1、f I. .i 7 TECZNICAL NOTES _.-. NBBI-ONAL-AD-VISORY- COKMITTEE FOR AERONAUTICS No . 684 . EXPEBI14ENTAL STUDY OF DFiFORtiTION IND.OF EFFECTIVE VIDTS IN AXI-LLLi LOADED SHEET-STZINGER PANELS By I?rAlter Ramberg, Albert E. XcPhersor, and Sam Levy National Bureau of Standards . . Fashfngton .February 19
2、39 I _ Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-., 7% I ,C NATIONAL ADVISORY COMITTEE FOR AERONAUTICS TECHNICAL NOTE NO. 684 EXPERIi03:TAL STUDY OF DEFORMATION AND OF EFFECTIVE TIDTH IN AXIALLY LOADED SHEET-STRINGER PANELS By Walter Ramberg, A
3、lbert E. McPherson, and Sam Levy SUMMARY The deformation of two sheet-stringer panels subject- ed to end compression under carefully controlled end con- ditions was measured at a number of points and at a number of loads, most of which were above the load at which the sheet 3ad begun to buckle. The
4、two panels were identical except for the sheet, which was 0.070-inch 24ST Alclad for specimenland 0.025-inch 24ST aluminum alloy for specimen 6. A technique was developed for attaching Tuckerman op- tical strain gages to the sheet without disturbing the strain distrihution in the sheet by the method
5、 of attach- ment. This technique was used to explore the strain dis- tribution in the sheet at various loads. The twisting and the bending of the stringers were measured by means of pointers attached to the stringers. The shape of the buckles in the sheet of specimen 6 was recorded at two loads by m
6、eans of plaster casts. The sheet and the stringer loads at failure are com- pared with thecorresponding loads for five similar panels tested at the Navy 3odel Basin. A detailed comparison is made between the measured deformation of the buckled sheet and the deformation calculated from approximate th
7、eories for the deformation in a rectangular sheet with freely sup- ported edges buckling under end compression advanced by Timoshenko, Frankland, and Harguerre. The measured effec- tive width for the specimens is compared with the effectfve width n;ivcn by nine different relations for effective widt
8、h as a function of the edge stress cr divided by the buck- ling stress ccr of the sheet. The analysis of the measure1 stringer deformation is confined to an application of Southwellts method of plot- ting deformation against deformation over load, If the stringer approaches instability in accordance
9、 with South- wells relation, the deformation will be a linear function Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 . . N.A; C.A. Technical Note No; 6.84. . _.-. . . . . . of the deformation divided by the load and the slope of the straight line
10、 obtained wil.1 be equal to the elastic ,. . . . buckling load. A good check with the observed ultimate load wag .obCained from.a plot of the twisting deforma- tion and of bending deformation as indicated by the pointer readings and of bending deformation as measured by differences in extreme fiber
11、strains in those cases in which all observed pointscould be brought to scatter about a common straight line. It was concluded that the stringer failure in both specimens was due to an insta- bility in which the stringer was simultaneously twisted and bent as a column. INTRODUCTION The strength of sh
12、eet-stringer panels in e,nd compres- sion has become a problem of importance with the increas- ing use of stiffened sheet to carry compres.siveloads in box beams for airplane wings and in other types of mono-. coque contruction. The buckling of the sheet,bstween stringers .in a. panel under end comp
13、ression;the strain distribution in the sheet, and the effective width of the sheet as a func- tion of the stringer stress, have been considered from a theoretical po,int (6) , ! . . . ,The corresponding, straight lines are shown dotted in fig- ure 11 for loads of5,000, 9,000,. and 13,000 pounds. The
14、 agresrhent between observedand calcu.lated strains be- low the load prddticfng,budkle.s in the, sheet iS seen to be satisfactory. Thesimple beam.foraula (equation (6) ceases to adscriBe the strain.distribution for loadsequal to or greater than 1,7;000 pounds. Beginning mith this load, the axial str
15、ain changes relatively slightly at a point midwaybetween stringerti,:while it, i,ncreases rapidly near the stringers. I. Theload carried by the sheet becomes L Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.L.A. Technical Note Xo.: 684 9 .a decr
16、eas,ing proportion“.ofVthe total load and the strain distribution takes onXa characteristbc wave pattern. ., : . . . . . . . I ;*. :It would not be correct to conclude from the. fairly regular wave patter,n of the axial median fiber strains that %he extreme fiber strainswould be e-qually symmetri- c
