Theoretical Analysis of Stress Distribution in Bonded Single Strap and Stiffened Joints

Transcription

1 56 Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts Abstract In ths paper, dstrbton of peeng stress n two types of adhesvey-bonded jonts s nvestgated. The jonts are a snge strap and a stffened jont. Theses jonts are nder nform tense oad and materas are assmed orthotropc. Layers can be dentca or dfferent n mechanca or geometrca propertes. A twodmensona eastcty theory that ncdes the compete stressstran and the compete stran-dspacement reatons for adhesve and adherends s sed n ths anayss. The dspacement s assmed to be near n the adhesve ayer. A set of dfferenta eqatons was derved and soved by sng approprate bondary condtons. Rests reveaed that the peak peeng stress deveoped wthn the adhesve ayer s a fncton of geometrca and mechanca propertes. FEM soton s sed as the second method to verfy the anaytca rests. A good agreement s observed between anaytca and FEM sotons. Behnam Ghoddos a a Yong Researchers and Ete Cb, Ahvaz branch, Isamc Azad Unversty, Ahvaz, Iran, b.ghoddos@aahvaz.ac.r Receved In revsed form..6 Accepted 6..6 Avaabe onne 9..6 Keywords Stress dstrbton, adhesve jont, strap jont, stffened jont, fnte eement, peeng stress INTRODUCTION Adhesvey-bonded jonts are wdey sed de to ther severa advantages over the other methods. Wder contact regon n adhesvey-bonded jonts s the case of more nform stress dstrbton. In the same weght, bonded jonts show more strength than the other common methods sch as threaded connectons, wedng and rvetng. Adhesvey-bonded jonts are stronger n fatge, fare and they are corroson resstant. Composte materas that are wdey sed these days are weak n oca stresses so t s crtca to se mechanca jonts de to ther stress concentraton. Adhesveybondng acts over areas not a snge pont so they are the best choce n bondng dfferent composte ayers. There are severa jont desgns for bondng the ayers sch as snge-ap, dobe-ap, snge strap, stepped-ap, stffened, scarf btt, etc.

2 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts 57 A nmber of stdes have been condcted to anayze the stress dstrbton theoretcay and nmercay wthn the overap ength of adhesve ayer. Ojavo and Ednoff (987), nvestgated the effects of thckness of a snge-ap jont nder tenson. They assmed peeng stress to be constant aong the thckness. Ther work showed that the peak shear stress occrs at the both ends of the overap regon. Hart-Smth (97), derved the teratve cosed-form anaytca sotons for sngeap adhesve jont whch acconted for adhesve pastcty and adherend stffness mbaance. Three dstnct effects, bendng de to eccentrc oads, shear and peeng stress were covered n hs anayss. He aso stded a dobe-ap jont and showed that the effects of peeng stress are more prononces n snge-ap jonts de to eccentrc oad path. Chan her (999), presented smpfed onedmensona modes for snge and dobe ap jonts based on cassca eastcty theory. He assmed shear deformaton constant across the adhesve thckness. Shahn and Taher (9), presented anaytca treatment of the deformatons n adhesvey-bonded jonts on eastc fondaton wth speca attenton to the specfc case of adhesve jont between the face sheets of sanch beams. They stded snge-ap, stffened and snge strap jonts sng stran energy method. They apped cyndrca bendng theory to determne some coeffcents to cacate moments on edges. Lo and Tong (8), presented a nove formaton and anaytca sotons for adhesvey-bonded composte snge-ap jont by takng nto accont the transvers shear deformaton and arge defecton n adherends. On the bass of geometrcay nonnear anayss for nfntesma eements of adherends and adhesve, the eqbrm eqatons of adherends are formated. They sed Tmoshenko beam theory to express the governng dfferenta eqatons n terms of the adherend dspacements. Ther obtaned sotons are apped to snge-ap jonts, whose adherends can be sotropc or composte amnates wth symmetrcay ps. They determned a new forma for adhesve peeng stress. L et. A. (999), performed a nonnear two-dmensona fnte eement anayss to determne the stress and stran dstrbton across the adhesve thckness of composte snge ap jonts. They showed that the tense peeng and shear stresses at the bond free edges change sgnfcanty across the adhesve thckness. Vabe et a. (6), sed bondary eement method to stdy stress gradent n adhesvey bonded jonts. Ther work ncded both snge- and dobe-ap jonts. Nmerca rests of snge- and dobe-ap jonts showed the potenta of bondary eement method n anayss of bonded jonts. Zhao and L (9), deveoped a genera two-dmensona anaytca approach capabe of provdng an expct cosed-form soton for the cacaton of eastc stresses n snge-ap jont, Assmng near dstrbton of a ongtdna norma stress n the jont thckness drecton. By treatng the adhesve ayer n the same way as the adherends, the two-dmensona stress and stran dstrbtons at any pont, and the tense force, shearng and bendng moment at any cross secton can be predcted accratey, n both the adhesve and adherends. Ther anayss was based on a two-dmensona eastcty theory that both ncdes the compete stress-stran and the compete stran-dspacement reatonshps for the adhesve and adherends. Ther method was capabe of satsfyng a the bondary stress condtons of the jont, ncdng the stress-free srface condton at the ends of the bondne. Sawa et. a. (), anayzed snge-ap adhesve jonts of dssmar adherends sbjected to tense oads as a three body contact probem sng two dmensona theory of eastcty. They examned the effects of Yong s mods rato between dfferent adherends thckness, the rato of the adherends ength and the adhesve thckness on contact stress dstrbtons at the nterfaces. Temz et. a. (5), sed FEM to anayze behavor of b-adhesve sed n Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

