ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Experimental Stress Analysis in Superpressure E. J. MICKEVICZ'
U. S.
W
Naval Ordnance laborafory, White Oak, Silver Spring, 1
HY should the superpressure designer be interested in ex-
perimental stress analysis? Because experimental stress analysis when properly applied can help him to determine and improve the mechanical strength of structures and machines. Although many excellent review articles on theoretical stress calculations have appeared in the technical press, experimental stress analysis has not always received the attention i t deserves. Such methods as photoelasticity, brittle lacquer examination, and strain gage studies can be and have been applied in the field of superpressure design with quite useful results. Photoelasticity is an optical method of determining the stresses in structures. Stresscoat is a largely mechanical means, and resistance strain gages are an electrical technique, After a brief description of each of these techniques, their application to specific problems in superpressure design is discussed. Photoelasticity, the optical method, utilizes a transparent plastic model which is subjected to simulated service loading while a beam of polarized light is passed through it. Under these conditions a pattern of alternating light and dark bands 1
Present position, General Electric Co., Special Defense Projects Dept.,
3198 Chestnut St., Philadelphia, Pa.
Figure 1.
854
Md.
called interference fringes is formed with monochromatic light. These fringes represent the loci of constant principal shear stresses. An analysis of these fringe patterns yields both qualitative and quantitative knowledge of the stress distribution within the model ( W W , % S ) . The apparatus used in making photoelastic anaIysis is called a polariscope; a simplified commercial model made by General Radio Corp, Cambridge, Mass., is shown in Figure 1. This diffused light polariscope consists of a lamp and housing, a diffuser, a polarizing screen, a pair of quarter-wave plates, a specinien holder and straining bridge, an analyzer, a monochromatic filter, and a camera, preferably one equipped with a ground-glass screen. Brittle lacquer examination, specifically the use of the proprietary material known as Stresscoat, sold by Magnaflux Corp., Chicago, Ili., is the process in which a brittle lacquer is sprayed on the structure under test and allowed to dry (15, 16). As the structure is stressed, the lacquer cracks a t right angles to the principal tensile stress indicating relative stress levels and areas of stress concentration during actual operation. The threshold sensitivity range of the Stresscoat, defined as the tensile strain which causes the initial appearance of a crack, extends from
Commercial model of a photoelastic polariscope
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 5
EXTREME CONDITION PROCESSING
Figure 2.
Calibration strip in strain scale
Initial pattern at 0.001 1 inch/inch strain or 33,000 Ib./sq. inch stress on steel
0.0002 inch per inch t o 0.001 inch per inch, corresponding to tensile stresses of 6000 and 30,000 pounds per square inch in steel. Detection of the initial crack can be made easier in some instances by the use of Statiflux technique, a method originally devised to locate ordinarily invisible cracks in nonmetals, ceramics, and porcelain-enameled steel (48). After the crack pattern has been developed, it can be dye-etched to render i t permanent and to simplify photographing the pattern. Figure 2 shows the crack pattern developed in a Xtresscoated caiibration strip used to determine the threshold sensitivity of the applied coating. Electric resistance strain gages, which are cemented to the apparatus at the points where a measure of the stress is desired, consist of a grid of fine wire which changes its resistance when stretched (44). By electronically monitoring this change in resistance a continuous measure of the development of stresses under operating conditions is obtained. Figure 3 is a schematic drawing of an SR-4 electric resistance strain gage manufactured by Baldwin-Lima-Hamilton Corp., Philadelphia, Pa. These gages are available in sizes ranging from a minimum of l/&nch grid length to a maximum 9-inch grid length (32). Another newer type of strain gage, known as a foil strain gage, also available from Baldwin-Lima-Hamilton Corp., operates on similar principles and is frequently applicable to the solution of similar problems (33, 40,47). Figure 4 shows a typical linear foil strain gage. Table I gives a comparison of the practical applications of these three techniques-namely, photoelasticity, brittle lacquer analysis, and strain gage studies. Typical design problems, among which are the measurement of operating loads, external and internal surface stresses, bending stresses, stress concentrations, high temperature effects, shrink-fit and residual forces, internal stresses, and others, have yielded to these experimental methods.
