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д! 20 M, M, Ep M s ^ M | ^ - M ; .220 Yechish
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д! 20 M, M, Ep M s ^ M | ^ - M ; .220 Yechish. В ta y a n c h in i ta s h la b , o ‘ r n ig a n o m a ’ lu m m o m e n t M B n i q o ‘ ya m iz. U n in g q iy m a tin i v a ld a g i b u ra lis h b u rc h a k la ri y ig ‘ in d is i n o lg a teng- lig i sh a rtid a n to p a m iz : M , a M 2( a + 6 ) + М в ( а + й + с ) G JP G JP G JP B u te n g la m a d a n M B= 2 2 0 M m t o p ila d i. A ta y a n c h d a g i m o m e n t M A= 4 0 0 + 2 2 0 -6 0 0 = 2 0 N m boMadi. B u ro v c h i m o m e n tla r epyu ra sin i k o ‘ ra m iz va undan e n g katta b u ro v c h i m o m e n t M ma,= 3 8 0 N *m n i a n iq la y m iz . V a ln in g d ia m e trin i m u s ta h k a m lik sh a rti b o ‘ y ic h a a n iq la y m iz : Шт % аш \ я[т] V Л--40 B ik r lik sharti b o ‘ y ic h a : - J - 32 ™ . - 5 . 7 5 » \ n G [ ( p \ V ^ - 8 - 1 0 4 - 0 ,2 5 ° D ia m e tm in g k a tta s i q a b u l q ilin a d i. 6.3. Kesim i doiraviy bo‘lmagan sterjenlarning buralishi M u h a n d is lik a m a liy o tid a k e s im i d o ira v iy emas, b a lk i to ‘ g ‘ ri to ‘ rtb u rc h a k , uchburchak, e llip s va boshqa s h a k lli k e s im la r k o ‘ p u ch ra yd i. B u n d a y no - d o ira v iy k e s im li s te rje n la r a y n iq sa s a m o ly o ts o z lik d a keng ta rq a lg a n . T a d - q iq o tla rn in g k o 'rs a tis h ic h a bu x ild a g i s te rje n la rg a yassi k e s im la r g ip o te z a - sin i qoMlab b o M m a yd i, c h u n k i ste rje n b u ra lg a n d a u n in g k e s im i q iy s h a y a d i, na tija da k u c h la n is h la rn in g ta rq a lis h q o n u n i m u ra k k a b tus o la d i. Shu sababli ke sim i d o ira v iy boMm agan s te rje n la rn in g a n iq h is o b in i e la s tik lik n a za riya - sin in g u s u lla ri asosida bajarish m u m k in , xo lo s. B u x ild a g i m a sa la la m i dastav- v a l S e n -V e n a n y e c h g a n e d i. B ir o q m a z k u r k u r s im iz d a b u h a q d a g i m a’ lu m o tla rn i toMa ta v s if e tish im k o n i b o M m a g a n lig i sababli, bu ye rd a faqat amalda q o M la n ila d ig a n fo rm u la la m i is b o ts iz bayon etish b ila n ch e kla n a m iz. M . U rin m a k u c h la n is h la rn in g eng k a tta q iy m a ti r mm = — - ; (6 .1 1 ) Wk M J toM iq b u ra lis h b u rc h a g i ------- ; (6 .1 2 ) <3Jk M - n is b iy b u ra lis h burch a g i 9 = — — (6 .1 3 ) G Jk fo rm u la la r o rq a li a n iq la n is h i q a b u l q ilin g a n . Н ТП Ттк A w С В h B u ye rd a Jk v a W k - s h a rtli ra v is h d a b u ra lis h d a g i in e rs iy a m o m e n ti va b u ra lis h d a g i q a rs h ilik m o m e n ti deb a ta la d i, oMcham b ir lik la r i a w a lg ic h a sm4 va sm 3. A m a liy o t d a k e n g ta r q a lg a n t o ‘ g ‘ r i Tmax t o ‘ r tb u r c h a k k e s im li s te r je n n in g b u r a lis h in i o 'rg a n a m iz . B u n d a y ke sim la rd a u rin m a k u c h la n is h la rn in g ta rq a lis h q o n u n i 6 .8 -ra s m d a k e l tirilg a n . R asm da ta s v irla n is h ig a k o ‘ ra k e s im n in g s irtid a g i m a ksim a l k u c h la n is h la r С v a D nu - q ta la rid a v u ju d g a k e la d i. A va В n u q ta la rd a g i k u c h la n is h la r ancha k ic h ik b o ‘ lib , r = v r max fo r- 6.8-rasm. m u la d a n a n iq la n a d i. M a k s im a l ku c h la n is h t max esa 6.11 fo rm u la dan a n iq la n a d i. B u y e rd a g i q a rs h ilik m o m e n ti q u y id a g i fo rm u la d a n to p ila d i: W k= ahb2. B u ra lis h d a g i in e rs iy a m o m e n ti Jt= b h b 3. B u n d a h - t o ‘ g ‘ r i t o ‘ rtb u rc h a k n in g k a tta to m o n i; b - to ‘ g ‘ ri t o ‘ rtb u rc h a k n in g k ic h ik to m o n i a , P, V- k o e ffits ie n tla r h i в nisbatga bogMiq holda 6.1-jadvaldan o lin a d i. T o ‘g ‘ ri t o ‘ rtb u rc h a k li ke s im uchun m u s ta h k a m lik va b ik r lik s h a rtla ri: r _ = — ^ < [ r ] ; (6 .1 4 ) в = _ ±r±6 a h e 2 ЪЛ p h e 3G (6 .1 5 ) B u ra la y o tg a n s te rje n n in g k o ‘ n d a lan g k e s im i teng y o n li tra p e ts iy a shak- lid a b