1、TECHEJI CAL NOTES BATIONAL ADVISORY COMMITTEE FOB AERONAUTICS - No, 752 - AN 53 1965 AN INVESTIGATION OF SHEET-STIFFENEB PABELS SUBJECTED TO COMPIIESSION LOADS VITH PART1 GULAR REFERENCE TO TORSIONALLY VEAK STIFFENERS By Louis (3. Dunn C8 1 if o rni a Ins t i t ?It e of Technology PROPERTY OF LTV VO
2、UGHT AERONAUTICS DIN LIBRARY - _- $1 I Vashing Fe bruaqi :ton 1940 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COhlMITTEE FOii AERONAUTICS -_- TECENICAL NOTE NO. 752 AH I ITYES T IGAT I ON OF SHEET-STIFFEMER PAT? EL S SSJBJECTEO
3、 TO COYPRESSION LOADS VITH PASTI CULAR REFEXEKCE TO TORSIONALLY VXAK STIFFENERS By Louis G. Dum / S U M MA BY A total of 153 panel specimens of 24ST zluminum alloy with nominal thicknesses of 0.920, 9.025, and 0.040 inch mith extruded bulb-anqle sections of 12 sbapes sgaced 4 and 5 inches as stiffen
4、ers mere tested to ojtain the Suck- ling stress ar,d the r,mplitv.de of the maximum nave when buckled. Bulb angles from .? to 274 inches long were test- ed as llin-end columns. The exoerimental data are presented as stress-strain and column curves and in tabular form. Some comparisons nith theoretic
5、al results are presented. Analytical methods are developed thzt make it possible for the desiqner to predict with reasonable accuracy the bucklin? stress and the maximum-mave anplituCe of the sheet in stiffened-panel combinations. The scope of the tests was insufficient to formulate general design c
6、riteria but the results are presented as a guid.e for desisn and an in- dication of the type of theoretical and experimental mork neched. INTRODUCTION This report ?resents t3e results of an investigation on the behavior of sheet-stiffener Fanels subjected to end c omp r e s si on . In ?art I nethods
7、 are developed for calculating: (1) The bucklinerioentnl results obtained by testing a 1zrge number of nanals in which the stifrc1-i- ers were bulb angles of the type commonly used in aircrzft constr.dction. The effective midth as a f-anction of t2e sti:.feil?r stress m2s determined for panels with
8、stiffen- ers of various cross sections and torsional ri:;iditics, I:?henonenon in stiffened panels indicates that a gradual twisting of the stiffener occurs rrith increasing load until near the failing load, mhen the buckling rapidly increases and causes failure of the Fanel. The degree of twisting
9、of tbe stiffener during loadins of the panel de- pends on the torsional riqidity of the stiffener and on the thickness of the sheet to which the stiffener is at- tached. The effect of the sheet on the stiffener nay be sum- marized as follows: . (1) When the sheet ouckles, the stiffener exerts a rest
10、raining moment on the sheet or, conversely, tho sheet imparts to the stiffener a twisting moment that. is proFor- tional to the cur.rature of the sheet. In the analysis of isolated columns, this interaction of stiffener and sheet changes the homogeneous yroblem of torsional stability to a nonhomogen
11、eous sroblem of gradual twisting for the case of open-section stiffeners attached to sheet. For torsion- ally weak stiffeners, it is important that the interaction of sheet and stiffener be taken into consideration. (2) A column that fails by twistins mill generally twist ajout an axis through its s
12、hear center. Owing to Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-the rilace. Thiz assumption is reasonable for the type of stiffened panels used in aircraft construction. (2) In order to eliminate secondary phenomena of in- stability in the stif
13、fener region, it will be assumed that the center of twist of the stiffener is at the edge of the sheet and., furthermore, that the stiffener is cor-nnntrated at the edge of the sheet (3) The material is 3omogeneous, isotropic, and obeys Eookes law of deformation. The qcneral case, in which bending o
14、f the stiffener is considered, has been investigated by E. Chwalla (refer- ence 6). The boundary conditions are, of necessity, rather complicated and the final solution is consequently too in- volved for general practical apFlication. The boundary conditions for t3e simplified case under considerati
15、on, with dimensions and loadint: as indicated in figure 2, are as follows: At x=O,x=a The boundary conditions are satisfied if the deflection Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 U.A.C.A. Technical Note No, 752 ., where f(y) is a functio
16、n of y only, ar?d A corresponds to a half-nave length, i.e., a/m, At y = b/2 w=o (4) A second boundary conditlon at the stiffener can be ob- tained RS follows (reference 7, p. 303): The bending mo- ments that appear nlonq the stiffener 6urin;i; buckling are proportional at each oint to the znglc of