Application of Stress Analysis Measurement of Operating Loads. Before the engineer can create a rational design some knowledge of the operating conditions to which the pressure vessel will be subjected is essential. If these conditions must be assumed, it is regrettable. If on the other hand some quantitative data are available, then the design process is based on firmer ground. Electric resistance strain gages are frequently used to measure the actual operating loads applied to a part. By properly instrumenting the member a continuous record of the load fluctuations with time can be obtained and made available t o the designer. Unexpected vibrations, transient shocks, and stress peaks may be discovered in this way. Locating the strain gages to best advantage is made easier if Stresscoat is applied first, and the regions of stress concentration thereby revealed. Care must be exercised in selecting recording equipment with a rapid enough response so that transient shocks may be faithfully recorded (68,30). Measurement of Stresses on External Surfaces. Early in the design stage photoelasticity is of great value in determining the optimum shape (31). I n Figure 5 the fringe patterns obtained May 1956
with a “two-dimensional” model of a pressure vessel bulkhead are shown. A comparison between different fillet radii waa made to determine the one most suitable for this application. I n this sample only one model was made and from i t each of the others was made in turn after each fringe pattern under load had been photographed. After the photographs were compared, one of the radii was specified on the drawings. This problem was successfully solved without the need for laborious computations to determine the actual value of the individual stresses; a qualitative examination was sufficient in this particular case. Once the actual apparatus is available, the other two techniques -Stresscoat and strain gages-come into play. Customarily Stresscoat is applied to the pressure apparatus which is then
hp
I \
STRAIN SENSITIVE
AXIS
i
YO01 DlA. WIRE BONDING
CEMENT
F E L T PROTECTION PAD
‘LEAD
WIRE’S
PLAN (FELT
Figure 3.
PAD R E M O V E D )
CROSS
S E C T I O N A-A
Plan and cross-section views of typical wire resistance strain gage
tested to the proof pressure. If there are no abnormal or unexpected indications developed during test, then the Stresscoat examination may suffice. But, if there are indications of stress concentrations or unexpectedly highly stressed surfaces, then this brittle lacquer examination should be followed with the application of strain gages. An externally pressurized vessel carrying instrumentation which permitted the remote monitoring of 72 channels of information is shown in Figure 6. Measurement of Stresses on Internal Surfaces. Here, again, photoelasticity is quite useful in establishing the optimum design, if applied early. A model can be made and loaded similarly to the expected operating conditions. After fringe photographs are made, minor changes can be introduced in the geometrical configuration and the loading pattern, while the behavior of the specimen to this range of conditions is checked. If the actual superpressure apparatus is a t hand, then the best
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
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ENGINEERING. DESIGN. AND PROCESS DEVELOPMENT ~~
To ble I. Desired design measurement External surface stresses
Application of Experimental Stress Analysis to Superpressure Design Ratin$ C
Photoelasticitya Lit. cited (19, 20, 22, 23, 30, 31, 34, 38, 55)
Ratingb B
Stresscoat Lit. cited (15, 16, 19, 31, 46)
Internal surface stresses
B
(20-23, 30, 37, 5-51
Stresses throughout member
A
Stress change as design is modified Stress concentrations
A
(19, 20, 22, 23, Not recommended 30, 31, 34, 55) (19, 22, 23, 30, B 31, 38, 55) (19, 20, 22, 23, B 30, 31, 34, 35, 37, 45, 51,55) (43) A
A
Not recommended
Residual stresses
Not recommended
Shrink fit stresses Stresses at high temperatures
B Not recommended
(22-24, 47)
Thermal stresses Bending stresses
Not recommended B
Not recommended (19, 20, 22, 23, Not recommended 3 0 , 3 1 , 34)
Mot recommended
Bo
