1、|li,j Iiq,_ 4 iCASE F|YNATIONAL ADVISORY COMMITTEEFOR AERONAUTICSTECHNICAL NOTENo. 1525STRESS AND DISTOI%TION MEASUREMENTS IN A45 SWEPT BOX BEAM SUBJECTED TOBENDING AND TO TORSIONBy George Zender and Charles LiboveLangley Memorial Aeronautical LaboratoryLangley Field, Va.WashingtonMarch 1948F:“ = I
2、t“ _,-_: t, “:,Ab FI:;L;.; ,_;:.LL: i:2 A:;_IfNATIO,.=,:,LAUv :;P,RY C.t);MI ii EE FOR AEROI,I,t1312- H -IR_,. N. W.WASi:,tNGION 25, b. Co-,E:,LITII:3Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or netw
3、orking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSTECHNICAL NOTE NO. 1525STRESS AND DISTORTION MEASUREMENTS IN A45 SWEPT BOX BEAM SUBJECTED TOBENDING AND TO TORSIONBy George Zender and Charles LiboveSUMMARYAn untapered aluminum-_lloy box beam, representing the
4、mainst_._ctural component of a full-span, two-spar, 45 swept wing wlth acarry-through bay, was subjected to tip bending and twisting loadsand its stresses and distortions were measured. Only symmetricalloading was considered and the stresses were kept below the propor-tional limit.The investigation
5、revealed that for bending the importanteffect of sweep was to cause a considerable build-up of normal stressand vertical shear stress in the rear spar (when considering the boxbeam as sweptback) near the fuselage. No such marked effectaccompanied torsion. The stresses in the outer portions of thebox
6、, both in bending and in torsion, appeared to be unaffected bysweep and agreed fairly well with the stresses given by elementarybeam formulae.The investigation further revealed that the spar deflections ofthe swept box beam could be estimated approximately by analyzing theouter portions of the box b
7、eam as ordinary cantilevers and makingadjustments for the flexibility of the inboard portion to which thecantilevers are Joined.INTRODUCTIONPresent designs of aircraft for transonic speeds call for wingswlth large angles of sweep. In order to study the structural problemsencountered in the design of
8、 swept wings a 45 swept box beam, shownIn figures 1 and 2, was subjected to symmetrical t_p loading and itsstresses and distortions were measured. This paper gives themeasured data and compares the stresses with those given by standardbeam formulas and the distortions with those estimated on the bas
9、is ofapproximate calculations.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACATN No. 1525SYMBOLSAAFEGIJKLMPQTVXabchZ_i, Z2stt at barea enclosed by cross section, square inchesarea of flange, square inchesYoungs modulus of elasticity (10,500 ksi
10、)shear modulus of elasticity (bOO0 ksi)geometric moment of inertia, inches4torsional stiffness constant, inchesshear-lag parameterlength, inchesbending moment, kip-inchesload, kipsstatic moment, inches 3torque, kip-inchesshear force, kipslongitudinal force, kipsdepth of box beam, incheswidth of box
11、beam, inchesdistance from neutral axis to any fiber, inchesdepth of spar web, incheslength of triangular bay, incheslength of portions of carry-through bay, inchesperimeter of cross section, inchesthickness, inchesthickness of spar web, inchesthickness of cover sheet, inchesProvided by IHSNot for Re
12、saleNo reproduction or networking permitted without license from IHS-,-,-NACATN No. 1525 3XYWWhcCL7W8Adistance from origin, inchesdeflection, inchesdeflection of front spar, inchesdeflection of rear spar, incheswarping displacement due to torque, incheswarping displacement at cross section hc due to
13、 bendingstresses, inchesrotation of cantilever portion due to flexdbility ofcarry-through bay, radiansshear strain of spar webrotation of cantilever portion due to flexlbility oftriangular bay, radlansangle of sweep, degreeslongitudinal stress, kslrotation of cross section due to torque, radlansTEST
14、 SPECIMENThe pertinent details of the swept box beam are shown in figure 3.(Hereinafter the box beam is referred to as sweptback rather thanswept, thus making it convenient to refer to the spars (or sidewalls)as “front“ and “rear“ without ambiguity.) The sweptback part8 con-sisted of two boxes with
15、their longitudinal axes at right angles,Joined by and continuous with a short rectangular carry-through bayrepresenting that part of the wing inside the fuselage. The materialof the specimen was 21_-T aluminum alloy except for the bulkheads.The bulkheads consisted of rectangular steel sheets with a
16、900 bendat each edge, forming flanges for attachment to the spars and covers.Bulkheads 2, 3, 4, and 5 were -_-Inch thick, whereas all other bulk-32heads were _-inch thick.6The cover sheet and front spar web, but not the rear spar web,were spliced at the center l_ne of the carry-through bay, and thes
17、tringers and spar flanges were spliced at the ends of the carry-through bay, as shown in figure 3. The front and rear spars were alsoreinforced at the ends of the carry-through bay where the box beam wassupported.Provided by IHSNot for ResaleNo reproduction or networking permitted without license fr
