78.365 7.8 180900000 3.097

4500 78.540 7.8 180900000 3.104

4510 78.714 7.8 180900000 3.110

4520 78.889 7.8 180900000 3.117

4530 79.063 7.8 180900000 3.124

4540 79.238 7.8 180900000 3.131

4550 79.412 7.8 180900000 3.138

4560 79.587 7.8 180900000 3.145


26/31

4570 79.762 7.8 180900000 3.152

4580 79.936 7.8 180900000 3.159

4590 80.111 7.8 180900000 3.166

4600 80.285 7.8 180900000 3.172

4610 80.460 7.8 180900000 3.179

4620 80.634 7.8 180900000 3.186

4630 80.809 7.8 180900000 3.193

4640 80.983 7.8 180900000 3.200

4650 81.158 7.8 180900000 3.207

4660 81.332 7.8 180900000 3.214

4670 81.507 7.8 180900000 3.221

4680 81.681 7.8 180900000 3.228

4690 81.856 7.8 180900000 3.235

4700 82.030 7.8 180900000 3.241

4710 82.205 7.8 180900000 3.2484720 82.380 7.8 180900000 3.255

4730 82.554 7.8 180900000 3.262

4740 82.729 7.8 180900000 3.269

4750 82.903 7.8 180900000 3.276

4760 83.078 7.8 180900000 3.283

4770 83.252 7.8 180900000 3.290

4780 83.427 7.8 180900000 3.297

4790 83.601 7.8 180900000 3.304

4800 83.776 7.8 180900000 3.310

4810 83.950 7.8 180900000 3.317

0

2

4

6

8

10

0 20 40 60 80 100

Torque,T

(Nm)

Angle of Twist, (rad)

Torque,T (Nm) versus Angle of Twist,

Aluminium


27/31

0

20000000

40000000

60000000

80000000

100000000

120000000140000000

160000000

180000000

200000000

0.000 20.000 40.000 60.000 80.000 100.000

ShearStress,

(Pa)

Angle of Twist, (rad)

Shear Stress versus Angle of Twist,

Aluminium

0

20000000

4000000060000000

80000000

100000000

120000000

140000000

160000000

180000000

200000000

0 1 2 3 4

shearstress,

Pa

Shear Strain

Shear Stress versus Shear Strain

Aluminium


2.Shear modulus of elasticity 14.2 GPa

3.Ultimate Shear Stress 1.81x10Pa


28/31

DISCUSSIONS

1. Compare and discuss on the experimental results with the theory.

From the graph plotted for torque, T against angle of twist, , we got a straight line from

the beginning original with a positive gradient. At this stage, when the torque is removed

and the specimen will go back to its original shape because it is in the elastic region.

Based on the graph,we know that the twist angle is keep increasing even the increment of

the torque is very small. After going through the elastic region, the specimen will enter

the plastic region and undergo plastic deformation and reach the ultimate strengh withthe

increasing in twist angle until fracture occurs.

For Aluminium:

From the experiment, we know that the twist angle is proportional to the torque. This is

because the aluminium is a ductile material and aluminium can returns to its original

shape when the torque is removed whereby the torque apply is less than the proportional

stage. However, the aluminium graph is not a straight line as a typical shearstressstrain

curve is presented a mainly brittle behaviour is observed. The twist angle will increase

even the torque is very small. This situation will continue until fracture occurs.

For Brass:

Similarly with the aluminium, we know that the twist angle is proportional to the torque.

This is because brass is also a brittle material and brass can returns to its original shape

when the torque is removed whereby the load apply is less than the proportional stage.

Followed by the increment in the twist angle even the torque is very small. It will

continuously happen until fracture occurs.

For Steel:

Based on the experiment, we know that the twist angle is proportional to the torque. This

is because the steel is a brittle material and steel can returns to its original shape when the

torque is removed whereby the torque apply is less than the proportional stage. After that,

the twist angle will increase even the torque is very small after that the specimen will

start to fracture and fully break finally. For the aluminium the theoretical value is

25.5GPa however the value of shear modulus that we get in experiment is 14.91GPa.