o ‘ lsa, h is o b la s h ja ra y o n id a uni e k v iv a le n t boMgan t o ‘g ‘ r i t o ‘ rtb u rc h a k b ila n a lm a s h tirila d i (6 .9 -ra s m ). B u n in g u c h u n tra p e ts iy a n in g o g M rlik m a rka zi С dan u n in g y o n to m o n la rig a C B v a C D p e rp e n d ik u la rla ri tu s h iri- la d i. В v a D n u q ta la rid a n v e r t ik a l c h iz iq la r o 'tk a z ila d i. H o s il boM gan abed t o ‘ rtb u rc h a g i iz la n g a n e k v iv a le n t (te n g k u c h li) t o ‘ r tb u rc h a k d ir . S hu t o ‘ rtb u rc h a k d a n fo y d a la n ib te n g y o n li tra p e t- siyada h o s il boM adigan eng k a tta u rin m a k u c h la n is h v a b u ra lis h b u rc h a g in in g ta q r ib iy q iy m a t la r in i a n iq la sh m u m k in . K o ‘ ndalang k e sim i e llip s shakliga ega boMgan sterjen buralganda undagi m aksim al u rin m a k u c h la n is h la r k ic h ik y a rim o ‘ q !a r b ila n e llip s n in g ke- sishgan nuqtasida h o s il boMadi (6 .1 0 -ra sm ). 6.9-rasm. Buralishdagi qarshilik momenti Wk, sm3 Eng kalta urinma kuchlanish hosil bo’lgan nuqtalar h b a P У 1 0,20S 0,141 1 1,5 0,231 0,196 0,859 1,75 0.239 0,214 - 2,0 0,246 0,229 0,795 2,5 0,256 0,249 - 3,0 0,267 0,263 0,753 4,0 0,2X2 0,2X1 0,745 6,0 0,292 0,299 0,743 8,0 0,307 0,307 0,743 10,0 0,313 0,313 0,743 00 0,333 0,333 0,743 Jk= phb3 Wk = a lib2 Uzun tomonlur o'rfasi; M. ; ,K Kalta tomonlar o'rtasi т — У Tm.i\ ■ Burchaklarda kuchlanish nolga teng. Fra w Щ ■к=- h<% + f>& - 6>r - Wk|-2 h o b ()6| Wk 2 = 2 h(i bn 8 2 Uzun (omonning • Мл о rtasi r. = —- ; W " 1 1 Kalta lomonning о rtasi r, = —- - IK., Ichki burchaklarda, materialning oquvchanlik chegarasiga yaqin miqdorda, kuchlanishlarning yuqori darajadagi kontsentratsiyasi yuz beradi. Burchaklar r radiusii yoyga ega bo'lsa, konlsenlnitsiya koeffitsienti a , = 1.74? bo'ladi ‘ 64 ' I W = irb 'h 1 б ~ Kichik yarim o'qlarning tashqi nuqtalarida M,; . r“ " wt ' Katta yarim o'qlarning lashqi т, = m nuqtalarida _ ™ > ;(i-g 4) 1 16(»r + l) _ xbl ~ 16 * x( 1 - a-4 )m Kichik yarim o‘qning uchida _M , . T""x IV, ' Katta yarim o'qning uchida r _ Гшк1- Қ Л! I — = —m> 1 Л, Aj К — = —= £Г < ) ^ 6, Jt = — — Г 2.6——: 1 1б1 d 1У = — X * 8 2 ,6--1 - > 0,5 ь d/D a P d/D a P 0,00 1.57 1,57 0,40 0,76 1,22 0,05 0,80 1,56 0,60 0,66 0.92 0,10 0,81 1,56 0,80 0,52 0,63 0,20 0,82 1,46 1,00 0,38 0,38 Wt — a —— * 16 0 ‘yiqning tubida г = —*■ W. K a tta y a rim o ‘ q b o ‘ y ic h a k e s im d a g i e n g k a tta u rin m a k u c h la n is h = boM adi; bu ye rd a m = h h . m D o ira v iy boMm agan ba’ zi k e s im la r uchun Jk va W k n in g b a ’ z i q iy m a t la ri 8 -ja d v a ld a k e ltirilg a n . A g a r b u ra la y o tg a n s te rje n n in g k o 'n d a la n g k e s im i m u ra k k a b s h a k lli boMsa, u n i o d d iy s h a k lla rg a a jra tila d i, bunda m u ra k k a b s h a k lli k e s im n in g in e rs iy a m o m e n ti Jk o d d iy s h a k lli k e s im la r in e r s iy a m o m e n tla r in in g y ig 'in d is ig a te n g boM adi: Jk = Jkl+ Зк2+ --- J| o d d iy k e s im la rn in g ra q a m la ri. B u rilis h b u rch a g i y a x lit kesim va u n in g o d d iy k e s im la ri u ch u n b ir x il _ м ье _ м Ь1е _ _ M hne b o M g a n lig i sa b a b li ^ ~ q j ~ q j ~ ~ GJ b u ro v c h i m o m e n t o d d iy k e s im la rg a u la m in g b ik rlik la r ig a p ro p o rs io n a l ra v is h d a ta q s im la n a d i: М „ = М „ 4 ^ M „ = M 4 ^ - : M „ = м / * '* •'к •'к K e s im n in g h a r b ir k is m id a g i eng katta u rin m a k u c h la n is h M h, M, ( w. V J к J . 4 Л r J л J ki w V ki \ n in g eng katta q iy m a ti Jki / W ki m a k s im u m boMgan e le m e n td a h o s il boM adi: M , w k (6 .1 6 ) bu yerda w К VVh у (6 .1 7 ) 6.5-misol. Ko'ndalang kesim yuzasi to ‘g'ri to'rtburchak bo'lgan p o 'la t sterjenga Mh = 1000 N m burovchi moment t a ’sir etadi. Buralishga ruxsat etilgan kuchlanish [t]=40MPa, tomonlari nisbati h/v=2,5 bo'Isa, ko'ndalang kesim о ‘Ichamlari topilsin. _ M„ r 1 Yechish. M u s ta h k a m lik sharti r max ~ цг dan s te rje n n in g b u ra lis h d a g i q a rs h ilik m o m e n tin i a n iq la y m iz : M 4 0 8 -ja d v a ld a n ЫЬ=2,5 ga m os k e lu v c h i a = 0 ,2 5 6 n i ta n la y m iz . K o ‘ nda lan g kesim o M c h a m la ri q u y id a g i fo rm u la d a n to p ila d i: W k= ahb2 = 2 ,5 ab 25 sm = 3,38sm; h = 2 ,5 6 = 2 .5 3 ,3 8 = 8 ,4 5 sm . 