1、NATIONAL ADVISORY COMMIITEE FOR AERONAUTICS TECHNICAL NOTE 3431 AN ANALYSIS OF THE STABILITY AND ULTIMATE COMPRESSNE STRENGTH OF SHORT SHEET-STRINGER PANELS WITH SPECIAL REFERENCE TO THE INFLUENCE OF RNETED CONNECTION BETWEEN SHEE T AND STRINGER By Joseph W. Semonian and James P. Peterson Langley Ae
2、ronautical Laboratory Langley Field, Va. Washington March 1955 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 3431 AN ANALYSIS OF THE STABILITY AND ULTlMATE COMPRESSIVE STRENGTH OF SHORT SHE
3、ET-STRINGER PANELS WITH SPECIAL REFERENCE TO THE INFLUENCE OF RIVETED CONNECTION BETWEEN SHEET AND STRINGER By Joseph W. Semonian and James P. Peterson SUMMARY A method of strength analysis of short sheet-stringer panels sub jected to compression is presented which takes into account the effect that
4、 the riveted attachments between the plate and the stiffeners have on the strength of panels. An analysis of experimental data shows that panel strength is highly influenced by rivet pitch, diameter, and loca tion and that the degree of influence for a given riveting depends on the panel configurati
5、on and panel material. INTRODUCTION Rivets have been used extensively for attaching the cover skin to the stringers and webs of aircraft wings. These rivets have been designed, to a large extent, by rule-of-thumb methods; yet, extensive experimental work of which reference 1 is representative has sh
6、own that the compres sive strength of stiffened panels is greatly influenced by variations in diameter and pitch of the rivets. References 2 to 4, in which the mode of instability of plates in compression known as wrinkling or forced crippling has been analyzed, show that the panel strength is influ
7、enced also by the location (rivet offset) as well as the pitch and diameter of the rivets. This mode of instability results from the existence of a flexible attachment between the plate and its supporting members and has occurred more frequently as the compression skins have become heavier and the s
8、upporting members lighter. The purpose of the present paper is to evaluate the strength of short compression panels and in particular to determine the influence of the riveting used to fasten the stringers to the plate on the strength of the Provided by IHSNot for ResaleNo reproduction or networking
9、 permitted without license from IHS-,-,-2 NACA TN 3431 panel. Figure 1 shows the variation in strength with rivet pitch and names the various modes of failure involved. Only rivet pitch is con sidered to be varied in figure 1 but variations in strength could be obtained also by varying the rivet dia
10、meter or the rivet offset. When the rivet pitch is small, the panel of figure 1 fails in the local mode; for larger pitches, it may fail in either the wrinkling or the inter rivet mode. Failures in the interrivet mode are not usually permitted in contemporary design; whereas, failures in the wrinkli
11、ng mode are common. The problem of evaluating the effect of riveting on the strength of panels becomes, therefore, primarily a study of the wrinkling mode of failure. The local-mode section of the curve of figure 1 is shown as a horizontal line. It is recognized that there may be some gain in streng
12、th with a favorable change in riveting after the riveting (pitch in fig. 1) is such that the local mode is obtained. The available test data indi cate that the gain in strength is small and it is neglected in the analy sis presented herein. A study of the wrinkling mode is made with the use of the p
13、rocedures established in references 3 and 4 in connection with the calculation of the strength of multiweb beams in bending. These procedures make use of a new structural parameter termed the “effective rivet offset“ which plays an important role in determining the strength of riveted structures suc
14、h as compression panels and multiweb beams and makes possible rela tively simple structural analysis. The effective rivet offset is evalu ated by using a relatively rigorous analysis of the initial instability of compression panels supplemented by experimental data and is applicable to the nalysis o
15、f multiweb beams as well as panels. A semiempirical maximum-strength analysis of panels which utilizes the effective-rivet offset concept is made and compared with a large number of test results to show the accuracy and generality of the analysis. The analysis is exemplified in the appendix. SYMBOLS
16、 bA width of attachment flange of stiffener (see fig. 2), in. bF width of outstanding flange of stiffener (see fig. 2), in. bn width of top of hat for hat-section stiffeners, in. bO geometric rivet offset (see fig. 2), in. bS stiffener spacing (see fig. 2), in. Provided by IHSNot for ResaleNo reprod