While for the brass the theoretical value of shear modulus, G is 37GPa but in our


29/31

experiment the value of shear modulus from the graph torque, T versus angle twist is

10.25GPa.However, for the specimen steel, the theoretical value of shear modulus is

79.3GPa but in the experiment the value of shear modulus we get is 13.98GPa.

2. Discuss on the mechanical properties of the tested specimens in shear.

The mechanical properties which can be obtained from the experiment are the shear

stress, shear stress proportional limit, ultimate shear stress and the modulus of rigidity.

a) Shear stress, is the stress applied parallel or tangential to the surface of a material.

From the results obtained, the shear stress of steel is the highest, followed by brass and

aluminium is the lowest.

b) Shear stress proportional limit is the limit where the specimen will return to its original

dimensions and shape when the load applied is removed. From the graph obtained, the

proportional limit of steel is the highest, followed by brass and aluminium is the lowest.

c) Ultimate shear stress is the maximum shear stress that can be sustained by a material

before rupture. It is the ultimate strength of a material subjected to shear loading. From

the graph obtained, the ultimate shear stress of steel is the highest, followed by brass and

aluminium is the lowest.

d) Modulus of rigidity, G can be obtained from the ratio of shear stress to the shear strain.

It is the rate of change of strain as a function of stress in a specimen subjected to shear or

torsion loading. From the experiment, the modulus of rigidity of steel is the highest,

followed by brass and aluminium is the lowest. This proves that the steel has the highest

brittleness while aluminium has the highest ductility.

3. Discuss on the factors that can be affected to the experimental result.

Factors that can be affected to the experimental result are:

a) The equipment used in our experiment was old and rusted and friction may be created

in the system, hence the value obtained will differ from the theoretical value.

b) In this experiment, the loads must be applied constantly to obtain a perfect rotation.

However, this experiment was done manually. As a result, it was impossible to apply a

constant load on the specimens. Thus, the values obtained from the experiment would

definitely different from the theoretical values.


30/31

c) The difference between theoretical and experimental value was caused by the purity of

the specimens used. In our experiment the specimen used was not fully pure since they

contain impurities and there are imperfections in their structures, contrast with the one

that being used in order to get the theoretical value.

d) In this experiment, the torsion force must be continuously and uniformly supplied. If

we did not control and turn the holder of torsion machine properly with constant force

and rate, it was difficult to get smooth cycle and this will affect our results.

e) Parallax error occurs when our eyes was not placed perpendicular to the scale of the

measuring instruments such as vernier caliper and protractor.

f) The time interval between taking the two continuous reading was very near, so we

cannot get the very accurate readings during the experiment because when the readings

shown by the torsion machine was not rigid and the same time we must get the next

reading within a few seconds.

CONCLUSIONS

1. From this experiment, the mechanical properties of the specimens such as the shear

stress, shear stress proportional limit, ultimate shear stress and the modulus of rigidity are

obtained. When a torque is acting on the specimens, the specimens would experience

torsion until the specimens have reached their fracture points. Furthermore, the modulus

of rigidity, G can be calculated by using the gradient of the graphs plotted for shear stress

against shear strain. From the experiment, the modulus of rigidity of steel is the highest,

followed by brass and aluminium is the lowest. This proves that the steel has the highest

brittleness while aluminium has the highest ductility.

2. Many mechanical structures are subjected to torsion during their operations. By testing

these materials used in these structures on torsion test, the manufacturers are able to

simulate real life service conditions, check products quality, verify designs, and ensure

proper manufacturing techniques as the shear stress, shear stress proportional limit,

ultimate shear stress and the modulus of rigidity of these materials are known.


31/31

REFERENCES

-http://www.sut.ac.th/engineering/metal/pdf/MechMet/10_Torsion%20test.pdf

-http://www.mae.wmich.edu/faculty/kujawski/torsion%20test.pdf

-http://www.instron.us/wa/applications/test_types/torsion/default.aspx?ref=http://www.

google.com.my/url

-http://www.scielo.br/pdf/mr/v11n3/09.pdf

Documents

Torsion report.pdf