Mile Maksić. Faculty of Mechnical Engineering, University of Niš, YU
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1 FCT UNIVERSITTIS Seres: Mens utot Control nd Robots Vol N o 00 pp 79-8 STBILITY OF THE FREELY SUPPORTE RECTNGULR PLTE STRENGTHENE WITH THE TRNSVERZL PROPPING IN THE PLSTIC RNGE UC 56:597:607/0705 Mle Msć Fult o Menl Engneerng Unverst o Nš YU bstrt Retngulr plte s loded b unorl dstrbuted ores o pressure n te d-sure It s reel supported on ll our sdes nd strengtened t one rbtrrl set trnsversl proppng Stblt o te plte s onsdered under te ssupton tt under even dstrbuton o pressure N v t bules n te dreton O nto snusodl l-ves In ts oposton requen equton s deterned or rel roots o te rerst derentl plte equton INTROUCTION ordng to te sll plsto-elst deorton teor reltvel to so lled "deorton teor" derentl equton o d-sure o retngulr plte n te plst rnge non n te lterture s Stoells equton s or 0 τ τ In ppers [5] [6] nd [7] probles o stblt o unstrengtened retngulr plte loded b unorl dstrbuted ores o pressure or derent ltng ondtons ere solved Supposed solutons stsed gven derentl equton n spled ors nd gven ltng ondtons Stblt o te retngulr plte reel supported on ll our sdes strengtened t one rbtrrl set trnsverzl proppng loded b unorl dstrbuted ores o pressure n te d-sure ll be onsdered n ts pper Reeved ugust 000
2 80 M MSIĆ PROPOSITION N SOLUTION OF THE PROBLEM Retngulr plte strengtened t one rbtrrl set trnsverzl proppng s presented n pture It s loded b ores o pressure N n O dreton ept bove entoned lodng plte s lso eted b pressure ro proppng s l oent o nert Proppng dvdes plte nto rnges nd e or tsel presents unstrengtened plte erentl equton under ondtons o proppng gven n pture : τ 0 N redues to net spler or 0 Soluton o ts derentl equton ll be sered or n or sn b t s supposed tt under eet o unorl dstrbuted pressure N plte bules n dreton nto snusodl l-ves Plte bulng n dreton s dened b untons ll be deterned lter Supposed deleton unton stses ltng ondtons on unloded sdes 0 nd on deletons nd oents re equl to zero Needed dervtves o deleton unton re: sn sn " sn " sn IV 5 B replng dervtves 5 nto derentl equton e get to oogenous lner derentl equton 0 " IV 6 Crterst equton o derentl equton 6 s 0 7 I e ntte r Fg
3 Stblt o te Freel Supported Retngulr Plte Strengtened t te Trnsverzl Proppng 8 8 roots o equton 7 n be rtten n te or ± ± 9 Here e ntte oeent o proportonlt to rtl ore o bulng N r 0 Roots o te rterst equton re rel ullled ondtons 0 0 nd te n be rtten s ± ± ± ± Solutons o derentl equton or rnges nd re s s s s b Roots re gnr ullled ondtons 0 0 so te n be rtten s ± ± 5 ± ± 6 Solutons o derentl equton or rnges nd re
4 8 M MSIĆ F B os B sn B os B sn 7 F B5 os B6 sn B7 os B8 sn 8 Roots re ople ullled ondtons < 0 0 nd te enrle sort ntervl o prtl probles Ltng ondtons on loded sdes 0 b re su tt deletons nd oents re equl to zero tt s or 0 0 n oter ords " ν 0 n oter ords or b 0 n oter ords b 0 ν 0 n oter ords " b 0 On te boundr o rnges nd o te plte strengtened t one trnsverzl proppng deletons nlntons nd bendng oents or rnges nd re equl t rbtrr dstne : η η η η " " η η 5 Lst egt equton or deternng 8 ntegrton onstnts s obtned ro ondton tt te derene beteen trnsverzl ores or rnges nd long te proppng represents te lodng b proppng tes eet on plte III III η η φ η 0 6 ere r represents te net ter φ Er I r 7 ere E r s Youngs odulus o elstt o proppng I r l oent o nert o trnsverse seton o proppng Fro te ondtons 9 e ve strengtened plte requent equton or te se o rel roots tt s se s η s η φ sηη sηη 0 tb tη For proppng postons! b/ b/ b/ ro 8 e get vlues 8
5 Stblt o te Freel Supported Retngulr Plte Strengtened t te Trnsverzl Proppng 8 b φ 9 b b t t b φ 0 b b b b t t t t b φ b b b b t t t t We n slrl get requent equton n se b en roots o rterst equton re gnr CONCLUSION ervted requent equton or rel roots o te rterst equton o bs derentl equton t deterned ters 9 long t usng te results o solutons or unstrengtened plte dependene o rtl ore o bulng ro relton o sdes b/ ould be deterned REFERENCES Z Stoell Uned Teor o plst Bulng o Coluns nd Pltes Report No 898 Ntonl dvsor Cottee or eronuts l97 V Joj Te Bulng o Renored Retngulr Plte I SP - Vol No0-l957 Joj J Nnov Stblt o pltes n te plst rnge Srjevo l980 S Voljr Stblt o sold sstes Mosv l967 5 MMs Use o ouble Trgonoetrl Seres t Solvng Proble o Stblt o Retngulr Plte n te Plst Rnge "IM-" Reser nd evelopent No rusev l995 6 MMs Use o Sngle Seres t Solvng Proble o Stblt o Retngulr Plte n te Plst Rnge Colleton o Ppers o Fult o Menl Engneerng n Ns Ns MMs Inluene o ltng ondtons on stblt o sure bes loded b ores o pressure n sll plsto-elst deorton rnge Tenque-Menl Engneerng STBILNOST SLOBONO OSLONJENE PRVOUGONE PLOČE OJČNE POPREČNIM URUĆENJEM U PLSTIČNOJ OBLSTI Mle Msć Prvougon ploč je opterećen rvnoerno rspoređen sl prts u srednjoj površn Slobodno je oslonjen n sve četr strne ojčn jedn prozvoljno postvljen poprečn urućenje Rztr se stblnost ploče pod pretpostvo d se pod dejstvo
6 8 M MSIĆ rvnoerno rspoređenog prts N zvj u prvu O u snusodln polutls U ovo rdu se određuje reventn jednčn z relne orene rterstčne derenjlne jednčne ploče
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Proble (0 ponts): The plstc block shon s bonded to rgd support nd to vertcl plte to hch 0 kp lod P s ppled. Knong tht for the plstc used G = 50 ks, deterne the deflecton of the plte. Gven: G 50 ks, P 0
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