3 58 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts reparng of damaged parts. In a dobe-strap jont wth an embedded patch, patch was embedded nto the adherents for strctra reqrements. In addton, to ncrease the strength of the jont, two adhesves were sed to bond the adherends. They sed nonnear fnte eement method to predct the fare oads to assst wth the geometrc desgn and to dentfy effectve ratos of szes to maxmze jont strength. Shshesaz and Bav () had an nvestgaton on vod and debond effects n a dobe ap jont. For symmetrc debonds and vods wth reatve engths of.8, the same effects were observed. In a comparson for defects between snge-ap and dobe-ap jonts they reported that the ncrease n stress s hgher n snge-ap jont than n dobe ap jonts. Karachaos et a. (), stded the effect of defects on the strength of a snge-ap jont wth varos adherend and adhesve materas. Two dfferent types of adhesve were stded wth dfferent degrees of dctty snce the stress dstrbton aong the overap depends on the adhesve s capacty to deform pastcay. Stee adherends were sed from ow strength and hgh dctty to hgh strength. Rectangar and crcar defects ocated n the mdde of the overap were stded. The artfca defect conssts of a thn fm of Tefon paced n the mdde of the overap, ths creatng a dsbond of the reqred sze. When a toghened strctra adhesve s sed wth a hgh-strength stee, there s an amost near decrease n jont strength as the defect area ncreases. In the case of the brtte adhesve, the redcton n strength, as the defect sze ncreases, s not proportona for sma defect szes, ndcatng that the end of the jont becomes more mportant de to oca strans exceedng mtng vaes. Ghoddos and shshehsaz (6), nvestgated an adhesvey-bonded stepped-ap jont sfferng from a vod wthn ts adhesve ayer. They sed cassca eastcty theory to determne shear stress fed n the separated sectons of the adhesve ayer aong the overap ength. They decared that the stepped-ap jont performed better n stress dstrbton wth vod rather than snge-ap and dobe-ap jont. In ths paper, peeng and shear stress dstrbton n the mdde of the adhesve ayer and peeng stress fed between adhesve and adherends n a snge strap jont and a stffened jont are stded. The adherends are orthotropc and t s assmed that the adherends have bendng deformaton besde ongtdna dspacement. The adhesve ayer shows shear defamaton. Longtdna and transversa dspacement eqatons are consdered as a near fncton n the thckness drecton. Shear stress s assmed to be constant across the adhesve ayer and the ayers can be ether smar or dssmar n geometry or mechanca propertes. The anaytca soton can satsfy the bondary condtons competey. Theoretca rests are verfed by FEM rests whch obtaned from ANSYS software. ANALYTICAL SOLUTION. Stffened Jont In a stffened jont, an extra ayer as a dober s bonded to the prmary ayers and mproves the strength of the jont. The ayer cases moment n the jont and shear and norma stresses n the adhesve and adherends ayer. The externa tense oad s nne and there s no eccentrc oad. The jont s conssted of two composte ayers wth orthotropc strctres. Mechanca and geometrca propertes of theses ayers sch as thckness, Yong s mods and Posson s rato can be dfferent. Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

