‘ ADAPTING A REENFGR‘CED PLASHC AND FOAM §N£ULATED SAN§W§CH TO A RIGED FRAME DESIGN Thesis for {he Degree of M. .5. MECHEERN SR'E’E UNEVERSETY Jacob Pos .1961 \/ e . This is to certify that the thesis entitled Adapting a Reinforced Plastic and Foam Insulated Sandwich to 8 Rigid Frame Design presented by Jacob Pos has been accepted towards fulfillment of the requirements for | - 1‘ rwmfinfif .‘ .1 .,:;.::.3R .4 .- 2 g lln ! llrfl\fin -‘f ‘1; 4w: --7 “our. 32"“. ALdegree in Agricultural Engineering November 22, I)ate 0-169 ADAPTING A REINFORCED PLASTIC AND FOAM INSULATED SANDWICH TO A RIGID FRAME DESIGN By Jacob Pos AN AB STRAC T Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering ABSTRACT ADAPTING A REINFORCED PLASTIC AND FOAM INSULATED SANDWICH TO . A RIGID FRAME DESIGN by Jacob Pos The primary obiective of this investigation was to design a reinforced plastic and foam insulated sandwich as a structural component for farm building design. A review of literature indicated that, except for some research by the Canadian Department of National Defence, very few fabricators have combined reinforced plastic skins and plastic foam insulation to produce a structural sandwich component. The rigid frame chosen for this investigation is composed of compound curves and deep contours to provide rigidity and resistance to bending moments. The complex shape was created to provide a uniform distribution of stress throughout the entire arch for a uniformly distributed load. A three foot width of section would allow the installation of standard doors and windows and also allow convenient building construc- tion . Based on a preliminary investigation, a polyester resin with a single layer of IO oz. plain weave'glass cloth and a single layer of 2 oz. glass mat reinforcement was used as the outer skin; and a polyurethane foamed-in-place insulation was used as the core for the model frame. A model analysis of the frame was made to facilitate the investigation. True models were used and prediction equations for stress and deflection derived to test the hypothesis. Two models were built using a layout and section scale of 3, that is, the models were l/3 the span and section of the prototype. The models were tested under short term static loads on a special horizontal test floor in the Farm Structures Research Laboratory at Michigan State University. The loads were applied perpendicular to the span through a system of hydraulic cylinders and loading shoes, and applied in increments to establish definite load- deflection and load-stress relationships for each frame. Deflections were measured by dial gage indicators and strains by electric resistance strain gages. ADAPTING A REINFORCED PLASTIC AND FOAM INSULATED SANDWICH TO A RIGID FRAME DESIGN By Jacob Pos A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering I96] f -7] ’7 I -- ":- .’—- :3 / ;,.-. “‘ L,» r/‘J‘ , r '4’- ’ ' ” ,4; 2. J. Pos Chemical and mechanical properties were determined for each frame from samples of laminate removed from excess flange material. A complete combustion of the laminate provided a measure of per cent silica present; the moduli of elasticity in bending and tension were used to estimate stress and deflection of the frames. Measured stresses and deflections were compared with estimated values with reasonable agreement in all comparisons. From the results of the investigation, the following conclusions were made: I . Polyester resin with glass reinforcing may be combined to produce a laminate for structural components with excellent mechanical properties, and high moldability, water resistance and rot resistance. 2. Wood can be used efficiently and economically for the construction of patterns for practically any shape. 3. Polyurethane foamed-in-place insulation provides an excellent low density core for light weight sandwich construction. 4. Electric resistance strain gages are easily mounted on, or imbedded in, the plastic laminate. 5. The horizontal test floor and hydraulic load system can be used satisfactorily to apply static loads to structural components; but for small models requiring light loads, an inverted vertical procedure would provide more accurate and convenient results. ACKNOWLEDGEMENTS Appreciation is herewith acknowledged for the patient support of my wife Daisy, and my two children, without whose sacrifice this work could not have been accom- plished. Special thanks are extended to Dr. J. S. Boyd, my Maior Professor, for his wise counsel and patient encouragement throughout this proiect. I am greatly indebted to Dr. R.A. Aldrich, not only for his personal assistance in this proieCt, but also for having pioneered this work at Michigan State University and constructing the test facilities. I wish to thank Mr. James Cawood in the Agricultural Engineering Research Laboratory for his interest in this proiect and in supplying the necessary tools and materials. Sincere appreciation is expressed for the interest and valuable suggestions concerning the program from Dr. M.L. Esmay, Dr. T. Triffet, members of the guid- ance committee, and Dr. C.E. Cutts, head of the Civil Engineering Department. Thanks are given to Mr. G. Miller and his staff of the Dow Chemical Company at Midland, Michigan, for their assistance in providing advice, labour, equipment and material in casting the plastic cores for the two model arches. TABLE of CONTENTS Page INTRODUCTION ............................................... l LITERATURE REVIEW ............................................ 2 Plastics ............................................... 2 Classification .................................. 2 Polyester resin ................................. 3 Catalysts ...................................... 4 Promoters ...................................... 4 Parting agents .................................. 4 Fillers ........................................ 5 Reinforced Plastic Laminates ............................. 6 Properties of glass fibers ......................... 7 Glass fiber reinforced laminates .................. 8 Mechanical properties .......................... 9 Design theory of reinforced laminates ............. 12 Application of reinforced plastics ................. l4 Urethane Foams ........................................ l6 Physical and mechanical properties ............... lo Rigid Frame Analysis ................................... l8 Model Analysis ........................................ 18 Prediction equations ............................ l9 Theory of models ............................... l9 Structural models .............................. 2l Distorted models ............................... 22 THE RESEARCH PROJECT ....................................... 23 Preliminary Investigation ................................ 23 Rigid Frame Analysis .................................... 24 Model Analysis ........................................ 29 Prediction equation for stress ..................... 29 Prediction equation for deflection ................ 30 Frame analysis for the model ..................... 3I TABLE of CONTENTS (Cont.) Page Experimental Investigation ............................... 33 Model construction ............................. 33 Test facilities .................................. 37 Instrumentation ................................ 3‘? Determining material constants ................... 42 Model testing .................................. 52 Longterrnstaticloading................' ......... 56 RESULTS AND DISCUSSION .................................... 59 Mold Fabrication ....................................... 59 Laminate Materials . . . . . . . ............................... 59 Properties of the Glass Resin Laminate ..................... 60 Glass content of the glass resin laminate .......... 6I Tensile properties .............................. .. 6I Flexure properties .............................. 63 Evaluation of the Model Analysis ......................... 65 Long-term Loads ....... ‘ ................................ 66 CONCLUSIONS.................... ........................... 67 SUMMARY" .................................................... 69 BIBLIOGRAPHY ............................................... 7l Figure I. I0. ll. l2. I3. l4. l5. LIST OF FIGURES Effect of glass fiber content on mechanical strength of polyester laminate. Stress-strain diagrams of glass fiber A and two resins, B and C. Resin B is a hard, high strength material; and resin C is of inter- mediate strength and hardness. Foam-density curves for polyurethane and polystyrene rigid insulation. Rigid frame and section details. Load and moment diagrams for the rigid frame. Half-frame section and table of design calculations. Successive operations in the laminating process. Equipment used to foam in-place the polyurethane insulation. Courtesy Dow Chemical Co. Midland, Michigan. Placing liquid polyurethane insulation. Model under test in Farm Structures Research Laboratory, Michigan State University. Typical strain gage application on model arch and Ames gage test stand for deflection measurements. Load-strain curves in bending as determined by deflection transducer and SR-4 strain gage mounted on the bending specimen as shown. Testing'and recording equipment for determination of material constants. Flexure (a) and tension (b) specimens under test. Typical records for flexural test (a) and tension test (b) as recorded by Sanbom Recorder. Page II l3 I7 25 27 28 34 36 36 38 38 40 4l 4] 43 Figure l6. l7. l8. I9. 20. 2l. 22. 23. 24. 25. 26. ' 27. 28. 