B- Thick cylinder

Calculations: [ d = 37 mm, D = 150 mm, L = 203 mm, E = 73 GPa, = 0.33 ] 1- Draw the relation of the applied pressure with each of the hoop & radial strains that are recorded before for different radius.

P 1 2 3 4 5 6 7 8 9 10 11 12 13

0 0 -3 0 -2 -3 -1 -1 0 -1 -3 -1 -3 -2

1 7 -15 5 -7 -1 -5 0 -2 1 -4 15 -1 -1

2 15 -25 10 -13 1 -9 0 -6 3 -7 33 -4 -3

3 25 -36 15 -20 6 -14 3 -8 6 -8 54 -4 0

4 36 -44 23 -26 9 -16 5 -10 7 -11 72 -5 0

5 47 -56 30 -30 14 -19 80 -10 10 -11 94 -3 3

6 57 -64 36 -36 19 -20 12 -12 13 -13 113 -4 5

P H1 R2 H5 R6 H9 R10

0 0 -3 -3 -1 -1 -3

1 7 -15 -1 -5 1 -4

2 15 -25 1 -9 3 -7

3 25 -36 6 -14 6 -8

4 36 -44 9 -16 7 -11

5 47 -56 14 -19 10 -11

6 57 -64 19 -20 13 -13

2- Calculate the theoretical hoop and radial stress at all the given radius in the

-80

-60

-40

-20

0

20

40

60

80

0 1 2 3 4 5 6 7str

ain

p

H1

R2

H5

R6

H9

R10

experiment [from the inner radius (18.5 mm ) up to outer radius ( 75 mm )] for internal pressure of 3 & 6 MPa

H theo = 3*0.06478*(1+((0.075*0.075)/(0.075^2)))

=0.38868MN/m^2

r theo =3*0.06478*(1+((0.075*0.075)/(0.075^2)))

=0MN/m^2

p radius H theo R theo p radius H theo R theo

3 0.0185 3.388387 -

2.99971 6 0.0185 6.776773 -

5.99941

3 0.028 1.58868 -1.2 6 0.028 3.17736 -2.4

3 0.036 1.03783 -

0.64915 6 0.036 2.075659 -1.2983

3 0.045 0.734173 -

0.34549 6 0.045 1.468347 -

0.69099

3 0.056 0.542925 -

0.15424 6 0.056 1.08585 -

0.30849

3 0.063 0.469765 -

0.08109 6 0.063 0.93953 -

0.16217

3 0.075 0.38868 0 6 0.075 0.77736 0

3- Draw the theoretical and derived hoop stresses and the radial stresses with variable radius ( r ), and estimate the difference between theoretical & experimental

results.at pressure =6 MPa

radius H theo R theo

0.028 3.17736 -2.4

0.036 2.075659 -1.2983

0.045 1.468347 -0.69099

0.056 1.08585 -0.30849

0.063 0.93953 -0.16217

radius H exper

R exper

0.028 1.759668 -

2.63131

0.036 1.181304 -

1.50817

0.045 0.304747 -

1.06743

0.056 0.139266 -

0.68404

0.063 0.276075 -0.7119

H = [ E / ( 1- 2 )] * ( H + R )& R = * E / ( 1- 2 )+ * ( R + H )

H= 81921.22096*( 36 +0.33*-44)/1000000

R =81921.22096*( -44 +0.33*36)/1000000

-3

-2

-1

0

1

2

3

4

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

R exper R theo

H exper

H theo

H exp

R exp

36 -44

23 -26

9 -16

5 -10

7 -11

4- Calculate the longitudinal stress & strain for all the pressure.

L = p r i 2 / ( r O2 r i2)& L theo= [ L - * ( H + R )] / E L=1*0.0185^2/(0.075^2-0.0185^2)& L theo=(0.064786-0.33*(1.12946225+-0.99990225))/73000=0.301802

= 0.064786MN/m^2

p L L theo L

0 0 0 -3

1 0.064786 0.301802 -1

2 0.129573 0.603604 -4

3 0.194359 0.905405 -4

4 0.259145 1.207207 -5

5 0.323932 1.509009 -3

6 0.388718 1.810811 -4

5- Draw the theoretical and measured longitudinal strain with the variable

pressure.

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7

L theo

L theo

-6

-5

-4

-3

-2

-1

0

0 1 2 3 4 5 6 7

L

L

p

p