IBIJCIKLING Of CUM, 'PLYWOOD PLATES IN AXIAL COMPRESSION

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1 IBIJCIKLIG f CUM, 'PLYWD PLATES I AXIAL CMPRESSI Information Reviewed and Reaffirmed January 1953 IFRMATI REVIEWEb AD REAFFIRMED 16 This Report is ne of a Series Issued in Cooperation with the ARMY-AVY-CIVIL CMMITTEE on AIRCRAFT DESIG CRITERIA Under the Supervision of the AERAUTICAL BARD o. ltail UITED STATES DEPARTMET F AGRICULTURE FREST SERVICE FREST PRDUCTS LABRATRY Madison 5, Wisconsin In Cooperation with the University of Wisconsin

2 BUCKLI' F THI CURVED PLYWD PLATES I AXIAL CMPRESSI/ By EDWARD ':'3. KUEZI, Assistant Engineer Summary This report presents the results of tests made to determine the buckling stress of thin, curved, plywood plates under axial compression. The tests were made in an apparatus that was arranged to prevent change of curvature at the ends of the plates and to provide guides, not clamps, for the edges. The plates can thus be thought of as being simply supported. While it is apparent that a plate supported in this manner is not found in industrial or commercial products where the edges are usually fastened to stiffeners, this method of testing provides means of determining the effectiveness of thin plates in carrying loads without the complicated analysis that would be necessary if stiffeners were incorporated. The conclusions are briefly that the buckling stresses of thin, curved plywood plates in axial compression are approximately equal to those of thinwalled plywood cylinders provided the width and length of the plates are each greater than their radius of curvature. It seems likely that the length effect on the buckling stress of such curved plates is the same as for thinwalled cylinders in compression. Plates of smaller widths and lengths exhibit higher buckling stresses. Scope of the Work The major portion of the testing was conducted on thin, curved, plywood panels of widths from 1/2 to 4. and lengths from 1 to 6 times the radius of curvature of the specimen. Both axial and circumferential directions of the face plies were used in the principal series of tests, and a few check tests were made on specimens having, the grain direction of the plywood at an angle of 45' with the vertical. As a check on the effect of the edge guides a few tests made on cylinders fitted with internal "spiders" to restrain buckling; were compared with tests on curved panels of matched material. 1 This mimeograph is one of a series of progress reports prepared by the Forest Products Laboratory to further the ation's war effort. Results here reported are preliminary and may be revised as additional data become available Mimeo. o

3 Buckling stresses of restrained cylinders were also compared with theoretical buckling stresses of unrestrained cylinders. Description of Specimens All specimens were made of yellow birch or yellow-poplar aircraft grade veneers, rotary cut at the Forest Products Laboratory. The plywood was glued into flat sheets in a hot press using Tego film glue. To form these flat sheets to the proper radius af curvature they were wet and bent he ceiinder over a hot mandrel. Prior to forrdnge t the / sheets s *ere scarf cut. The scarf gluing was accomplished on the hot mandrel. Sheets of matched material were pressed flat and subsequently cut into minor coupons for testing in bending, compression, and tension. The matching was accomplished by using veneers obtained from the same portion of the loc. as were the veneers in the curved plates and cylinders. While none of the material was conditioned prior to testing, it was allowed to remain in the testing laboratory for about a week and then tested. The major portion of the plywood consisted of 3-ply material with faces of 1/1-inch veneers and cores of 1/4-inch veneers. Some of the plywood used in the restrained cylinder study was of 5-ply material with all veneers 1/1-inch thick. All specimens in this study, curved plates and cylinders, were formed to a 5-1/4-inch radius of curvature. Apparatus and Testing Methods The apparatus used to test the curved plates was arranged to simply support the vertical edges of the plate (fig. 1). The top of the specimen was allowed to bear on the edge guide support plate fastened to the upper head of the testing machine, and the bottom rested on a flat plate mounted on a spherical bearing on the lower head of the machine. The bottom plate was adjusted to assure uniform bearing, and screw jacks were placed to prevent tilting. A strap of we'ebiag was passed around the ends of the cylinder to hold the ends tightly to the end plates. The separation of the edge guides to receive the specimen was adjusted by means of feeler gages to Provide a uniform clearance of about.2 inch along the entire length of the specimen. The edge guides were such as to restrain the curved dates inthe radial direction only and afforded no restraint in the circumferential direction. The load was applied at a slow uniform rate until failure occurred. The cylinders that were fitted with internal restraining spiders were loaded in the same manner as the curved plates. The internal spider was arranged to prevent the cylinder from buckling in certain places by holding 6 or 12 equally spaced radial vanes against the inner wall of the cylinder. Mimeo. o