6.6-misoL Uzunligi 5m, ko'ndalang kesimi 6.11-rasm, a da ka'rsatilgan po 'lat sterjenning ikki uchiga Mh =500 N m burovchi moment ta ’sir etadi. Po 'lat sterjenda vujudga keladigan eng katta urinma kuchlanish va bura lish burchagi aniqlansin. Yechish. E n g a w a l m u ra k k a b s h a k ln i o d d iy e le m e n tla rg a a jra ta m iz (6 .1 1 -ra s m , b ), s o 'n g ra h a r q a ysi e le m e n tn in g g e o m e trik ta v s ifla r in i a n i q la y m iz : •Л = Jk\ + •Л-з + ^кЪ B ir in c h i e le m e n tn in g o M ch a m la ri h ,= 4 5 m m ; b t= 3 5 ; h,/Z > ,= l,2 8 5 ; Jk,= p 95 4 6 .1 1-rasm. h , / i , 3. 6 .1 -ja d v a ld a n h , / t , = 1,285 boMgan nisbat u c h u n a ,= 0 ,2 2 1 ; p ,= 0 ,1 7 2 . U h o ld a Wn = a , h t f = 0 ,2 2 1 • 4 ,5 • 3 ,5 2 = 12, I s m 2; J tl = P fab] = 0 , 1 7 2 - 4 , 5 - 3 , 53 = 3 3 ,2 sm*; ^ * L = 1 M sm = 2,12sm . Wt, 1 2 ,2 S hu y o ‘ sinda oM cham lari h2= 8 0 m m ; 6 2= l0 m m ; h ,/6 ,= 8 boMgan ik k in c h i ele m e n t uchun q u y id a g ila rn i a n iq la y m iz : Wk 2 = а ,Қ Ь 1 = 0 , 3 0 7 - 8 - 12 = 2 , 5 s m 3; J k2 = PjhJ>l = 0 ,3 0 7 • 8 • 1:2 = 2 ,5 s in * ; ^ = 1 sm Wк 2 S terjen k o 'n d a la n g k e s im in in g 3 -q is m i oM cham lari h 3= 9 5 m m ; Z>j=20mm; h 3 9 5 — = 4 ,7 5 - B u la rg a mos g e o m e trik ta v s ifla r: Wk 3 = a,h 3b; = 0 ,2 8 8 • 9 ,5 • 2 2 = 10,9 sm 3; J „ = P A hl = 0 , 2 8 8 -9 ,5 - 2 3 = 2 1 , 9sm 4; i = ^ = 2 sn,. Wk, 10,9 S hunday q ilib , J k = J k] + J k2 + J k3 = 3 3 , 2 + 2 ,5 + 2 1 ,9 s m4 = 5 7 , 6 s m 4 E ng ka tta n isb a t Jki / W ki b irin c h i elem e n tg a t o ‘ g ‘ ri k e ly a p ti, shuning u ch u n eng katta u rin m a k u ch la n ish x shu ele m e n t katta to m o n in in g o 'rta s id a h o s il boM adi: Wk = - Jk = = 2 1 , 2 s n f ; J J W kx 2 ,7 2 M„ 5 0 0 - IO"6 r = ----- ----------------- — = 2 3 , 6 M P a : 1 Wh 2 1 ,2 -1 0 г к S te rje n n in g b u ra lish burchagi М. Л 5 0 0 -1 0 -5 a = ------- = -------- - ----------------- - = 0 ,0 5 4 2 rad 6.4. Buralishga hisoblashda o‘rgatuvchi kompyuter texnologiyasi { M } = GIp / \ M a z k u r p a ra g ra f buralishga is h la yd ig a n e le m e n tla m i S h E H M y o rd a m i da hisoblashga bag‘ ishlangan. Chap u ch i m ahkam langan va k o 'n d a la n g k e s im i d o ira v iy b o 'lg a n ster je n n in g boshqa u ch ig a m o m e n ti M ga teng b o 'lg a n j u f t k u c h q o 'y ilg a n . B u ju f t kuch s te rje n n in g k o 'n d a la n g kesim yuzasida y o ta d i ( 6 . 12-rasm ). M a z k u r j u f t k u c h ta ’ s irid a ste rje n n in g e rk in k o 'n d a la n g ke s im i m ahkam langan kesim ga nisbatan a yla n ib , sterjen d e fo rm a tsiya la n a d i. S te rje n n i b u ra lis h g a h is o b la s h d a b i k r li k m a trits a s i tu z ila d i. B u n d a c h o 'z ilis h d a g i k o 'c h is h o 'm ig a buralish burchagi aniq la n a d i, e la s tik lik m o d u li va k o 'n d a la n g kesim yuzasi esa mos ravishda s iljis h m o d u li v a q u tb in e rs i y a m o m e n tla ri b ila n a lm a s h tirila d i: ' 1 - 1 - 1 1 _ S te ije n la m in g bura lish in i hisoblash uchun m azkur dastur tuzilgan. D astlab k i m a ’ lu m o tla m i E H M g a k iritis h ta rtib i va hisob n a tija la ri q u yid a k e ltirilg a n . D a s tla b k i m a ’ lu m o tla m i k ir itin g (n is b iy q iy m a tla r) A k e s im id a g i m o m e n t = -3 ,0 0 N .m В k e s im id a g i m o m e n t = - 2 ,0 0 N .m С k e s im id a g i m o m e n t = 1,00 N .m 1 -o ra liq u z u n lig i = 1,00 m 2 -o ra liq u z u n lig i = 1,00 m 3 -o ra liq u z u n lig i = 2,00 m M n in g q iy m a ti (N ) = 5000.00 N m R uxsat e tilg a n k u c h la n is h (M P a ) = 70,00 M P a Q ayta к о 'r ib c h iq is h ke ra km i? U /N 1 -o ra liq 2 -o ra liq 3 -o ra liq “ + + A В 4 С к 1.0 1,1.0 I. 2 .0 [ 6 .12-rasm. N a tija la r . Y u q o rid a k o 'rs a tilg a n k iris h a x b o ro tin i ta yyo rla g a