18、om IHS-,-,-4 NACATN No. 1525METHODOFTESTINGThe setups for bending and twisting tests are shownin figures iand 2, respectively. The box was supported by steel rollers, withaxes parallel to the direction of flight, at the four corners of thecarry-through bay, and loads were applied at the tips of the
19、box.(The bulkheads at the ends of the carry-through bay and the verticalreactions provided by the rollers taken together were assumedtorepresent the restraint that might be provided by a fuselage to thewing.) All loads were applied symmetrically at both tlps by meansof hand-operated winches. At each
20、 tip the load was transferred fromthe winch to a horizontal steel I-beam and then to the tip bulkheadin such a manner that the resultant load applied to the box was avertical force acting through the center of the tip cross sectionfor bending or a pure torque acting in the plane of the tip crosssect
21、ion for torsion.Forces exerted by the winches were measuredby meansof dyna-mometerson which the smallest division was equivalent to approximatelylO pounds. Strains were measuredonly on the right half of the boxbeamby meansof Tuckermanoptical strain gages. A 2-inch gage length(smallest division, 0.00
22、0004 in./in.) was used for the measurementofall stringer strains; strains at a 45 angle to the spar-_eb centerlines, used to determine shear stresses, were also measuredwith a2-1nchgage length (smallest division, 0.000002 in./In.). A 1-1nchgage length (smallest division, 0.000004 in./in.) was used t
23、o obtainall other strains. Stringer and flange strains were converted tostresses using a value of E = 10,500 ksi; shear stresses wereobtained from shear strains using a value of G = 4000 ksi. Spardeflections were measured by means of dial gages along the topflanges of the spars. The smallest divisio
24、n of these gages wasequivalent to 0.001 inch in the bending tests and 0.0001 Inch in thetorsion tests.RESULTSStresses due to bending.- The normal stresses in the stringers andflanges due to tip bending loads of 2.5 kips are shown in figureand are compared with the stresses given by the formula Mc of
25、Ielementary beam theory, shown by means of dashed lines. The top-coverand spar shear stresses due to the same bending loads are shown _nfigure 5 and are compared w_th the stresses VQ of elementary beamIttheory. The dotted parts of the stress curves in flgures 4 and 5 inthe inboard region of the rear
26、 spar are extrapolations representingthe stresses that would exist If there were no reinforcement of thespar where it entered the carry-through bay.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATNNo. 1525 5Stresses due to torsion.-The shear str
27、esses in the top cover andspar webs due to tip twisting moments of 43.42 kip-inches are given InTfigure 6 and are compared with the stresses ?A-_ of ordinary shelltheory. The stringer stresses developed by the same twisting momentsare plotted in figure 7. The stringer stresses near the center llnebo
28、x beam in figure 7 are compared with the _-stress due toof thethe component of the tip torque which produces bending of the carry-through bay.Distortions due to bending.- The measured spar deflections due totip loads of 2.5 klps are given in figure 8(a) and are compared withcomputed spar deflections
29、 shown by means of dashed curves. Thecomputed deflection curves were obtained by assuming the beam to beclamped as a cantilever at bulkhead 6 and superimposing on the canti-lever deflections the deflections due to the flexibility of the innerportion of the beam. A detailed description of these compu
30、tations Iscontained in appendix A.The measured and computed spar deflections shown in figure 8(a)were used to calculate the rotations (in their own planes) of crosssections perpendicular to the spars and cross sections parallel tothe direction of flight. These cross-sectional rotations are shown_n f
31、igure 8(b).Distortions due to torsion.-The measured spar deflections due totlptwisting moments of 43.42 kip-inches are given in f_gure 9(a) andare compared with computed spar deflections, shown by means of dashedcurves, obtained by applying ordinary torsion theory = _-j tothe outer portion of the be
32、am and then superimposing rlgid-bodytranslations and rotations due to the flexibility of the inner portionof the beam. The details of these computations are in appendix B.The measured and computed spar deflections shown in figure 9(a)were used to calculate the cross-sectional rotations shown infigur
33、e 9(b).DISCLNSSIONStresses due to bending.- The comparisons of experimental andcomputed results in figures 4 and 5 reveal that the stresses in theouter portions of the sweptback box beam, between the tip and a crosssection about one chord length from bulkhead 6, are substantially thesame as those gi