17、uction or networking permitted without license from IHS-,-,-NACA TN 3431 / 3 bW depth of web of stiffener (see fig. 2), in d f . p AZ E Etan R rivet diameter, in. effective rivet offset (see fig. 5), in. buckling-stress coefficient failing-stress coefficient rivet pitch, in. allowable rivet pitch, i
18、n. radius of bend between attachment flange and web of stiffener (see fig. 2), in. plate thickness (see fig. 2), in. stiffener thickness (see fig. 2), in. cross-sectional area of Z-section stiffener, in.2 plate flexural stiffness per unit width, Ests;i2(1 _ 2), kips/in. flexural stiffness per unit w
19、idth of web, Ewtw2(1 _ 2), kips/in. Youngs modulus, ksi secant modulus, ksi tangent modulus, ksi Youngs modulus of plate material, ksi Youngs modulus of stiffener material, ksi rivet tensile strength, kips required rivet tensile strength, kips Provided by IHSNot for ResaleNo reproduction or networki
20、ng permitted without license from IHS-,-,-4 C1Z . crp NACA TN 343l rotational stiffness per unit length (see fig. 5), kips lateral deflection of plate, in. plasticity factor buckle length, in. Poissons ratio buckling stress, ksi average stress in panel at failure, ksi average stress in panel at fail
21、ure in local mode, ksi failing stress of plate, ksi crippling strength of Zsection stiffener, ksi deflectional stiffness per unit length, ksi The designation for the various aluminum alloys has recently been changed. The old designation and the corresponding new designation for the aluminum alloys m
22、entioned in this paper are as follows: Old designation New designation 24s-T3 2024-T3 75S-T6 7075-T6 Al7S-T3 2ll7-T3 2S-F llOO-F Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 343l 5 STRUCTURAL ANALYSIS A panel typical of those analyzed is s
23、hown in figure 2. The panel is considered to be short enough so that the column bending mode can be neglected yet long enough so that various local modes can form freely without end effects. The panelis considered to be wide with many equally spaced stringers but the results of the analysis can be a
24、pplied to panels with as few as four stringers without appreciable error. The analysis is presented in four sections. The first section develops an initial-instability analysis which together with available experimental data is used in the second section to establish the effec tive rivet offset as a
25、 function of appropriate panel parameters. The values of effective rivet offset thus established are used in the third section to formulate a semiempiricl maximum-strength analysis. Finally, the fourth section is devoted to developing criteria which limit the pitch and diameter of rivets required to
26、 achieve the predicted strength of panels. Initial Instability of Panels The panel shown in figure 2 usually will buckle into either the local mode which has been analyzed in reference 5 or the wrinkling mode which will be analyzed herein. Another mode termed the “torsional cum local“ mode was analy
27、zed in reference 6. This mode may become the pre dominant mode when the width of the outstanding flange of the stiffener becomes small (say b:F 0.90) and the chart should not be used for much smaller values of rivet diameter without confirmation. Figure 8 is applicable to multiweb beams as well as p
28、anels and can be used in the application of the formulas and design charts of refer ence 4 to the analysis of the bending strength of multiweb beams. Failure of Panels The failure of short compression panels usually, results from a growth of either local or wrinkling type of buckles. Less frequently
29、, failure Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3431 9 may result from rivet failure or growth of an interrivet type of buckle. The first two types of failures will be discussed in this section and the last two types will be conside
30、red in the next section where rivet criteria are developed that can be used to prevent such failures. Failure in the wrinkling mode. - Panels which buckle initially in the wrinkling mode usually fail in a similar mode. The plate configuration at failure, however, is simpler than the initial buckling
31、 configuration because, as the initial buckles grow with an increase in applied load, the plate buckle shape becomes more and more cylindrical until at failure it may be assumed to be cylindrical and the plate may be treated as a column on an elastic foundation. The plate in the column mode appears
32、much like the well-known interrivet mode except the length of buckle is grpater than the rivet pitch. The stringer, however, has a very differ ent configuration. In the interrivet mode the stringer cross section may remain essentially undistorted while the plate and stringer separate. In the wrinkli
33、ng mode of failure the attachment flange of the stringer follows the plate contour and causes the other plate elements of the stringer to distort also. The similarity between the appearances of the wrinkling mode and the interrivet mode has caused investigators to make strength calculations with int