n d a n s o 'n g m ashina a v to m a tik ravishda ko n stru ksiya n i hisoblaydi va ekranga q u y id a g i k o 'rin is h d a n a tija la r c h iq a zad i. 1 -o ra liq 2 -o ra liq 3 -o ra liq + + A В I 10 L 1.0 I. 2.0 B u ro v ch i m om en tlar epyurasi 1.00 -4 .0 0 K o ‘ chishlar -5.00 B u n d a n k o ‘ rin a d ik i, dastur v a d a s tla b k i m a ’ lu m o tla r ta y y o r boMsa, z a ru r boMgan h is o b n a ti- ja la rin i o lis h q iy in emas ekan. X u lo s a . Shunday q ilib , m a z k u r bobda b u ra lis h d e fo rm a tsiya si h o la ti b ila n ta n is h ib c h iq ild i. B u ra - la yo tg a n sterjenlarda v u ju d g a ke la d ig a n u r in m a k u c h la n is h la r va b u ra lis h b u rc h a k la rin i a n iq la y d ig a n fo r m u la la r b e r ild i. B u ra lis h d a g i m u s ta h k a m lik va b ik r lik s h a rtla ri b a y o n e tild i. F o r m u la la m i qoM - lashga d o ir m is o lla r va k o m p y u te r te x n o lo g iy a s i k e ltir ild i. B ilim in g n i s in a b k o ‘ r 1. B u ralish d efo rm a tsiy a si qanday y u z beradi? 2 . V a l d eb n im ani aytilad i? 3. B u ralish d agi g ip otezalar. 4 . B u ralish bu rchagi n im a v a u qanday top ilad i? 5. Q utb in ersiy a m o m en ti n im a va u n in g oMcham b irligi qanday? 6 . E n g katta k u ch la n ish v a ln in g q aysi n uqtasid a h o sil boMadi? 7. V a ln in g k o 'n d a la n g k esim i b o 'y ich a urinma kuchlanish qanday taqsim lanadi? 8 . D o ira v a h alq a u ch u n qarsh ilik m om en tlari qanday form ulalar yordam ida top ilad i? 9 . B u ralish d agi m u stah k am lik sharti qanday form u la b ilan ifodalanad i? 10. T o ‘g ‘ri t o ‘rtburchak k e sim li vallarn in g qanday nuqtalarida m aksim al urin m a k u ch la n ish h o s il boMadi? 1 1. M urakkab sh ak lli k esim lard a m aksim al urinm a k u ch lan ish qanday top ilad i? 12. M urakkab sh ak llard a bu ralish burchagi qanday top ilad i? 13. S h E H M da b u ra lish g a h iso b la sh jarayoni qanday operatsiyalardan tashkil topad i? 14. E H M natijalarni q an day k o ‘rin ishda beradi? v n B O B . E G I L I S H Mavzu mazmuni. Ushbu bobda egilishga ishlaydigan elementlaming kuchlanish - deformatsiya holatlari tahlil etiladi. Eguvchi moment va qir- quvchi kuchlanishlami, normal va urinma kuchlanishlami aniqlash usullari bayon etiladi. Formulalami qo ‘llashga doir misollar keltiriladi. 7.1. Egilishga oid tushunchalar A g a r to ‘ g ‘ r i o ‘ q li sterjenga, u n in g o ‘ qid a n o ‘ tu v c h i te k is lik d a y o tu v c h i ju ft ku ch y o k i k u c h la r sistem asi q o ‘ yils a , sterjen e g ila d i. E g ilis h g a is h la y digan s te rje n la r balka deb ataladi. 7 .1 -rasm da ba lka ga ta ’ s ir e tu v c h i k u c h la r sistem asi ta s v irla n g a n ; bu k u c h la r b a lk a n in g s im m e triy a te k is lig id a y o ta d i. A g a r k u c h la r sistem asi s im m e triya te k is lig id a yotm asa, u h o ld a ba lka e g ilish d a n tashqari q iy s h a y a - di ham. 7.1-rasm. H iso b la sh ta rx la rid a (s x e m a la rid a ) im o ra t y o p m a la ri ham , to ‘ s in la r ham , v a g o n la m in g o ‘ q la ri ham , s a m o ly o t q a n o tla ri ham ba lka deb q a b u l q ilin a d i (qar.1.3), (sh u n in g uch u n b a lk a n i - to 's in deb o ‘ g irib boM m aydi). S hunday balkalardan b ir i 7.2-rasm da ta svirla n g a n . B a lkaga y o y iq q (N /m ), y ig ‘ iq F (N ) va j u f t ku ch M (N -m ) q o 'y ilg a n . B u k u c h la r ta ’ s irid a b a lk a e g ila d i, y a ’ n i egilish deformatsiyasi s o d ir boMadi. A ta y a n c h i s h a m irli-q o ‘ z g ‘ almas ta ya n ch deb a ta lib , unda ik k it a reak- s iya k u c h la ri Қ , v a H a paydo bo M ish in i ilg a ri (1 .3 .) k o ‘ rib o ‘ tg a n e d ik . В ta y a n c h i s h a m irli - q o ‘ zg ‘ a lu v c h i tayanch deb a ta lib , unda b irg in a re a ksiya k u c h i R ft h o s il boM adi. S h a m irsiz q is tirm a ta y a n c h la rd a esa u c h ta re a ksiya k u c h i R * H a, M a paydo boMadi (7.3 -ra sm ) T e k is y o y iq k u c h la r intensivlik, y a ’ ni b a lk a n in g u z u n lik b ir lig ig a tc /g ‘ ri k e lg a n m iq d o r q b ila n