ICUL'I',.LL ROOM PUCICLING Of SIMPLY SUPPORTED RECTNGULR SNDWICH PNELS SUBJECTED TO EDGEWISE PENDING March 1959 N. 1868 This Reprt Is One f a Series Issued in Cperatin with the NC-23 PNEL ON COMPOSITE CONSTRUCTION FOR meta VEHICLES f the Departments f the IR FORCE, NVY, ND COMMERCE FOREST PRODUCTS LBORTORY MDISON 5, WISCONSIN UNITED STTES DEPRTMENT OF GRICULTURE FOREST SERVICE In Cperatin with the University f Wiscnsin
BUCKLING OF SIMPLY SUPPORTED RECTNGULR SNDWICH PNELS SUBJECTED TO EDGEWISE BENDING! By W. E. JHNKE, Engineerand E. W. KUENZI, Engineer Frest Prducts Labratry,..4. Frest Service U. S. Department f griculture Summary The buckling f rectangular flat sandwich panels when subjected t edgewise bending was investigated experimentally. Panels f tw sizes were tested; each had thin aluminum facings bnded t an aluminum hneycmb cre. In each test, the lad at which buckling ccurred was determined frm facing lad-strain data. Buckling lads als were cmputed theretically. The bserved buckling lad was 102 percent f the theretical value in ne test and 87 percent f the theretical value in the ther test. Intrductin The stresses that can be resisted by sandwich cmpnents subjected t edgewise lad are ften limited by the resistance f the sandwich t buckling,!this prgress reprt is ne f a series (NC-23, Item 56-5) prepared and distributed by the Frest Prducts Labratry under U.S. Navy, Bureau f ernautics Order Ns. Ner 01835 and 01853 and U.S. ir Frce Cntract N. DO 33(616)58-1. Results reprted here are preliminary and may be revised as additinal data becme available. Maintained at Madisn, Wis., in cperatin with the University f Wiscnsin. Reprt N. 1868-1-
rather than by prprtinal limit, yield stress, r strength f the sandwich materials. Buckling lads r stresses may be cmputed theretically if adequate infrmatin is knwn cncerning the panel gemetry, applicatin f lad, edge cnditins, and mechanical prperties f materials invlved. theretical analysis fr the determinatin f buckling lads f simply supprted rectangular sandwich panels subjected t cmbined edgewise bending and cmpressin has been presented in a previus reprt.! In a supplement4 t that reprt, design curves fr the predictin f buckling lads were cnstructed fr panels subjected t pure edgewise bending. The purpse f this wrk was t prvide experimental verificatin f the theretical analysis fr the buckling stresses f sandwich panels subjected t edgewise bending. Test Specimens Tw sandwich panels f similar materials and cnstructin but f different size were fabricated. Bth panels were tested in edgewise bending as beams simply supprted at the ends and laded symmetrically at tw pints alng the span. sketch f the test panel shwing lading and supprting apparatus is presented in figure 1. Facings were 0.032-inch sheets f 2024-T3 aluminum ally. Lading strips f Duglas-fir, 1 by 3 inches in crss sectin, were riented perpendicular t the panel length and bnded flatwise t bth facings as shwn in figure 1. The ends f these strips extended 1 inch beynd the edges f the panel s that lads culd be applied t these prtruding ends withut applying any lad t ther pints alng the span. Since the purpse f this investigatin was t determine the effects f pure edgewise bending f panels, the nly area f the panel f vital interest was that lcated between the tw strips at the lad pints. This area f pure bending was 45.7 by 46.1 inches in size. T reduce the pssibility f buckling f the end sectins f the panel, which were under cmbined bending and shear lads, stiffening strips f 1- by 3-inch Duglas-fir were bnded t the facings as shwn in figure 1. sketch f test panel 2 is shwn in figure 2. Facings f this panel were 0.063-inch sheets f 7075-T6 aluminum ally. The lading strips and imel, W. R. Elastic Buckling f a Simply Supprted Rectangular Sandwich Panel Subjected t Cmbined Edgewise Bending and Cmpressin. Frest Prducts Labratry Reprt N. 1857, 1956. 4 --Kimel, W. R. Supplement t Elastic Buckling f a Simply Supprted Rectangular Sandwich Panel Subjected t Cmbined Edgewise Bending and Cmpressin. Frest Prducts Labratry Reprt, N. 1857, 1956. Reprt N; 1868-2-
