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ii К A 2 1 С A = «2. «22 «2 и = *2, *22 b2n .«»1 «m2 «inn _ 1 О s K,2 bu ye rd a atj = b(/ ( / = 1 ,m j = 1, /г) u h o ld a bu m a trits a la m i t e n g m a t r i t s a l a r deyish m u m k in . A g a r A m a tritsa n in g q a to rla rin i ustunga, u s tu n la rin i esa qatorga a y la n tirib yo zsa k, u h o ld a A m atritsaga nisbatan A -1 - tra n s p o n irla n g a n m a tritsa h o sil b oM adi, y a ’ ni «и «12 « . / «12 «ml A = «21 «22 «2 л A' = «12 «22 «m2 .«»1 «,„2 .«1 n «2 „ «„m. U s tu n m a tritsa A n in g tra n sp o n irla n g a n k o ‘ rin is h i q a to r m a tritsa boMadi: А ,= [а ,...а т ] 1.6-rasm da s h a rn irs iz q o ‘ z g ‘ alm as ta y a n c h n in g k o n s tru k s iy a s i (a ) v a sodda ta s v iri (b ) b e rilg a n boM ib, bunda ste rje n u c h i tayanchga b ir ik tir ilg a n ; sterjen g o riz o n ta l va v e rtik a l y o ‘ nalishda q o ‘ zg‘ a lis h y o k i ta y a n c h k e s im i a tro fid a a yla n is h im k o n ig a ega emas. B u n d a y tayanchda u ch ta re a k s iy a (Ra, Ha, Ma,) v u ju d g a k e la d i. 1.4. Y u k lar tasn ifl In sh o o tg a ta ’ s ir etadigan har qanday ta sh q i k u c h la r yuklar ( н а г р у з к и ) deb ataladi. Y u k la r ta ’ s ir etish xa ra kte ri, ta ’ s ir e tish k o ‘ rin is h i, ta ’ s ir etish u s u li, ta ’ s ir e tish jo y ig a qarab tu r li x illa rg a b o ‘ lin a d i (ta s n ifla n a d i). 1. Y u k la r q o ‘ y ilis h v a q tin in g d a v o m iy lig ig a qarab statik va dinam ik y u k la rg a b o ‘ lin a d i. Statik yuklar in s h o o t y o k i u n in g e le m e n tla rig a shun- c h a lik o h ista q o ‘ y ila d ik i, n a tija da e le m e n tla rd a h o s il boM adigan te z la n is h - la r n in g q iy m a ti h is o b g a o lm a s a b o M a d ig a n d a ra ja d a k i c h ik b o M a d i. B oshqacha q ilib aytganda, s ta tik y u k la r ta ’ s irid a in sh o otd a te b ra n ish y o h o sil boM m aydi, y o k i h o s il boMsa ham ju d a k ic h ik boMadi. D inam ik y u k la r ta ’ s irid a in s h o o t v a u n in g e le m e n tla rid a te z la n is h u y g ‘ o n a d i, bu esa o ‘ z n a vbatida te b ra n is h la m in g v u ju d g a k e lis h ig a sabab- c h i boMadi. 2. T a ’ s ir erish k o ‘ rin is h ig a qarab y u k la r doim iy va m uvaqqat (v a q tin - cha) boM ishi m u m k in . M u v a q q a t y u k la rn in g o ‘ z i o ‘ z navb a tid a , uzoq m u d - d a tli, qisqa m u d d a tli va m axsus yu k la rg a boM in a d i. Doimiy y u k in s h o o tn in g x iz m a t q ilis h m u d d a ti m o b a y n id a o ‘ z q iy m a ti va y o ‘ n a lis h in i o ‘ zg a rtirm a g a n hold a m u tta s il ta ’ s ir e tib tu ra d i. B unga in - s h o o tn in g x u s u s iy o g ‘ ir lig i, tu p ro q v a suv b o s im i k a b ila r m is o l b o ‘ la o la d i. Uzoq m uddatli m uvaqqat yuklarga uzoq vaqt x iz m a t q ila d ig a n t u r li j i - x o z la r (m asalan, ku tu b xo n a la rd