oMchanadi va N /m b ila n ifo d a la n a d i. N o te k is y o y iq k u c h la m in g in te n s iv lig i b a lka n in g u z u n lig i b o 'y la b o ‘ zgaradi v a q x b ila n b e lg ila n a d i. M a ’ lu m k i, b iro r ko n stru ksiya n i hisoblashdan ilg a ri u n in g h iso b la sh ta rh i ta n la n a d i. H is o b n a tija la ri toM aligicha ana shu ta rh n i qanday ta n la n ish ig a bogM iq. A y n iq s a tayanch x illa rin i to ‘ g ‘ ri b e lg ila n is h i m u h im aham iyatga ega. O datda b a lk a la r kam deform atsiyalanadi, undagi k u c h la n is h la r ham elas t ik lik chegarasida boMadi. A y ta y lik , m etall y o k i y o g ‘ och to ‘ s fn n in g u c h i gMsht d e v o rg a b ir o z k ir itilg a n boMsin. T a ya n ch y u za si k ic h ik boM g a n i sababli t o ‘ s in n in g u c h i o zg in a m iq d o rd a ogMshi m u m k in . S h u n in g o ‘ z i ta ya n ch n i s h a m irli deb qabul qilish g a asos boMadi. A g a r to ‘ sin d evor orasi- ga k o ‘ proq k ir it ilib , beton va arm atura yo rd a m id a m ahkam lansa, ^ b unday ta y a n c h n i s h a m irli deb boM m aydi, albatta, uni sh a m irsiz q is tirm a tayanch deb qabul q ilin sa , t o ‘g ‘ riro q boMadi. ф —о S ta tik a n iq b a lk a la rn in g ta y a n c h re a k s iy a la rin i a n iq la s h u c h u n s ta tik a n in g u ch ta m uvozanat te n g la m a la rid a n fo y d a la n - a m iz . B u n d a X o ‘ q i - b a lk a n in g o ‘ q i b o ‘ y la b , Y o ‘ q i esa - tik y u q o rig a y o ‘ n a ltir ilib , k o o rd in a t boshi b iro r ta ya n ch s h a rn iri- n in g m a rk a z id a o lin a d i. A w a l g o riz o n ta l reaksiya k u c h i a n iq la n a d i. B u n in g uchun l x = 0 te n g la m a s id a n fo y d a la n ila d i. V e rtik a l re a k s iy a k u c h la ri v a ta y a n c h m o m e n ti lm = 0 va £ y = 0 te n g la m a la rid a n to p ila d i. M o m e n t n u q ta s i s ifa tid a b iro rta ta ya n ch s h a m irin in g m a rka zi q a b u l q ilin a d i. E y = 0 te n g la m a sid a n to p ilg a n re a k s iy a la m in g t o ‘ g ‘ r i y o k i n o to ‘ g ‘ r i e k a n lig in i te k s h iris h u ch u n fo y d a la n is h ^ ^ m aqsadga m u v o fiq . 7 4-rasm A 7.3-rasm. S huni ham ta ’ k id la b o ‘ tis h jo iz k i, agar balkaga q o ‘ y ilg a n k u c h u n in g o ‘ q i b o 'y la b y o ‘ nalsa, k u c h n in g m a ’ lu m q iy m a tid a ba lka da bo 'ylama egi lish d e fo rm a tsiya si so d ir boMadi. B u m asala a lo h id a m u a m m o boM ib, bu haqda 9 -bobda ba ta fsil to ‘ x ta Iib o 'ta m iz (7 .4 -ra sm ). 7.2. Eguvchi moment va ko‘ndalang kuchlarni aniqlash B a lk a egilganda u n in g k e s im la rid a n o rm a l ст va u rin m a z k u c h la n is h la r h o s il boMadi. B u k u c h la n is h la m i a n iq la sh u ch u n b a lka k e s im la rid a tashqi k u c h la r t a ’ s ir id a v u ju d g a k e la d ig a n , * ic h k i k u c h la r ( M , Q , N ) n i a n iq la s h ta la b e tila d i. S h u n g a d o ir b ir m is o l k o ‘ r ib o M a m iz . Ik k i ta y a n c h li b a lk a o ‘ q ig a t i k ra v is h d a F „ F 2 v a F 3 k u c h la r q o ‘ y ilg a n , d e y lik (7 .5 -ra sm ). B u k u c h la r ta ’ s irid a b a lk a e g ila d i (s o lq ila n a d i).B u n d a b a lk a n in g A u c h i- Re dagi ke sim o g ‘ a d i, В u c h id a g i kesim в ham o g ‘ adi, ham g o riz o n ta l y o ‘ n alishda s i lj iy d i ( c h u n k i В ta y a n c h i s h a m ir li q o ‘ z g ‘ a lu v c h i ta y a n c h ). S h a m ir li q o ‘ z g ‘ alm as A tayanchida ik k ita R a va H a re a ksiya k u c h la ri, В ta ya n ch id a esa b irg in a R 6 reaksiya ku c h i v u ju d g a k e lis h i m u m k in . R eaksiya k u c h la ri b a lk a n in g q u y id a g i m uvozanat te n g la m a la rid a n to p ila d i. £ M , = F,a, + F2a n + F3a3 - R b l = 0 ; = R J - F,{1 - a,)-- F2(l - a2) ~ F3b = 0 ; ^ X = Ha = 0 . B ir in c h i tenglam a balkaga q o ‘ y ilg a n b archa k u c h la m in g A nuqtasiga nisbatan m o m e n tla r yigM ndisi, ik k in c h i te n g la m a esa В n u q ta sig a nisbatan m o m e n la r yig M n d isi, u c h in c h i te n g la m a esa barcha k u c h la m in g X o ‘ qiga boMgan p ro e k s iy