34、ven by elementary beam theory. Only the remainingportion of the box beam appears to be appreciably affected by sweepbackand shear-lag effects.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACATN No. 1525The important effect of sweepback, as indic
35、ated in figures 4and 5, is to cause an increase of normal stress and vertical shear Inthe rear spar immediately outboard of bulkhead 6 and a correspondingrelief of stress in the front spar outboard of bulkhead 6. Thenormal stress in the rear spar outboard of bulkhead 6, extrapolatedto eliminate the
36、effect of local reinforcement, was 1.40 times theMc-stress and the vertical shear stress, also extrapolated, wasI1.33 times the vertical shear stress at the tip.The build-up of stress in the rear spar near the carry-throughbay can be explained qualitatively as follows: If the elasticrestraint provid
37、ed by the portion of the box beamInboard ofbulkhead 6 were symmetrical, the stress distribution in the portionof the box outboard of bulkhead 6 would be as shown_n figure lO(a).Actually, because of the triangular bay between bulkheads 6 and 8,more restraint is offered to the rear spar than to the fr
38、ont spar,and ama result the front spar rotates more in _ts own plane atbulkhead 6 than does the rear spar. The result is a warping ofthe cross section at bulkhead 6. Such a warping can be producedby meansof a self-equilibrating antlsy_etrlcal stress d_stributlonapplied to the portion outboard of bul
39、khead 6 as shownin figure lO(b).By the principle of superposltlon, the stress distribution of thatportion of the sweptback box beam.outboard of bulkhead 6 can beobtained by superimposing the stress distributions showninfigures lO(a) and lO(b). The resulting stress distribution _s shownin figure lO(c
40、) and is seen to be in good qualitative agreement, asfar as the main characteristics are concerned, with the measuredstressdistributions outboard of bulkhead 6 shownin figures 4 and 5.Calculations madefor the box beamdescribed herein and for asmall Plexlglas box beam, similarly constructed and slmil
41、erly loadedbut having a solid carry-through bay clampedbetween two supportblocks, indicate that the shear-leg part of the stress d_strlbutlonat bulkhead 6 (f_g. lO(a) can be estimated by replsclng thetrianguler bay by a rectangular bay clamped at its inboard end, witha length equal to 15 percent of
42、the length of the front spar of thetriangular bay, and making a conventional shear-lag calculstion(reference I) for the resulting cantilever box beam. The unknownmagnitude of the torsion-bending part of the stress distribution(f_g. lO(b) could be estimated by applying the pr_nclple that thewarping o
43、f the cross section at bulkhead 6 due to the stresses Infigures lO(a) and lO(b), when the cross section is considered part ofthe inner portion (made up of the triangular end carry-through bays),must be the sameas the warping when the cross section is consideredpart of the cantilever outer portion (s
44、hown In fig. 10). Suchestimates would be necessarily crude because no theoretical dataexist on the response of the inner portion to the stress distributionsProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN No. 1525 7shown In figures lO(a) and lO
45、(b), although the response of the outerportion can be calculated from existing formulas (reference 2).Stresses due to torsion.-The comparisons in figure 6 reveal thatthe top-cover and spar shear stresses due to tip twisting moments aresubstantially the same as those given by the elementary formula _
46、LRAt(for torsion with constant rate of twist) in the outer portion of thebeam, extending from the tip to a cross section about one chord lengthfrom bulkhead 6. From this cross section inboard to bulkhead 6 thecover and spar shears change slightly from their elementary values as aresult of the restra
47、int against cross-sectional warping provided bythe triangular bay. This restraint against warping produces longi-tudinal stringer stresses (fig. 7) about half the magnitude of theshear stress T-L at bulkhead 6. From bulkhead 6 toward bulkhead 82Atin the triangular bay both the cover and spar shears
48、show a markeddecrease Calculations show that, for the purpose of estimating the coverand spar shears and the bending stresses due to torsion Just outboardof bulkhead 6, the triangular bay may be replaced by a rectangularbay of half the length clamped at its inboard end. The resultingstructure is an
49、ordinary cantilever box beam and the theory andformulas of reference 2 may be applied.Distortions due to bending.-The reasonably good agreementbetween the theoretical and experimental spar deflections in figure 8(a)indicates the correctness of the basic assumption used in appendix Ain estimating the spar deflections. This assum
