Stress State for Pipes Made of a Concrete and Fiber Glass when Change the Angle of the Reinforcing

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1 Intentionl Jounl of Science nd ngineeing Investigtions vol. issue 5 Apil 0 ISSN: Stess Stte fo Pipes de of Concete nd Fie lss when Chnge the Angle of the Reinfocing ymo Aed Alstt Sediq echnicl duction osul echnicl Institute osul Iq (tymoed@yhoo.com Astct- he pupose of this ppe ws to ovecome economic issue which is one of the mjo ies of the use of FRP in civil engineeing. he nlysis of the methods of definition of elstic chcteistics of septe lyes einfoced y high-module fies on the mco level is given. In the cse when the composite itself epesents set of lyes with diffeent diections of einfoce the technique of the given elstic chcteistics definition nd component of mtixes of igidity of ll lyes pcge s whole is offeed. Keywods- fie glss concete pipes stess stte composite mteils einfocing. I. INRODUCION Composite is defined s mechniclly seple comintion of two o moe component mteils diffeent t the molecul level mixed puposefully in ode to otin new mteil with optiml popeties diffeent thn the popeties of the components (definition sed on [ -. Composite mteils hve een used in constuction fo centuies. One of the fist ws the use of stw s einfocement in mud nd cly ics y the ncient gyptins [4. he comintion of einfocing steel nd concete hs een the sis fo nume of stuctul systems used fo constuction fo the lst centuy. he new clss of composite mteils gdully gining cceptnce fom civil enginees oth fo the ehilittion of existing stuctues nd fo the constuction of new fcilities e fie Reinfoced Polyme composites pimily developed fo the eospce nd defense stuctues. Fie Reinfoced Polyme composites e the comintion of polymeic es cting s mtices o indes with stong nd stiff fie ssemlies which ct s the einfocing phse [. he comintion of the mtix phse with einfocing phse poduces new mteil system nlogous to steel einfoced concete lthough the einfocing fctions vy considely (i.e. einfoced concete in genel ely contins moe thn 5% einfocement whees in FRP composites ccoding to vious souces [ - 5 einfocing volume fction nges fom 0-70%. Although the steel einfocement in concete stuctue is potected y concete ggessive envionmentl condition cn stimulte the contion of concete nd the fomtion of hydted feous oxide in steel esulting in splling of concete cove. he pimy cuse of deteiotion of concete pipe is the coosion of steel einfocement. Since FRP composite execises high coosion esistnce it cn e used to eplce steel einfocement in the foms of es fo flexul nd she einfocements nd tendons fo pestesg o post-tensioning. FRP e nd tendon cn te the fom of one dimensionl o multidimensionl shpe depending on type of ppliction. hee hve even een some ttempts to incopote wieless seng into infstuctue ug FRP einfocement. Howeve thee e sevel chllenges in ug FRP e nd tendon. One issue is the line elstic ehvio of FRP e when loded to filue. his mens tht concete element einfoced ug FRP e my not hve the sme ductile filue of steeleinfoced element. Its lowe modulus of elsticity lso leds to seviceility polems such s lge deflection nd lge cc widths [. he im of this ppe is to pesent FRP composites s the new mteil used fo the puposes of civil engineeing nd pepe the stte of the t in pipes stuctues ug FRP composites fo stuctul elements s the sustitution of tditionl mteils. II. HORICAL ASS OF CALCULAION OF LASIC CHARACRISICS OF ULILAYR ARIALS Fo othotopic mteil clculted ccoding to the elstic popeties of high-modulus steel lye hve the fom [6: ( ( 87

2 ( K v v ( ( ( ( ( v v ( ( ( ( v ( v ( ( ( ( ( ( ( ( K v ( ( ( ( ( v. v v ( v ( ( ( ( / / ( ( tix stiffness nd pliility K - n othotopic lye in the diection of symmety xes espectively. Whee the suscipt "в" efes to the einfocement (steel "м" efes to the inde (concete - the eltive volume content einfocement lye in the diection of xes ( nd ( (see Fig.. She modulus of the steel nd concete e detemined y the dependencies. ( ( V ( V Whee: в м ( - Poisson's tio coefficient of einfocement which chcteies the eltive volume content of steel cn e detemined y the fomul: ( d i ( 4h Whee: steel dimete ( h thicness of the einfoced lye i fequency of einfocement (к ( ( к d - detemined ug empiicl eltionships nd s typiclly ( к ( к chnges in the intevl ( he geomety of the einfoced lye is shown in (Fig... All quntities with index (K efes to the K- lye shell. lsticity eltionships fo n othotopic unidiectionl einfoced lye in its xis of symmety ting into ccount physicl nd technicl constnts ( - ( in mtix fom e s follows: (4 [ [ column mtix of stess nd stin lye in the diection of xes of symmety (Fig. Figue Unidiectionl steel einfocement scheme Solving two systems of equtions (4 with espect to stiffness ( we cn find the following eltions: (5 55 â. 55 Complince coefficients cn e witten y technicl constnts (: Intentionl Jounl of Science nd ngineeing Investigtions Volume Issue 5 Apil ISSN: Ppe ID: 5-6