29. LIST of FIGURES (Cont.) Typical stress-strain curves in tension for polyester, resin-glass reinforced laminate from model plastic arch number I. Typical stress-strain curves in tension for polyester, resin—glass reinforced laminate from model plastic arch number 2. Typical stress-strain curves in bending for polyester resin-glass reinforced laminate (cloth down) from model plastic arch number I. Typical stress-strain curves in bending for polyester, resin-glass reinforced laminate (mat down) from model plastic arch number I . Typical stress-strain curves in bending forpolyester, resin-glass reinforced laminate (cloth down) from model plastic arch number 2. Typical stress-strain curves in bending for polyester, resin-glass reinforced laminate (mat down) from model plastic arch number 2. Deflection of model arch number I at crown due to a uniformly distributed load. Load-stress curves in bending for model arch number I at crown due to uniformly distributed load. Arrows point to tension failure in the outer shell of the sandwich arch of the haunch ioint of the arch frame. Deflection of model arch number 2 at crown due to a uniformly distributed load. Load-stress curves in bending for model arch number 2 at crown due to a uniformly distributed load. Deflection of model arch number I at crown with a constant uniform load of 3l .3 pounds per foot of beam. Matched patterns used as molds to cast the two surfaces of the plastic arch shell. Long-term static loading-test on model arch number I subjected to a uniformly distributed constant load of 3l .3 poundsper foot of beam. vi Page 44 45 46 47 48 49 50 SI 53 54 55 57 58 58 Figure 30. 3I. LIST of FIGURES (Cont.) Typical failure of flexure specimen with cloth (top side) in tension and mat in compression, tested with cloth down. Typical failure of flexure specimen with mat (top side) in tension and cloth in compression, tested with mat down. vii Page 64 LIST of TABLES Table Page I . Comparison of Mechanical Properties of Plastics and Metals. 6 2. Typical Mechanical Properties of Polyester Resin, Polyester Laminates, Structural Steel and Aluminum. 9 3. Mechanical Properties of Polyester Resin Laminates as Determined from Samples taken from the Flange Laminates of the Model Frames (l). l0 4. Flexural Fatigue Characteristics of Two Glass Fiber Reinforced Laminates. ll 5. Tensile Stress-rupture Properties of 0 Fabric Reinforced, Rigid, General Purpose Polyester. l2 6. Physical and Mechanical Properties for Rigid Urethane Foam Board Stock. l6 7. Mechanical Properties for Polyester Resin, Glass-Reinforced Laminates as determined from Samples taken from the Flange Laminates of the two model frames. 52 8. Glass Fiber content of Polyester Laminate. 6l 9. Estimated and Measured Values of Deflection and Extreme Fiber Stress at the Crown for the two Arches. 66 viii INTRODUCTION Research for better farm buildings is constantly seeking new building mate- rials and more efficient construction practices. While the traditional materials used in farm buildings may have proven adequate for their reSpective purposes, the com- plexity of modern form practices is placing new demands on properties of building materials. ’A material is needed that combines the durability and fireproof qualities of concrete, the light weight and rust resistance of aluminum, the strength and decay resistance of steel, the workability and attractive features of wood, and the thermal properties of foam plastics. The reinforced plastic and foam insulated sandwich proposed in this study not only embraces all of the above requirements, but when designed and fabricated as structural units, they can be speedily erected to form a building pleasing in desigi and adaptable to a variety of uses. The procedure entailed: (I) a study of the available literature to provide basic information for the selection of the most suitable materials to be used in this investigation, (2) the design of a variable sandwich section to provide uniform stress distribution over the entire arch, (3) the design and construction of matched molds for the fabrication of a scale model, (4) the testing of the model, as well as representative samples of the laminate, to assist in predicting the ultimate behaviour of the prototype. LITERATURE REVIEW Plastics - ’Plastics are synthetic materials combined by laboratory processes for the explicit purpose of assembling qualities and economies of manufacture not available in natural materials. The present concepts of plastics began with the discovery, by Dr. Leo H. Baekeland (7) about I906, of a practical way of utilizing the long- known reaction between phenol and formaldehyde. Plastic chemistry generally begins with the so-called intermediates. Acet- ylene, acetone, phenol, formaldehyde, benzene, and many similar compounds which are polymerized to form elementary plastics. These elementary plastics are then converted to useful products by a combination of mechanical and chemical processes . Classification Plastics are classified in several ways, but the more general method is to divide them into two broad groups according to their behaviour pattern. lh_er_r_n_op_lcls_t_i_c_s_ are those plastics which soften under heat and harden again when cooled. No internal chemical change takes place. They are like paraffin in this respect. There are roughly l4 basic materials in this group with a softening point ranging from I40 to 220 degrees fahrenheit. They vary greatly in their mechanical and electrical qualities within the range of their optimum operating temperature. Some have excellent qualities all the way down to -60 degrees F. Some have a sharp softening point, while some get progressively softer as their temperature approaches liquefaction . Ilfllngetfllgflgstigiare those plastics which soften only once under heat and then undergo an internal chemical change which makes them hard and impervious to further applications of heat up to the charring or disintegration point, which ranges from 250 to 300 degrees. F. There are only three of these plastics in current (J) use, phenol formaldehyde, urea formaldehyde, and melamine formaldehyde, more frequently called: phenolics, ureas, and melamines. ' From a review of the many resins commercially available, a polyester type resin was chosen to be used in this study. No attempt is made to present the chem- ical; formulation as it is considered to be outside the scope of this investigation. Polyester resin Polyester resins are solutions of unsaturated polyesters in reactive monomers such as styrene or diallylphthalate. The polyesters are obtained from an unsaturated dibasic acid or anhydride, by reaction with a dihydric alcohol. Maleic anhydride and diethylene glycol are typical materials used. The esters produced are linear in structure with recurring maleic double bonds and the monomer can co-react with these reactive bonds to give insoluble and infusible cross linked chains. The properties of the resins can be varied by substition of part of the maleic anhydride with other dibasic anhydrides or acids or by the use of different dihydric alcohols. Also the type of monomer used can influence the properties of the resins. With simple precautions against exposure above normal room temperature, the basic resins are stable for several months. Cure is developed by the addition of a catalyst capable of initiating the cross linkage mechanism . The cure of the liquid polyester resin takes place in two distinct stages. After suitable catalyzation the first stage is the formation of a soft gel. This stage ‘ may require but a few minutes or may take several hours, or even days, depending on the temperature and the catalyst system used. Little or no heat is evolved during this step. Immediately following gelation the cure is rapidly propagated with con- siderable evoluation of heat. In a large mass of resin or under well insulated conditions the heat of reaction may carry the temperature to as high as 460 degrees F. with extreme rapidity. This was experienced by Aldrich (l) , who observed a change in viscosity of the resin at peak temperature. Apparently when the laminate thickness and consequently the resin content was built up too quickly, the reduced viscosity at peak temperature resulted in a runout of resin and left a resin starved laminate. In addition an extremely rapid increase in temperature in a mass of resin during its transformation from a soft gel to an infusible solid can set up internal strains leading to cracking or crazing. Sometimes the temperature may rise above the boiling point of the monomer before it has entirely reacted causing bubbling and creating voids in the cured resin . I The use of catalysts and promoters is an important part of the technology of polyester resins. The conversion of the liquid resin to a solid infusible condition can be induced by the use of a catalyst, usually an organic peroxide, and the application of heat. Promoters are used to activate the catalyst to develope cure at room temperature or to accelerate heat cure. Catalysts The most widely used perioxide catalysts are benzoyl peroxide, cumene hydroperoxide, and methylethylketone peroxide. Benzoyl peroxide is best suited for high temperature applications and methylethylketone peroxide for low tempera- tures. The latter is most frequently used as a 60 per cent solution in dimethylphthalate for hand lay-up fabrication at room temperature. Promoters Cobalt napthenate is the most widely used promoter for low temperature work. The commercial solutions usually contain 6 per cent cobalt metal. A corn- bination of 2 per cent methylethylketone peroxide (60 per cent solution) and 0.25 per cent cobalt napthenate (6 per cent cobalt) will provide l0 - I5 minutes