stiffening strips fr this panel were 1 by 4 inches in crss sectin. The pure bending sectin f this panel was 26 by 26 inches in size. The cre f the pure bending area f bth panels was aluminum hneycmb f a density f 3.05 punds per cubic ft. This cre was made f 0.002-inch perfrated fil f ally 3003-H19, frmed t 3/8-inch hexagnal cells. Cre was riented in the panel s that the cre ribbns were parallel t the length f the specimen. Because this investigatin was cncerned with the effects f pure bending, it was imprtant t prevent any failure in the specimen befre buckling ccurred in the pure bending sectin. The end sectins f the beam had t withstand shear stresses cmbined with bending stresses, and in rder t prevent failure in these ends, plywd was used as a cre fr the end sectins instead f aluminum hneycmb. The plywd cres were made f 5 plies f Duglas-fir veneer glued with a phenl-frmaldehyde resin film glue. Specimen Preparatin Bth sandwich test panels were fabricated at the Frest Prducts Labratry. Sandwich facings were cut t apprximate size frm sheets f clad aluminum ally with a metal-cutting bandsaw. Surfaces f each sheet were rubbed with a clth, which had been saked in acetne, t remve such freign materials as wax and dirt. Each clean sheet was inserted flatwise int a large, shallw plyethylene tray that cntained an etching slutin f sdium dichrmate, sulphuric acid, and water preheated t 170 F. fter 5 minutes f immersin and agitatin, the sheet was remved and turned ver and again immersed fr 5 minutes s the etching f bth sides wuld be alike. When the etching was cmpleted, the sheet was remved frm the tray f slutin, rinsed with a spray f tap water, and air-dried in frnt f a fan. primer f diluted FM-47 adhesive was sprayed, t a thickness f abut 0.001 inch, nt the surface areas where cres and Duglas-fir strips were t be bnded. The primer adhesive was cured fr 40 minutes at 300 F. by passing the sheets thrugh a veneer dryer. Slices f aluminum hneycmb were available nly in small pieces, sme as small as 3 by 6 inches in size. These pieces were spliced tgether with cntact cement t frm cntinuus sheets f cre large enugh fr the pure bending sectin f the panels. Surface areas f the specimen facings were much larger than the platen area f the steam-heated press that was used fr curing the resin bnd between the facings and cres; therefre, it was necessary t fabricate the panel by Reprt N. 1868-3-
bnding first the central sectin that had hneycmb cre, and then bnding each f the tw end sectins that had plywd cre. The hneycmb cre was bnded t the facings with an epxy resin that was applied t bth sides f the cre with a rller and t the crrespnding areas f the facings with a ntched spreader. The hneycmb cre was inserted between the tw facings s that it was lcated at the center f the facing length with cre ribbns parallel t that length. This assembled sectin was inserted between the platens f the press t cure the resin bnds fr 90 minutes at 200 F. under a pressure f 15 punds per square inch. fter the resin was cured, the press was allwed t cl t rm temperature. Pressure was maintained until the panel cled t rm temperature. The plywd cre was cated n bth surfaces with a phenl-resrcinl glue, and then inserted between the facings adjacent t the hneycmb cre. Each assembled sectin f plywd sandwich was inserted between the platens f the press t cure the resin fr 12 hurs at 73 F. under a pressure f 15 punds per square inch. fter the sandwich panels were cmpletely fabricated, they were trimmed t crrect dimensins using an electric handsaw. The 1-inch lading and stiffening strips f Duglas-fir were cated n ne flat surface with a phenl-resrcinl glue. The strips were then bnded t lcally primed surfaces f the aluminum facings at lcatins shwn in figures 1 and 2. Weights were used t apply 150 punds cmpressin between the strips and facings while the glue was cured fr 48 hurs at 73 F. s a precautin against any pssible peeling r lcalized tensin failure f the bnd