Strain Gages Ratingb Lit. cited A ( 4 , 5 , 26, 27, 30, 32, 38, 40, 41, 49, 53) A ( 8 , 12, 26. 27, 30, 32, 33, 35, 40, 42, 49,50) Not recommended
( 1 5 , 16, 30, 38, 46) (15, 16, 30, 39, 45, 46) (20, 30, 36, 46, 54) (48)
e
( 4 , 30, 32, 38)
c,
( 4 , 26, 27, 30,
39,45) ( 2 , 21, 29, 30, 36) ( 3 , 9-11, 25, 56)
13
( 9 , 1 0 , 56) ( 4 , 6, 30, 32)
Imposed operating loads Not recommended B ( 1 5 , 1 6 ,46) Not recommended Operating stress level used to Not recommended control equipment 0 The photoelastic approach necessitates manufacture of a model; this technique is not applicable to measurement of actual stresses or strains in an operating superpressure vessel. b Letters give estimated order of performance in practical design of superpressure equipment. c Stresscoat All-Temp, a ceramic-base material, may be applicable.
means of investigating inner surface stresses is to use electric resistance strain gages. Many investigators have cemented strain gages to the inner walls of pressure vessels and operated them a t high pressures (8, 12, 41). To bring electrical information into and out of pressure vessels at these pressures, a number of electrical seals have been developed. Seals are described by Bridgman (7), Steele ( 5 0 ) ,and the National Bureau of Standards (4%'); the latter seal is stated to be operable up to 100,000 pounds per square inch A large measure of care must be exercised in interpreting strain gage readings obtained in this manner. Clough, Shank, and Zaid (ib) say that the deviation in output between a pair of strain gages cemented to two identical blocks and subjected to direct pressure can be as great as 26 microinches per inch per 1000 pounds per square inch; a quantity great enough to mask the actual stress reading in the inner wall. (This phenomenon appears to be due to nonuniformity in bonding the different gages.) Riickevicz reports a similar coefficient for foil strain gages but of lesser magnitude in the order of 2 microinches per inch per 1000 pounds per square inch (40). If designers are not aware of this effect under superpressure environments, misinter-
Figure 4.
856
pretation of the experimental data may result. T o minimize the danger of misinterpretation, the use of multiple strain gages on the interior walls is recommended; comparison of the readings among similarly placed strain gages should allow an estimate of the "best" gage reading t o be made. Unfortunately, to return the apparatus to a no-load level after cycling to pressure and then to examine the zero shift of the strain gages are not generally sufficient to detect the appearance of this effect. Bending Stress Measurement. If the existence of bending stresses is suspected in the pressure vessel shell and their magnitude is desired, two methods of applying strain gages are available to measure this data. In the first method strain gages are placed a t selected locations on the outer wall of the vessel and then mating gages are placed on the inner wall a t congruent locations. Comparison of the two gage readings will give a measure of the bending and direct stresses. If the inner mall is inaccessible, then the same information may be obtained through the use of a method originally described by Brewer (6). I n this technique a separate bridge is built spanning the strain gage on the surface. When operating, readings are taken of the gage on
Typical linear foil strain gage
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 5
EXTREME CONDITION PROCESSING
Figure 5. Photoelastic study of fillet radii in pressure vessel bulkhead
* the surface and also on the bridge. By introducing these values into the relationships given by Brewer, it is possible to calculate the magnitude of the bending and direct stresses individually. Stress Concentrations. Many stress concentration factors have been determined both theoretically and empirically. (Theoretical stress concentration factors are discussed by Neuber in his book, “Theory of Notch Stresses-Principles for Exact Stress Calculation,” Translation 74 by the David Taylor Model Basin, Carderock, Md.) Several excellent handbooks are available giving the stress concentration factors, usually determined by photoelastic analysis, for a large number of geometrical