Modulus of Rigidity_Calculations

7/23/2019 Modulus of Rigidity_Calculations

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Sample Sr.No

Angle of Twist

At 400mm from fixed end At 200mm from fixed end

Degree Radian Degree Radian

1 2 3 5 3.5 0.01745 0.02618

2 4 6 10 5.5 0.01745 0.07854

3 6 9 14 7.5 0.01745 0.11345

4 8 12 18.25 9.5 0.01745 0.15272

5 10 15 22.5 11.25 0.01745 0.19635

6 12 18 27.5 14 0.01745 0.23562

Length 10

Diameter 0.198

1.51E-04

Slope " m " 72.808

G 4.83E0!

"oad#$#

% N &

Tor'(e

##

% Nmm &

Steel Rod%4!0mm x )mm dia&

Polar oment o!nertia " # "

0.01000 0.06000 0.11000 0.16000 0.21000 0.260000

5

10

15

20

f(x) = 72.7526571842x + 0.765070543

R = 0.9976791058

Relationship between Torque & Angle of Twist

Deection ( mm )

Loa ( ! )


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Angle of Twist

At 400mm from fixed end At 200mm from fixed end

Degree Radian Degree Radian

3 5

6 10

9 14

12 18.25

15 22.5

18 27.5

Length 10

Diameter 0.198

1.51E-04

Slope " m " 72.808

G 4.83E0!

"oad

#$#

% N &

Tor'(e

##

% Nmm &

Polar oment o!nertia " # "

0 5 10 15 20 25 300

5

10

15

20

f(x) = 0.6799106186x " 0.5202179436

R = 0.9988210755

Relationship between Torque & Angle of Twist

Angle of Twist ( radians )

Torque ( Nmm )


3/8

Spe,imen

Torsion Test on"engt/ of ar +00mm

Radi(s of S/aft +)mm

Diameter of ar !mm

$olar oment of 1nertia 2+.23

Sr.No

Angle of Twist

At 400mm At 200mm

Degree Radians Degree Radians

1 3 150 1 0.017

2 6 300 3 0.052

3 9 450 5 0.087

4 8 600 7 0.122

5 10 750 9 0.157

6 12 900 11 0.192

7 14 1050 13 0.227

8 16 1200 15 0.262

9 18 1350 17 0.297

10 20 1500 19 0.332

11 22 1650 21 0.367

12 24 1800 23 0.401

13 26 1950 25 0.436

14 28 2100 27 0.471

15 30 2250 29 0.506

16 32 2400 31 0.541

17 34 2550 33 0.576

18 36 2700 35 0.611

19 38 2850 37 0.646

20 40 3000 39 0.681

mm#

"oad

#N#

Tor'(e #Nmm #


4/8

Solid -ir,(lar ar

765450000

510300000

459270000

437400000

425250000

417518181.818182

412165384.615385

408240000

405238235.294118

402868421.052632

400950000

399365217.391304

398034000

396900000

395922413.793103

395070967.741935

394322727.272727

393660000

393068918.918919

392538461.538462

od(l(s of Rigidit*# G #

$%ic& 'e(e fo


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)(a*+


6/8

Sr. No

1 150 0.0174532925

2 300 0.0523598776

3 450 0.0872664626

4 600 0.1221730476

5 750 0.1570796327

6 900 0.1919862177

7 1050 0.2268928028

8 1200 0.2617993878

9 1350 0.2967059728

10 1500 0.3316125579

11 1650 0.3665191429

12 1800 0.401425728

13 1950 0.436332313

14 2100 0.471238898

15 2250 0.5061454831

16 2400 0.5410520681

17 2550 0.5759586532

18 2700 0.6108652382

19 2850 0.6457718232

20 3000 0.6806784083

Tor'(e% Nmm &

Angle of Twist% radians &

50

100

150

200

250

300

350

Applied Tor'


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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

f(x) = 4!"#$%&4'&4%$x "

$+a(t ,it%e

Angle of Twist % radians &

e % Nmm &


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Modulus of Rigidity_Calculations