17、rotation of the edye. The angle of rotation of the stiffener durinq buck- 1in /awl 0 -IT2 in nx an 2 2 - (-) dx = fo“ - 2 1 ax / ax = - cosa - 4h“ fo 2h2 / h , 0 0 Substitutin? in equation (16) 2nd. solving for fo/X gives: The preceding equation may be mritten in the form: vhpre cSt is the unit defo
18、rmadtion of the sti-fener (CTst/Est) and cC is the Tiiiit deformation of t5e sheet at bucklinq ( O?/E, j. 3cyond the prcL3ortion:il limit, the valuc of cst should be dctcrnined from the stress-strzia curve of tTe StifTPner. The wlue of J, is obtained from t:ie curves 01“ figurc 3. allles of fo/h for
19、 stifen- cr strerses up to 27,090 ?sounds yer square inch 1?;Lvc 5qen o-stained brr cxperincntal methocis. m Frocedure, Consequently, in addition to determin- ing the ultimate load of the panel, stiffener deformations were measured at internediate loads and records were made of the mave pattern of t
20、he buckled sheet. Knowing the stiffener deformation for a given load, a curve of average stress as a function of stiffener strain could be plotted. 1% was then possible, with the aid of the stress-strain dia”;am of the stiffener alone, to determine that portion Of the total load carried by either th
21、e stiffeners or the sheet throughout the entire range of load. From these data, the effective width of the sheet acting with the stiffeners at any stiffener stress could be calculated and plotted. Column curves of the average stress at failure were plotted as a function of the effective slenderness
22、ratio of the 3anels. These curves indiczteci tile effect of the column length on the ultimate stresses. The anve-gattern records were used to check the theo- retically calculated. values of the buclrlfnc: stress and the maximum-nFve am-olitude of the sheet. Provided by IHSNot for ResaleNo reproducti
23、on or networking permitted without license from IHS-,-,-16 N.A.C.A. Technical Note Bo. 752 The theoretical analypis also inc?icated that a knowl- edge of the torsj.onal rigidity of the stiffeners WV:IS re- quired. The torsional riridity of bulb-antgle sections being rather difficult to calculate, th
24、is property was ex- perimentally determined. Mat e r i a1 s The extruded SulS-angle sections used in the tests v:ere fabricated from 24ST aluminum alloy. (See fi2. 6.) The shTet 1va.s also of 24ST alloy with a norriinal thickness of 0.020, 0.025, and 0.340 inch. The strensth properties of five of th
25、e bulb-angle sections are given in figure 7 and table I . Test Specimens The panel lengths “ere so cbosen ES to cover the com- plete range of bulkhead spacings that might %a encountered in current aircraft design practice arid were such as to cover tile norrial short-column range and, in certain in-
26、 stances, depending on the dimensions of the bulb ancrle, were uch as to reach the long-column rance. The number of stiffeners was varied in order to in- vesti2;atc the effect, if any, of tSP number of stiflen- ers on the ultimate stiffener stresses. A typical examgle of on* of the 183 :a.i:el speci
27、mens is shown in fiyures 8 and 9. The riir.!ensions of the spec- imens and the test data are 4iven in tables I1 to VII. For :ia:iels 148 to 183, the stiffener s2acing mas 4 inches. On all other panels, the spacing was 5 inches. The rivet seciner of stiffeners. t, sheet thickness. k, ratio between lo
28、ad carried by each effective width of sheet and aciditional load carried by outside sheet panels due to edge suports. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-20 N.A.C.A. Technical Note No. 752 Evzluation of .- The effect of the tube over the
29、- - kL rep edqe of the panel is to stiffen thc sheet between the sti+fener and the tu3e; and, in effect, the panel width is 2.5 inches rather than 5 inches. Secause the panel width is decreased, the critical buckling stress of the -beet is increased znd the sheet bettvecn the tube and the sti-fener
30、will be acting at a hicher average stress than the sLFet betrrecn the two julb engles. The effective wiuerre su Calculate the bucklincl; stress of the sheet, be- tween the stiffener and the tube, assumins the conditions of support at the tube to 5e the same as those at the stif- fener. (1) Calculate
31、 the buckling stress assumins simFle suPport at both stiffener and tube. The value of ocl was then assumed to be the averase of the two calculated Suckling stresses. A plot of k, as a function of stiffener stress, for the various sheet and stiffener combinations, is shown in fi;-ure 14. Knowing the
32、value of k, as a function of the stiffener stress, the average effective width was calcu- lated by means of equation (3). The stiffener area and the skin thickness used in these calculations were comput- ed from the neasured dimensions of each stiffener. The stiffener stress ost and the total load P
