1、TECHNICAL NOTE 0-424 INVESTIGATION OF THE BUCKLING STRENGTH OF CORRUGATED WEBS IN SHEAR, By James P. Peterson and Michael F. Card Langley Research Center Langley Field, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON June 1960 Provided by IHSNot for ResaleNo reproduction or networking p
2、ermitted without license from IHS-,-,-L 9 5 9 NATIONAL AEBONAUTICS AND SPACE ADMINISTRATION TECHNICAL NOTE D-424 INVESTIGATION OF THE BUCKLING STRENGTH OF CORRUGATED WEBS IN SHEAR By James P. Peterson and Michael F. Card SUMMARY Design charts are presented from which the buckling strength of corruga
3、ted shear webs can be determined. The charts are applicable to webs with supported edges in which the edge rotations of the web along lines of support may range from unrestrained (simply supported edges) to completely restrained (clamped edges). In addition, the results of shear tests on seven beams
4、 with corrugated webs are presented and discussed. INTRODUCTION The geometric properties of corrugated sheet adapt it particularly well to certain structural applications, one of the more important of which is the shear web. Corrugated sheet has been recognized for some time as an effective medium f
5、or transmitting shear loads (see, for instance, ref. l), but it has not been generally used for this purpose because of certain inherent difficulties associated with fabrication and stress analysis. More recently, however, corrugated webs have been considered in structural applications where the web
6、s are required to perform dual functions. high-temperature environment applications for their thermal stress- alleviating properties as well as for their shear-carrying properties, or they may be used in a sandwich-covered wing structure where fewer webs than usual are employed and where each web is
7、 required to possess a relatively large crushing strength as well as a large shear buckling strength. For instance, corrugated webs may be used in The design information available is generally inadequate to predict the buckling behavior of corrugated shear webs. Buckling charts are available for ort
8、hotropic plates in shear with either clamped edges (see ref. 2) or simply supported edges (see ref. 3 or ref. 4, p. 384) but nothing is available for orthotropic plates with edge-support conditions falling between these limits, the range in which most practical corrugated webs will fall. The use of
9、charts for simply supported shear webs will Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 predict buckling at unduly small loads in most practical applications. The amplitude of corrugations in corrugated webs is relatively large compared with th
10、e thickness of a conventional plate with the same bending stiffness. Thus, there is a greater opportunity for restraining the rotational deformation along the edges of the corrugated webs. On the other hand, the edge support is not likely to be such that deformations are completely restrained in any
11、 practical application. Hence, design information for webs in which the rotational deformations along the edges of the web are only partially restrained is needed. Design information is also needed regarding the effect of restrained warping on the buckling load of corrugated webs. The only informati
12、on available on this effect is in reference 5, where buckling loads are given for long clamped corrugated webs with complete restraint against warping along the edges. corrugation shape (square wave) and indicate that the effect of restrained warping on buckling may be considerable. neglected in usu
13、al orthotropic plate analyses of corrugated webs. The calculations were made for a specific This effect is The present paper extends previous calculations to include edge support conditions between clamped and simply supported edges for ortho- tropic shear webs with geometric properties characterist
14、ic of corrugated webs. The effect of restrained warping on buckling is taken into account in an approximate manner by an extension of the work of refer- ence 5. webs are presented and discussed. In addition, the results of some tests on corrugated shear SYMBOLS plate flexural stiffness in longitudin
15、al direction, x- in-kips ; 12 -2 plate flexural stiffness in depthwise direction, = Etp , in-kips D2 pxD2 + p D 2 + 2D plate stiffness, Yl w, in-kips D12 plate twisting stiffness, in-kips Dxy E Youngs modulus, ksi M moment per inch of length of plate, kips Provided by IHSNot for ResaleNo reproductio
16、n or networking permitted without license from IHS-,-,-3 L 9 5 9 NxY P S b kS 2 P t - t t A W X, Y 7 r 6 E shear load per inch of plate, kips/in. beam load at web failure, kips shear load in web, kips effective depth of corrugated web between attachment members, in. amplitude of corrugations in corr