gel time. Parting agents' A parting agent is a material which promotes easy separation of a molded article from the mold. A wide range of materials is available. The choice for a particular application depends on several factors such as the type of mold, the condition of the mold surface, the importance of the surface appearance of the finished molding, the method used for molding, and the characteristics of the particular resin used. Films or film-forming material should be used as the parting agent on porous molds such as those made from wood or plaster. Polyvinyl alcohol film is an effective material, but is relatively expensive. Cellophane film is inexpensive, but is useful only on relatively flat surfaces. Polyvinyl alcohol solution is a film-forming mate- . rial which can be brushed or sprayed and on drying forms a film with excellent release. It is particularly suitable over complex shapes and compound curves. Lubricants or waxes are used on non—porous metal surfaces, such as steel or aluminum . Johnson's paste wax has been used effectively as a mold release, not only on non-porous surfaces, but also on heavily lacquered porous surfaces. ‘ Fillers When polyesters are reinforced with glass fibers, it is common practice to ‘ incorporate mineral fillers as resin extenders; special grades of calcium carbonate and aluminum silicate are often used. They are normally mixed with the polyester when the pigments and catalysts are added. Fillers are used essentially to reduce the material cost. The addition of I fillers dilutes the resin filler mixture with a subsequent reduction in cure shrinkage. When the shrinkage is reduced, there is less tendency for the resin to pull away from the glass fiber surface; thereby improving its water resistance. The mechanical properties of the molding are not harmed by the incorporation of fillers. However, it has been suggested (6) that the total resin content of a laminate should not be below 25 per cent. Fabric laminates generally contain from 25 to 40 percent resin, and thus, the replacement of some of the resin by filler reduces the resin content to a danger- ously low figure. Therefore, the use of more than 5 per cent filler (of the resin- filler mixture) is not recommended when fabrics are used . Chopped strand laminates contain from 55 to 80 per cent resin, consequently a higher percentage of the resin can be safely replaced. Polyester resins shrink when they cure (from 4 to 8 per cent by volume), mainly due to the shrinkage of the cross-linking monomer. When glass fiber reinforcement is used, the shrinkage causes a raised-fiber surface pattern in the molding because the part pulls away from the mold surface; also the resin tends to pull away from the glass fiber surface. The polyester resins are not without their limitations. Although better than many plastics in respect to flammability and heat resistance, most types will burn and they have definite temperature limitations. When glass fiber reinforcement is Used, the subtle but very important drawback of shrinkage during cure makes smooth surfaces difficult to obtain and can cause poor water and weathering resistance. Reinforced Plastic Laminates A variety of reinforcing materials, including paper, have been used for specific applications. A few of these materials and the resulting mechanical pro- perties of the reinforced plastic laminates are included in table I. The geatest mechanical strength is obtained through the use .of glass fiber reinforcement. Table I. Comparison of Mechanical Properties of Plastics and Metals (7) Sp. Tensile Compressive Modulus of Specific Gr. Strength Strength Elastici Modulus (psixl0-3)(psixl0 3) (psixi0- (psix 10"6) Magnesium alloy I .8l 46.0 35.0 6.50 3.60 Stainless steel 7.85 l85.0 l50.0 30.00 3.80 Pregwood l .30 30.0 l5.0 3 .70 2.80 Chrome-moly steel 7.85 l80.0 l50.0 29.00 3.70 Aluminum alloy 2.80 62.0 40.0 l0.40 3.70 Paper laminate l.33 l2.0 35.0 3 .00 2.25 Glass-fabric laminate g l.50 l4 .0 40.0 2.00 l.34 Impact phenolic, molded l.38 7.0 35.0 l.80 l.30 Wood-flour phenolic, " l.36 8.5 30.0 0.96 0.70 Asbestos-paper laminate I .80 10.0 38.0 l.50 0.84 Canvas-fabric laminate l .33 9.5 38.0 I .50 l . l2 Properties of glass fibers Glass fibers are made from a lime-alumina-borosilicate glass which is relatively soda-free. The raw materials are mixed in accordance with formulae adapted to the end uses of the fibers. The subsequent molten glass flows to marble forming machines which turn out small glass marbles, 5/8 inches in diameter. Recent improvements in glass refining indicate that textile fibers may be drawn direct from the original melt, eliminating the marble operation. The basic fibers are inorganic, incombustible and durable and will neither shrink nor swell with moisture changes. The yarns are flexible and may be used for weaving or braiding. During the manufacture of glass yarns, a lubricating size is applied to the glass surface to assist in the forming operation. This size is removed after the strands have been fabricated, and a surface treatment known as a "finish" is then applied. Several finishes, designed primarily for use with polyester resins, are available. The "general purpose" finish provides a balance between good handling characteristics of the glass and good adhesion between the resin and the glass. This is a low-cost finish and is recommeded where maximum laminate strength is not required. The "high performance". finish is designed for maximum resin-to-glass adhesion, thus yielding maximum laminate strength. An example of the latter is recognized by the tradeename "Volan A" . The special conditions existing as the fibers are formed modify their properties. The tensile strength is about 400,000 psi. measured on single glass filaments with diameters from 0.00020 to 0.00l00 inches. The modulus of GIOSlIle)’ 0f the fibers IS about I0.5 x l06 psi ., and remains relatively unaffected by environment or treatment. The specific modulus of glass fibers is approximately the same as that of aluminum and steel, Table l. The glass fiber is a perfectly elastic material, following Hooke's law to rupture. The fibers stretch elastically about 3.5 per cent before breaking, and are unique in that there is no measurable difference between their yield and ultimate strengths. Glass fibers show neither creep nor hysteresis at room temperature. Fatigue, as applied to glass, is different from fatigue as ordinarily considered _in metals. In the latter, a loss in strength occurs due to an internal adjustment to applied loads that is described as cold working. In glass, 0 loss in strength occurs due to surface attack by the environment. By adequate protection of the surface, this loss in strength can be reduced to practically zero. Glass fiber reinforced laminates The greatest mechanical strength in laminates is developed through the use of glass fiber reinforcement. The values for characteristics such as flexural and tensile strengths are highest with woven glass cloth. However, the use of cloth.is limited by its cost and the difficulty in applying it to complex designs with features requiring deep draw or sharp curvature. When maximum strength is required and the configura- tion of the structure permits the use of cloth, selection may be made from several types with weaves 'varied to emphasize specific properties. Unidirectional woven fabrics have large amounts of relatively heavy yarn in the warp, and a small number of lighter yarns in the fill. This orientation of the maior fibers permits the development of maximum impact, flexural, and tensile strength in one direction. Plain (or square) woven fabrics have essentially a "balanced" construction, i.e. , the same yarns in equal amounts running in the warp and fill directions. The use of conventional plain cloth gives uniform orientation of mechanical properties, but the peak strength values obtainable with unidirectional cloth cannot be developed. Because of the relatively high cost, the use of glass cloth may not be adapt— _ able to many structural designs. The greatest versatility in design at relatively low cost is realized through the use of glass fiber mat or preforms made from chopped rovings. Mat is composed of chopped strands of glass fiber assembled in random order into a thin layer and then bonded with 2 to 5 per cent of binder resin, which when cured will hold the fibers in place during handling. This random orientation of the fibers, in mat reinforced materials, yields equal strength and elastic properties in all directions in the plane of the plate, i.e. , they are essentially isotropic. Mechanical properties Research by government and industrial laboratories has provided considerable information relative to the mechanical properties of glass fiber reinforced plastics. Table 2 gives typical mechanical properties characteristic of polyester resin and glass fiber laminates in comparison with clear cast polyester resin, structural steel and aluminum )l2). Table 2. Typical Mechanical Properties of Polyester Resin, Polyester Laminates, Structural Steel, and Aluminum Clear l2 Ply ll Ply ' Structural Aluminum ' Cast Laminate Laminate Steel Property Resin 3/4 oz. l8l-ll4 Glass mat Glasscloth Flexural strength ult. psi l3000 32400 47000 40000 45000 Flexural moduls psi 0.65). 106 1.65x106 2.7x 106 28x 106 10 .3). 106 Tensile strength psi 8000 25000 36l00 42000 45000 Izod impact (notched bar) 0.4 l7.7 l2.9 45 25 Specific gravity l. l0 l.55 l.8l 7.85 2.77 Specific flexural strength l2000 26000 26000 5l00 l6200 Specific flexural modulus 0.54x 106 0.78.. 