34、errivet-type formulas on panels which failed in the wrinkling mode . (See, for instance, ref. 11.) The panels of this reference evidently failed in the wrinkling mode and the strength of the panels can be calculated by the methods developed herein. The stability criterion for the plate in the wrinkl
35、ing mode of fail ure is given as (see ref. 12) The support stiffness was determined by trial to give the best corre lation between panel strength and calculated strength. It was found that the support stiffness could be taken as (6) This equation is identical to equation (2) except the rotational st
36、iff b ness a-li has been replaced by a constant value of 3. In the trial Dw Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 NACA TN 3431 calculations used to determine the support stiffness, othr values bW of CL-Dw tion (2), were tried, including
37、the apparent value as given by equa bi but the value CL - =3 was considered to give the best agree-Dw ment between calculated strength and panel strength over a wide range of panel proportions. It gave particularly superior correlation compared with the apparent value when the webs of the stiffeners
38、 were relatively unstable because the apparent value (eq. (2) gave the restraint at the onset of buckling of the webs and not the restraint offered the skin at b panel failure. The value CL -li = 3 was also used in reference 4 to cal-Dw culate the strength of multiweb beams in bending. With the simp
39、lification implied by equation (6), that the support stiffness is independent of the buckle length, equation (5) can be sim plified to read kt.t = 2 _, S_ Rb3 . 1t4ns after kt.t is minimized with respect to buckle length. Equations (6) and (7) have been solved and the. results are presented in figur
40、e 9 which gives the maximum stress that the plate can carry in the wrinkling mode. At this stress, the lateral deflections of the plate, and therefore the lateral forces on the stringers, become large and destroy the capacity of the stringers to carry additional load except for unusual panel proport
41、ions. Experience in testing panels and multiweb beams indicates that a plate in the wrinkling mode suffers a relatively moderate redistribution of stress after initial buckling. The load-shortening curVe for a plate in the wrinkling mode, therefore, nearly coincides with the stress-strain curve of t
42、he plate material until just prior to plate failure. The stringer on a panel which has ,buckled in the, wrnklingmode appears very much like a stringer on a panel which has buckled“ in the local mode and evidently suffers much the same redistribution ostress and loss of axial stiffness. In order to c
43、alculate the strength of a panel, it is necessary to know the load carried by the stringers at panel failure. (The plate load is given,by fig. 9.) The load carried by the stringers depends on the proportions of the panel. If the stringers are relatively sturdy (13 1), the stringers will not be loade
44、d as heavily as the plate. An approximation which gives predictions which are slightly high when the stringers are unstable but which gives satisfactory results over the entire practical range of panel proportions is that the stringers take the same stress as the plate as long as that stress is not
45、greater than the stringer crippling stress, in which case the stringers take their crippling stress. In addition, the calculate load carried by the panel must always be greater than the crippling loadof the stringers tested without being fastened to the plate. This criterion takes care of the case w
46、hen the area of the stringers is large compared with the area of the plateand.the attachment between the plate and the stringer is so flex ible that wrinkling occurs at a load less than the crippling load of the stringers. For this case, the lateral forces on the stringers are compara tively small a
47、nd do not affect the strength of the stringers. Further more, at the shortening necessary for the stringers to achieve their crippling stress, the load being carried by the plate has fa+len to a negligible uantity and it may be assumed that the entire load is being carried by the stringers. The valu
48、e of the plasticity factor to be used with figure 9 is given by euation (4). The use of a plasticity factor which is a function only of the stress-strain curve of the plate material and is applied to the average stress in the plate at failure may seem to be rather arbi trary for panels on which the
49、proportions are such that the panels buckle at loads that are considerably less than the loads that the panels ulti mately carry. Panels which buckle fnthe local mode, for instance, expe rience a severe redistributi0n of stress as the panel is loaded beyond the buckling load. The factor may not be too arbitrary for panels which fail in the wrinkling mode, ho
