1、ARB June 1942 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ORIGINALLY ISSUED June 1942 as Advance Restricted Report TEE STRENGTH AND STIFFNESS OF SHEAR WEBS WITH AND WITHOUT LIGHTENING HOLES By Paul Kuhn Langley Memorial Aeronautical Laboratory Langley Field, Va. WASHINGTON NACA WARTIME REPORTS are r
2、eprints of papers originally issued to provide rapid distr-ibution of advance research results to an author ized gr oup requiring them for the war effort. They were pre viously held under a security sta tus but are now unclassified. Some of these reports were not tech nically edited. All have been r
3、eproduced without change in order to expedite general distribution. L - 402 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I“ I I L I I NATIONA!, ADVISORY COMMITTEE FOR AERONAUTICS ADVANCE RESTRICTED REPORT THE STRENGTH AND STIFFNESS OF SHEAR WEBS W
4、ITH AND WITHOUT LIGHTENING HOLES By Paul Kuhn SUMMARY Nearly 200 tests were made on the strength of shear webs of 24s-T aluminum alloy, vTi th and without lightening holes. The testa were madein a jig of the singl-specimen t ype, in which the specimen is free to collapse completely without developin
5、g diagonal tension . The lightening holes were circular and had either flanged edges or beaded edges, the specimons with flanged edges constituting by far the largest test gtoup. The following equations were found for the shear stresses T causing colla.pse, 1.11 stresses being given in kips per squa
6、re inoh: (a) Solid webs: Tcoll = (37 - 0.283 hit) if hit 60. The second formula applies only to sheet 0.036 inch thick; for other thick nesses, the colls.paing stress may be obtained from a graph (b) Webs with flanged holes: (c) colI (net) = k:cr + (ult - Tcr) D/b where the shear stress is based on
7、the net section 3/4 Webs with beaded holes: Tcoll:= 4!0 (t/h) . where the shear stress 1s based on the gross section. Within the rather narrow test range, the size and the spacing of the holes has a practically negligibl e effect on the strength of webs with beaded holes. In these equations, h is th
8、e width of the sheet; t, the thickness; D, the hole diameter; bj the hole s pacing; k, a correction factor (not differing greatly from unity), which depends Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 on t he sheet thickness; Tcr the buckling s
9、tress; and T ul t , the ult imate shear strength of the material . Simple empir i cal formulas are 8i ven for the h()ar stiffne s s appropriate to various groups of specimens. For webs with flanged holes, design charts are presented; these charts make it possible t o determine by inspect ion the pro
10、portions of the l i1test web for a given set of design c ondi tiona. INTRODUCTION The shear webs emp l oyed i n aircraft struct ures are fre quen t ly perforated with r egularly spaced h910s to l ighten the web or to provide a ccess to t!18 interior of the str uct.v.re . Round hol es with flanged ud
11、ges were used in airship girder3 before the metal monocoqus s t.ructure came into gener a l use for airplanes, and t ha. - The cliliiensions of the shear H webs without holes and the mcximutn) oads .c?-rried by thenlare gf veIl .:In table 1. The experiln.enta1shear stresses causing the webs to colla
12、pse T coll were calculated., from the t(;ist load. causing the specimen to collapse Pcoll, by the formula TCQ1 :ol (1) La t the effect;!,yelength . Le being taken as (see fig. -5) , 1 . ,Lo :. L -h1 2 (2) for bar supports as well as for rod supports. This correction for 1neffoa;t1 veness at the free
13、 ends was also used by SchUss,ler (refel“Qnce 1) alid is based on photoelastic tests reportod in ref0reroe 3 (p. 6Q,5). Strain measurements made on the upper half of one speclmen wi thber supports showed stresses equal to 79 and 99 per-cent of the calculated stress at distances of 0 .3111 d 0.4h1, .