17、al. Figure.12, which show-sboth the axial extreme fiber stratns. and the medfan fiber strains .along the transverse center line of specimen 1 fox the 25,;000-pound load, fn- dica,tes almost no bendin the buckle pattern in a givenbay between two string- ers seemed to be independent oftho buckle patte
18、rn in ad- jac.ent bays up to a load of 25,000 pounds. . The beginning of buckling in the shect.was indicated by a sudden increase in the bending strain as measured by the diffekence in reading on .str.ain gages on opposite sides of the sheet.Thi% in clearly shown in figure 13 for the readings of the
19、 trarisver.se. strain gages. The bending strain increased ten times a.s-the stringer stress increased 17 percent from 12,000 to 14,000 pounds por square inch. ,. All the strain gag.es were removed from the sheet at a load of 26,000 pounds. and only the three pairs of gagee shown in figure.14.aere ke
20、pt on to indicate stringer strains for loads above 26,000 pounds. The strain readings on the stringer gages are plotted against .load in figure 15. . Figure 16 shows the axial strain distribution for .specfmen 6. Buckling of the sheet in the case of th-is specimen was observed at a load betweenl,OOO
21、 and 2,600 pounds corresponding to an average stree the buckle pattern in aglven bay between two s-tringers seems to be unaffected by the buckle pattern of adjacent bays up to hload of 10,900 pounds. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10
22、 N.A.CA.; Technical Not.e Xo. .684 Th,e measurements af axial strain .along the transverse center line. of specimen 6 were followed by measurements of transverse and of axial strafn in other portions of the specimen. In the course, of. these measurements, it appeared that the stratn readings ,at .a
23、given load and a given loca- tion could be repeated ,within the observational error in successive tests It was concluded that the measured strain distributions could be superposed on each other just as if they had all .been det,ermined simultaneously and that t?tey could be applied in ca,lculating s
24、tresses from strains, 4 . The, distribution of axi.al, median fiber strains .a.long the transverse center, line. was obtain,ed from strain gages mounted on the .spectmen in: the ,same.loca.tions as shown in figure 9 for,specimen* l.:,. Transverse strains were measured along three l-inch ga,gs lines
25、onthe transverse center line as shown in, figures .18 and, .19. :The ,results of these, measurements for bay 3 (between stringers S and R) are shown graphically .in .fP,gur.e 20. . : Figure.21. shows the .di stributi.on. of both axial and transverse ,me:dian. f,iber. strain ,al,ong, an .axial line m
26、idway be- tvoen. two stringers, as: obtained . . .The twist 6, about the axis of the stringer is seen . . from ffgure 31 to alternate at low loads from posttive to negative values corresponding roughly to the buckles, which are shown di.agr,ammatically,beJ.o the.curves;, As the load increases, a twi
27、st of the stringer as a whole is superposed on the alternating twist. . rhe twist -6y about the axis normal to the stringer in plane.of the sheet; which.is shown in figure 32, aitshows dscil- , lations that are probably,due to the buckles in theadja- cent sheet. I ,. , : . . . . . . . 1. J The curve
28、s Ey(x) and 8,(x), must have in average . : . . # :. * : . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 N,A.C.A. Technical ,vote.No. 684 .I . , value of zero to satisfy the condi,tion of zer.0 displace- sent v, w at the ends of; the stringer; t
29、his requirement follows directly from the relations Cy = dw/dx and e = z dv ,/dx connecting w and v with 6 Y and es, re- spectively. Actually, 6y and 6, were found to have average values definitely higher than zero. An examina- tion of the data showed that this discrepancy could be as- cribed to a s
30、mall displacement to one side of the equidis- tant vertical wires B-B (fig. 30), the displacement in- creasing with the Load. No attempt was made to correct the curves in figures.32 and 33 for this displacement, since the correction would only,involve downward displace- ment of each curve as a whole
31、, The deformation of the stringers of specimen 6 was also measured with pointers. *A different method was used which gave greater accuracy and was more conv,enient than the method applied to specimen 1. The twists Gx, E , Y and 6, were measured by the relative displacements Vl -v3, u1 - u3, and ua -
32、 us, of three black crosses that were marked on cardboard glued to sheet aluminum pointers attached to the web of the Z-section at the cen- troid as indicated in figures 34 and 35. The twists of the section about axes through the centroid are given by (see fig. 35): Vl 7 v3 8, = - % - u3. U2 - U3 I
33、cy = 9 c13 c13 ez = - b23 (8) where cl3 and b, are the distances between the crosses indicated in figure 35 and where ul U2 and u3 denote displacements of the crosses 1, 2, and 3, parallel to the stringer, and v1 and v3 denote displacements of the crosses 1 and 3 normal to the stringer and parallel