4 These vanes were not glued to the specimen. The vanes were made about 1/4 inch shorter than the length of the specimen so that they would carry no load. Methods of testing minor coupons in bending, compression, and tension are described in the appendix. Results of Tests All specimens (curved plates, cylinders, or restrained cylinders) failed by buckling of the plywood. 1Tnile this was usually a sudden failure. all buc'eles appearing instantly, it was occasionally of a progressive nature, that t6, an initial buckle would develop, then a second, third, and so on until maximum load was reached. The progressive buckling occurred rapidly, and the difference between the load at the initial buckle and the maximum load was usually indiscernible. In general, the shape of the buckles (figs. 2, 3, 4, and 5) was,essentially the same as those found in cylinders under compression, although the size and the aspect ratio changed when the width of the plate was decreased below the radius of curvature of the specimen. The size of the buckle appearing in the narrower plates was smaller than in cylinders, and the aspect ratio approached unity. Long specimens, 1/2 radian wide, of plywood with the face grain direction axial, flattened when the load was applied because of the small stiffness of the panel in its circumferential direction. Cylinders fitted with restraining spiders failed by buckling. The shape of the buckles was the same as that of the curved panels of comparable widths. It was difficult to adjust the vanes on the spider to fit the exact inside of the cylinder. Evidence substantiating this was seen occasionally when the width of the buckle was greater than the spacing of the vanes. This also ma ny have been due to the fact that buckles in adjacent bays caused some increase in diameter of the specimen thus allowing the buckle to increase in width. Computation of Results The buckling stresses were computed ie the usual manner, by dividing the buckling load b y the loaded area. Prom previous work the buckling stress for thin-walled plywood cylinders in axial compression was found to be expressed by the formula: p e ke r...yameo. 7o. 1322, "Buckling of Long, Thin, Plywood : Cylinders in Axial Compression." Mieo. o

5 where: p = buckling stress E k = a constant depending on the ratio 1 and defined in Mimeo.1322 El + E2 = modulus of elasticity of the veneers measured parallel to the grain h = thickness of the plywood r = radius of curvature of the plywood Values of E L were determined from bending, tension, and compression tests on minor specimens of the plywoods. The method is discussed in the follbwing: For any plywood construction having the grain of the face plies either parallel or perpendicular to the span, the modulus of elasticity (E 1 or E 2 ) in bending is related to E L by the formula: i=n \ E. I 7. 1 i=1 El or E2 = E L = KE L where: I = moment of inertia of the entire cross section about its bh 3 centerline (I - Tr-) Ii = moment of inertia of the i th ply about the neutral axis of the cross section Ei = modulus of elasticity of the ith ply, measured parallel to the span (for plies having the face grain parallel to the span Ei = EL ; for plies having face grain perpendicular E.=.45EL ' for yellow birch and E. =.37E for yellowpoplar) L The values of El and E2 ware determined from the test data on a plywood beam simply supported at the ends and loaded at the center, by using F13 the formula E -. The values of E L were then computed by use of the A I values of K given in table Table 1 is the same as Table 7 of Forest Products Laboratory Mimeo B. Mimeo. o