a g i k ito b la r), om onat p a rd e vo rla r va boshqalar k ira d i. Qisqa m uddatli m uvaqqat yu klar to ifa s ig a sham ol, iq lim iy ha ro ra t ta ’ s iri, sh u n in g d e k , q o r, o d a m la r va m e b e lla rn in g o g ‘ ir lig i k a b ila r k ira d i. Z ilz ila v a p o rtla s h t a ’ s ir la r i, g ru n tla r n in g n o te k is c h o ‘ k is h i - m axsus (особы й ) m uvaqqat yuklarga k ira d i. 3. T a ’ s ir e tish u s u lig a k o ‘ ra y u k la r b irk a rra li, ta k r o riy -o ‘ z g a ru vch a n va ha ra ka tla n u vch a n x illa rg a b o ‘ lin a d i. Birkarrali yuklarga in sh o otg a n o ld a n to o x irg i q iy m a tig a qad a r b ir v a ra k a y ig a q o ‘ y ila d ig a n k u c h la r sistem asi k ira d i. Takroriy о ‘zgaruvchi yu klar in sh o otg a ta ’ s ir etayotgan k u c h la r siste- m a s in in g b ir ta s h k iliy q is m id ir-k i, b u q ism sistem adagi boshqa k u c h la rg a b o g ‘ lanm agan h o ld a o ‘ z in in g m iq d o r v a y o ‘ n a lis h in i o 'z g a rtira o la d i. M a salan, s h a m o l in s h o o tg a b o shqa k u c h la rd a n m ustasno ra v is h d a is ta lg a n y o ‘ n a lis h d a v a q iy m a td a ta ’ s ir eta o la d i. Inshootga ta ’ s ir eta d ig a n h a r qan- da y tra n s p o rt v o s ita la ri harakatlanuvchi yuklarga m is o l b o ‘ la o la d i. 4. T a ’ s ir e tis h jo y ig a k o ‘ ra y u k la r b ir nuqtaga to ‘plangan ( y ig ‘ iq ), uzun- l ik y o k i y u za b o ‘ y la b yoyilgan (y o y iq ) ham da hajmiy y u k la rg a boM in a d i. T a ’ k id la b o ‘ tis h jo iz k i, real h o lla rd a y u k n i b ir nuqtaga to ‘ plab boM m aydi. A s lid a y u k m a ’ lu m yuzachaga ta ’ s ir etadi. A g a r y u z a c h a n in g oM cham lari k o n s tru k s iy a e le m e n tla rin in g oM ch a m la rig a nisbatan k ic h ik b o ‘ Isa, m a ’ lu m x a to lik la r g a y o ‘ l q o ‘ y g a n h o ld a , y u k y u z a c h a n in g o g ‘ i r l i k m a rk a z ig a q o ‘ y ilg a n , deb q a b u l q ilin a d i. Jism s irtig a ta ’ s ir e tu v c h i y u k la rd a n tash q a ri u n in g h a jm i b o ‘ y la b ta ’ s ir e tu v c h i k u c h la r ham boM adi. J is m n in g x u s u s iy o g M rlig i, in e rs iy a va m ag- n e tiz m k u c h la ri ana s h u la r ju m la s id a n d ir. H is o b ja ra y o n id a u la r ham jis m h a jm in in g m a ’ lu m n u q ta s ig a t o ‘ p la n a d i. Sanab o ‘ tilg a n y u k la r t u r la r i 1.7-rasm da sx e m a tik tarzda ta svirla n g a n . K o ‘ r ib o ‘ tilg a n ta sh q i y u k la rd a n ta sh q a ri in s h o o tla rg a ta ’ s ir eta d ig a n boshqa ta ’ s irla r ham m a v ju d . M a sa la n , h a ro ra t o ‘ zgarganda e le m e n t d e fo r- m a tsiya la n a d i, dem ak unda q o 's h im c h a ic h k i k u c h la r paydo boMadi. In s h o o t la r u c h u n z ilz ila k u c h la ri ta ’ s iri ham x a ta rlid ir. B in o v a in s h o o tla rn i b u n day k u c h la r ta ’ s irig a h is o b la y d ig a n a lo h id a u s u