Ap HHlK. AAHHJ\O P AlilKOBH'Fl

TABJ\. I1UE H3

OTTIOPHOCTH MATEPHJAJ\.A e"'AAI OVIO 1I6'f1Y~

xm Jil3ME.If,EHO Jil3.llAH>E

\. \

" r PAD E B 11 H C K A KID liT A"

Ii EO r P A)l, 1985.

PeueH3CKT

Jlp HHlK. KATYlUA)(EJlPI1X. B8Hp. npoq,.

MawHHCKor $aKymCTa y HHWY

3a HPO "rpal)eaHHexa ""'MrS": MwtSH BKWlbHh - rnBBHK ype,aHKIC, MwtHUB .uOJlKh

- onroaoplDl YPCIl/IIIJC, OnTa BaCHJloCBKh - ypeJlHIIJC, ' lOBO KapauKh - TexHH'OOI

YPCIl/IIIJC, CHeJIClIH8 HeuHh - H8C110BHa C\llaHa

1'Hp8llC: 5.000 npKMep:uca

UJT8Mna: UJTaMnaPKjs .Ba~ap" Bop

nPEllrOBOP llBAHAECTOM H311Al-bY

OBO 1131131he Tu6.1uqa U3 OiJiiiOPHOCiJiu .lfaiJiepujaAa HCTO j c Kao II

npeTXO-UHa H3-ua1h3, aJJH cy nornYHO 113MelheHe MepHe je-UHHHue nojellH­

HHX BeJJHqHHa II Y reKCTY H Y TafiJJHllaM3 y -uyxy 33KOHa 0 MepHHM j e­-UIIHHU3M3 II MepIIJlIIM3 (CJJYlKfieHH JlIICT C4>PJ 6p. 13/76, QpaH3 341).

Ii

oeorp311, 17. jaHyapa 1982. rO-UIIHe. ll. P.

llPE,UrOBOP

,Ua 611 CTYAeHTH npH peWaBaH>~' 3allaTaKa 113 OTnoplt0CTU .IUlTepu)ClAc.

Mor JlH JlaKWe KOPHCTHTH pa3He HYMepl1'1Ke H npaKTH'IHe no-uaTKe. aBe cy

To6J1u~e H311BojeHe H3 YI,l6eHHKa 36uPKa 3aaaTaKa IL3 OT1lOPHOCTU AtaTe­pujClAa. OHe ey YCKJlaljeHe ca MOjHM yufieHHl\HMa OTTlOpHOCT AtaTcpujClAa

11 36upKO 3aaaToKa U3 o'rnopHocTU AtaTepujClAa, na cy cnpoaelleHa MeTa ofieJle>KaBalha Kao H y y ufir·HHllI1Ma.

TafiJlHl\e ey npBeHeTlleHO HaMetbeHe CTYlleHTHMa MalUHHeKHX q,a­

KYJlTE1Ta, aJlH >ly. MOry KOPHCTHTH H cry,lleHTH ,lIpyrnx q,aKYJlTeTa, BHCC;-:fX H BHWKX WKOJla na H TeXHH'{KHX WKOJIa.

no JKeJbH eTY,lleHaTa AonYlbeHe ey TafiJlHlle eJlaCTH'IHHX JlHHHja H

pa3HH MaTeMaTH'IKH ofipacUH Y l\HJbY OJlllKlllatba HYMepK'O<Or pewetba eJlOJKeHKX npo6.neMa H3 OTIlOPHOCTH MarepHjBJIa M TeopKje OCl\KJlaUl11a. C Ofi3HpOM Ha BeJIHKY npll1\leHy JlOrapMTMapa ,lIO,lla'r je O,llCJbaK 0 PAA)! ca JlOrapHridapoM.

npoq,. lIP HHJK. M. Tp60jeBHII fiPHJKJbHBO je npo'lHTao pyxonHC M y'lHHHO MH KopHCHe npHMeAfie Ha '1eMY My ee HajcpJl.8'1Hltje. 3axBaJbyjeM.

3aXB3JbyjyllH ,.rpa~ea · ItHCKoj K>I>U3U'-' y neTOM M311aIbY ,lIO,llaTa jc

npoWHpeHa Ta6JIMlla XnI. Y WecTOM M3,l131bY (M3 1965. ro,llKHe) ,lIO,llaTa je TafiJlHl\a XVIII . .. noaa~u 0 CTaHaapduMQ "peMa JY10CA08eHCKUAt cra'" oapalUUl Jye", a y OBOM - oeMOM - H3,l1aH>Y H Ta6J1u~e xunep6oAw .. Kl&I

4>YHK~uja 3a apeaHOCTW Oil x=O IlO x = 2r.. CeM TOra OTKJlOIbeHH cy YO'le­

HH wTaMnapcKH He,llOCTRl\H. Pa./lM eMaH>elba TpowKoBa WTaMnatba yufieHHKa HHCY ee MOrJle M3-

MeHHTH MepHe jeAHHHl.\e noje./lHHHX BeJlH'floIHa Y AYXY 33KOH3 0 MepHItM je./lMHMl\aMa (CnYJKfieHH JlIiCT C4>PJ fip. 45/61), na npH '1IiTaIbY Tpe6a

KOPHCTIiTH 03HaKe H je,llHHHl.\e ,lIaTe Y TafiJlIiUH Ha HapeJlHoj CTpaHIt.