between facings and lading strips, a pair f blts were lcated at each end f the lading strips t hld the strips and sandwich tgether. Electrical resistance-type strain gages were cemented t the pure bending sectins f the facings. Lcatin and directin f the strain measurements are shwn in figures 1 and 2 fr the panels. Test pparatus and Prcedure Edgewise flexure tests were cnducted at rm temperature. Lad was applied in a vertical mechanical testing machine and measured at ne reactin with a hydraulic lad cell (fig. 3). T prevent lateral buckling f the edges f each sectin f the test panel, wd rails were grved t a depth f abut 1/4 inch and fit snugly alng the panel edges between the lading strips, as shwn in figures 1, 2, and 3. Reprt N. 1868-4-
These rails were made slightly shrter than the panel edges between lading strips s that they wuld carry n lad during the test. Each panel was munted n edge fr test with the length hrizntal. One end rested n a hydraulic lad cell. The ther end rested n a nest f rllers that was pivted, as shwn in figure 4, t allw fr rtatin in the plane f the panel as bending ccurred. lng the upper edge f the panel, the lad was transmitted thrugh tw flat nests f rllers that rested n the ends f the strips f Duglas-fir at the tw lad pints. When the panel was munted in place, a flexure lad f 500 punds was applied. Held lightly in place by this lad, the panel was carefully alined s that all f the lading strips n each facing were lcated in ne vertical plane. Ends f the lading strips were restrained t prevent lateral buckling f the panel as a whle by steel rller bearings munted against each lading strip at the end ppsite the pint f applicatin f the lad r reactin, as shwn in figures 1, 2, and 5. The rllers, munted with axes hrizntal, prevented lateral mtin but allwed vertical mtin. Where the lads r reactins were applied t the ends f the lading strips, frictin prvided adequate lateral supprt. Facing strains were measured t determine if the lading was symmetrical and if pure bending was being applied t the central sectin f the test panel. t midspan, n the cmpressin side f the beam, the maximum lateral deflectins f the pure bending sectin f the panel were measured with a dial gage, as shwn in figure 5. Deflectins f the neutral axis f test panel 1 were measured with dial gages lcated at the midspan and lad pints, as shwn in figure 3. ls at midspan and near each f the lad pints f bth test panels, strains in the facings were measured with electrical resistance-type strain gages lcated and riented as shwn in figures 1 and 2. t each lcatin, facing strains parallel t the neutral axis f the panel were measured. lng the neutral axis f the panel, strains at the lad pints were als measured at angles f 45 and 90 with the neutral axis. t midspan n the cmpressin side f the beam, strains f bth facings were measured at the pint where maximum lateral deflectin was expected. The flexure lad was applied in equal increments. Strains f the facings, vertical deflectins f the neutral axis, and lateral deflectins f the panel were determined fr each increment f lad. These data were taken thrughut the test until buckling f the panel ccurred. Reprt N. 1868-5-
Theretical Cnsideratins Buckling Lad If the cre f a sandwich cnstructin is rthtrpic, is subjected nly t antiplane stress, and has an infinite transverse mdulus f elasticity, and if the facings are hmgeneus and istrpic, then the theretical buckling lad per inch f edge at the utermst fibers f a rectangular sandwich panel subjected t pure edgewise bending is given by the frmula:± N = ( 1 2 D k (1) where b is depth f beam and k is critical lad factr fr the given panel and lading. D - E f (c + f) 2 1 - v 2 2 ( 2 ) where E is 'effective mdulus f elasticity f facings, v is Pissn' s rati f facings, f is thickness f facing, and c is thickness f cre. The facing stress at the edge f the panel is S- 2f and the ttal flexure lad t prduce this facing stress is P = 2Sfb 2 3a where a is the mment arm between the reactin and nearest lad. Fr a given sandwich cnstructin, the critical lad factr (k) may be determined frm theretical curves that shw the factr as a functin f the panel aspect rati and the parameter:± w cf Tr)2 2-1; E 1 1 - v 2 G (5) where G is the shear mdulus f the cre assciated with relative displacement f the facings in the directin parallel t the neutral axis. Families f these curves are pltted fr cre materials that have shear mdulus values in the directin parallel t the neutral axis, which are either 40 Reprt N. 1868-6-