3 55 If the thic-wlled element consists of unidiectionl einfoced lyes the xis of locl coodinte systems tht do not coincide with the xes of the glol coodinte system tht is fo exmple in coss-einfoced shells it is possile to vy the mteil popeties due to the ngle of einfocement shell xes ( Let - the ngle etween the xes of symmety lye ( ( nd the diections of coodinte lines т.е. cone einfocement. It is nown tht in the otted ( ( einfoced lye hs nisotopic popeties nd hs one plne of elstic symmety. hen ecoming fi tio of elsticity: ( (6 Whee ( tix of stiffness coefficients n of n nisotopic lye in the diection of the mjo coodinte lines [ [ Column mtix of stess nd stin lye in the diection of the mjo coodinte lines. tix coefficients e expessed though the coefficients of the mtix ( with dependencies: 4 4 cos cos cos 4 cos 4 cos cos cos cos 55 cos cos 6 cos 55 cos cos cos cos 6 6 cos cos cos Fo futhe pesenttion of the mteil system of equtions (6 (7 conveniently epesented s: ( (8 Whee in eqution (8 intoduced the following nottion: [ [ ( ( ( 54 ( 45 ( 55 ( ( [ [ ( ( ( ( 6 ( ( ( ( 6 ( ( ( ( ( 6 ( ( ( ( (9 In the cse whee the composite is set of n diffeent oiented lyes of unidiectionl mteil contined elstic chcteistics of the pcge lyes e the ovious with eltions: Whee (0 n h( h( h( / h eltive thicness of the -n lye. he elstic constnts of multilye stc in tension cn e otined y tnsfoming the system of equtions (0 to men Sustituting ( in the fist eqution of the system of equtions ( nd pe-expesg stin with ssistnce fom the emining (-x equtions ( it is esy to find the vlue : Intentionl Jounl of Science nd ngineeing Investigtions Volume Issue 5 Apil ISSN: Ppe ID: 5-6

4 det ( Whee mino element of the mtix. Similly thee e othe vlues of the constnts: det det - ( Young modulus det ( ( 55 (4 She modulus - (5 Poisson's tios. he emining thee vlues of Poisson's tio e ug the well-nown eltions ( i j. (6 j ji i Hee the fist index of the Poisson coefficient indicted diection of lod ppliction the second one demonstted diection of the ltel defomtion which ws induced y this foce. On the sis of the poposed lgoithm ug n pplied pcet of PC AHCAD 4 pogms we otined numeicl vlues of elstic chcteistics of the einfoced mteil. III. SRSSD SA OF ULI-LAYRD CYLINDRS UNDR ACION OF INRNAL PRSSUR. In [7 solution of polem of stess-defomed stte of n nisotopic cylindicl shell of finite length induced y n ction of intenl nd extenl hydosttic pessue fo the cse of stte without moment ws poposed to e solved simil to solution of Lme polem fo thic-wll isotopic cylinde. Unde n ction of only intenl pessue p expessions fo solution of lme polem fo thic-wll isotopic cylinde. Unde n ction of only intenl pessue P expessions fo noml pessue tngents fo cylindicl coodinte system (Fig. should e witten s: ( p ( (7 ( p ( (8 p ( ( g 45.( ( g (9 45 ( p g g ( 0 (0 Whee noml stesses espectively in the dil cicumfeentil nd longitudinl diections she stesses in the cicumfeentil nd dil diections inne nd oute dii of the cylinde coodinte of the cylinde ( i j... 6 coefficients complince mtix einfoced mteil nd tht e ssocited with coefficients stiffness mtices (0 eltions = (. = ( In ddition in (7 - (0 intoduces dditionl nottion: g 6 6 g 6 i j ( i j ( Dependences (7 to ( wee deived ting into ccount n ssumption tht n elstic symmety which ws pependicul to noml to middle cylinde sufce ws pesent in evey point of the cylinde. In this cse of nisotopy unde n ction of noml pessue the thicwll cylinde will not only chnge the cuvtue dii of tnsvesl coss-sections ut lso chnge the initil length nd e whiled. mploying fomuls (7 to ( to deive the vlues of mximl nd miniml stesses ting plce t points of the intenl nd extenl sufces of the consideed cylinde seems to e not complicted (. We should lie to note tht clculting the stessed stte of nisotopic cylindicl shells employing the fomuls (7 to ( theoeticl esult fo thin-wlled cylindes could e deived with pcticlly ssumed ccucy( / 0 8. In this cse the indicted dependences do not llow one to detemine chnges of the cylinde stessed stte induced y pesence of mteil inte-phse stuctue defects nd n influence of conditions of ends fixtion. 6 Intentionl Jounl of Science nd ngineeing Investigtions Volume Issue 5 Apil ISSN: Ppe ID: 5-6