5. MapTa 1961. rOAHHe

7. q,efipyapa 1971. rO./ll1He Beorpa./l

.II P.

MEPHE JEnYlHYlUE nPEMA 3AKOHY 0 MEPHI1M JMI1HI1 UAMA (c,1\,>t-:6cHIi ; IIICT C<PPJ Gp. 13/76, CTpaHa 341.}

~ l "-,

Mr plIa Rl',l lC'IHtU\

I. Ay>t'HHn

2. n ORp wHHa

3. 3anp~MHHa

4. Yrao

5. Bp. " e

6. 6p'HHa

7. 'y 6 p38tbC

~ . Milea

9. Cne1lH~1I1{1I8 lr.Ia·

~a - r.rrTlilla 10. CHAa. T\')KHHI

OJt13Ka

L

MepH e j C411HHU C

Mer.p. : rn = 10 drn = 100 ern = 1000 mrn; MHKpOH (1') = MH,pOMerap (I' rn); MH.1KMHKpOH (m Il) = HaHo~leTap (om).

A Im'; ap. I • = 100m'; ""TaD. 1 ha = 10< m'; I kmt = lOa m2; 1 dm:l = 10- : mt; 1 em! = 10 ~ rna; 1 mm2 = 10- 1 rna.

VIm'; km' = 10' m'; 1 dsm' - 10' m'; 1 dm' = ; = 10- 1 m'; 1 em' = 10-' m';

'Hrap. 1 I = 1.1000 028 dm' ~ I dm'; 6po~e.a TOHa. I hI = 2.8J2 m'.

rad 1 1° L CTrnr H. 1° = 90 L ; "HHyr •• I' = 60 ; ee'YHn ••

T

,.

" 'M, m

r= MfV

F; 0

I' 1 1" = - ' rpa.yc Ig = - -L ' p·'H)· ...

60' . • 100' - .

180 200 = 1 rad = -- L = -- g r.dusa .

, " l'(, K~ f H .1a · ( S); !-HtUyTB (I min = 60 s) ; l'aT U.nH 'UIC

(1 h = 60 min) ; na. (1 d = 2~ h).

m/s ; m min ; kUl/h ; qBOP (knol) = I nmUe/h = = 1.851 km/h.

mIs' I .H.orp'w (kg) ; ;rOHa. 1 I = 10' kg: .,iI.HT .. Hnll M"UOeKa Ue,na. 1 q=IOO kg; rp .... \ ' g.....:O.OOI ·kg:·

kg/m': I g/cm'= 10' kg/m' = I,OO!) 028 gfrom'.

"'YTH (newlon). l N =1. kgm/s'; KHJl1nOHll. I kp _ =9."116 65 N; MerlnOH4. ·Mp=IO' kp;noH4, I p = U.ool kp; ".'.1I0H4. I mf'..., 10-" ·kp.

II. Cn tu . <I>H~. TellC. 1'",=01 V N 'm' : 1 kp{dm' = I plem' = II 806, 65 N/ru'.

12. Hlnoll , npHTHcaK 0', r, ·p

13. Pa4, elll'pn'j;o A, 1:.

H . CHa... f'

N 'm'; 6ap (bar) : 1 bar = H),' N/n,'; kp/m'; TrXM II""" .. "oc<I>"p. (al) ; 1I0p ....... (<I>H3H"'0:) aT­"oc<l>epa (' aim); ... JlH .. eT.p <Tvn'll lIC .ne (mm Hg) 1 .'m = l,n:\3 227 al = 1.013 250 bar = 101 325,U N/m' = 760 mm Hg.

VY~ (i'l,I_). I J = I Nm; 1 kpm = 9,81l6 65 J ; .." 'C, I Wh = :. 600 J .

. " ,

BaT (w.II), I W = 1 J 's ; "Olbe.s (.1 ... , I KS = = 75 kpoo 's < 7;15,5 W.

Q 6pUOB8tt.e ""0 *."111 K AtJlOHI "(.'I,II IIX jt:Jl HHHUI BPWH t't: l103.81Ialbt"M "pe a ­

M("TKI Hc' npeA je llt lllllte :

repa (Tl 10 ":

rH". (U) 1011 ;

Nl',,> (M) 10' :

I<H.O (k) Ill-'

'CKTO (il) to':

lleK" (d.) 10 :

4tllll (0) 10-' ;

Ut' IiTH (to) I U-"t;

MHJlII (m) 10-:1;

MHKpU (1\) 10 e

lIaHO (n) 10-'

nllKO (p) 10-".