14、 respectively, from the end; the measured stress at the middle of -liha spepimen was 105 percent of the. calculated stress. This OXOO38 at th middle is explained qualitatively by tho fact that the 10a(1 i applied in concontratecl form, as mentioned in th.o discussion of the test jig. The fact that a
15、 5-percent excess was l1easurod inst;)ad of a 2-perce;lt excess, 0.13 est1matecl, may be clue to experimental error) inadequacy of the simple formula usec1 for making tho esti1ll.s;pe, local overstressing due to oversized holes, and finally to tho high load carriedin the solid s,)0c:i.ln.en. Tho exp
16、erimental values of T 0011 are shown in figure 6. The evidence is not so complete as might be desired but appears to warrant the conclusion that the method of eclge sUI)port dOGS not affeot the collapsing load For values of hit 60, the curves separate for different thick nesses, the thinner sheets d
17、evelop higher stresses than the thicker sheets. For a thickness of O.Q36 inch, tho oxperimental curve for hit. 60 can be expressed by the empirical fornula or coll = 1,200 t/h kips per square inoh (4) No attempt was mde to eXpress the .ourves for other thicknesses in a.na.ly tical form For compariso
18、n, figure. 6 a.lso shows the wellknown theoretical curves for the critical shear stresses 7 cr These curves are valid only as long as the stress in the material rAS not passed the 11rli t of proportionality; beyond this point, corrections must be made analogous to the case of column curvos at low sl
19、enderness ratios. Thero is no established llethoCl, of nUlkng such corrections in the case of critical shear stress, but an upper liJ.:lit for T or may obviously be obtained by using T coll whenever it is lower than Tor. 1he strength of shear webs with flanged hqles. Because webs wi th round flanged
20、 11g.1.tening holes are widely usocl, an effort was made to devolop an empirical strength formula. ofsuch1a fornl that it could be used for extrapola.tion beyond the test range with a reasonable degree 01 accuracy. The fOlTlUla developed. is , where 1 Formula. (5) for the strength of shear webs with
21、 flangt7d lightening holes, as given in this report, was based ona fairly large number of tests (119 tasts). The range of SOIle of tho variables was, howover , quito lmi ted; in particular, there were practica.lly no to s taw! th a dia.me ter;“to -depth ratio grea tGr than 0.5. Addi -tional tests ha
22、ve been started to extend the range of variables; only a few of these tests have now been carpleted (Sept. 1942), but they appear to indicate defin:ttoly tha.t the foula. becos UIlconservat1ve outsicLe the test range. Pending the completion of these tests, .it is, rec.ommnded tha 1?Pe appllcaifion o
23、t:. !ormula (5) be strictly confined .t2l!9bs falip.e; wi thin test lanse. which DUlY be defiri2 as fo).10J1S: D/h 0.32 inch Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-0J :J I H j 9 Tcoll (net) shear stress that causes oollapse, based on the net
24、 . section. The net sect:t.on per inch run is taken as t(l -nib) T cr critical stress at which the sheet would buckle. if it .had no hol.es T ult ultimate shear stress of material D clear diameter of holes b center-tocente:t spac:tng of holes k “ 0.675 + 7.5 t (t l to T call (net) : kT ult, which in
25、dicates a net shear stress lower than Tult for thin sheet, increasing to a net shear stress somewhat larger than T ult for thick sheet. Th5.s excess, which has a maximum value of 5 percent according to formula (6), can probably be explained by the fa.ct tha.t the value. of or ult asobtained from ref
26、erence 4 is somewhat. conservative. When the holes become vanishj.ngly small but a fini te. spacing is still maintained or “rhen the spacing becoroos very large for any arbitrary size of holes (D/b 70), formula (5) reduces to . T coll (net) = kTcr This value is conservative for large ratios of hit a
27、nQ apprOXimately correct for low ratios of /t provided that the T coll curve is used as a cut-off curve for T cr as suggested in the diSCUSsion of the strength of solid webs. The linear dependenoe of T coIl on nib was established empirically; a sample test plot is shown in figure 7. It was first Pro
28、vided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 believed that the change of T coll should (legend on a functj.onof D, b, and. h, tho most obvious one bolng :rf Ibh that expresses the amount of lightening (ratio of area removed to original area) excep
29、t for inessential constants. It was found,hoWGver, that Y!1uch closer gorrelation could. be obtained wi.th the para.meter Dlb than wi th D Ibh. . Tables 2, 3, and 4 give the dir.ensions of the test specinns, t,he test loads, the experimental values of T coli and the calculated. values of T call for
30、the shear webs wi t11 flanged lightening holes. The experimental valUGs of Tcoll were calculatd by tho formula where the effectiv net crosssoctional area Ae was taken as Ae = (n 1) (b - D)t(8) n being tho nur.1ber of holes in tho specimen . . The cOrrection for ineffectiveness at the enels includod
31、in f01“Dula (8) is based on -ello Q.ssUIJ?tion that tho materlal outboard of the last holo on each end carries no stress. ualitativoly, this correctionsoelUS more aprJropria te for p0rforatocl 8:pecimens than the correction used for solid spocin.ens, and. it does not differ greatly from the correcti