lla r bor. B a ‘ z i in s h o o tla r yongM n (o lo v ) ta ’ s irig a ham h iso b la n a d i. B u n in g saba- b i s h u n d a k i, b a ’ z i k o n s tru k s iy a la rn in g m a te ria li y u q o ri h a ro ra t ta ’ s irid a o ‘ z in in g m e x a n ik x u s u s iy a tin i k e s k in o ‘ z g a rtira d i va b u n in g o q ib a tid a bu - z ilis h s o d ir boM ishi m u m k in . T a ’s ir e tis h T a ’s ir e tis h T a ’s ir e tis h T a ’s ir e ti s h jo y i ------- u s u l i --- k o ‘r i n i s h i --- x a ra k te ri T o ‘ p la n g a n ( y i g ‘ iq ) k u c h la r Y o y ilg a n ( y o y iq ) k u c h la r H a jm iy k u c h la r U z o q m u d d a tli Q is q a m u d d a tli M axsus (о с о б ы е ) 1.5. Ichki kuchlar. Kesish usuli. Kuchlanishlar A g a r b iro r jis m y o k i elementga tashqi kuch ta ’ sir etsa, ana shu jis m y o k i elem entda o ‘ sha kuchlarga q a rsh ilik k o ‘ rsatuvchi ichki kuchlar paydo boMishini a y tib o ‘tgan edik. Tashqi kuchlar jis m n i deform atsiyalaydi, ic h k i ku c h la r esa bunga q a rs h ilik k o ‘ rsatadi. M a te ria lla r qarshiligi fa n in in g vazifasi ic h k i ku ch la r q iy m a tin i aniqlashdan iborat. C hunki ic h k i k u c h la m in g qiym atiga qarab, y u - q o rid a aytganim izdek, elem entning m ustahkam ligiga baho beriladi. J is m n in g b ir o r k e s im id a v u ju d g a k e la d ig a n ic h k i k u c h la rn i a n iq la s h u c h u n kesish usulidan fo y d a la n ila d i. B u usul keng tarq a lg a n u s u lla rd a n b ir i b o ‘ lib , m o h iy a ti q u y id a g ila rd a n ib o ra t. A g a r b iz n i ix tiy o r iy shaklga ega boMgan jis m n in g (m asalan, p riz m a tik sterjenning, 1.8-rasm, a) b iro r ke sim id a g i ic h k i k u c h la r q iz iq tira d ig a n boMsa, sterjenni o ‘ sha kesim b o ‘ y ic h a xa yo la n kesib ik k i boMakka ajratam iz va b ir boM agini, m asalan, chap q is m in i tashlab yu b o ra m iz. K esishdan ilg a ri sterjen tashqi k u c h la r ta ’ s irid a m uvozanat h o la tid a edi, o ‘ ng boM akning m uvozanat h o la tin i saqlab, q o lis h uchun chap q is m n in g o ‘ ng qism ga boMgan ta ’ s irin i ic h k i k u c h la r b ila n alm ashtiram iz. B u k u c h la r butun p rizm a uchun ic h k i kuch, a jra tilg a n boMak uchun esa tashqi ku ch va z ifa s in i o ‘ ta yd i. Ic h k i k u c h la r as- lid a bu tu n kesim b o ‘ y ic h a tarqalgan boMadi, b iro q u la m i u m u m iy h o ld a b itta bosh v e k to r R va b itta bosh m om ent M b ila n alm ashtirsa boMadi. A g a r q irq im s te rje n n in g b o ‘ y la m a o !qiga t ik boMsa, hisob ancha sod- da la sha d i. K o o rd in a ta o ‘ q la ri X , Y , Z n in g boshi k e s im n in g o g M rlik m a rka - z i О ga jo y la s h tirila d i (1 .8 -ra sm , b). B u n d a O X va O Y o ‘ q la ri ke s im te k is - lig id a y o ta d i. B o sh v e k to r R ni k o o rd in a ta o ‘ q la ri b o ‘ y ic h a u ch ta ta s h k il b) 1 ft ft Is) ~ a r . ' «22 B = bn Ьгг К . « 3 ! « 3 2 . A . b 22 Ь 23_ A g a rd a A va В m a trits a la rin in g ta a llu q li ta rtib la ri teng b o ‘ lm asa, u la rn i k o ‘ p a y tirib boM m aydi va b u n d a y m a trits a la r m o s b o ‘ 1 m a g a n m a t r i t s a l a r d e y ila d i. M asalan, y u q o rid a g i В v a A m a trits a la r o ‘ zaro mos emas, c h u n k i u la r ni В A k e tm a -k e tlik d a k o ‘ p a y tirib boM m aydi. A k s in c h a , ik k i m a tritsa A va В o ‘ zaro m os boM ib, u la m in g k o ‘ p a y tm a la ri m a vju d : A = C h u n k i m a tritsa a m a lla rid a А В * B A boMadi. B u te n g s iz lik ik k i m a trits a k v a d ra t v a te n g ta r tib li (m os m a trits a la r) boMganda ham saqlanadi. K v a d ra t m a trits a la r u c h u n q u y id a g i k o ‘ p a y tm a la r boM ishi m u m k in : A " = A n_l • A = A • A " '1 = A , R - bu tu n son A m a tritsa sin i a m ik d o rg a k o ‘ p a y tiris h q u y id a g ic h a b a ja rila d i: С - a A - a U m u m a n , m a trits a la m i k o ‘ p a y tiris h d a q u y id a g i a lg e b ra ik bogM anish- la rd a n fo y d a la n is h m u m k in : ( a + P)A = a A + (ЗА a ( A + B ) = a A + a B ( a p ) A = a ( p A ) = (3(aA ) ( A 3 )C = A (B C ) a ( A B ) ■= ( a A ) B = (a B )A (A + B)C = AC + B C C ( A + В) = СА + C B A E = A M a trits a la m i k o ‘ p a y tiris h d a q u y id a g i x u s u s iy h o la tla r boM ishi m u m k in : 1. H a d la ri b ir x il boMsa, h o s il boMgan m a trits a q u y id a g i k o ‘ rin is h g a ega boM adi: «11 «12 a \« ' a a u a a l2 « « . „ " «2! «22 a 2„ — a a 2 \ a a 22 a a 2„ a a „ 2 .«»1 «„2 a m ат «2п ‘Д _ап{ ап2 аш 2. Ik k i diagonal m a trits a la r k o ‘ paytm asi A C =A B = 0 Pi A . BA 0 a„ ko m m u ta ts io n xu su siya tg a ega. 3. T e n g ta r tib li ustun m a trits a A n i q a to r m a tritsa В ga k o ‘ paytm asi shu ta rtib g a teng k v a d ra t m a tritsa h o s il q ila d i: C = A 5 = 4. T e n g ta r tib li q a to r m a tritsa A n i ustun m a tritsa В ga k o ‘ paytm asi s ka lya r С ga te n g d ir: a2 [b{ b2 b, ] = ' a A а2Ь\ °\b2 a2b2 a A ° lK an _aA aA <*A_ C = [ a x a2 a „ ] 5. K v a d ra t m a tritsa A n in g v e k to r ustun В m atritsaga k o 'p a y tm a s i us tun m a tritsa С ga te n g d ir: C = A B - au a M °2\ U22 an\ an2 I n bi 1 G " 1 Ь2 = C2 1 1 1 1 c, = £ aub, j = i M a te ria lla r q a rs h ilig i fa n id a q o ‘ lla n ila d ig a n m a trits a la rn in g a ks a riy a ti te n g la m a la r tiz im in i tu z is h va u la m i y e ch ish ga q a ra tilg a n . A g a r A va В m a trits a u la rn in g k o ‘ paytm asi A B v a B A b ir lik m atritsa g a teng boMsa, u la r te ska ri m a tritsa h iso b la n a d i: A B = B A = E. C h iz ik li m atem atikada A m a trits a s in in g te ska ri k o ‘ rin is h in i A ' 1 deb, y o k i В = A '1 d e b qabul q ilin g a n . H a r qanday to ‘ liq k v a d ra t m a trits a o ‘ z in in g te ska ri m a tritsa sig a eg a d ir va u q u y id a g ic h a ifo d a la n a d