I

2

3

4

5

I. T ABJII1UA

0) e6PAC~H

3Ka'lelbC o6pacua 06pa3aa

1. JlHHeapHo CTalbe Haopeaalba

HanoH. 3a npoH3Bo.'bHY .. paBaH (ca HopManoM n)

llHnaraunja

Hcre3Ha KPYTOCT

flOnpeQH3 .llHJlaT3UHja

Poisson~oB ' KoecjJHUH-je"T

-f -+ ... ....

Pn = a. n + TnT T + T.N N

61 F F o. e=-=-=-=-, I EA 91 E

9l=EA dim91=dimF; INr

6 Koecj>HUHjeHT enaCTH'I- m<> 1/11; a .. liE HOCTH . .

7 KOHTpaKUKja npeceKa ~/ ... A.-A', .100'/. A.

8 AI", FIIEA = FI

9 Hooke'oB saKOH ,a=Ee

10 HanoH 3a ynpaBHH a~=a,-FIA npeceK

II CTeneH cHrypHocTH¥ v = aM/a.

12 flpnpawTaj 3anpeMlfHe 6 V = V' - V "" (1-2 Il) I: V WTana

.. 13 TBp.lloha n6 BrineU'y IJa - 2 Flrr. D (0 - VO-::::-· -d'-:::)

(Fz3kN: 0 -10 mm; d npe .. I.K· OC:II01e ccj>epHor oTce'!K.)

• v= 4 31 "RPRO onTepehe.e (\).

..

,

2

14 HanOHH 3a KOCH npeceK

TOTanHH

HopMallllH

TaHreHUHjallHH

je.a.Ha'!HHa Mohr'oBor Kpyra

15 ~'h.a.ylKelbe no.a. YTH­uajeM conCTBeHe Te­lKHHe

npIt3MaTH'IHH WTan

HanOH

KPYlKHO KOHH'!HH WTan

HanoH

16 YTHUaj ueHTpHlflyrallo

He CKlle Ha HanOHe

rYCTHHa MaTepHjalla

HopMallHH HanoH .

yraoHa 6p3HHa o6p-Taiba .

6poj o6pTaja y MH­

"YTY

17 YTHUaj TeMnepaTYP­CKe npOMtHe Ha Ha­nOHe

Ji,HlIaTllUHja

HanoK' (KoHiaKTHH)

TepMH'!KH Koe­(j)HUHjeHT wHpe­Iba

p. = FIA' = (FIA) cOS'll = a. cos 'P

an='/.a. (I:+-cos2rp)

". '" 'I. o. sin 2 'I'

0nmox::::Oz 3a ,=0°;

" ..... ='/,a. 3a '1'= ±4So

(0. - 'I. a. )' +fo' ''' ('I. d. )'

O=y", AI

-. . .. .~.

a.= y .. (I-Z); \ ~I~~.= . Y .. 1 /' ~ z"O;

Adz- edz = (fJ,/f) dz; AI <=: QI/2fA . 01/291.

a,='/. y,. (I-z); a, .... = 'I. y .. l

A/-Ym l'/6E .. 01/2EA, ; A . ~A sa Z DO,

- .. '

p= ),,,,/g

30l/2.ae ....

n =" V pit [o/miD)

a (Ta6l1Hua II)

.-.. .

", .

OJ A.-.-----,.-, --;;-r " - - ,'.

r ,' , -r"+--<' : r ~ \ I I I I )------- - ~-J-.- --r-;o'

, .. -- -- ... ' In I

f-,--- l !-6l-j

Alrcwar.llo IIlJiiproolJl'

Oy toy _ (J{!Sln'l'

/

lJoOproo"e Ij gbo f;oriJuo

zj t ~ (

~:--

--~/ I ...

: 1"~

" ,-~--",,""'---

/ . .r

1I00p(JJ:Jne V iUpu 0.0001/0

/"_-1-___ 1

" r I , I l.t, ,

!/fJUJOIDIJ (fEo{JJtJJO)

v

t r . ~ r r----- ' ~ ' .. (1 • -iF -:, ~ ~> - -- ~"': --'-

/

, , , ~------ ---

/(Ol'lOO;JQuii}I1/lJJU UOJoIJU

l/uctJ.·o CY L lIen,' ..