106 l.5x 106 3.57x106 3.7x 106 Specific tensile strength 7300 l6l00 20000 5350 l6200 Specific impact strength 0.4 ”.4 7.l 5.7 9.0, Per cent resin l00 46 36 The values in Table 2 show that on an equal weight basis glass fiber rein- forced laminates can equal or excel metals in certain mechanical properties, notably ultimate flexural and tensile strength. However, the laminates in Table 2 are pressure molded and high in reinforcement content. Most commercial assemblies, especially those molded from glass mat at contact pressure, will have a much higher resin content and consequently lower values than those recorded in Table 2. IL: This fact is evident when comparing the results of aldrich (I), Table 3, with comparable values in Table 2. Table 3. Mechanical Properties of Polyester Resin Laminates as Determined from Samples taken from the Flange Laminates of the Model Frames (l) 4 Ply Laminate l0 oz. ‘ G lass cloth Maximum strength in bending (psi x l03) 23.3 Maximum strength in tension (psi x l03) 17.3 Modulus of elasticity in bending (psi x l06) 2.3 Modulus of elasticity in tension (psi x l06), (a) l.5 Modulus of elasticity in tension (psi x l06), (a) l .7 (a) Model P025l00 (b) Model P025050 The values given in Table 3 were derived from samples taken from two models. The laminates were fabricated by the hand-lay-up process. There was no reference as to the per cent resin content in the samples. Figure I shows the effect of the percentage of glass fiber reinforcement on the mechanical strength of polyester resin laminates (l2). When glass fiber reinforced laminates are exposed to extremely cold con- ditions, they exhibit higher strengths and less brittleness than are shown at room temperature. The increase in strength is attributed to the glass since the resins themselves become brittle. When the laminates are exposed to heat, they exhibit a loss in strength. Some resins have a maximum service temperature of 200 degrees F., when used with glass fiber reinforcement, and other special resins are usable at temperatures approaching 500 degrees F. Upon being exposed to weather, glass fiber reinforced polyester resin laminates increase in flexural strength for the first few months, and then drop off in strength to a point approximately 80 per cent of original strength. The initial strength increase II 35 // FLEXURE 30 /, 25 20 /// /, ,/ "' TENSION l5 / l0 ULTIMATE STRENGTH (psi x 10'3) IO 20 30 4o 50 60 7o 80 90 PER CENT GLASS ' Figure I. Effect of glass fiber content on mechanical strength of polyester laminate. is attributed to additional curing of the resin by ultra violet light and heat from the sun . Sonneborn (6) in reviewing the literature to date has'stated that glass rein- forced laminates do show fatigue and stress rupture, Table 4 and Table 5 respectively, but creep appears to be very low. Table 4. Flexural Fatigue Characteristics of Two Glass Fiber Reinforced Laminates Original Endurance Per cent of Material Flexural Limit at Original Strength l0 x l06 Strength (psi) Cycles (psi) l8l Fabric (plain weave), high performance finish; rigid general 65,000 l5,000 23 purpose polyester; glass content for 30 minutes at 250 degrees F . 12 Chopped strand mat, rigid general purpose polyester; glass content 33,000 7,000 2l 38 per cent by weight. Cured for 30 minutes at 250 degrees F. Table 5. Tensile Stress-rupture Properties of 0 Fabric Reinforced, Rigid, General Purpose Polyester Condition Rupture Stress 300 hours; unnotched 60 per cent of static unnotched tensile 300 hours; notched 55 per cent of static notched tensile Design theory of reinforced plastics Dietz, in his discussion of the theory of reinforced plastics (6), states that any material, when stressed, stretches or is otherwise deformed, and in the case of reinforced plastics, if the resin and the fiber are firmly banded together, the de- formation in each component is the same. But the fiberglass, being more unyielding than the resin, will develop a higher stress for a given deformation or strain. If the stress to strain relationships of fiber and resin are known, the stresses developed in each for a given strain can be computed, and hence their combined action determined. Stress-strain diagrams for glass fiber and for two resins are shown in Figure 2. Curve A, typical of glass, shows that stress and strain are directly proportional to each other. , Stiffness, or modulus of elasticity, as measured by the ratio of stress to strain, is high . Curve 8 represents a hard resin. Stress is directly proportional to strain when both are low, but stress gtadually levels off as strain increases. The modulus of elasticity, as measured by the tangent to the curve, is much lower than that of glass. Similarly curve C which represents a softer resin has a lower modulus of elasticity than the hard resin . Dietz applied these stree-strain diagrams to the investigation of a rod in which half the total volume is glass and half is resin. Assuming that the glass fibers are l3 55 ' . FVGLASS FIBER A 50 45 A 40 A 35 1° 9 30 X :9:- 25 l/ m I WANGENTIO B m 4 4 A E; 20 ,' * .' 5 I , 14/ RESIN B '5 I ///1= / ,’ Io , , ’ ,I‘Z—TANGENT to C 5 l L?- t t LRESIN C l l 0.5 1.0 1.5 2.0 2.53.0 PER CENT STRAIN Figure 2. Stress-strain diagrams of glass fiber A and two resins, B and C. Resin B is a hard, high strength material; and resin C is of intermediate strength and hardness. laid parallel to the axis of the rod and the rod is stretched 0.5 per cent, then, from stress-strain diagrams, Figure 2, a value of 50,000 psi is obtained for the glass, and 7,500 psi for hard resin, B. If, for example, the rod has a total cross section of one-half square inch, then the total load in the glass is one-quarter times 50,000 or l2,500 pounds. Similarly the load in resin B is l,875 pounds. Therefore the load required to stretch the com- posite rod is the sum of the loads in the glass and the resin, or £4,375 pounds. l4 Dietz puts this in the form of an equation: 0A =0fAf+OrAr ...................................... (l) where 0 - mean stress intensity on the entire cross section (If - stress intensity in the fiber 0r - stress intensity in the resin A - total cross-sectional area Af - cross-sectional area of the fiber Ar - cross-sectional area of the resin For a cross-section made up of different materials, the equation is generalized by Dietz to: i=n 0A=Z aiAi ........... . ............................. ..(2) where 0 i - tensile strength Ai - cross-sectional area of any component of the section Application of Reinforced Plastics The continued expansion of the plastics industry has opened so many new horizons for the application of glass reinforced plastics that only one area will be considered in this report. In the rather narrow field of structures, one fabricator (l4) has included the following items in his advertising literature: Radomes, ware- houses, barns, silos, sheds, aircraft hangers, garages, implement sheds, portable _ shelters, tank covers, and all-year swimming facilities. One of the many applications of special concern is sandwich construction . Its principle is that of high strength skins separated by a low density core. The skins are usually glass fiber resin laminates, and the core (whose main purpose is to l5 keep the skins in place) may consist of balsa wood, foamed plastics, or honeycomb construction. Sandwich panels are light in weight, strong and rigid. In addition, the low density core provides excellent insulating qualities making the panels well suited to refrigerated storages, and unitized truck trailer, boat hull, and aircraft design . Now that the general public has accepted prefabrication in house design, it is only natural to expect new and exciting designs utilizing the versatile properties of reinforced plastic panels. One such development is the completely prefabriCated sections 6f the plastic house co-sponsored by MIT and Monsanto Chemical Company (ll). Because of the relatively complex design, full scale prototypes of the house sections were fabricated and tested. The floor sections were essentially hollow girders consisting of an outer molded surface and an inner flat surface. Both surfaces consisted of woven-roving—reinforced polyester resin laminate. Full de- sign load, held on the floor for six weeks, produced no appreciable Creep. The National Research Council and the Plastics Industry of Canada have teamed up to build a polyurethane radome for the Royal Canadian Airforce guided missile program (I0). The final design was the result of experimentation with three different methods of radome fabrication and several different combinations of mate- rials. The resulting structure is 26.5 ft. in diameter and is built up of panels roughly 4 ft x 4 ft x 3.5 in . thick, and 6 lb per cu ft density. One of the test _ radomes was erected using expandable polystyrene bead panels'4 in. thick with a 2.5 lb per cu ft density. In order to protect the low density polystyrene foam from weathering and accidental mechanical damage, the outer surface was covered with a layer of glass cloth cemented to the foam with epoxy resin. The mechanical tests showed that the polystyrene radome would stand up to a maximum wind velocity of 250 mph. The erected radome after nearly three years, is in good condition although exhibiting some evidence of creep. The latest developments in foam and foam mixing facilities have opened a whole new field in the design of structures. These developments have led to the conception of the so called "foamed in place“ technique. One of the more common materials used for this purpose is polyurethane. I6 Urethane Foams Urethane foams (9) are thermosetting plastics which can be produced with varying degrees of