6 For any plywood construction having the grain of the face plies either parallel or perpendicular. to the direction of the applied load the modulus of elasticity (E a or Eb ) in tension or compression is related to EL by the formula: i=n Tr-Ai E _ i=1 ul A EL = CEL where: A P area of the entire cross section (A=bd). th A.=area of the ply Values of El. and Eb were obtained from compression and tension test PI data by using the formula E = The values of E L were then computed by Ae use of the values of C given in table 1. Values of EL as, found from several tests of each kind (bending, tension, and compression) and in each direction on coupons from the matched flat plates of plywood were averaged to get the value applicable to a particular curved plate or cylinder. The values of E 2 as found from the bending tests of the plywood were erratic, and many were for this reason omitted from the averages. Furthermore, the valid values were too few to be used as E 1 a basis for computing the ratio for use in finding the value of k to E 1 + E2 K 1 be used in the buckling formula. Consequently, the equivalent ratio K1 K2 was in each instance computed from the data of table 1 which have been derived from more adequate tests and are hence considered more appropriate 1 1 fr the purpose. Using these computed values of, - values 1 + K2 ni + n2 of k for use in the buckling formula were read from the graph in figure 6. Discussion of Results Experimental values 'of k as computed from the results of tests on curved plates using the relation k = a- with values of p as found in these E L h tests and values of E L as derived from coupons taken from matched plywood panels are listed in column 7 of tables 2 and 3. Column 8 lists for comparison theoretical values of k as found by the use of figures 6 from the ratio Mimeo. o. 158

7 K 1 The actual buckling stress as found in test is shown in column 4 K1 + K2. and the theoretical value in column 9. The theoretical value was found from the buckling formula (p = kel 17) using the theoretical values of k and the values-of EL derived from tests on the coupons from matched panels. Curved Plates -- Face Grain Axial and Circumferential The effect of length of specimen as shown in figure 7 is greater for specimens with face grain direction axial than for specimens with face grain direction circumferential. In both instances the length effeot is not significant until the length is shorter than twice the radius of curvature of the specimen. A decrease in length from two radii to one radius increases the k about 2 percent. The effect of width of specimen as shown in figure 8 is not apparent until the width is less than one radian. A decrease in width from one radian to one-half radian increases the k about 1 percent. The points plotted in figure 9 show about the same scatter as paints in a similar plot for thin plywood cylinders in compression (fig. 1) Curved Plates -- Face Grain at 45 Degrees Figure 11 presents a comparison between curved panels of plywood with the grain directions of the veneers at 45 to the axis of the plate and cylinders of matched material. Experimentally determined values of k are plotted. The points representing specimens of lengths greater than the radius of curvature agree closely with theoretical values inasmuch as k is essentially the same for plates and cylinders. The points representing shorter specimens show an increase in the buckling stress of the curved plate as compared to that of the long cylinder. This increase is about 2 percent, or about the same as for specimens having face grain directions 'axially or circumferentially. Restrained Cylinders Face Grain Axial and Circumferential Table 4 presents the data obtained from tests of restrained cylinders. The experimental results agree fairly well with theoretical values. -Figure 3 from Mimeo. 1322, "Buckling of Long, Thin Plywood Cylinders in Axial Compression." 158

8 Curved Plates Compared with Restrained Cylinders -- Face Grain Axial and Circumferential Table 5 and figure 12 present the results of tests on curved plates compared with restrained cylinders in compression. Due to the difference in edge conditions, the restrained cylinders exhibit buckling stresses about 2 percent greater than the curved panels. The curved plate edge is free to hinge and free to move circumferentially, while in a cylinder the continuation of material over a restraining vane provides more of a fixed edge con-. dition. In general, much of the variation in test results is accredited to the fact that small initial imperfections may cause buckling. This variation may also be due to differences in the dimensions of the specimen and in the mechanical properties of the materials. Factors affecting thicknesses may be due to difficulties encountered in manufacture, such as the cutting of the veneer, shrinkage during drying, pressing the plywood, and many others. Because of the variation of the mechanical properties of the material it is conceivable that even though a minor specimen was cut from a portion of the.log adjacent to the major specimen and had a similar specific gravity and moisture content, the mechanical properties might differ to some degree.a Figure 13 presents a design curve for long, thin-walled plywood cylinders and can be used for designing curved plates. Conclusions The buckling stresses of thin, curved, plywood plates simply supported at the edges and loaded in axial compression are approximately equal to those of thin-walled plywood cylinders provided that the width and length are each greater than the radius of curvature of the specimen. A decrease in width from one radian to one-half radian increases the k about 1 percent. A decrease in length of specimen from two radians to one radian increases the k about 2 percent. APPED IX Tests of Minor Specimens Flat plates of plywood that matched the material of the cylinders and curved plates furnished specimens for minor tests in bending, tension, and compression. 2See points on curves for strength-moisture and strength-specific gravity relations for mod as given in Technical Bulletin 479, "Strength and Related Properties of Woods Grown in the United States." Mimeo. o