• ,[x, /:

[r .. : ~ • " , r

3

II

4

2. Hanpeaalba Y Asa npaB~a (PasHO CTaibe Haopeaalba)

18 KOMnoHeHTHe AHJlaTa­

UHje

19 HopManHH HanOHH

20 KOMnoHeHTHH HanOHH

HOPM3J1HH

T3HreHUHjaJlHH

r n3BHH Ka nOHK

JeA~a'lHHa Mohr'oBor

Kpyra

EJiHnca K3nOHa

" .. " . 21 H3npe331be TdHKKX

22

23

CYAOB3

OCI' lIHa jeAHa­qV Ja

C!pepHH CYA

KOHHtlHH c Y Jt

HopMaJl'HH HanOH~

.a. = 'I. (a. + a,) +'/. (a. - CI.) cos 2 '9

~"= '/.(a.-a,) sin 21'

O",.mo%::; (1", - 01 3a CPm =0°

a"mi,,=Oy=a. 33 'Pm;:!/:"

...... = ±'/.(a.-a,,) 3a 'Pm'" ±'/.n

[a. - 'I, (a. + a,)J' + ,", - [' I,(a. - a,)]'

x' y' -+ -= 1 0 2 cst . "

, t a,.IR .. ~'" (a,IRe) = (r/")

0' = pR 12. B; 0'111 :2 CJc :- a

a, = pRI", am = a. = p1?/2"

p=(H":" ~}r.; a, .... - (r .H'lga}/4ocosIX

am ~.' ';'-(3 y. H'Ig a)/1 fj 6 cos a · · .;,

3. CMKu.albe

E E 0.1[ =0 =

1+f1 E" 0, - - 0= - -- e

1+1\ '

24 KOMnoHeHTHH HanOHK

Y KoeOM npeceKY

HopManHK a,,~a cos 2 'l'

TaHrCHUKjanHH t.= a sin 2"

cKCTpeMIjH 0'''''''.' -=!: 3,n q> - 0- ~ a,.."", ~ - c 3.1 -9\ '

t._.= ±a 31 ,. - :1:45'

~ f F f 25 Knl\3albC y - 2a ~2 f- ---• £ 0 0 a: 26 CMKWljHa KPYTOCT (!cOA

27 MOIJ.'j1l KIIK3a_ (CMH- G-£ £ --ua]"H 1I0lJ.ynl 2(1+1') 2,6

28 .lJ.HMeH3HOHHC3lhe f-F/A<t, •

29 3aKHBUH

IJ.HMeH3HOHHcalhe f ~ FINA-lJ, <: fd .... '1. a"

aKcHjallHa CHna F~ 1,57, a",-2.SNd&J"

Moh Howelb. F AI" F=0.785 d&J,

IKTIIBUI DOSP- A.-(b-dJ & WHKa IIHMB

1J.0380lb4!HK Ha-nOK

cneUlicliH.jHH OT-

nop Tpelhl CI" -FIA <'cr..,

4. Haape3albe y Tpll np.a~. (OpoCTOPHO CTalb1! Mupeaa .... )

30 3aTeJalb4! y TpH

npaaua

IJ.M1IlITaUHje 1

~.- £ (Or-I'(G,+",l).

1 !, - E (<1,-1' (": "<I.)}.

1 ~ ,- E I", -1' ('. + ",)1.

6

31

32

33

34

35

36

37

38

HopManHH HanOHH

Ky6Ha JlHllaTSUHja

XHJlpOCTaTHQKH npH-THcaK

MOJlYIl KOMnpeclljc

i1HsapHjaHTe

HanOIHI

JlHII3Tau.Hja

Lame'ose KOHCTaHTe

Hooke'os JaKOH .

HanoH 32 npOH380Jb ' Hy paBaH (ea HOp­... MallO", n)

HanOHH 3a KOOPJJ:H­HaTHe pasHH

£ a. = -(I - fl) e. + fl (~ y +e.)J,

A

ay = ~ ((I-fl) Ey+fl(e, +e. l] ,

a,e ~ [(I-fl) e,+fl (e.+ey)]

A=(1 +fl) (1-2)1)=£flj).

) - 2fl &v=AV/V- e.+&y+e,_ E «(1.+'1,+:1,)

S (d • + l = e.r T Ey 6, = £ V

:1 (I + fl) G

3(1-2\1}

20p.

1-2fl

a. =1.Sf+20e.. T%~Oy ..

Yx"'y,i', tz=>r,,; ... Ty - Gyy ,

' .' . . r~-Y''''t "",=1':%;

a,=1.S!+2Ge •• 't.+Gy ..

Y,=rx::1' t',-'fay;

-+ -+ ..... -+ -+... ~ P.-P. a+pyll+p, y-p •• i+ p.yj +Pn. k

..... ..... -+ -~

n=ai+~j+yk; a-eosa; ~=COSIl;

y = COS y; a1 + fll + y' - 1

~ ... .. ..... p.-a. i + 't.y j +'t .. k

-+ -+-+ ... py = Ty. i+ay j +Ty,\(

... ..... '. ..... P. = T,.i+Tl1 j +'1, k