a la ri yig M n d isi n o lg a te n g e k a n lig in i ifo d a la y d i. B u tenglam alardan no m a ’ lu m re a k s iy a k u c h la rin i to p a m iz . Ra = - ^Fx{ l - a , ) + F2 { l - a 2) + F3b ]; М ^ Ғ м + Ғ л + Ғ ^ ) . Ra Ha Ft nd-. A Ra A ^ <2j X & e a2 I F, & r, \F‘ 7.5-rasm. E g u v c h i m om ent v a k o 'n d a la n g k u c h la m i a n iq la sh uchun kesish u s u li- dan fo y d a la n a m iz . B u n in g u ch u n b a lk a n i ix tiy o r iy X masofada kesib, ik k i q ism ga a jra ta m iz (7 .5 -ra sm , b). Q irq ilg a n q is m la m in g m u vo z a n a tin i saqlab q o lis h u ch u n ke sim la rg a M x m o m e n ti v a Q x k u c h in i q o ‘ya m iz. H a r ik k a la q ism uchun m u vozanat te n g la m a sin i tu z a m iz : C hap q ism uchun U s h b u teng la m a la rg a asoslanib, eg u vch i m o m e n t v a q irq u v c h i k u c h la r u ch u n u m u m iy q o id a n i ta ’ rifla y m iz . Kesimda vujudga keladigan eguvchi momentning qiymati, shu kesim ning og 'irlik markaziga nisbatan kesimdan bir tomonda yotgan barcha tashqi kuchlardan (tayanch reaksiya ham shunga kiradi) olingan momentlaming algebraik yig'indisiga teng. Kesimda ко ‘ndalang kuchning qiymati shu kesimdan bir tomonda yo t gan barcha tashqi kuchlaming (tayanch reaksiyasi ham shunga kiradi) ver tikal о ‘qqa bo ‘Igan proeksiyalarming algebraik yig 'indisiga teng. Ishora qoidasL A g a r balka egilganda uning qabarig‘ i pastga qarasa, moment ishorasi musbat, qabariq yuqoriga qarasa ishora m a n fiy olinadi (7.6-rasm, a). A g a r balkadan a jra tib o lin g a n , u z u n lig i d x boMgan e le m e n tn in g chap k e s im id a g i k o ‘ n d a la n g k u c h y u q o rig a , o ‘ n g k e s im d a g i k o ‘ n d a lan g ku ch pastga y o ‘ nalgan boMsa, k o 'n d a la n g k u c h n in g ish o ra si m usbat o lin a d i; bu- Mx = Rax - Қ (jc — cr,) Qx = R a - F [ 0 ‘ ng qism uchun Mx = R b ( l - x ) - F 3 ( a 3 - x ) - F2 ( a , - x ) Qx = - R b + F3 + F 2 M - m usbat Q - musbat -M M - manfiy dx Q - manfiy n in g aksi b o ‘ lsa, ishora m a n fiy o lin a d i.. Boshqacha aytganda agar k o 'n d a la n g kuch la rd a n ta s h k il topgan j u f t ku ch e le m e n tn i soat strelkasi y o ‘ n a lis h id a aylantirsa, k o 'n d a la n g ku ch ishorasi musbat, te ska ri y o 'n a lis h d a a yla n tirsa manfiy o lin a d i. 7.3. Eguvchi moment, ko'ndalang kuch va yoyilgan kuch intensivligi orasidagi differensial bog‘lanishlar Ix tiy o r iy y u k la r ta ’ s irid a g i b a lkadan c h e ksiz k ic h ik elem ent a jra ta m iz ( 7 .7 -ra s m ). A jr a t ilg a n e le m e n tn in g u z u n lig i ( d x ) c h e k s iz k ic h ik b o ‘ lg a n lig id a n y o y ilg a n y u k te kis taqsim la n g a n deb qarash m u m k in . E le m e n tn in g chap k o ‘ nda lan g ke s im ig a M x va Q x , o ‘ ng k o ‘ ndalang ke s im ig a esa M x + d M x va Q x + d Q x z o 'riq is h k u c h la ri ta ’ s ir etadi. M a z k u r elem ent ana shu k u c h la r ta ’ s irid a m uvo za n a td a boMadi (7 .7 -ra sm , b). 7.7-rasm. U o ‘ qiga nisbatan m u vo za n a t te n g la m a s in i tu z a m iz : ^ Y = Qx - qdx - ( Ox + dO x) - O, dQx bundan dQx = -q d x y o k i (^ .1 ) k e lib ch iq a di. D e m a k, k o ‘ ndalang k u ch d a n abssissa x b o ‘ y ic h a o lin g a n b irin c h i h o s ila teskari ishora b ila n y o y iq ku ch in te n s iv lig ig a teng boMar ekan. E n d i e le m e n tn in g o ‘ ng to m o n id a g i k e s im in in g o g M rlik m a rka zi О ga nisbatan m o m e n tla r te n g la m a sin i yo z a m iz : ^ M o = Mx + Qxdx - qdx ■ ~ - ( Mx + dMx) = 0 bundan dMx = Q x d x - q k e lib c h iq a d i. B u ifo d a d a g i ik k in c h i ta r tib li k ic h ik m iq d o r e’ tib o rg a o lin m a sa , q u y id a g i fo rm u la g a ega boM am iz: dMx = (7 .2 .) dx D e m a k , e g u v c h i m o m e n td a n abssissa x b o ‘ y ic h a o lin g a n b ir in c h i h o s ila m a z k u r k e s im d a g i k o 'n d a la n g k u ch g a te n g b o ‘ la r ekan. Q x n in g q iy m a tin i (7 .2 ) dan (7 .1 ) ga q o 'y s a k , q u y id a g i fo rm u la k e lib c h iq a d i: d ' M - * r = - q (7 ' 3 -> D e m a k, b ir o r kesim dagi e g u v c h i