4 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts 59 The mode of the jont can be redced to a two-dmensona mode becase the oad s nform and shear and norma stresses are not vared n the z drecton. Fgre shows a mode of the jont. Fgre : stffened ap jont confgraton. E x and E y are the eastc mods of the ayers n x and y drectons. f are nterna forces n the nt of wdth n the ayers and respectvey. F s xz and zx are Posson s rato. f and the externa tense force apped nformy to the jont n x drecton. The foowng assmptons are assmed n ths anayss. The mode of ths anayss s pan stress. It means that the stresses n z drecton are constant. Shear stress s assmed to be constant throgh the adhesve ayer. Dfferenta eqaton of transversa and ongtdna dspacements n the adhesve s assmed to be a near fncton. Axa force s gnored n the adhesve ayer de to the sma Yong s mods of adhesve rather than the Yong s mods of adherends. Cyndrca bendng theory s sed to cacate deformatons n the adhesve and adherends. Free body dagrams for an nfntesma eement n the overap regon are shown n Fgre., are shear stresses and y, y are pee stresses n ayer and. From the eqbrm n x and y drecton: df df dq dq (-a) (-b) () y () y Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

5 6 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts d t ( ) (4) y y Fgre : Free-body stress eqbrm dagram. From the moment eqbrm n ayer and : dm dm t Q (5-a) t (5-b) Q ( ) x m s the shear stress n adhesve. y, y are pee stress between adhesve and ayer and respectvey. The reatonshp between force and moment n the ayers wth axa stress n x drecton s: f t 6 M ( ) t (6) x y t, y t (,) (7) From the eastcty theory and eqbrm: x x (,,) y (8-a) y y (,,) x (8-b) Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

6 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts 6 The sbscrpts, and denote the pper adherend, ower adherend and adhesve, respectvey. Sbstttng Eqatons 8-a, 8-b nto 6 and sng the Eqatons -a, -b,, and 4: Where, ( ) 6 Q ( ) t (9-a) ( 4 ) 6 Q ( ) t (9-b) (-a) (-b) Sbstttng Eqatons 9-a, 9-b nto 8-a, 8-b: Where, d y t( ) y ( ) (-a) d y t ( ) y ( ) (-b) d y y t (.5) (-c).5 ( y t ).5 () Constants of ntegratons for the Eqatons -a and -b are determned by Eqaton and for the Eqaton -c, Eqaton s sed..5 () y y pckng, and sng the Eqaton -c ead to cacate peeng stress n the mdde of adhesve ayer m. sng Eqaton -c and pckng.5 and.5: y y d t m m (4-a) d t m m (4-b) Reatonshp between shear stress and shear mods s shown n Eqaton 5. xy (,,) (5) G Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

7 6 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts Stress-stran reatonshp for orthotropc materas s depcted by Eqaton 6. E xz E y x D D x x xz Ey E y y y (,) D D xy G (6) D (7) xz zx Peeng stress and stran s derved from Eqaton 6 as foow: y Ey v xz Ey x (,) D y D (8) v A E E y xz y x x y y (9) Where, A E E D (,) E x y xz y () For transversa dspacement of the ayer, by sbstttng Eqatons 6 and -a nto Eqaton 9 and then ntegratng by : v v At xzey x E x y d 4 4 d v At Ex t y 4 6M xz AE x f ( ) t () v s the transversa dspacement for top srface of the ayer. Transversa dspacement between adhesve and ayer s derved by contnty of dspacement and sng Eqaton as foow: v v v At E AE f d t y ( ) x xz y () By sbstttng Eqaton nto Eqaton : Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

8 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts d v v At Ex t y 4 6M xz AE y f( ) ( ) t () Smary for the ayer : 4 4 d v v AtEx t y 4 6M xz AE y f ( ) t (4) From contnty of dspacements: v v, v v, (5) For ongtdna dspacements: v (,,) y x (6) By sbstttng Eqaton nto Eqaton 6, sng Eqaton 5 and ntegratng by : (7) dv ( ) t( ) Q xzaey ( ) G d d y x t At E t xz AEy xz AEy ( ) G (8) For the ayer smary: Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

