Mechanical Engineering Lab report

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OAKLAND UNIVERSITY School of Engineering and Computer Science

ME 361 Mechanics of Materials

Laboratory 3

STRESSES IN A PRESSURE VESSEL

1. Objective To study stresses in a thin walled pressure vessel and to compare experimental results with theoretical

values.

2. Reference 2.1 Class Notes 2.2 Mechanics of Materials, 4th Ed., by Beer and Johnson, Mc Graw-Hill, Inc., 2005.

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3. Apparatus/Materials 3.1 Strain gauged pressure vessel.

3.2 Compressed air source

3.3 VISHAY strain gauge Indicators.

4. Procedure 4.1 Figure 1 is the schematic of the pressure vessel and pressure gauge you will use in the experiment.

Connect it to the compressed air source available in the lab room (this would be done by the

Teaching assistant). NOTE: Pressure limit warning on the equipment and do not exceed this

limit (60 psi recommended).

Fig.1 Schematic of apparatus

4.2 As you use each strain gauge on the tank, the strain gauge indicators must be connected, calibrated and balanced to measure strain. Refer to the following procedure:

4.2.1 As the single gauges are used in the experiment, the quarter bridge should be used. Make sure that the most-right button is on the 1/4 -1/2 position (Black, unpressed). The two

cables from the connector of the gauge should be connected to P+ and S- of the indicator.

Also due to the resistance value of the gauge is 120, the jumper line will be connected between S- and D120 connectors.

4.2.2 Check the AMP to be zero: push the “AMP ZERO” button to make sure it is zero. Otherwise, you can make adjustment by turning AMP ZERO knobby hand on the left side

of the board.

4.2.3 Check the Gauge factor: Push the “GAUGE FACTOR” button to make sure it is in the

right value. In this experiment the gauge factor is 2.045  0.005.

4.2.4 Final step is to balance (at least one gauge should be balanced).

4.3 After connecting strain gauge indicators to the particular gauge for which measurements are to be made, pressurize the tank to 10 psi and balance the instrument (At least one gauge should be

balanced and in this case record the other strain gauges). Then increase the pressure from 10 to 50

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psi and note the strain. For each gauge used, the tank must be depressurized to 10 psi and the

indicator balanced and calibrated if necessary.

4.4 For cylindrical section of tank, measure and record hoop strain at gauges 1, 3, 5 and 9: measure and record longitudinal strain at gauges 2, 4, 6 and 10.

4.5 For spherical section of tank, measure and record hoop strain at 7, measure and record strain at gauge 8.

4.6 The following information should be recorded also 4.6.1 The direction of orientation of each gauge used. 4.6.2 Location of each strain gauge on the pressure vessel.

5 Parameters: E = Modulus of elasticity of Aluminum = 10.16 × 10 6 psi

 = Poisson’s ratio, 0.34

D = 5.077 in, outer diameter of cylindrical section

r = Inner radius of cylindrical section as well as inner radius of spherical portion

 = Strain gauge readings in inch/inch (Note: the strain gives only  values) t = Thickness of pressure vessel for each location

t 1,2 = 0.079 in

t 3,4 = 0.08 in

t 5,6 = 0.079 in

t 7,8 = 0.109 in

t 9,10 = 0.076 in

P = Internal loading pressure

Gauge factor = 2.045  0.005

Resistance value of the gauge is 120 

6 Calculations 6.1 Calculate the theoretical values of circumferential and longitudinal stress for each strain gauge

position studied.

For cylindrical portion:

t

rp x

2

  (Longitudinal stress)

t

rp y

  (Hoop stress)

For spherical portion:

t

rp yx

2

  

6.2 Calculate the experimental values of circumferential and longitudinal stress for each strain gauge

position from the strain gauge output using the formula:

4

)( 1

)( 1

2

2

xyy

yxx

E

E

 



 



 



 



6.3. Compare, in a table, the theoretical and experimental values of stress. Explain difference, if any,

between experimental and theoretical values.

7 Questions (answers to be included as part of discussion) 7.1 Is it better to have a hemi-spherical or flat ends for a cylindrical pressure vessel? Explain this

aspect with respect to the stresses that you may observe in a flat end vs. a hemi sphere end.

7.2. What would be the maximum pressure that the pressure vessel can withstand without failure?

Assume that the factor of safety is 3 and the ultimate normal stress u = 38 ksi and the ultimate

shearing stress u = 24 ksi for this aluminum material.

7.3. From the answer provided in question 7.2, where do you think this cylindrical pressure vessel with

hemi spherical ends will fail first? Why?

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SAMPLE OF EXPERIMENTAL DATA

Pressure Gauge 1*

90o

Gauge 2

0o

Gauge 3

90o

Gauge 4

0o …

Gauge 9

90o

Gauge 10

0o

10Psi ∆p 0 ∆εy 79 ∆εx 29 ∆εy … ∆εx ∆εy ∆εx

20Psi 10Psi 19 19 85 6 58 29 … …

30Psi 10Psi 40 21 92 7 86 28 … …

40Psi 10Psi 63 23 98 6 116 30 … …

50Psi 10Psi 85 22 104 6 145 29 … …



y 

21.3μ

 x

 6.3μ



y 

29μ  x

 y

 x

*Only Gauge 1 is balanced here.

Experimental values at the point (i, j) on cylindrical surface:

ijxyy

ijyxx

E

E

)( 1

)( 1

2

2

 



 



 



 



the x

 and y

 is average value for ∆p.

Theoretical values at the point (i, j) on cylindrical surface:

ij

x t

rp

2

  (Longitudinal stress)

ij

y t

rp   (Hoop stress)

In which (i, j)=(1, 2),(3, 4),(5, 6), (9, 10)

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NOTICE: (a)Check the two valves to be sure that they are closed before power on the air compressor;

(b) Pressure limit warning on the equipment and do not exceed this limit (60 psi recommended); (c) At

the end of experiment, close the two valves and disconnect the high-pressure pipe from the strain gauged

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vessel. Pull deflator to deflate the air compressor. Open the valve A of the strain gauged vessel to deflate

strain gauged vessel.