flexibility ranging from very flexible comfort cushioning to rigid insulating boards. The degree of rigidity is controlled by the chemical formulation of the component materials used. The two basic components are polyol (Experimental Plastic Q 4I97.6))x and semiprepolymer (Experimental Plastic Q 4l99.2). Polyol is formulated with a fluorocarbon blowing agent, trichloromonofluoromethane. The polyol also contains the cell control agent and catalyst. The prepolymer is a reaction product of an excess of toluene diisocyanate with a controlled hydroxyl content. Chemical reaction occurs between the isocyanate groups in the prepolymer and the hydroxyl groups in the polyol to produce a thermoset, crosslinked polymer. During this reaction the fluorocarbon blowing agent previously added to the polyol is vaporized and expanded in gaseous form by the heat of reaction. This causes a foam to be produced. Physical and mechanical properties The following properties have been determined for rigid urethane foam board stock (l3) Table 6. Physical and Mechanical Properties for Rigid Urethane Foam Board Stock L Property Value Density I .8 to 2.3 lb. per cu. ft. Compressive yield strength (77 degrees F) 30 to 50 lb. per sq. in . Compressive modulus " l000 to I500 " Flexural strength " 40 to 60 " Flexural modulus " 650 to l000 " Shear strength " 22 to 28 " Shear modulus I " 300 to 500 " -xCode used by the Dow Chemical Company, Midland, Michigan l7 Thermal conductivity _ " 0. I6 to 0. l7 BTU Water absorption I .2 to 2.0 per cent by volume Water vapor transmission'rate I .6 to 2.5 Perms per in. Linear thermal coef. of expansion 0.000025 to 0.000030 Adhesives Resorcinal, rubber emulsion, rubber solvent, epoxy resin, polyester resin and bituminous compounds. The thermal conductivity value represents the long term equilibrium value for cut boards. Initially the thermal conductivity or "K" factor, is in the range of 0.“, to 0.I3. This low value is due to the high concentration of the fluorocarbon blowing agent in the closed cells of the foam. However, nitrogen and other gases in the air will diffuse through the cell walls at a very slow rate. Since these gases have relatively higher thermal conductivities than the blowing agent, the combination results in an increase in the overall "K" factor of the foam. 4 / POLYURETHANE %/ 3 / j / TENSILE STRENGTH (psi x 10'2) N ’ I § OLYSTYRENE 5 l0 l5 FOAM DENSITY (lb/cu ft) Figure 3. Foam-density curves for polyurethane and polystyrene rigid insulation. The curves in Figure 3 give a comparison of tensile strength at various densities between polyurethane and polystyrene. For foam densities greater than 5 lb per cu ft, polyurethane has increasingly higher strength values. l8 The exposure of urethane foam to sunlight or artificial light with a high content of ultraviolet will eventually deteriorate the surface of the foam. The use of most conventional prOtective finishes will eliminate this surface degradation problem, and a wide selection of coatings can be used because of the foam's excellent solvent resistance . Rigid Frame Analysis Statically indeterminate frames with members of variable cross section have found considerable application in modern construction. While several methods for the analysis of rigid frames are presented in structural design text books, only a limited number provide a convenient method of solving rigid frames of variable section. Leontovich (4) has developed an approximate method based on the method of elastic centers augnented by the concept of elastic parameters. Attention is given to the development of formulas in a convenient form for algebraic solution. Numerical values of elastic parameters and load constants for straight and curved members of variable cross section are provided in charts and tables. A more exact method based on the method of "Virtual Work" and using the summation of moments on relatively small increments of frame length has been pre- pared by the American lnstitute of Steel Construction (8). For steel structures, deformations due to shear, direct stress, and temperature are normally neglected in rigid frame analysis. This practice is usually entirely justifiable since, for the average frame, the stresses due to all of the foregoing rarely amount to more than 2 or 3 per cent of the total (8). Model Analysis Before an expensive engineering project is undertaken, it is sometimes ad- visable to study the performance of a small scale model of the prototype that is to be constructed. In the case of structures, deflection tests and static destruction tests are performed on models in order to predict how well the prototypes will fulfill their purposes. This is especially true when a prototype structure is not available or ex- pendable, or if the—testing of the prototype would be difficult or costly. l9 It must not be assumed, however, that model studies provide ready answers to all questions. As a general rule, suitable model tests cannot be devised, nor can their results be interpreted without an understanding of the basic theory of the phenomenon under consideration . Prediction equations The general form of the equation for any phenomenon may be determined by dimensional analysis. This method has been attributed to E.W. Buckingham (5). In itself, dimensional analysis gives qualitative rather than quantative results and also provide certain prediction equations. Given a set of physical quantities which describe a phenomenon, a set of dimensionless and independent terms can be established by a combination of dimension- al analysis and the Buckingham Pi Theorem. This theorem states that the number of dimension less and independent quantities required to expressa relationship among the var- iables in any phenomenon isequal to the number ofquantities involved minus the number of basic dimensions in which these quantities may be expressed. In equation form: 5 = n-b ............................................ (3) where s - number of Pi terms n - total number of quantities involved b - number of basic dimensions involved The hypothesis is organized in such a manner so that one Pi term is expressed as a function ot the remaining terms, i.e.; 77' =‘F(7l'2,7l'3,W4,...7Ts)..................‘ ......... ..(4) The only restrictions placed on the Pi terms is that they be dimensionless and in- dependent. Theory ot models A general theory of model design may be developed by a simple extension 20 ot the general type equation (4). Since this equation is entirely general, it applies to any other system which is a function of the same variables. Hence it applies to a specific system called the model. 7T [m = F(7T 2m] 7F 3m, 1T4m, o on. 5m) .................... (5) An equation for predicting 7T, from it ,m may be found directly by dividing equation (4) by equation (5). fl' = FUZ’P’H‘I’WWSI .................. (6) 7T 7T 7rlrn F(772m, 3m, 4m,-'-7Ism) Now, if the model is designed and operated so that: “IT 2m = 7r 2 7r3'1n = 7T3 71'4m = ”4 .................. (7) Tl'sm = ITS it follows that: F(1r 27n3,1r4,...7rs)= F(7r2m,1r3m,7r4m,...1rsm) ......... (8) Therefore N, = "1m ...................... (9) Equation (9) constitutes the prediction equation, which must be valid if the design and operating conditions, equation (7), are satisfied. Equations (7) are known as the design conditions, and from them certain generalizations may be drawn. If all of the design conditions are satisfied, the model may be considered to be a "true" model in that it will give accurate informa- tion concerning the behaviour of the prototype, provided that all of the pertinent ~ quantities are included in the analysis from which the Pi terms are obtained. If all of the design conditions cannot be satisfied, the behaviour of the model may be distorted with reference to the factors included in the corresponding Pi terms and the 2l prediction equation may be affected materially. In general the design conditions will involve distances indicative of the size of the model and prototype. The ratio of some pertinent distance or length of the prototype to the corresponding distance in the model is called the length scale, and is designated as n. L = nL .......................................... (l0) m Structural models Structural models are built primarily for the purpose of supplying information about the structure under load. This information is evaluated in terms of resistance to failure caused by either deformation, fracture, buckling, or undesirable inelastic action. Consequently the basic consideration is one of evaluating deflection and stress. The deflection's and stresses are functions of (a) statics, (b) geometry, and (c) properties of the material. The effect of two resultant forces on a short section of a structural member is one or more of the following: I . Axial tension or compression 2. Cross shear 3 . Torsion 4. Bending The response of the member to the action of these forces is a function of the geometry of the section and the properties of the material. If a member is subjected to bending, the principal moments of inertia and distances from the neutral axis are the significant geometrical characteristics, while the modulus of elasticity and some measure of flexural strength are the required properties. For a model in which only stress is to be evaluated, the proportional limit is the only pertinent property of the material to be considered. However, from the practical standpoint, a knowledge of the modulUs of elasticity is essential, since stresses are not measured directly but are evaluated from measured strains. ' 22 Distorted models The requirement of complete geometrical similarity between model and prototype is essential for a true model, but it may not always be feasible either practically or economically. For example Aldrich (I), in establishing the design conditions for his plastic arch, found it necessary to use a different scale for the cross-section in comparison to the layout scale, otherwise an extremely thin skin section would have caused considerable difficulty both in construction and in be- haviour under load. A model so designed that one or more of the design or operating conditions is not satisfied is known as a distorted model. Consequently any one or a combination of the three principle factors involved in structural analysis, viz. , statics, geometry, and the properties of the material may contribute to a type of distortion . The prediction equation for a distorted model may be established by determining a prediction factor 8 so that 7TI : aTT‘m ........................ (ll) Murphy (5) gives prediction factOrs for stress and deflection based on the four fundamental types of loading. The prediction factor, a , is given in terms of a distortion factor 0 . Values of a are given for exact, partial, and no similarity of cross section between model and prototype. THE RESEARCH PROJECT ‘ Preliminary Investigation The review of literature has clearly shown that more and more designers are turning toward reinforced plastics because the cost of experimenting with unusual forms is no longer prohibitive. Clay, plaster, or wood provide inexpensive molds for contact pressure fabrication . This equipment may not represent automation, but the investment is low and volume production is not necessary to amortize costs. Dr. Aldrich, on reviewing his research project, made the following sugges- tions for further study: I . Investigate the use of glass reinforced plastics for particular farm building application. 2. Investigate building element cross-section and layout to determine the most economical unit of reinforced plastic suitable for clear span construction for farm buildings. 3. Investigate the use of glass reinforced plastics in thin shell construction. 4. Investigate the use of different forms of fibrous glass as plastic resin reinforcing materials. 5. Investigate the possibilities of developing standard size prefabricated building elements of reinforced plastics which would permit flexible building arrangement. Taken separately these recommendations would entail considerable work. However, combining the suggested items into a single project appeared feasible. Hence the work was reduced to designing a rigid frame as a prefabricated building element (item 5), using glass mat as another form of fibrous glass (item 4), in a thin shell construction as surface skin for a sandwich laminate (item 3), of variable cross-section (item 2), and for the particular application (item I) as a controlled- atmosphere storage building. In the interest of farm building flexibility and usefulness, the 40 ft span 24 appeared to be the most suitable width of building for most farm enterprises, Figure 4. With the increased use of fork-lift trucks capable of stocking produce in vertical tiers, 0 l2 ft height to the eaves appeared to be the most convenient for economical storage and efficient use of loading equipment. This height would also permit trucks to enter the building for direct loading or unloading. Designing the structural unit as a 3 ft module would permit speedy erection and also provide sufficient width for prefabricating door and window sections. I The cross-section design was inspired by the work of Buckminster Fuller and his concepts of strength and rigidity in geodesic shapes. The curved arch shape in the crown section A—A, Figure 4, with its tangents perpendicular to the longitudinal axis of the rigid frame and elongated to parallel the span dimension, was an out- growth of this inspiration. At the inflection point of the moment distribution diagram, the convex surface of the crown was transformed to a concave surface which terminated to a maximum depth at the haunch, section B-B, Figure 4. This transition from the high crown convex to the deep section concave surface resulted in a steeper pitch than appears evident from the elevation view. This unusual design should improve the aesthetic appearance of the final structure. The sandwich construction was designed for 3 inch thickness of urethane foam insulation, using a 5 pound per cubic foot density to provide maximum insulation as well as some resistance to buckling. Adjacent units are locked together in a similar manner to that of corrugated metal roofing. The point of contact of the lower skin surface is treated with a resin adhesive to provide a resin weld between units and insure gas-tight construction for controlled—atmosphere storage buildings. Rigid Frame Analysis The rigid frame was analyzed using the "precise method of analysis" proposed by the American Institute of Steel Construction. This method is used most frequently in the case of frames composed of members having non-uniform moments of inertia. The design criteria is theoretically considered to lie within the boundary limits of a fixed-end condition and a hinged-end condition. However, since a 25 A‘l l 4I—0" -‘ —- - ‘ - ~ 12-0" (UUUUUUUIUU C 3I_0ll SECTION A-A F” '- u at”... .f I! 5 .J. ¢)t#ll 9.1..1330... imfnvu «Hm.- . (e um... . .c\fi’-r’0l‘§ 1" .u m. . Kw .. SECTION” B-B . u. . ”1...: E3... u .A' .WNDLHMC 3......» ,g. «Loo! . ‘0 *4. u an... er... 3:... .. \ .tfinmm. a o. r .0 \ dram m. s . w... .. .. In ..... arm». traumas“... \. . , 0 H~ I a. n . wear ham 3 Pl V .. \ .0. any. ‘DDU-xlm' subway: . “n on V. a.» NO.I?~I“¥“I§I-.uo . .mtfihsuandfio. J I a . '-'UWI 0‘0. I vJa I I. ‘1‘ u “ mun... Insular-W“ . at ~ ‘I ”We. _ QM..- mug...” Mr...“ we... , 1: "I... m. , P.” u. .. 7- Iwuhmmw WNW. to! v .I J ”yam"... .Ioh.’ , rt f , I SECTION C—C Figure-4. Rigid frame and section details. 26 1 practical fixed-end support is difficult and costly to construct, the actual joint more nearly approaches a hinged-end support. Therefore the frame is analyzed assuming hinged-end supports. The rigid frame of Figure 5-a is statically indeterminate to the first degree. In order to analyze it, the horizontal reaction component at E is selected as the redundant so that the reduced structure is treated as if it were free to move horizontally at E, Figure 5-b. The problem is now reduced to evaluating XE such that the horizontal displacement at E is equal to zero. For convenience a pair of coordinate axis is drawn through E. Moments which cause compression on the outside of the frame are positive, therefore with a virtual unit load placed horizon- tally at E in the direction of XE , Figure 5-c, the virtual moment at any point is equal to -Y. Equating to zero the horizontal displacement at E due to the load plus the displacement due to X E 2 fm Mw ds + XE m2 ds =.- 0 ................ .(l2) El El Canceling E, which is constant, and writing m as -y the equation becomes, -f‘LMW—di+xE/-L2-—di=0 ................. (13) l I Over the regions of constant I, the integrals could be evaluated by integation. However, a summation of finite terms would have to be made at the haunched knee and over the arch section, therefore a summation is used over the whole structure. Each half of the frame is divided into 9 sections of length, measured along the neutral axis. Mw, y, and l are determined at the midpoints of the sections. Evaluating the integrals in Figure 6 as summations, substituting their values in equation (l3), and solving for Xe' x = l3,750,778 w = 9.6V, E 1,431,204 27 W/ft. W/ ft. IIIIIIHIIIIIIIIIIIIJJ LIIIIITIIIIIIIIIIIII] B DJ: A r E_l_ . XE L/ ,1 Original Structure Reduced Structure (0) (b) E 44- Moment distribution on reduced structure due to the unit load at E. ' (c) w / ft. Fllllllllllllllllnlj II E E Moment distribution on reduced structure due to the uniformly distributed load. (0') _.I n._ Final moment distribution on the frame. (e) Figure 5. Load and moment diagrams for the rigid frame. 29 The moment at the‘ haunch is ll5.2 w-ft, and at the crown, -42.8 w-ft. The maximum stress will be at the joint, therefore, with a design load of 90 lb per ft of beam and u§ing the cross-section first on the beam side of the haunch and then on the column side, the stress in the outer fibers of the frame will be 5,4l2 psi and 4,608 psi respectively. The maximum stress value is well below the ultimate value of I7, 300 psi, Table 3. Assuming a maximum tensile strength of l7,300 psi, this would provide a stress factor of safety of 3.2. The final moment distribution for the frame is shown in Figure 5-e. I . From research conducted by Aldrich (I) it was proven that true and distorted models can be used to predict the behaviour of the prototype. Therefore, to reduce the cost of labor and materials, a model analysis was completed which permitted the fabrication of a reduced scale model of the rigid frame. Model Analysis The model analysis involves the selection of a suitable scale, the shape of the variable sections, the material to be used, and the development of prediction equations to study the behaviour of the design. The two factors which best describe the behaviour of a structural member under load are stress and deflection. Hence the first consideration is the develop- ment’of prediction equations for stress and deflection of the model using the method outlined in the review of literature. Prediction equation for stress The variables and their respective dimensions are as follows: Variables Symbol Dimensions of variables Span . S L Load per ft. of beam W F/L Stress ¢ F/L2 Scale ’9 - L Modulus of elasticity (tension) E F/L2 The stress, f = F(S,W,,3, E) 28 Soto—30.00 cmfiop mo DEE pco cozoom oEotltoI .0 6.59“. uO " nZl amenofli v8.5... 