percent, 100 percent, r 250 percent f the shear mdulus values in the directin perpendicular t the neutral axis. Theretical Deflectin f Neutral xis t midspan, the theretical deflectin f the neutral axis f the sandwich beam laded symmetrically at tw pints under ttal lad P is: - Pa, (3L 2-4a2 ) (6) m 8Efla where L is the span. t the lad pints the theretical deflectin f the beam is: Pa DL = (3L-4a) 2Efb' The tw test panels were designed fr as widely different values f parameter, W, as pssible with the materials usually used fr sandwich. The facings f bth panels were aluminum, which has a mdulus f elasticity f 10 millin punds per square inch and a Pissn' s rati f 1/3. The cres f bth panels were f aluminum hneycmb, frmed int 3/8-inch hexagn cells frm 0.002-inch fil; this hneycmb has a shear mdulus f 29,100 punds per square inch parallel t the ribbns and 12,800 punds per square inch perpendicular t the ribbns.5 Fr cnstructin 1, the fllwing values were determined: W = 0.0056 frm equatin (5), D = 8,950 frm equatin (2), k = 23.1 frm the theretical curves 4, and N = 975 punds per inch f edge frm equatin (1). t this lad the facing stress at the panel edge is 15,200 punds per square inch frm equatin (3), and the flexure lad t prduce this stress is 15,200 punds frm equatin (4). Fr this panel the theretical deflectin at midspan is 0.0091 inch per 1,000 punds f ttal lad and at the lad pints is 0.0078 inch per 1,000 punds f ttal lad. Fr cnstructin 2, the fllwing values were determined: W = 0.037 frm equatin (5), D = 26,000 frm equatin (2), k = 17.8 frm the theretical curves±, and N = 6,760 punds per inch f edge frm equatin (1). t this lad the facing stress at the panel edge is 53,600 punds per square inch frm equatin (3), and the flexure lad t prduce this stress is 38,000 punds frm equatin (4). 5 --Kuenzi, E. W. Mechanical Prperties f luminum Hneycmb Cres. Frest Prducts Labratry Reprt N. 1849, 1955. (7) Reprt N. 1868-7-
Test Results and Discussin Cnstructin 1 Relatinships between flexure lads and deflectins f the lad pints and midspan f cnstructin 1 were determined. t midspan, the deflectin increased at the rate f 0.0097 inch per 1,000 punds. This was abut 7 percent greater than the theretical deflectin cmputed frm equatin (6). t the lad pints the deflectin increased at the rate f 0.0079 inch per 1,000 punds, which was abut 1 percent greater than the theretical deflectin cmputed frm equatin (7). Facing strains measured at the neutral axis f the panel are shwn at varius lads in figure 6. Strains measured in the directin f the neutral axis were apprximately zer. This wuld be expected nly fr measurements f strain alng the neutral axis. t angles f 45 and 90 with the neutral axis, the measured facing strains als were apprximately zer, thus indicating that very little shear ccurred in the central sectin f the panel. Facing strains measured near the edges f the facings are shwn in figure 7. During the linear prtin f these curves, all f the strains measured n bth tensin and cmpressin sides f the beam at a distance 15-3/4 inches frm the neutral axis increased at a rate f abut 75 micrinches per inch per 1,000 punds f lad. This was abut 109 percent f the theretical rate f strain f the facings. Because strains at the neutral axis were nearly zer and als tensin and cmpressin strain rates near edges were nearly alike, the test area was subjected t pure bending. Increasing the lad beynd 13,000 punds caused the rates f strain n the cmpressin side f the beam t change but had n effect n the strain rates fr the tensin side f the beam. The buckling