5 AL COPARISON OF PROPRIS OF VARIOUS CONSRUCION ARIALS O FRP COPOSIS [5 Figue Design scheme of the pipe in cylindicl coodinte system IV. ARIALS PROPRIS A fie is mteil mde into long filment. Accoding to [5 gle fie usully hs dimete up to 5 um. igge dimetes genelly incese the poility of sufce defects. he spect tio of length nd dimete cn e nging fom thousnd to infinity in continuous fies. hey usully occupy 0-70% of the volume of the composite nd 50% of its weight. he min functions of fies e to cy the lod nd povide stiffness stength theml stility nd othe stuctul popeties to the FRP [. o pefom these functions the fies in FRP composite must hve high modulus of elsticity high ultimte stength low vition of stength mong fies high stility of thei stength duing hndling nd high unifomity of dimete nd sufce dimension mong fies. siclly the popeties of FRP einfoced composites depend on the popeties of its components thei volume tio the oienttion of the fies in the mtix nd popeties of the fie-mtix ond [8. he type of fies used s the einfocement is the sics fo clssifiction of FRP composites. hee e thee types of fies dominting civil engineeing industy: glss con nd mid fies. he tle elow pesents popeties of vious inds of fies. concet = 0 P υconcet = 0.4 nume of fie glss lyes. Popeties of glss mid nd con fies (le. Compison of popeties of vious constuction mteils to FRP composites (le.. V. RSULS AND DISSCION On the sis of the pesented clcultion models nd techniques which wee developed fo clcultion of such clss of polems the stessed stte of the concete nd steel cylinde which hd the intenl sufce dius 0 9 м ws studied. he shell ws ficted y eeling up glediected glss stip. As whole such cylindicl shell ws composed of gle-diected lyes. he eeling ngle of evey lye ws detemined ug code of mteil stuctue. otlly 0 vesions of the shell einfocing wee consideed (le.. NO. AL H SRUCUR OF H LAINA PIP. Code [ 0 0 /0 S [ 0 / 0 /0 / 0 /0 / 0 /0 / 0 /0 / 0 /0 S [ 0 / 45 /0 / 45 /0 / 45 /0 / 45 /0 / 45 /0 S 4 [ 0 / 60 /0 / 60 /0 / 60 /0 / 60 /0 / 60 /0 S 5 [ 0 / 75 /0 / 75 /0 / 75 /0 / 75 /0 /75 /0 S 6 [ 0 / 90 /0 / 90 /0 / 90 /0 / 90 /0 / 90 /0 S 7 [ 0 / ±0 /0 / ±45 /0 / ±60 /0 /0 S 8 [ 0 / ±0 /0 / 0 / ±60 /0 /0 S 9 [ 0 / ±45 /0 / 0 / ±90 /0 /0 S 0 [ 0 / 5 /0 / 0 /0 /45 /0 / 60 /0 / 75 /0 S AL PROPRIS OF LASS ARAID AND CARON FIRS [5 hicness lye is δ =.9 mm the othe chcteistics of the monolye components e con elie. Fo ny given stuctue of concete nd steel wee found physicl nd mechnicl chcteistics s composite mteil with one plne of elstic symmety (le 4. In this Cte coodinte system (Fig. is eplced y cylindicl (Fig.. Intentionl Jounl of Science nd ngineeing Investigtions Volume Issue 5 Apil ISSN: Ppe ID: 5-6