308.80.38.02 ngmm 8 88. «.8 3.. 8.22 d swvodtnzomee 858 v8 88. 0.8 _.2 «find m 3.868.388. 3.58 am 88. 3.8 92 82: a 38.88.3096. 85.5 8 88. 3.8 92 «.22 e 8858:8802 83.: 8k 88. n8 3.. mm on m 88.83238. 838. 08 88. «.8 3.. me on a. 3368 28.8 80.3 .8 E8. 0.8. 8.2 my, on m 268.8 22.8 we}... now 38. 0.8m mum. m._ .5 m 0.0 0.0 80.8 83 88. v.3 cs 0.0 .2 _ _ 82.: _ u we v.5 é. a: e :2 .332 .2 em> s _ a > x e -33 waste... \ A ‘l\ I I‘ll“ 0 .\ \R \. "Pl OZ "ll? "Pl .1 " t9l ll 30 Since there are five variables and two fundamental quantities, there will be 5 - 2 =3 Pi terms. 77.25 71'2a 31 773=SE w ' S ‘W‘ Similarly for the model: Tilmzsm Wm, ”ma-:Lml 7T3m._-_—._SmEm Wm Sm Wm The design conditions are: is “ m '7 SF The operating conditions are: E __ SmEm WQWm And the prediction equation for stress is: S = Sme W Wm Prediction equation for deflection The variables and their respective dimensions are as follows: Variables Symbol Dimensions of variables Deflection D L Span S L Scale [3 L Load per ft. of beam W F/I- Modulus of elasticity (tension) E F/L2 TIze deflection, D = F (5,13 ,W.E.) Since there are five variables and two fundamental quantities, there will be 5 - 2:3 Pi terms. 3l :1 N m jg :j M II elm \ 4 (A) It 2| m Similarly for the model: Tl'ma Dm' N2m=flm, 7T3m= SmEm Sfl't Sm Wm The design conditions are: The operating conditions are: iE_ = SmEm W Wm And the prediction equation for deflection is: D__Dm S Sm The design conditions indicate that the model and prototype should be geometrically similar and the operating conditions give the load relationship. A scale of three was used, or S 35m. This scale was used both for the span length and the cross-section, including the laminate thickness. Therefore the model is a true model, and the prediction equations for stress and deflection become : _ me 6‘- 3Wm D=3Dm Frame analysis for the model The method developed for the analysis of the prototype was also used for the analysis of the model. Therefore appropriate expressions for S, X,Y, D and I, 32 Figure 6, for the model were substituted in equation (I3) giving: 90,166 w = 2.96 w XE 30,490 The moment at the haunch is then - ”.84 w ft. , and at the crown +6.33 The stress at the crown is: a' = fl, = $.33 wa2)(1.45) . ,. 2 l 1.19] = 92.4 ln/lf‘l. The deflection at the crown was estimated by the method of Virtual Work. A virtual unit load was applied at the crown in the direction of the expected dis- plaCement. The frame is indeterminate to the first deg'ee, hence the horizontal re- action at E was again assumed as the reductant to take advantage of the previous analysis. The value of XE determined due to a unit vertical load acting at the crown is 0.3I7 lb (8). The equation for deflection at the crown is: Performing the necessary calculations for each segment of the half arch and summing the total we have Dc 2 52.68“;le = 7,5IE36w‘ 33 Experimental Investigation Model construction The. model arches were constructed using the contact pressure or hand-Iay—up process. The patterns were made from laminated wood molded to shape with hand and power tools to provide matched molds for each surface of the sandwich panel. Since only two models were required .for the investigation, the patterns were pre- pared for use as molds. The preparation consisted of filling defects and joints with—a wood filler and then sealing the surface with repeated applications of lacquer until a smooth hard surface was obtained. A large amount of wood filler was required to fill the numerous knot holes, checks and gum pockets despite a careful selection of the material. Prior to the laminate lay-up, the molds were first given a coat of Johnson's paste wax. Then a layer of parting agent or mold release, which was sprayed on and allowed to dry, followed by a final application of paste wax. This preparation was necessary as an added precaution to eliminate the possibility of a bond between the laminate and the mold surface. The polyester laminating resin was prepared in small containers, each mixture consisting of l000 ml resin (polyester), I0 ml modulator (cobalt napthenate), and l ml catalyst (methyl ethylketone peroxide. At 70 degeeF room temperature the pot life after mixing was approximately 25 minutes. For vertical surfaces 0 thixotropic polyester resin was mixed with standard polyester resin in the ratio l:I . The laminating process is illustrated in Figure 7, and consists of the following steps: (I) apply a layer of resin to the mold surface, (2) place the glass fiber cloth on the freshly applied resin and work the resin up through the cloth, (3) apply a second layer of resin over the cloth working the resin into the cloth with a short bristled brush to insure proper wetting and also work out excess resin and air bubbles, (4) place the glass fiber mat on the resin, (5) apply a third layer of resin over the mat and thoroughly saturate the mat with resin applying successive (a) I ' ' (5) Apply resin to mold surface. Place glass cloth on wet resin. _ '(d) . . Place glass mat on wet resin. Final resin touch-up and trim operation. Figure 7. Successive operations in the laminating process. 35 layers of resin slowly so as to prevent rapid increase in temperature which will reduce the viscosity and cause the resin to flow out of the laminate. The absorptive properties of the thick mat produced a laminate thickness greater than that obtained in the laboratory where special care was exercised in squeezing out the air bubbles. Careful supervision of unskilled labor to this important detail in the shop environment was quite difficult, consequently the actual thickness of the finished laminate varied from 0.035 in to 0. I25 in. The cloth and mat was trimmed along the edge of the mold with cloth shears while the laminate was still in the soft gel stage. The resin became hard in approxi- mately 4 hours. The two half-shells were then removed from the molds and welded together with glass fiber tape and polyester resin; sanding the two edges and sur- faces of the half-shells before welding, to insure a good bond between the tape and the laminate. The mold was designed to provide a 2 in flat surface, along one edge, the entire length of the arch. This yielded ample material, from each arch, for a random selection of flexure and tension specimens. The welded laminate shell was then repositioned between the two mold sur- faces.~ The molds were then clamped together and shipped to Dow Chemical Co. , Midland, Michigan, for the final operation of placing the polyurethane insulation in the sandwich arch. The equipment used to mix and place the liquid into the laminate shell, illus- trated in Figure 8, consists of metering pumps, pump motors, reservoir tanks, mixing head, and control panel. It is operated by electrical services in the form of 440 volt, three phase and 220 volt, single phase current. In addition, a supply of inert gas at I20 psi was used. I The polyol and semi-prepolymer in 30 gallon drums, and the solvent in a 20 gallon drum were mounted on the frame to make the entire system portable. The chemical components were delivered through a mixing head powered by a two horsepower motor. Proper blending was obtained by the use of two pumps of 20 gpm capacity, ' ‘ Figure 8. Equipment used to foam in-place polyurethane insulation. Courtesy Dow Chemical Co., Midland, Michigan. Figure 9. Placing liquid polyurethane insulation. 37 each driven through a gear reducer by a two horsepower motor. Rectifiers were used to convert 220 volt AC to DC current to supply the pump motors. The rectifiers were equipped with variable rheostats to control the desired pump speed. Tachometers, mounted in the control panel, were used to indicate the rpm of each motor. The equipment was initially designed to foam I2 in thick sections in ship bulkheads with a capacity of 40 cfm. However the equipment was modified for this proje ct to produce approximately 6 cfm. To insure uniform density throughout the entire arch, it was necessary to calibrate one-second check points along the pour path of the arch. Each check point representing 0.09 cu ft of core volume. Then with the mix designed for a free-foam density of 5 lb per cu ft and a pour rate of 29 lb per min, the core volume of 2.7 cu ft was run in 28 sec, checking the rate of travel against the one-second check points with a stop watch, Figure 9. The laminate shells of the second arch were assembled in much the same manner as the first, with the exception of the initial paste coat of resin. The thick paste coat is normally applied to the mold surface and allowed to gel slightly before the laminating process begins, to insure a glass smooth surface on the finished pro- duct. However, to reduce the resin content of the finished laminate, only a light application of normal viscosity resin was used for the initial paste coat. Test facilities The model arches were tested in the Farm Structures Research Laboratory, Michigan State University. This laboratory is equipped with a special test floor designed so that structures can be loaded in a horizontal position by using a System of hydraulic cylinders and loading pads. The loading pads for this project were shaped to the contour of the arch and coupled together in pairs. The loads were applied through the hydraulic cylinders to the center of the cross linkage connect- ing each pair of loading pads. This arrangement, Figure I0, provided a uniformly distributed load perpendicular to the span and spaced on I0 in centers, which is equivalent to 30 in centers on the full scale arch. The reaction supports were of sturdy construction and tied securely across the span to insure no displacement other than the deflection of the arch under test. A one-half inch flange at the 38 Figure I0. Model arch under test in Farm Structures Research Laboratory, Michigan State University. Figure II. Typical strain gage application on model arch, and Ames gage test stand for deflection measurements. 