Thick Cylinders Lab Report
Design Analysis 2
FOA: Dr Tony Murmu
Submission Date: 18th December 2015
B00259331

Aim

The purpose of this experiment was to determine the distribution of stress in a thick cylinder when subjected to internal pressure. This experiment aids the understanding of how a cylinder withstands internal pressures and how the behaviour of stresses varies at different points along the cylinder radius.
Theory

Using Lame's equations for a thick cylinder subjected to an internal pressure, the following equations, based on pressure and geometry, may be obtained to calculate hoop and radial stresses:

σθ= PK2-1(1+ R22r2)

σr= PK2-1(1- R22r2)
Where:

P = Internal pressure
R1 = Internal radius of the cylinder R2 = External radius of the cylinder K = R2R1 r = Radius to selected strain gauge

Furthermore, equations based on material properties and experimental values may be used to calculate hoop and radial stresses: σθ=E1-v2(εθ+vεr) σr= E1- v2(εr+vεθ) Where: E = Modulus of elasticity v = Poisson’s ratio εθ= Hoop Strain εr= Radial Strain

Apparatus * “TQ” SM1011 Thick Cylinder * PC with “VDAS” software The SM1011 consists of an aluminium alloy cylinder where the two halves are firmly locked together and held using two circular, steel diaphragms. One face of the joint (at right angles to the longitudinal axis) between the two halves has a shallow groove turned eccentrically to the bore which contains ten active strain gauges (5 hoop, 5 radial) fixed as shown in Figure 1. The cylinder can be subjected to various internal pressures using the hand wheel attached. Cylinder Specifications: Dimensions (mm): 203(L); 150(ID); 37(OD) Material: Aluminium alloy HE15 Properties: E = 73.5GN/m2 v = 0.33

Figure 1: Location of strain gauges within the cylinder

Method * Switch on apparatus at least 30 minutes before commencing the experiment to allow for the strain gauges to adjust to the surrounding temperatures * Turn on the “VDAS” software for the thick cylinder * Using the “GUI” connect the device: Connection - Connect To Device * Create a new data reading series: Data - Maintain Data Series - New Data Series * Zero the strain gauges using the button positioned on the facia of the apparatus and using the “GUI” take reading for a pressure of zero: Data - Record Data Values * In increments of 0.5MN/m2, take stain gauge readings up to a pressure of 5MN/m2 * Once all reading have been taken they can be viewed: Data - View Data Readings * Export all readings to a file that can be viewed using excel for processing: File - Export - HTML

Figure 2: Strain Gauge Layout

Results
Table 1: Effect of internal pressure on hoop strains (and strains at circumferences)

Table 2: Effect of internal pressure on radial strains (and longitudinal strain)

The following charts display how the strain gauges responded to increasing internal Pressure:

N.B.
All charts shown are representative, due to fluctuations in the readings obtained from the SM1011 apparatus not all baseline values were set to zero. This has been accounted for in the charts for strain gauges: 2, 4, 6, 7, 9 and 13. The pressure values displayed in the charts have been rounded to one decimal place.
Calculations

P = 4.5 MN/m2 E=73.5GN/m2 v=0.33 R1 = 0.0185 m R2 = 0.075 m K = 4.054

Gauges 1 and 2:

a17Pa Pa and 2:one decimal place.es are alsos been accounted for in the charts for strain gauges: 2, 4, 6, 7, 9,13

Gauges 3 and 4:

Gauges 5 and 6:

Gauges 7 and 8:

Gauges 9 and 10:

Discussion
The theoretical results are noticeably similar to the experimental values. The theoretical stress values are consistently smaller than the experimental ones, however they appear to follow the same pattern of decrement so may be considered respectably accurate.