m o m e n td a n , sh u k e s im n in g abssissasi b o 'y ic h a o lin g a n ik k in c h i h o s ila te s k a ri is h o ra b ila n y o y iq k u c h in te n s iv - lig in i b erar ekan. B u d iffe re n s ia l b o g 'la n is h la r, k o ‘ p in c h a , J u ra v s k iy teore- m a si deb y u r itila d i. 7.4. Eguvchi moment va ko'ndalang kuch epyuralarini qurish M a ’ lu m k i kuchlanishlar ic h k i kuchlarga b o g ‘ liq boMgan m iq d o rla rd ir, ya’ ni katta k u c h - ka tta ku ch la n ish , k ic h ik k u c h -k ic h ik k u c h la n is h h o s il q ila d i. O d atda k o n s tru k s iy a e le m e n tla rin in g m u s ta h k a m lig ig a aynan k u c h la n is h la r o rq a li baho b e rila d i. B in o b a rin , k u c h la n is h eng k a tta boMgan k e s im xavfli sanaladi. Shu boisdan elem entlam i, masalan, b a lk a la rn i m u sta h ka m likka hisob lashda ana shu xavfli kesim izla b to p ila d i va ana shu k e s im n in g m ustahkam lig i te k s h irila d i. X a v fli ke sim n i aniqlashda «E pyura» deb nom langan g ra fik ju d a qoM k e la d i. H a r b ir ic h k i ku ch (m asalan, e g u v c h i m om ent, k o 'n d a la n g y o k i b o ‘ y la m a ku ch la r) n in g o ‘ ziga xo s e p y u ra la ri boM ib, bu e p y u ra la r balka b o 'y la b shu k u c h la m in g ta rq a lish q o n u n in i ifo d a la y d i. H iso b la n a yo tg a n b a l k a n in g o s tid a a lohida o 'q q a m a ’ lu m masshtabda te g is h li m iq d o rla m in g q iy m a tla ri oMchab q o 'y ila d i v a g ra fig i c h iz ila d i. Q u y id a M va Q e p yu ra la rin i q u rish g a d o ir b ir necha m is o lla r k o 'r ib o 'ta m iz . 7 .1 -m is o l. B e rilg a n b a lk a u ch u n e g u v c h i m o m e n t v a k o 'n d a la n g kuch e p y u ra la ri q u rils in (7 .8-rasm ). Q o 'y ilg a n tashqi kuch F ta ’ s irid a b a lk a n in g e g ilis h i rasm da u zu k c h i- z iq la r o rq a li tasvirla n g a n . H is o b is h la rin i ta ya n ch re a k s iy a la rin i a niqlash- dan b o s h la y m iz . а) b) d) 7&. TO A *1 77$ '777 7 в I M epyurasi MC Q epyurasi \ ж in. 7 . 8 -rasm. Q o ‘y ilg a n k u c h b a lk a o ‘ q ig a tik b o M g a n lig i u ch u n g o riz o n ta l re a ksiya H a = 0 . Ik k ita v e rtik a l re a k s iy a n i q u y id a g i te n g la m a la rd a n to p a m iz : Fb £ м л = Ral — F b = О , b u n d a n Ra = - j - Fo 2 X = ~ R b ( + F a = О , b u ndan Л й = - y - E p y u ra la m i q u ris h d a n o ld in to p ilg a n re a k s iy a la m i te k s h ira m iz . B u n in g u ch u n ^ Г У = 0 te n g la m a sid a n fo y d a la n a m iz : Z Fb Fa F ( a + b ) 7 = Д а - Ғ + Л 6 = 0, yoki — + — - F = 0; — ^-------- * - F = 0 . У I I I M u v o z a n a t te n g la m a s i q a n o a tla n tirild i. D e m a k, re a ksiya k u c h la ri t o ‘ g ‘ ri to p ilg a n . Eguvchi m om ent va k o ‘ndalang kuch epyuralariga d o ir tenglam alam i tuzish uchun balkani uchastkalarga boMib chiqam iz va har b ir uchastka uchun tegishli tenglamani tuzam iz. Ik k i k u c h oraligMdagi masofa uchastka deb ataladi. Rama- Iarda tugundan kuchgacha boMgan masofa ham alohida uchastka tariqasida qa raladi. B iz hisoblayotgan balka ik k i uchastkadan iborat: Ra dan F gacha boMgan A C masofa 1-u ch a stka ; F dan Rb gacha boMgan B C masofa 2-uchastka. A v v a l M e p y u ra s in i q u ra m iz . A ta y a n c h id a g i ix tiy o r iy x , m asofada b a l kani kesam iz. Shu k e s im n in g o g M rlik m a rka zig a nisb a ta n m o m e n tla r te n g la m a sin i tu z a m iz . M a M u m k i, te n g la m a k e s im n in g b ir to m o n id a y o tg a n k u c h la r u ch u n tu z ila d i. B iz n in g m is o ld a ke sim d a n chapda b irg in a R a k u c h i, o ‘ n g to m o n d a esa F v a R b k u c h la ri b o r. Is h n i y e n g illa s h tiris h u c h u n ch a p to m o n g a te n g la m a tu z a m iz : w n Fb Mx - Ra x ] = — • * , . H o s il boMgan te n g la m a to ‘ g ‘ ri c h iz iq n i ifo d a la y d i. T o ‘ g ‘ ri c h iz iq n i c h i- z is h u c h u n u n in g ik k ita n u q ta sin i b ilis h k ifo y a . B ir in c h i uchastkada x, n in g o ‘ zgarish chegarasi: 0 < x, < a. x , = 0 boMsa, M A = 0; w Fab x , = a boMsa, M c = - j - boMadi. Shu is h la rn i ik k in c h i uchastka u ch u n ta k ro rla y m iz r.r F - a Mx = R b - x 2 = —— x2 ; 0 < x2 < b. x 2 = 0 boMsa, M „ = 0; , , Fab x 2 = b boMsa, M c = —— boMadi. , / X u s u s iy h o ld a , F k u c h i b a lk a n in g o ‘ rta s ig a q o ‘ y ilg a n boMsa, a = о = — FI boM adi. 4 K u c h q o ‘ y ilg a n n u qtadagi m o m e n t m a k s im a l m o m e n t h is o b la n a d i. E n g k a tta k u c h la n is h shu ke sim d a h o s il boMadi. E n d i b a lk a n in g o s tid a abssissa o ‘ q i o ‘ tk a z a m iz va y u q o rid a to p ilg a n q iy m a tla m i masshtab b o ‘ y ic h a shu o ‘ qqa jo y la s h tira m iz . H o s il boMgan g ra fik M e p y u ra s i deb a ta la d i (7 .8 -ra sm , b ) Ishora qoidasi. E g u v c h i m om ent ish o ra sig a d o ir u m u m iy q o id a d a n k e lib c h iq q a n h o ld a (q a b a riq pastga q a ra sa -m u sb a t, y u q o rig a qarasa m a n fiy ), m u s b a t is h o ra li o rd in a ta la r o ‘ qdan pastga, m a n fiy o rd in a ta la r o ‘ q dan y u q o rig a q o ‘ y ila d i. E p y u ra n i q a ysi to m o n g a jo y la s h tiris h g a d o ir ya n a b ir q o id a b o r. B u q o id a g a m u v o fiq e p y u ra e g ilg a n s te rje n n in g to la la ri c h o 'z ilg a n to m o n g a c h iz ila d i. B iz n in g m is o ld a b a lk a n in g p a stki to la la ri c h o ‘ z ilg a n . Shu bo isd an e p y u ra pastga c h iz ilg a n . B u qoid a ram a v a s in iq o ‘ q li b a lk a la rd a ju d a qoM k e la d i. S h u n in g u c h u n ham « Q u rilis h m e x a n ik a » s id a aynan shu q o id ad a n fo y d a la n ila d i. B ir o q a k s a riy a t « M a te ria lla r q a rs h ilig i» k ito b la r id a m u sb a t o rd in a ta la r o ‘ q dan y u q o rig a q o 'y ila d i. M a te ria lla r q a rs h ilig id a n k e y in q u ri- lis h m e x a n ik a s in i o ‘ q iy d ig a n ta la b a la rg a q u la y lik y a ra tis h m aq sa d id a ush b u k ito b d a b iz m usbat o rd in a ta la m i pastga jo y la s h tiris h u s u lin i ta n la d ik . Q e p y u ra s in i ham , M ep yu ra si s in g a ri, a w a l b irin c h i, s o ‘ n g ra ik k in c h i uchastka u c h u n q u ra m iz. B ir in c h i u ch a stka d a g i k o 'n d a la n g k u c h Q , tengla m a s in i tu z is h u ch u n ba lka o 'q ig a t i k boM gan o ‘ qqa k e s im d a n chap to m o n da y o tg a n k u c h la r p ro e k s iy a la rin in g y ig M n d is in i y o z a m iz . B u n d a y k u c h x, k e s im d a n ch apda b irg in a d ir. Q = + R a = — 1 / Ik k in c h i uchastka te n g la m a sin i X 2 k e s im d a ri o ‘ n g to m o n d a y o tg a n k u c h - la rd a n tu z a m iz : Q , = - № = ~ Q , ham Q 2 ham x ga bogMiq boMmagan o'zgarm as m iq d o rla rd ir. B u la m i masshtab b o ‘ y ic h a abssissa o ‘ qiga jo y la s h tira m iz . B u n d a m usbat ish o ra li o rd i- nata o ‘ qdan yuqoriga, m a n fiy o rd in a ta o ‘ qdan pastga q o ‘y i!a d i (7.8-rasm , d). E slab q o lin g : Q epyurasida k u c h q o ‘ y ilg a n k e s im la rd a sakrash y u z be ra d i va bu sa kra s h n in g q iy m a ti y ig M q k u c h n in g q iy m a tig a te n g boM adi. B iz n in g m is o ld a А , В , С k e s im la rid a sakrash y u z b ergan; b u sa kra sh la m - in g q iy m a ti Ra, R b va F ga te n g d ir. 7 .2 -m is o l. Bir uchiga F kuchi qo 'yilgan konsol balka uchun M va Q epyuralari qurilsin (7.9-rasm) B a lk a b itta uchastkadan ib o ra t. U n i ix tiy o r iy x m a sofada ke s ib , e g u v c h i m o m e n t v a k o 'n d a la n g k u c h te n g la m a - la r in i o ‘ ng to m o n u ch u n tu zsa k, A ta y - a n c h id a g i re a k s iy a k u c h la r in i to p m a s a k ham boM averadi. M x = - F x ; 0 < x < / Q x = +F. x g a q iy m a t la r b e r ib , m a s s h ta b b o 'y ic h a M e p y u ra s in i q u ra m iz . Q x ga b o g M iq b o M m a g a n o 'z g a r m a s m iq d o r b o M g a n i u c h u n , u n in g e p y u ra s i o d d iy t o ' r t b u r c h a k s h a k lig a e g a b o M a d i ( 7 .9 - r a s m ) . 156 R„ ( 1 , J 1 V J * M , i M epyurasi Download 78.98 Kb. Do'stlaringiz bilan baham: 
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