i: 4 , А г Ал л - ' = 1 4 , А г А„ D( A) Ал 4,2 А,, B u ye rd a A ^ - A m a trits a a n iq lo v c h is in in g a lg e b ra ik to ‘ ld iru v c h is id ir. A jj - m a trits a s in in g e le m e n tla ri A m a trits a s in in g a n iq lo v c h is id a g i i - q a to r v a j - u s tu n la rn i o ‘ c h irg a n d a h o s il boM gan a n iq lo v c h ig a (-1 ) n i k o ‘ p a y tirib hisoblanadi. Shunga e ’tib o r berish k e ra k k i, q u rilis h m exanikasi m asalalarini yechayot- ganda va tekshirayotganda, q u yid ag i bogManishlardan fo yd a la n ish m u m kin : x = - A ' 1 A E bu esa A 'A = E - b ir lik m a trits a s id ir. Y u q o rid a k o ‘ rsa tilg a n id e k, nomaM um h a d la r m atritsasi x = - A " ’ B teskari A ' 1 m a tritsa si o rq a li to p ila d i. A m atritsa D (A ) = 0 boMgandagina teskari A -1 matritsasiga ega boMa oladi. M is o l. A m a trits a n in g te ska ri q iy m a ti a lg e b ra ik to M d iru v c h ila r o rq a li to p ils in . B e rilg a n : A = 2 - 1 0 2 4 - 2 5 A lg e b ra ik to M d iru v c h ila r q u y id a g ic h a a n iq la n a d i: ' 0 2 - 2 5 4 i = = 4 . 4 m = 3 2 4 5 = - 7 . 3 0 2 - 1 = -6 • 4-> = = - 8 4 - 2 ^ 5 I- (N 1 D e m a k, te s k a ri m a tritsa A n in g to ‘ ld iru v c h is i 4 8 4 A = - 7 9 - 5 - 6 10 - 6 q u y id a g i a n iq lo v c h ig a ega b o ‘ lib : D{ A) = 16 + 6 + 4 - 3 0 = - 4 A~' =- 4 - 8 4 - 7 9 - 5 - 6 10 - 6 ga te n g d ir. T o ‘ r tin c h i v a undan y u q o ri ta r tib li m a trits a la m i a lm a s h tiris h v a u la m i teskari q iy m a tla rin i a niqlash ancha m u ra kka b masala h is o b la n a d i. S h u n in g u ch u n b u n d a y m a sa la la m i yechishda E H M va m a trits a am al- la rid a n fo y d a la n ila d i. Z a m o n a v iy E H M la rd a ta rtib i 5 0 -1 0 0 , h a tto k i 5 0 0 - 700 v a u n d a n y u q o ri boMgan m a trits a la rn in g teskari q iy m a tla rin i a n iq la sh im k o n iy a tig a ega boMgan standart d a stu rla r m a v ju d d ir. I I B O B . C H O ‘ Z I L I S H V A S I Q I L I S H M avzu m azm uni. Mazkur bobda siquvchi yoki cho'zuvchi kuchlar ta ’sirida sterjenlarda hosil bo ‘ladigan kuchlanish va deformatsiyalarni an iqlash usullari bayon etiladi; mavzuga oid misol va masalalar keltiriladi. Shuningdek, talaba sterjen materialining fizik-mexanik xossalarini tajriba yo'li bilan aniqlash uslublari bilan tanishtiriladi. 2.1. Cho‘zilish va siqilishda kuchlanish va deformatsiyalar. Guk qonuni In shoot va m ashina q is m la rid a c h o ‘ z ilis h va siqilishga ishlaydigan detal- lar, elem entlar k o ‘ plab uchraydi. B u la m in g m ustahkam ligiga baho berish uchun ulardagi ku ch la nish va d e fo rm a tsiya la rn i to p ish n i b ilis h im iz kerak. Sterjen n in g o ‘ q i b o ‘ y la b fa q a t b o ‘ yla m a k u c h q o ‘ y ilg a n sodda h o ln i k o ‘ rib o ‘ tam iz. K o ‘ nda lan g k e s im yuzasi A k u rs iv o ‘ zgarmas boMgan p riz m a tik ster- je n g a q a ra m a -q a rs h i y o ‘ n a lg a n b o ‘ y la m a k u c h G ‘ q o ‘ y ilg a n d e y lik (2 ,1-rasm , a). C h o 'z u v c h i ku ch ta ’ s irid a b o ‘ yla m a y o ‘ n a lish d a sterjen uzay- adi, k o ‘ ndalang y o ‘ n a lis h d a qisq a ra d i. S iq ilis h d a esa aksincha boM adi: ster je n uzunasiga q is q a rib , k o ‘ nda lan g kesim oM cham lari o rta d i. S te rje n n in g o ‘ qiga tik boMgan barcha te k is k e s im la r d e fo rm a tsiya n a tija s id a o 'z in in g te k is h o la tin i va n o rm a l o ‘ qqa t ik lig in i saqlab q o la d i, deb faraz e ta m iz. B u g ip o te za n i i lk b o r g o lla n d o lim i D .B e m u lli aytgan boM ib, tekis kesim lar gipotezasi deb a ta la d i. B u n d a n c h o ‘ z ilis h ja ra y o n id a s te rje n n in g b o 'y la m a to la la ri b ird a y c h o ‘ z ila d i, degan m a ’ no k e lib ch iq a di. B u gipoteza k o ‘ p s o n li ta jrib a la rd a tasdiqlangan. m a) b) 1 A I 2 ___ ____ __ _ . _____ ____________ _ _ ___ A l 2 n / d) Ab B o ‘ y la m a kuch ta ’ s irid a sterjen /, m m ga u za yd i desak, u h o ld a sterjen n in g d a s tla b k i h o la tig a n is b a ta n u z a y is h i Al = ^ - ( b o M a d i. B u n i c h o ‘ z ilis h d a t o ‘liq y o k i absolut u z a y is h , s iq ilis h d a esa to'liq y o k i absolut qisqarish deb ataladi. A b s o lu t u z a y is h n i s te rje n n in g d a s tla b k i u z u n lig ig a n isb a ti e = A l / l b o ‘ylam a nisbiy (leformatsiya y o k i nisbiy uzayish deb ata la d i. N is b iy uza yish nin g oMcham b ir lig i y o ‘ q, oM cham siz son. K o ‘ pincha fo iz la rd a b e lg ila n a d i: e = — -1 0 0 % = e - 1 0 0 % I K o ‘ ndalang d e fo rm a ts iy a la r ham shunga o 'xsh a sh to p ila d i (2,1-rasm , d); a oMcham y o ‘ n a lis h i b o ‘y ic h a s \ = A a / a \ b oMcham y o ‘ n a lis h i b o 'y ic h a s\ - - A e / e . M a n fiy ishora c h o ‘ z ilis h d a k o 'n d a la n g o M cham lar q is q a ris h in i anglata- d i. Iz o tro p m a te ria lla r uchun k o ‘ ndalang d e fo rm a ts iy a la r ha r ik k i y o ‘ nalishda b ir x il boMadi: s \ = e l = e x B u yerda ham E‘ oM cham siz s o n d ir. e va s ’ chiziqli deformatsiyalar deb ham y u ritila d i. C h o ‘ z ilis h va s iq ilis h d a k o ‘ ndalang n is b iy d e fo rm a ts iy a n in g b o ‘ yla m a n is b iy deform atsiyaga n is b a tin i k o ‘ n d a la n g d e fo r m a ts iy a k o e ffits ie n ti y o k i Puasson k o e ffits ie n ti deb ataladi: X I X asrning boshlarida fransuz o lim i Puasson tu r li m a te ria lla r uchun m a zku r nisb a tn in g o ‘zgarmas m iq d o r e k a n lig ig a e’ tib o m i qaratdi va barcha m a te ria lla r uchun unin g q iy m a tin i 0,25 deb o ld i. B iro q k e y in g i ta jrib a la r bu k o e ffits ie n tn in g q iy m a ti tu rli m a te ria lla r uchun tu rlic h a e k a n lig in i va bu q iy - m at 0 dan 0,5 ga qadar o ‘ zgarishi m u m k in lig in i k o ‘ rsatdi. H a r x il m ateriallar uchun Puasson k o e fits ie n tin in g o ‘ rtacha q iy m a tla ri 1.2-jadvalda berilgan. E ndi s iq ilis h va c h o 'z ilis h d a g i k u c h la n is h la m i aniqlashga o ‘ tam iz. Tashqi k u c h la r ta ’ s irid a k o n s tru k s iy a e le m e n tla rid a , m asalan, s te rje n la rd a ic h k i k u c h la r paydo bo M ish in i y u q o rid a aytgan e d ik . S te rje n b ir o r k e s im in in g m a ’ lu m nuqtasidagi ic h k i kuch in te n s iv lig in in g o M c h o v in i b ilis h m aqsadida k u c h la n is h tushunchasi k iritilg a n . D e m a k, k u c h la n is h deganda ke sim n in g m a ’ lu m nuqtasidagi ic h k i kuch in te n s iv lig i (m iq d o ri) tu s h u n ila d i. K u c h la n is h la m i aniqlashda kesish u s u lid a n fo y d a la n a m iz . B u n in g uchun p riz m a tik s te rje n n i ( m - n ) te k is lig i b o ‘ y ic h a x a y o la n k e s ib , ik k i qism ga a jra ta m iz . O l ng q is m in i tashlab, chap q is m in in g m u v o z a n a tin i te k s h ira m iz (2.1 rasm , b). C hap q is m in in g m uvozanatini saqlash m aqsadida ke s im yuza- siga t ik y o ‘ nalishda ic h k i elastik k u c h la m i (F ) q o ‘ ya m iz. B u k u c h la r o ‘ ng q is m n in g chap qism ga boMgan ta’ s iri v a z ifa s in i o ‘ ta yd i. A g a rd a B e m u llin in g te kis k e sim la r gipotezasini inobatga olsak, sterjen k o ‘ ndalang k e s im in in g , y a ’ ni sterjen b o ‘ y la m a o ‘ qiga tik (perp e nd iku la r) boMgan ke s im n in g b archa nuq- ta la rid a g i kuchlanishni 2.1-rasm, b ga k o 'ra q u yid ag ich a aniqlasa boMadi: X x = - F + cr A = 0 , bundan F (2 .2 ) b u ye rd a F - sterjenga ta ’ s ir e tu vch i b o ‘y la m a ku ch ; A - ste rje n n in g k o ‘ ndalang kesim yu za si; K u c h la n is h n in g oMchami SGS sistem asida kg /sm 2 y o k i k g /m m 2 X a lq a ro oM chov b ir lik la r i sistem asi SI da asosiy b i r li k H /m 2 y o k i Pa (P a ska l) b ila n ifo d a la n d i. U s h b u k u c h la n is h , tashqi kuch F s in g a ri, ke sim yuzasiga t ik y o ‘ n a lg a n lig i sab a b li normal ku c h la n is h deb ataladi. P riz m a tik sterjen s iq ilis h g a ish la - ganda ham n o rm a l k u ch la n ish ana shu fo rm u la o rq a li a n iq la n a d i,fa q a t isho- rasi m a n fiy boMadi. K o n s tru k s iy a elem entlarida vujudga ke la d ig a n k u c h la r va d e fo rm a tsiya la r o ‘ zaro bogMiq m iq d o rla rd ir: kuch boMmasa - deform atsiya boM m aydi; de- fo rm a ts iy a boMmasa - kuchlanish boM m aydi. Y u k ortgan sari e g ilis h n in g (de- fo rm a ts iy a n in g ) o rtis h in i, y u k kamaygan sari e g ilis h n in g k a m a y is h in i 1678- y ild a in g liz o lim i R obert G u k ta jrib a yoMi b ila n aniqlagan va o ‘ z in in g mash h u r q o n u n in i yaratgan. G u k qonuniga m u v o fiq defo rm a tsiya kuchga to ‘ g ‘ ri p ro p o rs io n a ld ir. C h o ‘ z ilis h va siq ilish d a bu qon u n q u yid ag ich a ifo d a lan a d i: a = Ее. (2 .3 ) A m m o b u p ro p o rs io n a llik n in g