Determination of stresses and strains in thick cylinders.
This assignment is based on the work done in the laboratory, in the field of stress analysis, and particularly about stress and strain applied in a thick wall cylinder and the reactions in this cylinder.
This apparatus enables the student to investigate the distribution of radialand hoop stresses and strains throughout the wall of a thick cylinder and to compare experimental results with the theoretical Lame predictions.
The cylinder is made from duraluminium in two halves cemented together. Other face of the joint has an eccentric shallow groove containing ten strain gauges at carefully determined radii and orientation. There measure radial and hoop strains for whichthe corresponding stresses are calculated. The groove is completely filled with jointing cement. Additional strain gauges on the inner and theouter walls enable the measurement of longitudinal and circumferential strains.
The cylinder is mounted in a sturdy frame and the whole unit complete with a hydraulic hand pump for applying pressure is fitted to a modular steel base.
All the straingauges are temperature compensated and forming a full bridge with stability circuit for each channel. Cylinder pressure is measured by an internal transducer and also by a Bourdon gauge. This provides a possible instrumentation based experiment in checking the calibration of the Bourdon gauge.
The aim of this experiment is to get familiar with the theory we have studied in class aboutthick cylinders and about the lame equations. Another thing is to use machines in the lab and know how they work and how to use them, paying attention to taking data, calibration and way of use. Other point is to use some pc program to put in order all the data collected and with this data analyze them and have some conclusions.
The steps we follow was first to calibrate the“cero” pressure and from that be possible to vary the pressure and take data. After it, we put in the cylinder pressure from one to six, and after, waiting few seconds to let the pressure act we took notes, once we reached six, we went down to one again until one. It was difficult to fix exactly the pressure in the pressure we wanted but was certainly close varying only for tenths or hundredths. Twoexperiments were done, one per group, and after the experiment we had to put them in common to make the average data and use that average to do the assignment.
1 ) Tables of experimental and theoretical data.
|Expe. | | | | | | |
|Gauge: |1 |2 |3|4 |5 |6 |
|Radius (m): |0.028 |0.028 |0.036 |0.036 |0.045 |0.045 |
| |ε hoop |ε radial |ε hoop |ε radial |ε hoop |ε radial |
|1MPa |0.011025 |-0.01155 |0.007925 |-0.0048|0.004675 |-0.00205 |
|2MPa |0.0207 |-0.02235 |0.014125 |-0.01025 |0.008625 |-0.004725 |
|3MPa |0.0307 |-0.033525 |0.0205 |-0.015725 |0.0127 |-0.007475 |
|4MPa |0.04065 |-0.044575 |0.026775 |-0.021325 |0.016825|-0.010175 |
|5MPa |0.0505 |-0.055525 |0.03285 |-0.0268 |0.02085 |-0.013025 |
|6MPa |0.0602 |-0.06635 |0.0391 |-0.03205 |0.0249 |-0.01575 |
|7 |8 |9 |10 |11 |12 |13...