33、 can be ob- tained from the curves (fi,as. 15 to 25) of average stress plotted against stiffener strain. By average stress is meant the applied load divided by the total cross-sectional area of the test panel. The strain against which the av- erase stiffener stress is plotted is an averaanels at fai
34、l- ure, even though the corrcs:ondin value of stiffener stress was quite uncertain. Column curves shoxinc”; the av- era$;c stress at failure as a function of L/p could thea be plotted for the various panels. The results are shown in fiCL as stiffeners. In order to obtain a proer roper alinement the
35、shear center of the Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.AC.A. Technicnl Note Xo 752 23 bulb anSle and the axis of rotation of the test xachine. The ends were cast in Woods metal and the tests therefore corresgonded to torsion with end r
36、estraint. The ayplied torsional mornent of five stiffeners is plotted aqainst the corresponding torsional deflection in figure 38. The torsional riqidity of the stiffener mas calculated from the equation where MT is the torsional moment, inch-o?ind.s Cp , torsional deflection, radians er inch. Colun
37、n curve of stifTeners alone.- - The experimental data of the stiffener tested as pin-end columns arc qiven in table VIII; the results are lotted in figure 39. Soagarisons of the results iTith the “straight-line formula“ and with the Johnson p,zrabolic forrriula are indi- cated in fiqure 39. For valu
38、es 01“ 80 ressive stress in stiffener. 0 - polar moment of inertia about axis of ttvist. torsional rigidity of stiffener. monent transferi-ed by buckled sheet to stif- f cner. torsional deflection cf stiffener. of m, is known and the end effects are neg- lected, the inclination p can be calculated b
39、y means of equation (25). This value of cp can be compared with a value of cp calculated from the assumptions that: (1) After buckling, D = D = constant at y = 0. (2) The wave form does not chanse. In order to sim-nlify the calculations. it was assumed that a stiffener as shown in fiqure 40 is attac
40、hed to a sheet having :?. thickness of Q.340 inch. The stiffener spacing mr,s assumed to be 5 inches and the axis of twist to be at the nosition indicated. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technical Note No. 752 27 If the assu
41、mptions (I) and (2) are compatible with the stiffener properties, the tmo calculated slopes should co- incide. From an examination of fiure 40, it can be seen that a fairly good agreement is obtained for stiffener stresses up to 20,000 pounds per square inch. Beyond this value of ox, the deviation i
42、ncreases rapidly with an in- crease in a,. It nay therefore be concluded that either assumption (1) or (2) or both are invalid, especially for high stiffener stresses. In view of the 5ood asreement obtained for the theoretically calculated maximum ampli- tude and the experimental values, it is felt
43、that assump- tion (2) is chiefly responsible for the discrepancy. A further refinement in the analysis is thus necessary and should be carried out. $ it should be noted that equation (25) describes only the case in which failure takes place by twisting of the column. The experimental observations ha
44、ve indicated that, for panel lengths near or in the Euler range, the stiffen- er may fail by combined trvisting and bending. This case is an important one because the critical stress will, in general, be lower than that given by either the Euler for- mula or by a formula derived for a pure twistins
45、failure. A theory that describes this type of failure as well as that for pure twisting should be of considerable impor- tance in airplane design and therefore deserves an exten- sive investigation. APPENDIX B Experimental Check of the Theoretical Buckline; Stress of the Sheet It mas desired to obta
46、in an experiment.al verification of the theoretical calculations of the buckling stress of the sheet for different values of v. Since p was rela- tively small for all the bulb angles tested, it mas nec- essary to design a panel having a larser value of p; that is, a value that more closely apyroache
47、d a simply support- ed edge condition. A stiffened panel was desisned in which the stiffeners consisted of bent-up angle sections, 0.051 by 3/4 by 3/4 inch, riveted to an 0.064-inch sheet. The panel was essentially of the same type as the bulb- anqle panels with the exception that the angles were ri
48、v- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-28 N.A.C.A. Technical Note No. 752 eted on each side of the panel, i.e., back to back. Three check panels designated panels A, B, and C of this design were tested and their dimensions and proncrties are ,.and C is, fron figure 38, 2 = ?dT/Ct3 = 250 Dound-inches“ c c Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technical Note No. 752 29 Since the sheet was stiffened by two angles, thg torsional riJ