32、on for soli(: s?eclmens wi thin tho tost range. Quantitatively, hm,rever, the correction is not vrified and conGtitutes the largest itGD of uncertainty in tho evaluation of the test data. The error dUG to this uncertainty is ostiLted to be, in most cases, less than 5 )orcent. The calculated valuesof
33、coll were obtainod by using fornulas (5) ei.nd(6). Tho valuos of T or nee;led for use with formula (5) were taKen from the curves shown :Ln figuro 8. These curves wereobtainecl by drawing tentative straight lines on all test plots, analogous to the Plot shown in :figure 7. Tho. tentativo values for
34、 cr obtamed in this Banner “Tere then plottod against, hit and. faired The n01ulus E was taken as 10,600 kips per square inch and the ultinate strength as T ult = 37 killS 1)01“ square inch, according to reference 4. It will be notecl that, for the two r.lain groups of to sts (with rear.1Gcl bolt
35、holes), fOT:lula (5) re:presents the test (lata quite well. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- Cl 6. 0 , , .:r H 11 Errors in excess of 10 percent are shown for 11 percent of 11 test and the maxiI:lUlD. errors are 22 percent on t.he con
36、aerva ti va side and 10 percent are shown for 11 percent of all tests, an.“l. the maximull1 errors are 22 percent on the conserva ti vs siele MellO percent a.:re shown by 16 percent of all test.s j the ma.xil:1urJl error on the conserva tive side is 24 percent and the Ina:lCimUITl error on the uncon
37、aervative side, 20 percent. Conpared. lit;h the formulas of reference 1, fomu1a (5) has, therefore, the twofold advantage of s01:16what better accuracy and of much greater usefulnoss for extlpolat1ne boyon the test range. The testgroU:p with drilled bolt holes averages 10 percent 10Vl, presUlll.!.l,
38、bljr reflecting the influence of. uneven 10o.el clistribution Causee,- by . irregular. ororsized holes. Tn!:, strnEth-.tJll$ffJb.!.!.tth.1?_ hole, The results of the tests on webs with beaded holes are given in table 5. Application of the formula deVeloped tor webs With f1ange(1 holes showed. large
39、irregular scatter, indicating that the behaVior of tho webs with boaded. holos differs conside.rably fron the behavior of the webs wi th flanged. holes. The bela stiffen a fairly lJ, curve- C through the test points for Wo b s with b:; 3 incha s The curve for b = 3 .5 inche swas OJI;Ii;!;tted to sir
40、l?lify the figUre. For the webs haying a.hole diaueter D = 1.60 inches, the tests indicate no l,elation between the allowable stress end the hole spacing. The mU:lbQr of tests is not sufficient to draw more definite conclusions on the influence. of hole size ani hole spacing. Provided by IHSNot for
41、 ResaleNo reproduction or networking permitted without license from IHS-,-,-12 Three beadedhole specimens were tested with bar supports. It will be noted that the test Ooints fall practically on the same . curves as points for tests with rod supports. The conclusion that the method of edge support d
42、oes not influence the strength of webs with beaded holes is in agreement with the conclusion first stated that this type of web fails in the srune eneral manner as a uniform sheet, because the tests on solid webs. indicated no influence of the method of edge support ori the strength. The strensth of
43、 webs with plain holes.- Since only four different sizes of webs with plain holes (without flanges) were tested, it is impossible to draw this load was chosen because, under present design reqUirements, the limit load is two-thirds of the ultimate design load. A simple formula for the shear-stiffnes
44、s factor may be obtained by assuming that the material between :the holes and the edges is entirely ineffective, leaving as effective material rectangular strips having a length (b-D) i the formula is evidently t) = 1 - D/b (11) Provided by IHSNot for ResaleNo reproduction or networking permitted wi
45、thout license from IHS-,-,-(J $ I H 13 If this formula is modified by introduc.ing an exponent m (lla) it may be adjusted to fit i.ndividual groups of test data as well as the scatter of the data will permit . The experimental displa.cement curves often exhfbi te.d marked irregularities; some of the
46、se irregularities were probably caused by lOuse fit of the bolts, some by buckling between the lightening holes. No attempt was made, therefore, to derive formulas of general. validity to represent the experimental shear-stiffness factors. Only the results for webs with rod supports are given. It is
47、 believed that the restraining influence exerted by the bar supports on the shear displacements is never approached in a practical struc.ture, and the results obtained wth bar supports are, consequently, of no practical interest. The stiffness o!1 webs;- By definition, the shear stiffness factor o e
48、quals unity for solid webs. If buckling begins at a load less than 2/3 Pooll, the value of Il tiill depend on the amount of buckling. The condition is similar to that in diagonal-tension fields .but is complicated by the fact that a web free to collapse is more sensitive to initial buokles than a dlagonal-tenslon web. There were additional experimSntal diffi cul ties in some cases, such as the small magnitude of the displaoe“ menta caused by hl being very smail, and unoerta1nties.ooncerning the fit of the bolts. As a result,the