17、ugated plate, in. (fig. 4) effective rivet offset, in. (fig. 10) attachment angle dimension, in. (fig. 10) shear-beam depth measured between centroid of compression cover and centroid of tension cover, in. shear buckling coefficient, unsupported length of web between end buffer bays, in. pitch of co
18、rrugations in plate, in. (fig. 4) thickness of sheet in corrugated plate, in. area per inch of corrugated plate expressed as equivalent sheet thickness, in. thickness of attachment angle, in. (fig. 10) plate deflection, in. coordinates measured along and depthwise of web, in. shear strain bending-to
19、rsion constant of corrugated plate, in .5 lateral deflection of web, in. restraint parameter, M 1 D2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-edge rotation of web, radians wave length, in. Poissons ratio Poissons ratio associated with bending
20、of corrugated plate in x- and y-directions. The product p p is taken to be zero in this paper. XY radius of gyration of corrugated plate about centroidal axis, in. shear stress, ksi efficiency parameter, ksi (eq. (12) Subscripts : av average cr critical e edge eff effective el elastic limit max maxi
21、mum CALCULATIONS The differential equation employed in the calculations was taken from reference 5. In the notation of the present paper, it is 2 aw = 0 (1) q,m aw4 + 2D12 that is, most of its stiffness is attributable to in-plane bending (so-called “bending stresses due to torsion“) and the associa
22、ted shear stresses. term neglects this important property of corrugated sheet and The use of equation (1) without the The second characteristic is associated with the small twisting For practical purposes the stiffness stiffness of corrugated sheet. parameter - is so small that it can be taken to be
23、 zero with neg- ligible error. The effect of this simplification is indicated in fig- D12 m ure 1, where the buckling coefficient is plotted against - D12 . Values of the parameter - D12 corrugations of current interest in structural applications. The curve shown was computed for clamped-edge condit
24、ions (E = m) but applies with negligible error to webs with other values of the edge-restraint parameter E. are generally less than 0.05 for the types of pz A solution to equation (1) can be obtained in the same manner as that employed in references 6 and 7 for shear buckling of isotropic Provided b
25、y IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 plates. The same stability equation applies in this case if the same boundary conditions are employed, that is, if plates with edges elas- tically restrained against rotational deformations are considered. The
26、stability equation is given by 2ap(4y2 - $)(cash 2a cos 2p - COS 47) + br2(u2 - p2) + ( a2 + p2)2 + (472 + u2 - p sinh 2a sin 2p + ea(4y2 + u2 + p2)cosh 2a sin 28 where Mb E =- I D2 (3) and a, p, and 7 for the case under consideration are given by the following relationships: where . Provided by IHS
27、Not for ResaleNo reproduction or networking permitted without license from IHS-,-,-7 and NVb2 kc = tP D1D2 3 The notation of references 6 and 7 is retained where between the curves is not known. It is known, however, that edge warping deformations are extremely difficult to prevent, and therefore th
28、e condition of complete restraint (E = m) is not likely to be approached in corrugated shear webs of conventional design. edge conditions may be such that some restraint is provided which can- . not be properly accounted for with the use of figure 3. however, that this effect will generally be small
29、 and that the On the other hand, It is expected, .I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-9 conservative assumption of unrestrained warping along the supported edges should suffice in most cases. Figures 2 and 3 will be used later in assess
30、ing the behavior of some tests on corrugated shear webs. TESTS Shear tests were conducted on seven beams with corrugated webs in order to obtain information regarding the buckling strength of such structures. The beams were of built-up construction and differed from one another only in depth. Test B
31、eams Details of construction of the test beams are given in figure 4 and table I. by a series of straight equal-length segments. tion of the segments was selected on the basis of an elastic weight- strength analysis of such corrugations in which the angle between adjoining segments was allowed to va
32、ry. series of tests include proportions of nearly optimum design. The web corrugations were composed of angular waves formed The particular orienta- Accordingly, the beams in this The test beams were constructed with short buffer bays at either end to facilitate the introduction of load into the spe
33、cimen in a uniform manner. The buffer bays must be short for this purpose because, as discussed earlier, the buckles tend to be short in the length direction. In a preliminary test of a beam with somewhat longer buffer bays than those finally used for the test specimens, buckling was observed to occ