39 support provided a seat for the column base and permitted the column to function as a hinged end column. Instrumentation To verify the design procedure, some measure of stress and/or deflection should be made. From our development of the model analysis, it is evident that both measurements are necessary to verify the analysis. Deflections can be measured by means of a dial gage deflectometer. Since stress cannot be measured directly, it must be obtained by measuring strain and then relating strain to stress through known stress-strain relationships for the material. Electric resistance strain gages, sensitive to small changes in strain are easily mounted to plastic surfaces, and for static strains require required only simple measuring instruments. Dial indicating deflectometers were used to record deflections at the crown and near the haunch, Figure II. Two additional gages were used, one on the outside of each column to check for symmetrical, lateral frame distortion. Type A-l, SR-4 electric resistance strain gages were mounted on the arch as shown in Figure ll . Two gages were mounted at the crown, one at the extreme fiber location on the bottom surface. Four additional gages were mounted along the arch and on the column. The gage signals were relayed through a switching device and interpreted from a standard 2-arm bridge Young Strain Indicator. The complete test procedure is illustrated in Figure l0. A representative sample of the flexure specimens was prepared for laboratory testing with a Type A—l, SR-4 gage mounted on the glass fiber cloth side to check the response of SR-4 gages on the glass fiber reinforced laminate, and to compare the deflections recorded from the SR-4 gage with those recorded from a differential deflection force transducer. The specimen was loaded in the same manner as the samples used to determine the modulus of elasticity in bending. A check of strain versus load indicated a difference of 4 percent at 70 percent maximum load, Figure I2. 40 Vtmm pco cooapmcot cozootflo .3 pofiecohop no @5953 E .3536 523600.. .N_ $507. 626;... no cosmooam @5185 of :0 $3256.: omom Sat... E}: 20:63.8 o_. 00. mo. no. 00. no. #0. mo. «0. :5. see 3.30 l..\ \ \ \ L \/ «mUDOmZdD—h \\ 20:63.30 Zuzanamluln “95 ENE Em _. 4. an; t .\ _ . m a: d L 0— ON 0m 3» ('“III CIVO'I 4| Figure I4. Flexure (a) and tension (b) specimens under test. 42 Determining material constants Since the laminate design used in this project was a departure from normal practice, exact values for mechanical properties were not availabe; and only approximate values obtained by interpolation could be used in the original design calculations for the frame. Therefore, in order to check both the quality of the laminate produced and the design predictions, it was necessary to determine the material constants for the laminate used in the model arches. Hence flexure and tensile samples were cut from the excess material along one edge of the laminate shell. The test specimens were prepared and tested according to ASTM designations (2). ASTM designation D638—58T was used for the tension specimens and ASTM designation D790-58T was used for the bending specimens. The flexure and tension tests were carried oUt as illustrated in Figures I3 and I4, using a PS-60 Riehle 60,000 pound capacity, screw power universal testing machine to apply the loads, and a model 350-I I00 Sanborn Carrier Preamplifier with a phase correcting network and a Sanbom 6-Channel Recorder. The loads on the tension specimens were recorded through the use of a force transducer based on the proving ring principle and incorporating a sensitive differen- tial transformer motion transmitter. Dynamic loading was verified by observing pointer movement of the dial gage on the Riehle Testing Machine and instantaneously actuating the marker on the Sanbom Recorder at predetermined intervals. The strain was recorded by substituting 0 Displacement Transmitter (Differential Trans- former Transducer) for the dial gage of the Riehl Extensometer (two inch gage length). A typical record is shown in Figure I5 (b), for Specimen I T 2. The first figure of the code identifies the arch number, the T designating "tension" specimen and the remaining figures designating the sample number. A total of IO tension specimens were tested, 5 from each arch. Figure I4 illustrates the equipment and procedure for the tensile test, and the results are shown in Figures I6 and I7. The loads on the flexure specimens were applied and recorded in the same manner as those on the tension specimens. The deflections were recorded through the use of a model I02 A-400 Daytronic Displacement Transmitter with a linear range of 0.0 to 0.4 in. with zero suppression. Dynamic deflections were verified . . .. l :— l. I II. t . flirtlff ' .i ’ i‘ :"‘ o 3' o v 9. “.3 x 1‘: l .. .:: .‘ 2‘ °i. ' I A. 0‘. . , " m: (a) (b) Figure I5. Typical records for flexure test (a) and tension test (b) as recorded by Sanbom Recorder. 44 ._ 33:5: :96 23.0.1 .358 E9: 20:25: poocoafoc $o_mtc_mo._ .cmtoboa coh— co_mc£ c_ mo>So thmtmmohm 3033 3 Ducal me. x .535 2.3.: m. .2 m_ N. : o_ w w n o n v .8 .0 .30 \‘I E _ zmz_owa{\ 2.. 28.8% - .\\ \\\\\ \ X (9.01 X ‘U! 'b5/'ql) ssams \\ \ \ \ \ o_ I 45 .N 5383: 50:0 023?. _opoE E9.“— 20:_Eo_ 108350.. mm0_mI:_mo._ ccatoboa :0» 83:2 :_ 32:0 50.5-39.3 3033mm. 0.53”. $2 x e \ .5 2.5:... m. 3 2 N. .2 o_ a m N c w v m N _ i 3 .so _ N m \\ m 1.... \\ a. 3 m m \ / \\ o m. E 23.8%] m n i u \ k m N: 252.8% I.P\J\\\ m (A. \ . \ o— \ \ : L\ \ 46 ._ .0383: 39.0 0233 _0poE So: ?260 £23 030:_Eo_ 309.850.. 30_mI:_m0._ $7.033 com 95:03 :_ 32:0 :_0.=mtmm0hm _oo_ax._. .3 0.59”. ANS x e x a: 2:25 N 3 n v m N _ as \ “$200 . . \ N \\ s \ . E. \\ m m \N H \\V o. W \ \ s N 81.23288 IINIHV\\\ x u n u w a \ \ we m. oan“: 253.8% I W. (e \ 2 \ \ t\ on ix 8 47 ._ .695: :03 0:33 .002. :5... €320 .oEv 0.0562 1000..ou.:_0._ 303:5...0: 3.05020“. :0. @5203 :_ 0.0230 £93... 30...... 1003»... .0. 0.59... n o :2 x 5}: 22.5 m v J.“ .0 £00 92m“: 2525QO n\ M- V‘ 020": Zm<<_Ummm I o— N— v— o— 2 ON NN (9_01 x U! b's/ql) ssams 48 .N 63:5: 306 0.30:. _03oE E0... A5503 3.23 0.05:6_ 3006.50: $0_mn5m0.. £03032. .6. @5353 5 m0>50 :_0hmlmm0hm 306%. .ON 0.59. co. x 5}: 2.3.5 m 3 . m M V m N '— 3.. . .0 to . . \ \ \\ . o \\\ \ \ \ B \\ M S _ \ o. S CUTE Zm<<_Umn_m [vii \ mu; . T n u .. \ \ N— V Gnu—"5 Zm<<_Um_n_mlL N\\..\IV .w. \ \ .1 m \\ .\\ 3 O... \ . \ m— 9.\.\ . \\ ON NN 49 .N 63:5: 306 02.0.07. _03o:. 50... .5503 .05. 0.05:6_ 3006.50. 303158.. £030.32. .6. m53c03 5 «.0250 50...?305. 705%.. . _N 059. :2 x 5?: 2.3.5 N v m N _ 3.. 3 .60 02 N. N Zm<<_Um_n_m\l\ b b D 1 P p u d u 1 02 N. u. N Zm<<_Um..m \ § *\ o— N— 3 3— 2 ON NN (€_01 x U! bS/ql) ssams .voo. wflagttmv 35.83:: a 2 0% :320 :0 _ 03:5: :20 3on mo :ozu0t0o .NN 0.33“. :5 2265 2 20:03:: o n .v m N . _ 4.3 m 2 I 3 .30 . a. o “0 ON W 1 ‘Q IA . om m S I. 88550 \ m . n \f/WWM\ \ ow w \v4 \ \ Anv‘w \w .I \Ca.“ éq/m OW AVU _ Emma» NV»? 2 O \\G A»& . 8 H I4 \ GI \Aom/m \ 85202 :84 332 w m \ II on m. \ m. D \ w 1'. om ( \ #CGEGLDmOOE m0 #Cmom . . _ 5] ._000_ «00332.35 3:50:50 2 030 $590 :0 _ 03:5: 50.5 _0moE :om m::0:0a :_ m0>50 $0.:mlwoo._ .MN 059... A .2 x E: SmEm m N _ x? \ \ \ \\ n K“ - \\ \ \ N . x o. .0 .030 xxx \\\ m x x x w x xx \ om M 322:3 fl? \ x \ .. m. x xx x x cm W. xxx \\ m \ \ \ < I. \ xx I O? mu 8505.00 1%\ m on V \ . . K a . mx. ’1 \ \\ 00 / :o:00m..$o._U £03. 0mm3m50 30:311003 AN 05?”. (“1°99 J0 wa) 0vo1 aamamsm mwaoanNn 56 Subsequent increments were applied and corresponding values for deflection and strain were recorded to complete the cycle. The cycle was repeated 8 times and the arch was then removed from the hydraulic test jig. The results of the tests are shown in Figures 22 and 23. Model arch N0. 2 was tested in a similar manner as that for arch No. I; however the final cycle was loaded to failure. The arch failed at each haunch simultaneously in a combination of compression in the innerlshell and tension in the outer shell of the sandwich construction as illustrated in Figure 24. The arch was removed from the hydraulic test and cut through the sections at 10 inch intervals to examine the uniformity of the laminate thickness and insulated core density. The results of the tests are shown in Figures 25 and 26. Long—term static loading The short-term static load tests as described previously do not provide informa- tion on behaviour of the arch and materials if loads of considerable magnitude are impressed on the structure over a period of time. To determine the possible presence of creep in the material, arch No.1 was subjected to a uniformly distributed constant load of 3l .3 pounds per foot of beam (approximately 40 per cent of the static failure load), Figure 29. Observations of the deflection at the crown were made and recorded at intervals until the frame had reached an equilibrium position. The load was then removed and observations continued until the frame had again reached equilibrium. The results of the test are shown in Figure 27. 57 E003 00 :00“. :00 00:50:”. m. _m 30 3002 8:035 3:03:00 0 3:2, 950:0 :0 — :03c5: 30:0 _030:: 30 :0200—000 .NN 050E 0.: 02: 08: 8o 08 8: o8 8... 8:. 8m 08 8: 3.0 om>O<