configurations. There are perhaps two outstanding texts in this field-one written by Peterson (46)and the other by Lipson, Noll, and Clock (59). Stress concentration factors associated with a diametral hole drilled into a cylinder were measured a t the inner wall surface with an ingenious adaptation of the photoelastic technique. Lamble and Bayoumi (97‘) used a composite model and measured a stress concentration factor of 1.7 a t the inner wall for a ‘/‘-inch-diameter hole drilled in a a-inch-i.d..by 3-inch-0.d. cylinder. Stress concentration effects can also be measured with Stresscoat and strain gages, Figure 7 ( A , B, and C)shows a tubing sample in which the effect of different shapes of vents was investigated. The comparison was made between a circular hole and an elongated, circular-ended slot. Specimens were obtained and blind holes and slots were milled in the outer surfaces-Le., the hole and the slot did not penetrate through the wall of the tubing in
May 1956
Figure 6. Externally pressurized vessel carrying instrumentation which permitted remote monitoring of 72 channels of information
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
857
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Figure 9. Stresscoat residual stress patterns Y
t
f
1
i
1
i
t
SIMPLE COMPRES SlON
BIAXIAL COMPRESSION
BIAXIAL TENSION
SIMPLE TENSION
.
Figure 7. Stress concentration effects Tubing samples used to study effect of vent geometry 8. Stresscoat pattern in vicinity of elongated slots C. Stresscoat pattern in vicinity of circular vents
A.
Figure 8. Stresscoat isoentatic patterns surrounding tubing fittings in superpressure vessel
kb
858
Figure
10. Residual molding stresses in plastic fuze revealed by Stresscoat technique
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 5
EXTREME CONDITION PROCESSING any place, After this machining, the tubes were Stresscoated and subjected to dynamic pressure pluses ranging from 5,000 to 25,000 pounds per square inch lasting only a few milliseconds. The resulting Stresscoat patterns were then dye-etched and photographed. As the pressure pulse levels were raised, the crack pattern extended over a greater area of the tube. By comparing the pressure pulse required to crack the entire Stresscoat pattern to that required to initiate the first trace of a crack a t the vent, a measure of the stress concentration effect of the different vents was obtained, Strain gages were also applied to this problem but were not so effective because of their large gage length compared to the vent size. Another case of stress concentration measurement in a pressure vessel is shown in Figure 8. Here the effect of a tapped hole for a superpressure fitting was determined using Stresscoat applied to the outside surface. The development of the crack pattern is delineated by the heavy line drawn through the ends of the crack pattern. As the pressure level is raised the cracks develop and extend further, at which time another line is drawn through the ends. In this fashion a graphic indication of the development and growth of the stress distribution may be obtained. Stress Measurement at High Temperatures. Because of the complications introduced by temperature effects, stress measurement above room temperature generally requires special techniques. For temperatures up to about 500' F. phenolicbase, electric resistance strain gages cemented with baked phenolic adhesives are quite suitable. Precautions must be taken to evaluate correctly and compensate for the effect of temperature, on the strain gages; practical procedures are described by several writers (10, 1 1 , l J ) . For operation in therange -50" to350'F. strain gages are commercially available which are self-temperature compensating-Le., the thermal coefficients are matched to those of the material to which the. gages are attached so that there will be no response to purely thermal effects (3). Gages are available compensated for application to either steel or dural. Commercial strain gages are also available for operation up to 1000° F. and should be used when operation in excess of 500" F. is anticipated. The authoritative publication in the field of high temperature strain gages