34、ur in the buffer bay at a load of approximately 70 percent of that computed for the test section. Reinforcement strips were used at the top and bottom of the webs of the test beams to delay local buckling. Use of the strips was sug- gested by a preliminary test also. buckling of the elements of the
35、corrugation was expected to occur at about the same stress level as buckling of the corrugated web as an orthotropic plate. However, local buckling of the flat elements occurred earlier than expected. ported ends of the elements of the corrugations that were not attached to the web-attachment angles
36、 at a stress of approximately 85 percent of the buckling stress computed for the elements on the basis of simple support all around. The premature buckling triggered web instability soon thereafter. Consequently, 1-inch-wide strips of the same thick- ness as the web were bonded to the web of the tes
37、t beams at the top and bottom to provide support to the otherwise free edges. The design was such that local The buckles seemed to emanate from the unsup- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 Thestrips have the additional advantage of a
38、lleviating the com- c plexity of the problem of providing an adequate attachment between the web and the web-attachment angles; this problem arises because attach- ments to the web can be made only at the crests of the corrugations. The strips have the disadvantage of adding weight. The webs of the
39、beams were fastened at each wave crest to the web- attachment angles with three conventional rivets (see figs. 4(c) and 4(d). to be scalloped, as is often done. The edge reinforcing strips, which are nominally 1/8 inch deeper than the attachment leg of the web- attachment angle, are visible in figur
40、e 4(d) for beams 6 and 7. are on the other side of the web of beam 5. The light areas at the tops and bottoms of the webs are areas which were chemically cleaned during fabrication for bonding the strips to the web. The geometry was such that the attachment angles did not have They L 9 5 9 The speci
41、mens were constructed of 7On-S aluminum alloy. Typical Youngs modulus E material properties were used in reducing the data. was taken as 10,300 ksi, and Poissons ratio p was assumed to be 0.32. Procedure 0 The test beams were cantilevered to a heavy backstop and loaded at the tip with a vertically a
42、pplied load (see fig. 5). The load was A applied in small increments, and between load increments the webs were examined for evidence of buckling. To help further in detecting buckling, particularly local buckling of the flat-plate elements of the corrugations, strain measurements were taken on the
43、webs of the beams. The strains were autographically recorded during the tests. used to help detect buckling of the corrugated sheet as an orthotropic plate. A buckle bar was mounted on each side of the web and rested on the web. Any lateral movement of the bar resulting from web buckling excited a s
44、train gage whose output was autographically recorded during the test. of the web was replaced with two banks of three dial gages. gages were read between load increments and were removed prior to expected failure. Also, in the early tests buckle bars were For the tests of beams 5 to 7, the buckle ba
45、r on either side The dial Results The shear loads supported by the test beams at failure are given in table I. according to the formula The average shear stresses in the webs at failure computed 6 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-11 P
46、ht T=- (9) L 9 5 9 are also given. The shear stress in the webs at failure as deduced from strain-gage readings near the neutral axis of the beams was usually about 5 percent less than the shear stresses computed according to formula (9), and in the case of beam 4 was 10 percent less. crepancy, whic
47、h was greater at high loads than at low loads, is believed to be the result of some out-of-plane (buckling) deformations of the webs even at relatively low loads. shear web is not uniform; the areas near the flanges carry more than their proportionate share. uted to the so-called “portal-frame actio
48、n.“ estimate the load carried by the portal frame of the test beams, and it was found to be less than 1 percent of that carried by the web in every instance. This dis- The shear distribution in a buckled Very little of the discrepancy can be attrib- Reference 8 was used to Lateral deflections of the
49、 webs, measured with dial gages, are plotted in figure 6 as a function of applied load. loads are indicated by the curves. started to grow from the beginning of load application, and at the pre- dicted critical load for the webs (denoted by tick marks on the curves) had grown to approximately 2 percent of the web thickness