chegarasi bor. K u c h la n is h n in g q iy m a ti o rta b o rib , m a ’ lu m nuqtaga yetganda p ro p o rs io n a llik b u z ila d i. A n a shu nuqta proporsionallik chegarasi deb a ta lib , tu r li m a te ria lla r u ch u n ta jrib a yoM i b ila n a n iq la n a d i. (2 .3 ) fo rm u la ta rk ib ig a k iru v c h i E k o e ffits ie n ti b irin c h i tu r elastiklik moduli y o k i b u n i fa n o la m ig a o lib kirg a n o lim n o m i b ila n Yung moduli deb a ta la d i. Y e n in g oMcham b ir lig i k u c h la n is h n ik i b ila n b ir x il e k a n lig i fo rm u - Iadan k o ‘ rin ib tu r ib d i. B u n in g sababi e oM cham siz sondir. e = a / E (2 .4 ) ifo d a d a n k o ‘ rin a d ik i, e la s tik lik m o d u li m a te ria ln in g d e fo rm a tsiya g a qarshi- l ik q ilis h x u s u s iy a tin i ifo d a la y d ig a n m iq d o rd ir. K u c h la n is h n i o ‘ zgarm as deb olsak, katta E ga k ic h ik g va aksincha, k ic h ik g ga ka tta d e fo rm a ts iy a t o ‘ g ‘ r i k e la d i. T u r li m a te ria lla r u c h u n e la s tik lik m o d u lin in g q iy m a tla ri 1-jadvalda k e ltirilg a n . 1-jadval M ateria llarn in g nom i E lastiklik m oduli E P u asso n k o e ffitsien ti ц k g/sm 2 da in n /m ' da U s le r o d li n o ‘la t 2,1-106 2,1-105 0 ,2 4 -0 ,3 0 A lu m in iy q o tish m alari 0 ,7 2 '1 0 6 0 ,7 2 -103 0 ,2 6 -0 ,3 6 T itan qo tish m alari 1,12-10 6 1 ,1 2 1 0 s - M is ( 1 ,0 - 1 ,3 ) - 1 0 6 (1 ,0 -1 ,3 ) -10s 0 ,3 1 -0 ,3 4 P latina 1.7-106 1,7-105 0,39 C h o ‘yan ( 1 ,1 5 - 1 ,6 ) -IO6 ( 1 ,1 5 - 1 ,6 ) -I 0 5 0 ,2 3 -0 ,2 7 Q a ra g 'a y (0 ,1 -0 ,1 2 ) IO6 ( 0 ,1 - 0 ,1 2 ) -IO5 - T ek sto lit (0 ,0 7 -0 ,1 3 ) -106 (0 ,0 7 -0 ,1 3 ) -105 - B eton ( 0 ,1 5 - 0 ,2 3 ) -106 ( 0 ,1 5 - 0 ,2 3 ) -IO5 0 ,1 6 -0 ,1 8 R ezina 0 ,0 0 0 0 8 -106 0 ,0 0 0 0 8 -105 0,5 Shisha 0 ,5 6 -106 0 ,5 6 -m 5 0,25 Q o ‘r g ‘oshin 0,17-106 0,17-10 5 0,42 Jadvalda k o ‘ rs a tilg a n q iy m a tla r ta jrib a y o ‘ li b ila n an iq la n g a n . G u k qonuni formulasi (2.3) dagi cr va g ning o‘miga a = Ғ / A va s = M U ifo d a la m i q o ‘ysak, G u k qonu n in in g boshqacha k o ‘ rinishiga ega b o ‘ lam iz: F i M = — (2 .5 ) EA B u fo rm u la d a n k o ‘ r in a d ik i, a b s o lu t u z a y is h n in g q iy m a ti c h o 'z u v c h i (siq u v c h i) kuchga ham da steijenning uzunligiga to ‘ g ‘ ri proporsional, steijen- n in g e la s tik lik m o d u li va k o ‘ ndalang kesim yuzasiga teskari proporsional ekan. (2 .5 ) fo rm u la ta rk ib ig a kirg a n E A k o ‘ paytm a c h o ‘ z ilis h va s iq ilis h d a g i bikrlik deb ataladi. 2 .1 -m is o l. Dastlabki uzunligi / = 2 5 0 mm, cho‘zilgandan keyingi uzurt- ligi I = 2 5 0 ,5 mm bo'lgan sterjenning nisbiy uzayishi aniqlansin. Y e c h is h . S te rje n n in g a b s o lu t u z a y is h i Д / = / , - / = 2 5 0 , 5 - 2 5 0 = 0 ,5 ............................... A / 0 ,5 M M m m . S te rje n n in g n is b iy uza yish i g = — = 25QJV1M ~ ' |