9 64 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts v ( ) ( ( ) ) td x dv Q xzaey ( ) t G d d y x t At E t xz AEy xz A E G y (9) s the dspacement of top srface of ayer (bonded srface). Usng Eqatons and 6: M (.5) x td () f xtd () d t ( ) ( ) x xz y AE y x d t ( ) ( ) x xz y AE y x (-a) (-b) By sbstttng Eqatons nto Eqatons and and sng Eqatons to 4: dv AE xt d 6 d xz AE y 5 G AE xtd M A E 5 5t G t y y xz AE y y dv AE xt d 6 d xz AE y 5 G AE xt d M A E 5 5t G t y y xz AE y y (-a) (-b) Smary to Eqatons -a and -b: Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

10 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts 65 d 4 tae x d t xz AEy t d f AEy 5 5 5G t d y 6xzAEy 6M AEy y G t tae x 5 d 4 tae x d t xz AEy t d f AEy 5 5 5G t t 6 6 AEx 5 d y xzaey M AEy y G t (4-a) (4-b) Dfferenta eqatons of transversa and ongtdna dspacement are assmed to be near n the drecton..5( ) ( ) (5-a) v.5( v v ) ( v v ) (5-b) Where v s transversa dspacement and s ongtdna dspacement n adhesve. Shear stress n the mdde ne of adhesve thckness m s obtaned by sbstttng Eqatons 5 n Eqaton 6 and dervaton: ( ) dv dv m ( ) G t (6) Negectng axa oad n adhesve ayer ( x ), peeng stress n the mdde ayer of adhesve m s derved n Eqaton 7. ( ) v E E ( v v ) m y y t (7) Dervaton of Eqatons 6 and 7, sbstttng Eqatons and 4 and sng 4-a and 4-b ead to emnaton of y and y. 6AE y tf ( D D) m ( 7D 8) m ( tt) M t 6 6AE y tf ( t t) M t 6 (8-a) Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

11 66 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts M AE M AE ( D D) ( D ) (8-b) y y 7 8 m 4 5 m t t Where D=d/ and (,,...,) s a smpfer coeffcent and s reated to geometrca and mechanca confgratons of the adhesve and adherends. Dervaton of Eqatons 8-a and 8-b and sbsttton of dervaton moment by sng Eqatons and 5 create nonhomogeneos dfferenta Eqatons 9-a and 9-b 6 t t Q AE ( D D ) ( D D) 4 y m 7 8 m t 6 t t Q A E y t y y 7 8 m 4 5 m t t M and force f (9-a) QAE QAE ( D D ) ( D D) (9-b) Dervaton of Eqatons 9-a and 9-b and sng Eqatons, and 4 to emnate dervaton dq of shear force create two ffth order near homogeneos dfferenta Eqatons. ( D D D) ( D D ) (4-a) 5 4 m ( D D D) ( D D ) (4-b) m Shear stress dstrbton and pee stress dstrbton can be fond by soton of Eqatons 4-a and 4-b. In ths type of jont ayer s nder tense oad and ayer sn t sbjected. Ths, For the free srfaces of adhesve n ts ends: Fgre shows edge oads n adhesve regon. For the bondary condtons of oads shown n fgre : m m m (4) m x (4) x M Q f, M M, Q Q, f F (4-a) x M M, Q Q, f F, M Q f (4-b) Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

12 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts 67 Fgre : A secton of adhesve and ts edge oads n the stffened jont. Sbstttng Eqatons 4-a and 4-b nto Eqatons 8-a, 8-b, 9-a and 9-b determnes the other essenta bondary condtons to sove Eqatons 4-a and 4-b. the edges oad can be determned by cacatng deformatons n dfferent parts of the jont. As the jont s symmetrc, a haf of t s shown n fgre 4. Fgre 4: Defectons n dfferent secton of stffened jont. w C cosh x C snh x (44-a) w C cosh x C snh x (44-b) 4 To determne the set of C coeffcents for bondary condtons s needed. x x : w (45-a) x L, x : w w (45-b) L, x : (45-c) x : (45-d) Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

13 68 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts As the jont symmetrc: M M D (46) * * x L. Snge Strap Jont Snge strap jont s conssted of three composte ayer wth orthotropc propertes. It can be ether symmetrc or asymmetrc n geometry and property. Fgre 5 shows a two-dmensona mode of a snge strap jont. Fgre 5: Snge strap jont confgraton. Anaytca soton of the jont s smar wth the soton of prevos jont and derved dfferenta Eqatons expressed n Eqatons 4-a and 4-b are vad here. Fgre 6 shows edge oads n three dfferent sectons. Set of Eqatons 47 expressed defecton fncton of adhesve and adherends. Fgre 6: defectons n dfferent secton of snge strap jont. Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