lad ccurred at 15,500 punds when the cmpressin strain measured at midspan in ne f the facings reached a maximum value. This bserved buckling lad was abut 102 percent f the cmputed theretical buckling lad. fter reaching the maximum value f strain in ne f the facings, further increases in lad caused the strain t decrease. The lateral deflectin f the panel is shwn in figure 8. The discntinuity in the lad-deflectin curve at abut 7,000 punds was prbably caused by a. slight shift f the panel because f play in the testing machine lading screws as the 7,000-pund mvable head was lwered. In figure 8, the lateral deflectin f the panel was much greater fr lad increments beynd a ttal lad f 15,000 punds, than belw that lad. Increasing the lad t 18,000 punds caused the buckle t increase, but did nt cause nticeable failure f the panel. fter reaching this lad, the test was discntinued. Reprt N. 1868-8-
Cnstructin 2 Figure 9 shws facing strains measured at the neutral axis f the panel. In the directin f the axis, these strains were very small. t the neutral axis f a beam, these strains wuld be expected t be zer. t angles f 90 with the majr axis, the values f strain als were nearly zer, thus indicating that little shear ccurred within the central hneycmb sectin f the panel. Strains measured near the edges f the facings (10 inches frm the neutral axis) are shwn in figure 10. During the linear prtins f these curves, the strains n the tensin and cmpressin sides f the panel increased at an average rate f abut 97.5 micrinches per 1,000 punds f lad, which is abut 90 percent f the theretical rate f strain fr the facings. In figure 11, facing strains measured 5 inches frm the neutral axis are shwn. During the linear prtin f these curves, the strains increased at a rate f abut 48 micrinches per 1,000 punds. This was abut 49 percent f the strain bserved at 10 inches frm the neutral axis, thus indicating that the strains were directly prprtinal t the distance frm the neutral axis. Therefre, the central sectin f the panel was subjected nly t pure bending stresses. Increasing the lad beynd abut 28,000 punds caused the rates f strain n the cmpressin side f beam t change but had n nticeable effect n the strain rates fr the tensin side f the beam. The buckling lad ccurred at 33,000 punds when the cmpressin strain, measured in ne f the facings at midspan 5 inches frm the neutral axis, reached a maximum value (fig. 11). This bserved buckling lad was apprximately 87 percent f the cmputed theretical buckling lad fr this panel. fter reaching a maximum value f strain in ne f the facings, further increases in lad caused the strain t decrease. Effects f edgewise flexure lad n the lateral deflectin f the panel are shwn in figure 12. Increasing the flexure lad beynd 33,000 punds caused the buckle t increase until sudden failure ccurred at a lad f 36,500 punds. The failure that ccurred in ne f the plywd end sectins is shwn in figure 13. Cnclusin Fr the tw tests cnducted, the buckling f sandwich panels in edgewise bending was fairly well predictable by thery. Reprt N. 1868-9-
Figure 3. --Simply supprted edgewise bending specimen shwing lad cell at ne reactin. Dial gages are lcated at the midspan and lad pints t measure deflectin f the neutral axis f the test panel. Z M 110 173
Figure 4. --Simply supprted edgewise bending specimen befre test, shwing pivted nest f rllers at reactin (lwer right). Z M 110 172
Figure 5. --Lateral twisting f edgewise bending specimen was prevented by rller bearings at lading strips. Dial gage measured lateral deflectin. Z M 110 175
40 36 32 28 Cr; 24 O O 20 O O -4 /6 /2 8 n. n 0 0 n THEORETICL BUCKLING 1 OBSERVED BUCKLING n -0-0...-FCING...- FCING NO / LOD POINT / LEGEND: 0 0 90 c NO. / MIDSPN NGLE OF FCING STRINS FROM NEUTRL XIS C n p -0 0 0...- FCING NO 2 - LOD 0, POINT 2. 6,,-, 4 n 0 n n. -.400 X/0"6 STR/N (INCHES PER INCH ) LO LID 0 Figure 9. --Facing strains measured at the neutral axis f cnstructin 2. Reprt N. 1868
Figure 13. --Cnstructin 2 after failure f a plywd end sectin. Z M 111 197