9 Bending specimens were 1 inch wide and were tested on a span length 48 or :More times the thickness of the specimen for face grain direction parallel to the span and 24 or more times the thickness for face grain direction perpendicular to the span, thus eliminating the necessity of correcting for shear deformation. Specimens were cut so that the face grain direction was parallel to the span and perpendicular to the span. Specimens rested on end supports rounded to about 1/16-inch radius. The load was applied at the center with a bar of about 1/8-inch radius. The stiffer specimens were tested on an apparatus that measured the load by means of a platform scale reading to 1/1' pound. The rate of loading and the driving force was obtained from a testing machine on which the scale was mounted (fig. 14). Specimens not stiff enough to test on the platform scale apparatus were tested on an apparatus which used water as a load. The load increments could be read to 1 grams, and the rate of loading was controlled by the size of nozzle (fig. 15). Lmaediately after testing, a sample was cut from the specimen for moisture content determination. The specific gravity was obtained from measurements, and weights were taken before testing and subsequently corrected for moisture content. During the test, load-deflection curves were plotted. Properties computed from the test data were the modulus of elasticity, the fiber stress on the most remote fiber at the proportional-limit load, the modulus of rupture, the moisture content, and the specific gravity. The modulus of rupture could not always be computed because the specimen sometimes was pulled down between the supports and wood failure did not occur. The tension specimens were 1 inch wide and 11 inches long with face grain directions parallel and perpendicular to the direction of the load. The ends of the specimens were gripped in Templin grips fastened to the testing machine by bolts passed through spherical bearings. The strain over a 2-inch gage length was measured at the center of the specimen with a Tripolitis extensometer reading to.1 of an inch (fig. 16). The rate of loading was.5 inch par minute. During the test, load-deformation curves were plotted. Properties computed from the test data were the modulus of elasticity, the tensile stress at the proportional-limit load, the tensile strength, the moisture content, and the specific gravity. Moisture content and specific gravity were determined in the same manner as theywere for the bending specimens. The compression specimens were 1 inch wide and 4 inches long with face grain directions parallel and perpendicular to the direction of the load. Because of the thinness of the specimen an apparatus consisting of thin spring fingers was used to give lateral support (fig. 17).. The strain was measured over a 2-inch gage length with a Marten's mirror apparatus. Load-deformation curves were plotted as the test proceeded. Properties computed from the test data were the modulus of elasticity, the compressive stress at the proportional-limit load, the compressive strength, the moisture content, and the specific gravity. The moisture content and specific gravity were determined in the same manner as for the bending specimens. Yimeo. o. 158

10 Table 1.--Values of K and C used for computing EL Plywood construction 3-ply (1:1:1) 3-ply (1:1.25:1) 3-ply (1:1.67:1) 3-ply (1:2.5.1) (1:1:1:1:1) Bendinp, : Bending : Tension or : Tension or : parallel : perpendicular: compression : compression : parallel :perpendicular :Yellow:Yellow-:Yellow:Yellow-:Yellaw:Yellow-:Yellow:Yellaw- : birch: poplar: birch: poplar: birch: poplar: birch: poplar :TC K:K K:C:C:C: C K1 ' 1 2 ' K2 :.965 :.965 : :.682 :.679 :.363 : :.1 :.93 : :.413 :.48 : : : : :.836 :.834 :.29 :.23 : : : : :.427 : ply (1:1.25:1.25:1.25:1): :.31 :.295 :.584 :.582 :.461 : ply (1:1.67:1.67:1.67:1):.664 :.661 :.381 : : ply (1:2.5:2.5:2.5:1) :.547 :.544 :.498 :.493 :.498 :.493 :.547 :.544 r-(1: 1.25:1.67:1.25:1) `.724 :.722 :.321 :.315 :.613 :.61 :.432 : ply (1:1:1:1:1:1:1) :.724 :.722 :.321 :.315 :.59 :.588 :.455 : ply (1:1.67: :1) :.64 :.6 : :.534 :.57 :.53. : 9-ply (1:1. 1) :.681 :.678 :.364: ply (1:1.25:...:1) :.632 :.629 : :.556 :.552 : Mimeo. o. 158