34、to the plane of the sheet. Attachment of the pointers to the web of the Z section rather than to the outstanding flanges prevented errors from local buckling of the flanges of the stringer. The use of the third cross 3 permitted the meas- urement of twists without having to measure displacements rel
35、ative to a distant reference wire as in specimen 1 (fig. 30) and eliminated the errors from a displacement of the reference wires. The use of black crosses provided more accurate reference marks than the high lights on the rifle shot and permitted the measurement of twists E, and cY with a sensitivi
36、ty of about a0.0002rEdian. c Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C,A Technical Note No. 684 15 Figures 36 to.38:.show.the rotations ex, cy, and , * 8, for the central stringer R of specimen 6 forloads. ranging from 1,400 to 18,0OOpoun
37、ds. . . .:. Figure 36shows the.twLst . 6x about the axis of the stringer, Comparison with ffgure 31 shows a relative pre- dominance of the,over-all twF$t of the stringer as a rod twisted from,the,+nds onahich are super$osed the alter- nating twists due probablyto. the buckles-in the sheet. ., 2 Figu
38、re 37.sho?s the rotation Ey of stringer R due to bending-about an axis parallel to the plane of the sheet at right angles .to,the stringer. Comparison with figure 32 shows that,this bendingsis different in distribution and is of much lowsr,magnLtude, The experimental error in reading Ey,is,too large
39、 f establish the nature of the bending definitely; ffis.probably due in part to the ac- tion of the.buckles in the sheet while, for specimen 1, the bendj.n Comparison with figure.14 sho%s“that the 0.025-inch .sheet of specimen.6 ,buckled betweenrivets in anumber of places but,that there,was.no buckl
40、ingbetween rivets for the O.C7-inch sheet of specimen 1. “ . . . . . . ,CCMi?ARISON.IhE MODEL BASIN RESULTS : . I “Acomparison of“the test results from the two shoet- stringer $pocimens given horefn with five specimens of the Provided by IHSNot for ResaleNo reproduction or networking permitted witho
41、ut license from IHS-,-,-16 N.A.C.A. Technfcsl Note bTo. 684 same design and of various lengths. tested at the Navy model basin are shown in figures 40 and 41 and In table III. Eigure 40 shows the average load per stringer element and per sheet element plotted as a function of the external load on th
42、e specimen for the three 0.07Linch Alclad panels tested at the model basin and for specimen 1 tested at the National Bureau of Standards, The ., stringer load for speci- men 1 was calculated by multiplying the .average stringer stress for the three stringers by the btringer area, the stringer stress
43、 being determined from the measured stringer strains :(fig. 15) and the stress-strain curve of the stringer as given by the short-column test (fig. 4). The average plate load was then taken as one-!fourth the differ- ence between the total external load and the load on the three stringers. The point
44、s for the specimens tested at the model basin were taken from.curves giving stringer loads and plate loads, which were obtained from the Bureau of Aeronautics of the .Navy Dqartment. The stringer loads for these curves were calculated by multiplyfng the meas- ured average.stringer strain at the cent
45、er section by a Youngs modulus of 10.5 X 106 pounds per square inch and by the stringer area of 0.13 square inch. The points in figure 40.wsre copied from these curves, except for a small correction for yielding made with the help of figure 4. The Boints for the four specimens scatterabout a common
46、curve beginning with a straight-line portion, in which the ratio of stringer load to plate load remains constant up to an external. load of .about 20,000 pounds. Beyond this load, the sheet ceased to carry its full share of the,!oad because of buckling and the slope of thetwo curves changes to an- o
47、ther pair of stratght lines. The load at. failure varied through a small range frqm 36,OOOpounds to 37,000 pounds. Figure 41 shows the corresponding set ofcurves for the three 0.025-inch.specimens, two tested at the model basin and the .third at the National Bureau of Standards (specimen 6). In this
48、 case, .buckling of. the sheet occurred at a much lower load and the two curves cease, to be straight lines.through the origin beginning at a load of about 2,000 pounds., The stringer loads for the specimens tested.at the model basin were consistently lower than for specimen 6, the difference being as much as 8 percent for some of the points, There was also a considerable difference in the load at failure, which w W = Pst/Ast wo where P, and P,t are the measured sheet loads and stringer loads, w. = 4 inches is,the initial sheetwidth, and A, and Ast are t