6 AL 4 H LASIC CONSANS OF FIR AND CONCR. Vlues of noml nd tngentil stesses t points of the intenl nd extenl cylinde sufce unde intenl pessue intensity q 40Pа e pesented in (le. 5 Anlysis of esults demonstted tht chnged code did not pcticlly influence the vlues of noml stesses in cicle diection. In this cse n essentil chnge of stess vlues of tnsvesl she nd noml xil stesses too plce. Studies which wee pefomed fo stessed stte of multi-lyeed shell hving [ 0 / ±45 /0 / 0 / ±90 /0 /0 S code when the lye thicness ws successively incesed till given vlue (Fig. 5 e of inteest. As whole the shell thicness ws detemined y n expession h. he vlue shown in Fig. 5 vlue of the shell intenl sufce did not chnge nd ws equl 0 9 м to. lstic constnts fo the pesented set of lyes did not depend on the shell thicness. AL 5 SRSS SA OF HICKNSS CYLINDR (H = 40 Figue Reltion etween stess Figue 4 Reltion etween stess nd thicness of the pipe nd thicness of the pipe Figue 5 Reltion etween stess nd thicness of the pipe We should lie to note tht the incesed shell thicness did not pcticlly chnge diffeence of noml stesses in the cicle diection t points of the intenl nd extenl sufces. So fo exmple if the shell thicness ws - h 40мм this diffeence ws 5P if it ws Intentionl Jounl of Science nd ngineeing Investigtions Volume Issue 5 Apil ISSN: Ppe ID: 5-6

7 - h 80мм the diffeence ws 45P. Anlying dependences of stesses on the shell thicness one could notice tht in nisotopic shells when /h>0 essentilly high stess vlues ose. Such stesses could e eson fo destuction of the inde in consideed einfoced mteil. In this cse conditions fo n idel contct etween the lyes which wee consideed in continuous-stuctue theoy of nisotopic pltes nd shells tuned out to e essentilly violted. VI. CONCLUSIONS he ppe poposed method fo detemining the elstic constnts of nisotopic mteil which consists of set of einfoced lyes. Reviewed ten vints of multilye nisotopic hollow cylindes with diffeent stuctue einfocement. Fo ech vint of einfocement to detemine the stess stte of the cylinde unde the ction of intenl pessue. It is shown tht with inceg thicness of the memne noml stess in diection θ (σθ incese ut noml stess in diection (σ deceses. VII. SUARY he nlysis of septe lyes einfoced y high-module fies on the mco level elstic popeties definition methods is offeed. In the cse when composite is set of lyes with diffeent e-enfocement diections methodology of detemintion the educed elstic popeties ove ll lyes in pcge in tote is offeed. he deflected mode of multilyeed hollow cylinde with the diffeent vints of eenfocement of its septe lyes unde intenl pessue is nlyed. RFRNC [ L. C. n Composites fo Constuction - Stuctul Design with FRP teils John Wiley & Sons Inc pp. -9 [ C. ut Use of Fie Reinfoced Polyme Composite in idge Stuctues sschusetts Institute of echnology 005. pp. 50 [. Kelle Use of Fie Reinfoced Polymes in idge Constuction IAS Stuctul ngineeing Documents No pp. 9- [4 R. Lope-Anido. Ni meging teils fo Civil Infstuctue. Stte of the At Ameicn Society of Civil nginees 000. pp. [5 H. Zoel osty ompoytowe 50. Juileusow Konfeencj Nuow KILiW PAN i KN PZI Kynic 004. p. 9 [6 S.. Veeshch Fo discete-stuctul theoy of multilye shells with stuctul defects / / ulletin of NU "KPI". Collection of scientific ppes. Specil Issue: Dynmics nd stength of mchines. - Khov: NU "KPI" S [7 S.. Lehnitsii he theoy of elsticity of n nisotopic ody. - oscow: Nu 977. pp. 46. [8.A. J studio de l plicilidd de mteiles compuestos l diseno de estuctus de contencion de ties y su inteccion con el teeno p su empleo en os de infestuctu vii - esis doctol Univesidd Politecnic de did..s. de Ingenieos de Cminos Cnles y Puetos Deptmento de Ingeniei y ofologi del eeno did 008. p. 46. Intentionl Jounl of Science nd ngineeing Investigtions Volume Issue 5 Apil ISSN: Ppe ID: 5-6