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15 Figure 1.--Apparatus for testing curved plates in axial compression. The edge guides can be removed and the bottom head blocked so that short specimens can be tested. Width adjustment is obtained by fastening the edge guide supports at different positions in the upper plate. Z M F

16 Figure 2.--Buckling failure of a curved plywood plate in axial compression. The plywood is 3-ply yellow birch. The faces are of.1-inch veneers, and the core is of.25-inch veneers. The face grain direction is axial. The specimen is formed to a 5-1/4- inch radius and is 2 radians wide and 3 inches long. Z M F

17 Figure 3.--Buckling failure of a curved plywood plate in axial compression. The plywood is 3-ply yellow birch. The faces are of.1-inch veneers, and the core is of.25-inch veneers. The face grain direction is axial. The specimen is formed to a 5-1/4- inch radius and is one radian wide and 3 inches long. Z F

18 Figure 4.--Buckling failure of a curved plywood plate in axial compression. The plywood is 3-ply yellow birch. The faces are of.1-inch veneers, and the core is of.25-inch veneers. The face grain direction is circumferential. The specimen is formed to a 5-1/4-inch radius and is 2 radians wide and 3 inches long. Z / F

19 Figure 5.--Buckling failure of a curved plywood plate in axial compression. The plywood is 3-ply yellow birch. The faces are of.1-inch veneers, and the core is of.25-inch veneers. The face grain direction is axial. The specimen is formed to a 5-1/g inch radius and is one radian wide and 3 inches long. Z x F

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23 / A A A. t") L1/4 8 C3 at > k et. 1/4,k.6 1/ ;t kj Lu. 2 o 13 a o c AL A w A, 2. tl b/c LEGED: '' --2s A FACE GRAI AX/AL A FACE GRAI CIRCUMFERETIAL -THERETICAL 44 C), 4'1 4-4 / CMPUTED BUCKLIG STRESS f CMPLETE CYLIDERS (EXPERIMETAL PRPRTIAL LIMIT STRESS) Figure 9.--Comparison of test and computed buckling stress to show effect of approach of buckling stress to stress at proportional limit in compression for thin, curved, yellow birch plywood plates under axial compression loads. All plates were 3-ply with faces of.1-inch and cores of.25-inch veneers, and were formed to a 5-1/4-inch radius. Each point represents the results of three major tests. Z If 64187

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25 2 3- D/ 3-2. s-/ -ir--- THERETICAL If 3 - (95-$2 5-I TE: FIRST UMBER AT A P/T DETES LEGTH F CURVED PLATE / ICHES ;SECD UMBER, WIDTH / RA/AS i I /2. /6 2 CURVED PAEL BUCKLIG CSTAT(If--P-9 ELh Figure 11.--Comparison of buckling constants of thin, curved, plywood plates in axial compression with those of thin, plywood cylinders in axial compression. The curved plates were formed to a 5-1/4-. inch radius and were in widths of 2, 1, and 1/2 radians and lengths of 3, 15, and 5 inches. The cylinders were 1-1/2 inches in diameter and 3 inches long. All plywood was 3-ply. The faces were.1 inch thick with the grain at -45 and the cores.25 inch thick with the grain at +45 to the axis of the specimen. Z M r

26 LEGED: PACE GRAI DIRECTI AXIAL A--FACE GRAI DIRECT/ CIRCUM- FERETIAL. a A /6.2 CURVED PAEL BUCKLIG CSTAT(Ire6) Figure 12.--A comparison of buckling constants of thin, curved plywood plates in axial compression with those of restrained plywood cylinders in axial compression. The curved plates were formed to a 5-1/4-inch radius and were in widths of one or one-half radians and lengths of 3 inches or 5 inches. The cylinders were 1-1/2 inches in diameter and 3 inches long. Some were restrained with 6 vanes and some with 12 vanes. For details as to plywood and sizes see table 5. Z x F

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