is entitled, "Summary Report on High Temperature Strain Gage Research" (62). Also applicable to the measurement of stresses at high temperatures is a brittle coating known as Stresscoat All-Temp. This is a ceramic-base material which is applied similarly to Stresscoat and then fired. After firing the apparatus is operated and the coating cracks in similar fashion. The disadvantage of this technique is that superpressure equipment must be sent t o the manufacturer for spraying and subsequent firing. Thermal stresses in superpressure vessels are probably most easily investigated using strain gages selected to function successfully a t the operating temperature. The work by Campbell, formerly of the National Bureau of Standards, is very helpful in this regard (9). Shrink Fit Stresses. Two methods can be applied to the measurement of shrink fit stresses incurred in making multilayer vessels. Photoelasticity has been applied to the study of this problem in models (84, 47). Another technique applicable to full scale apparatus is the use of electric resistance strain gages cemented to the inner walls of the inner shell. If the shrink fit is made by heating the outer shell, placing i t over the inner shell, and then allowing it to cool, this technique should work quite well and provide a continuous record of development of the shrinkage stresses. Residual Stresses. Residual stress measurement is generally a destructive method because some drilling or cutting of the material is required (8, 64). If this procedure can be tolerated in the actual apparatus, the residual stresses can generally be measured. Otherwise, the stresses in a prototype might be measured and the results extrapolated to the actual case. SomeMay 1956
times residual stress measurement makes its first appearance a t the post-mortem of a pressure vessel when the cause of accidental] premature failure is being investigated. Both Stresscoat and strain gages have been used in this work. For example, Stresscoat is sprayed on the specimen and allowed to dry. Then by drilling small holes through the Stresscoat and into the metal the material is free to deform in accordance with the existing stress distribution. This deformation cracks the Stresscoat in characteristic patterns as described by Heindlhofer (29)and shown in Figure 9. From the appearance of the crack pattern the original stress distribution may be deduced by comparison with Figure 9. The magnitude of the stresses is estimated from a knowledge of the calibrated threshold sensitivity of the Stresscoat (16). In Figure 10 the application of this technique to study of molding stresses in plastic fuzes is shown, After the fuzes were Stresscoated they were drilled along a line, and the crack pattern was studied as a function of the hole position. It was clearly demonstrated that a relatively high, residual, biaxial tensile stress existed near the base of the plastic molding of sufficient magnitude to initiate and propogate a failure crack in storage or when the fuzes were temperature cycled. Design modifications were suggested based on these Stresscoat indications. A similar procedure may be followed using electric resistance strain gages (3). I n this case the strain gages are cemented around the point under investigation, and the hole is similarly made. Strain gage readings are taken before and after drilling, and the stress distribution is computed from these values. The relationships needed for computing the residual stress distribution in cylinders and pressure vessels are given by Sachs (SO). Other techniques for residual stress measurement are very thoroughly discussed (8, 89, $6). The effects of residual stresses on the strength of pressure vessels are described by Faupel and Furbeck (18)who give the theoretical relationships between the residual stresses and the initial yielding pressure. Parsons (43) has reported encouraging results on the possibility of photoelastically studying residual quenching stresses in cylinders caused by heat treatment. Interior Stress Measurement. When a knowledge of the stresses existing throughout the cross section of a structure is desired, the simplest, most practical approach is to build a