14 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts 69 M F D D ( w ) (47-a) M F D D w ( tt ) M F t w D D (47-b) (47-c) Genera soton of Eqatons 47-a to 47-c s derved n set of Eqaton 48. w C cosh x C snh x (48-a) w C cosh x C snh x ( t t ) (48-b) 4 w C cosh x C snh x (48-c) 5 6 To determne the set of C coeffcents sx bondary condtons s needed. x x : w (49-a) x L, x : w w (49-b), : L x (49-c) x, x : (49-d) x, x : w w (49-e) x (49-f) L : Fnay, determnaton of edge oads s done by sng Eqatons 5-a to 5-d M D (5-a) * x L M D (5-b) * x Q D (5-c) * x L Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

15 7 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts Q D (5-d) * x FINITE ELEMENT MODEL The fnte eement method was sed as the second method to verfy anaytca soton. A twodmensona mode was created by ANSYS. Eement PLANE 8 was chosen to mesh the geometry mode. Ths hgh order eght-node eement has two degrees of freedom at each node, (transaton n the noda x and y drectons). Externa tense oad (.6kN/mm) was apped to the rght edge of Layer and the eft edge of ths ayer was constraned both n x and y drectons. The adhesve ayer s Epoxy and adherends are made of amnm wth ther nomna mechanca propertes expressed by tabe. The geometry of jont s reported by tabe. Fgre 7 shows the meshed FEM mode. E(GPa) ν Adherends 69. Adhesve.5 Tabe : Mechanca propertes of the adherend and adhesve. Fgre 7: FEM mode of a stffened jont. t. t t Tabe : Geometry detas of the mode (mm). Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

16 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts 7 4 RESULTS AND DISCUSSION Derved anaytca eqatons showed that geometry, matera propertes and oad condton affect shear and pee stress dstrbton aong the jont ength. These effects are stded n ths part besde comparsons of soton methods empoyed n the artce. 4. Stffened Jont Peeng and shear stress n a stffened jont are shown n Fgre 8 and Fgre 9. Rests of nmerca and anaytca method for stress dstrbton can be compared n the Fgres. Fgre 8: Peeng stress m p dstrbton n overap regon of the stffened jont. m Fgre 9: Shear stress dstrbton n overap regon of the stffened jont. Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

17 7 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts Fgre 8 ndcates that peak peeng stress m p s at both ends of overap ength. Ths type of stress s n ts mnmm vae at the mdde pont of the jont where x.peak shear stress occrs at a pont near two ends of overap ength as Fgre 9 shows. Fgres and depct peeng stress dstrbton between the adhesve and ayer, y and the adhesve and ayer, y, respectvey. Comparng Fgre and reveas that peak peeng stress between ayer and adhesve s mch more than peak peeng stress between the adhesve ayer and ayer. Vaes of y and y are zero except ther severe gradent at % of both overap ength ends. Except for the end regons of overap ength, FEM rests shows good agreement wth anaytca rests. Smpfcatons de to the apped assmptons may have a roe n the ncompatbty of rests n the end regons. m Fgre : peeng stress dstrbton between the adhesve and ayer n the stffened jont. 4. Snge Strap Jont Fgre shows peeng stress dstrbton n the mdde of adhesve ayer of the snge strap jont. Pay attenton to the coordnate axs, where x. Fgre shows that the stress s near zero aong the vast ength of jont n the mdde of adhesve and ts peak s at the end of ower adherend by the centerne of jont. Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

18 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts 7 Shear stress dstrbton n the adhesve ayer (n ts mdde of thckness) aong the overap s depcted n Fgre. Fgre : peeng stress dstrbton between the adhesve and ayer n the stffened jont. Fgre : peeng stress dstrbton n the mdde of adhesve ayer n stffened jon. Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

19 74 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts Fgre : shear stress dstrbton n the mdde of adhesve ayer n stffened jon. Shear stress dstrbton n Fgre decares peak of shear stress s near the nterna edge of ayer. Its vae s abot zero n aong the 75% of overap ength. Shear stress at the eft edge of adhesve s abot % of the peak. Rests show that two methods of soton are n good agreement bt FEM s more conservatve n estmatng of maxmm stress. Fgres 4 and 5 depct peeng stress dstrbton between the adhesve and ayer, and the adhesve and ayer, y, respectvey. y Fgre 4: peeng stress dstrbton between pper adherend and adhesve. Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