photoelastic model of the apparatus. By carefully loading the model and recording the resulting fringe patterns using either two-dimensional or three-dimensional analysis it is possible to get an indication of the stress distribution throughout the cross section of the model (88). If a sound dimensional analysis has been made then the results may be extrapolated to cover the actual apparatus ($0). Monitoring of Operating Stress Levels. A possible field of application for electric resistance strain gages may be in the control of euperpressure process equipment. There is no reason why strain gages cannot be applied to critically stressed sections of the equipment and wired into relay circuits so that when the stresses exceed a predetermined level an alarm is sounded and the process is brought to a temporary halt. Similar functions currently being performed by strain gages are the weighing of selected amounts of process chemicals and the weighing of trucks while traveling at normal highway speeds (27). It has been possible to give only a brief survey of the applications of these experimental techniques to superpressure design problems. Many other techniques exist, and many other applications have been made. T o gather the information presented into a concise and usable form, Table I, which lists the stress measurements to be made, the applicable techniques] and the references to consult for details, has been prepared. Many useful experimental methods, such as the use of mechanical or optical strain gages and x-ray stress analysis, have been deliberately omitted in favor of photoelasticity, Stresscoat, and electric strain gages. These latter techniques are emphasized because
INDUSTRIAL AND ENGINEERING CHEMISTRY
859
ENGINEERING, QESIGN, AND PROCESS DEVELOPMENT t h e y a r e believed t o be of wider application a n d t o provide a better measure of critical stress levels faster and more economically t h a n other methods. The tools oE experimental stress analysis, intelligently applied, can help the designer throughout the entire development of superpressure process equipment. F r o m the selection of t h e optimum design configuration t o t h e measurement of actual operating stresses and t h e preparation of manufacturing, testing, and operating specifications these tools find wide application a n d to safe a n d economical superpressure a p p a r a t u s
Literature Cited Baldwin-Lima-Hamilton Corp., Testing Topics 10, No. I (1955). Baldwin, W. bI.,Jr., “Residual Stresses in hletals,” 23rd Edgar Marburg Lecture, Am. Soc. Testing Materials, 1949. Barker, R. S., Proc. SOC.Erptl. Stress A n a l . 11, No. 1, 119 (1953). Baumberger, R., Hines, F., Ibid., 2, No. 1, (1945). Brewer, G. A., I b i d . , 5 , N o . 2, 88 (1949). Ibid., 10, No. 2 , 1 (1953); 6, No. 1, 123 (1949). Bridgman, P. \I7., “Physics of High Pressure,’’ 1st cd., Bell and Sons. Ltd.. London. 1949. Brunot, ,4.W., Schmittner, W. G., Proc. SOC.E x p t l . Stress A n a l . 4,No.1,49 (1948). Campbell, W.R., A’atl. Advisory C o m m . Aeronaut. Tech. X o t e 1011,Apri11946. Ibid., 1656, July 1948. Carpenter, J. E., Morris, L. D., Proc. SOC.Ezptl. Stless A n a l . 9;No. 1, 191 (1952). Clough, TI’. R., Shank, 11.E., Zaid, LI.,Ibid., 10, No. 2, lG7 (1953). Day, E. E., Ibid., 9 , KO.1 , 141 (1951). Durelli, A. J. .Okubo, S.,Jacobson, R. H., Ibid., 12, KO.2 , 55 (1955). Durelli, A. J., Tsao, C. H., Ibid., 11, KO.1, 181 (1953). Ellis, G., Ibid., 1, No. 1,46 (1943). Eng, IVews-Record 155, S o . 8 , 28 (1955). Faupel, J. H., Furbeck, A. R., Trans. Am. SOC.Mech. E n g r s . 75, No. 3, 345-54 (1953). Fessler, H., Rose, R. T., B r i t . J . A p p l . Phys. 4, No. 3, 76 (1953). Fessler, II., Rose, R . T., J . Mech. Phys. Solids 2, X o . 2, 127 (1954). Ford, H., “Symposium on Internal Stresses in Metals and Alloys,” The Institute of Metals, London, 1st ed., 1948. “Photoelasticity,” 1st ed., vol. 1 , Wiley, New Frocht, h1. M., York, 1941. Frocht, AT. M., “Photoelasticity,” 1st ed., vol. 2, Wiley, Kew York, 1948. Gibson, W.H. H., J . I n s t . Engrs., A u s t i a l i a 9, 228 (1938). Gorton, R. E., Proc. SOC.Esptl. Stress A n a l . 9, KO. 1 163 (1952). Gross, N.. B r i t . W e l d i n g J . 1, S o . 4, 149 (1954).