20 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts 75 It s observed that peeng stress that s toerated by the jont between the pper adherend and adhesve s abot zero aong the overap except the mdde regon of jont at the nterna edges. In ths regon the peak stress s occrred. The stress fed shown n Fgre 5 has a smar shape to depcted fed of Fgre 4 bt t s cear that the peak peeng stress between the pper adherend and adhesve s greater. Peak peeng stress between the ower adherend and adhesve s abot 56% of ts correspondng vae for peeng stress between the pper adherend and adhesve. FEM method agreed anaytca soton. In edges some ncompatbty are observed and they are consdered to be the rest of stress concentraton. Fgre 5: peeng stress dstrbton between ower adherend and adhesve. 5 CONCLUSION A stffened and a snge strap jont were stded. The jonts were nder nform tense oad and the ayers behaved as near eastc. The anayss were two-dmensona and eastcty theory was sed to estabsh stress-stran and stran-dspacement reatons. Derved dfferenta eqatons were soved sng approprate bondary condtons for each jont desgn. In a stffened jont peeng stress between adhesve and the ower adherend was mch more than ts vae between the stffener and adhesve so the crtca component n ths jont desgn was ower adherend that toerated the externa oad. Peak of shear stress and peeng stress n adhesve occrred at abot the mdde of the snge strap jont near ts centerne. Vaes were neggbe n the other ponts aong the ength. Peeng stress between adhesve and adherends were greater than ts vae n the adhesve ayer n both of the jonts. FEM predcted a more conservatve answer for shear and peeng n the snge strap jont and was n a good agreement wth anaytca sotons for both of the jonts. Fnay Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76

21 76 B Ghoddos / Theoretca Anayss of Stress Dstrbton n Bonded Snge Strap and Stffened Jonts externa edges n the stffened jont and nterna edges n the snge strap jont were observed as crtca ocatons n desgns. References Chn, H. (999). Stress anayss of adhesvey-bonded snge-ap jonts, J. of Composte Strctre 47: Ghoddos, B., Shshesaz, M. (6). Investgaton on Vod Effect on Shear Stress Fed n Bonded Stepped-Lap Jont, J. of Latn Amercan Jorna of Sods and Strctres : -4. Karachaos, E.F., Adams, R.D., Da Sva, L.F.M. (). Strength of snge ap jonts wth artfca defects, J. of Adheson and adhesve 45: L, G., Svan, L.P. (999). Thrng RW. Nonnear fnte eement anayss of stress and stran dstrbtons across the adhesve thckness n composte snge-ap jonts, J. of Comp. Strct. 46: Lo, Q., Tong, L. (8). Anaytca sotons for adhesve composte jonts consderng arge defecton and transverse shear deformaton n adherends, J. of Internatona Jorna of Sods and Strctres 45: NASA-CR-5 NASA Langey contract report. Hart-Smth, L.J., (97). Adhesve-bonded snge-ap jonts. Ojavo, U., Ednoff, H.L. (978). Bond thckness effects pon stresses n snge-ap adhesve jonts, J. of Amercan Insttte of Aeronatcs and Astronatcs Jorna 6: 4-. Sawa, T., L, J., Nakano, K., Tanaka, J. (). A two-dmensona stress anayss of snge-ap adhesve jonts of dssmar adherends sbjected to tense oads, J. of Adheson Scence and Technoogy 4: Shahn, K., Taher, F. (9). Deformatons n adhesvey bonded jonts on eastc fondatons, J. of Composte Strctre 9: 4. Shshesaz, M., Bav, N. (). Shear stress dstrbton n adhesve ayers of a dobe-ap jont wth vod or bond separaton, J. of Adheson scence and technoogy: -9. Temz, S., Adn, H., S, I.Y. (5). Behavor of B-Adhesve n dobe-strap jont wth embedded patch sbjected to bendng, J. of Theoretca and Apped Mechancs 45: Vabe, M., Reddy, J. (6). Bondary eement anayss of adhesvey bonded jonts, J. of Adhes. 6: 44. Zhao, B., L, Z.H. (9). A two-dmensona approach of snge-ap adhesve bonded jonts, J. of Mechancs of Advanced Materas and Strctres 6: -59. Latn Amercan Jorna of Sods and Strctres 4 (7) 56-76