(27) Gross. N.. Lane. P. H. R.. Enoineerino 174. S o . 4513. 97 (1952). Hathaway, C. M., PTOC. ‘Soc.”EzpfZ.Stress A n a l . 7 , NO.'^, 119 (1950). Heindlhofer, K., “Evaluation of Residual Stress,” 1st ed.. &ICGraw-Hill, New York, 1948. Hetenyi, M.,“Handbook of Experimental Stress Analysis,” 1st ed., Wiley, New York, 1950. Heywood, 1%.R., “Designing by Photoelasticity,” 1st ed., Chapman I% Hall, London, (1952). Institute of Physics, “hleasurement of Stress and Strain in Solids,” 1st ed., London, 1948. Jackson, P., I n s t r u m e n t Practice ( L o n d o n ) 7, 7’75 (1953). Jessop, H. T., Harris, F. C., “Photoelasticity: Principles and Methods,” 1st ed., Dover Publ., New York, 1950. Kimble, E. L.,Proc. SOC.E x p t l . Stress A n a l . 3, No. 2, 53 (1948). Ibid., 12, No. 1,91 (1954). Lambert, J. W., Lamble, J. H., Bayoumi, S. E. A., Proc. I n s t . Mech. Engrs. ( L o n d o n ) lB,575 (1952-53). Lee, G. H., “An Introduct’ion to Experimental Stress Analysis,” 1st ed., Wiley, New York, 1950. Lipson, C., Noll, G. C.. Clock, L. S., “Stress and Strength of Nanufactured Parts,” 1st ed., McGraw-Hill, New York, 1950. Miclrevicz, E. J., M.S. thesis, University of Maryland, College Park, &Id.,1955. N a i l . B u r . Standards ( U . S.), Circ. 528, 1954. N a t l . B u r . Standards U . S. Tech. *Yews Bull 39, S o . 5 . 71 (1955). Parsons, K. A., J . A p p l . Phya. 24, No. 4 , 4G9 (1953). Perry, C. C., Lissner, H . R., “Strain Gage Primer,” 1st ed., blcGraw-Hill, S e w York, 1955. Peterson, R . E., “Stress Concentration Design Factors,” 1st ed., Wiley, New York, 1953. Rockey, K. C., T r a n s . I n s t . M a i i n e Engrs. 63, No. 3, 43 (1951). Iiosenberg, P. R., “Proc. 13th Semiannual Eastern Photoelasticity Conference,” Cambridge, Mass., 1941. Singdale, F. N., Proc. SOC.Erptl. Stress A n a l . 11, No. 2. 173 (1954). Steele, PI. C., Eichberger, L. C., “Overstraining of MediumCarbon Steel Thick-Walled Cylinders,” University of Illinois, Urbana, Ill., April 1955. Steele, hl. C., Eichberger, L. C., “Use of Foil Gages to Measure Large Strain Under High Fluid Pressures.” University of Illinois, Crbana, Ill., July 1954. Sugarman, B., “Symposium on Internal Stresses in AIetals and Alloys,” 1st ed., The Institute of Metals, London, 1948. Tatnall, F., “Summary Report on High Temperature Strain Gage Research,” Baldwin-Lima-Hamilton Corp., contract ONR 845(00) and W7405-Eng. 26, subcontract No. 513. Tatnall, F., “Testing Pressure Vessels,” n’elding Research Council B u l l . 4, February 1950. Tokarcik, A. G., Polzin, & I . H., Proc. Soc. Ezptl. Stress Anal. 9, KO.2,195 (1952). Weydert, J. C , , Proc. Soc. E r p t l . Stress A n a l . 11, Yo. 1, 39 (1954). Yarnell, J , , “Resistance Strain Gages,” 1st ed., Electronic Engineering, London, 1951. RECEIVED for review December 15, 1935.
ACCEPTEDMarch 31, 1956.
STANDARD PUMP
A
Basic design of standard and superpressure pumps
SUPER 860
PRESSURE PUMP
COURTEGY RUFKA INSTRUMENT CO.
INDUSTRIAL AND ENGINEERING CBEMISTRY
Vol. 48, No 5
