CIVE 310 Lecture 5, Fall 2011

STRAINS “|. ial Stans P——Shar Sins —~ Lael Ses, Lateral Shains SS reer ‘Tensile Force (P) Agia tee Ps ae Compressive. Force (P) ~~ Axial Shortening bx seiait Sanne SCO Socom SEs re ng ee ae ans ESE a _ Lateral Expansion. . _L Lateral Cntr. a E —Eigypp= i | — cat Sb 8 Por... Elastic > Plomogentous.,..and. Ssotropic...matenal.... defines... | adefunite Ploperly. of material. » just. like called. (oissons. Rakio,V vy. lateral strain =. en leral shine ve od > Concrete. axial straine axial strain— OD OF mye Steel. = 0:5 —» Hubber [Vol db te AV = YY... _ A B~ 2b Sb | i i | L i! \ A OS a AVS OW shoes le SReoritical. values of V varies between. 0. and o.5 j | Vso. => Ey = 0 ....Cno. lederal. strains). | yYv =m 0.5. => E€.. -. = -05.€, . I Consider Br®. ee L oo, Inbal Volume Ve BL I ; Final. Volume = Ve = (hs) (Lea). Lee. ne m. ue, a BA-2bSL. a \ A _-4-Dilatation = near -Change.. 1... lume. per. unit. Volum = AV. ee VA But € = VE, => 2. =-VDS | | again; Yeo.=p AV= HA .. CIncompressible).. en | | Volumetric Strain. eae ete eae 7 q > Sarre — | Sperm Data 2... FP AOR KINA . axial.elig..os N= 0.249 Ye | dons vedlaclon xb. $D=D, mal =.= D.01215. mm... |..Comapuele.. Yand._ 2. wand. AY.2.... sesso hm t seemeseit a | A) {t Ip | 8 N D t aS i 8 S s WN 8 N m ' a a =p =~ 0.000243 mm we onternnenennen ae sh io b) S wr a Wn Elaterat 0.000243 = 0333. a i Ex oO o00FS a cot Ble 2 Be O;. a — ie P ——s __100 — = 0 0pm. i es 6,.A O1000F3 & FC5O)” ry? — a a Or Te FO GPa... — tie. Dilataho. Ye... BY. a2. ne Soe Avs Vp My en sn ne ee nee nn ne eee nnn eect merge ent nes ye fennnmnant ¢ em ee C50)" 4 ie . ZO so. SANE. 6 nl... fms ass i ae * D H . OI ae IIE IES 2 —Aps Ze Ep = 1962544 mat, ae Me = 5BIUIZ.2. mt... eee _ly = Sod. 249... mK O0.249 mom. J _ -y_AVn 589/92.2 — 58901. = BG rune. AY. =.0: 000243 22m | ; 4 i ' 1 | i = ! i { \ { 4 | { i | { i | i i ORS. an 5 OV = = Aveo ae A» C120). ee _ = Zebay #02194 C1 240.333) = 143.3 mag. LB. 6. Coca x (le we 0.00073.5.C1-2.(0:333)) = 0. wots ae am u m3 a i { | iy i § 4 hear Strain - Sbvss. Soin Feelations hip { i ! 1 | oof i { pone nn fm | Cttre. Shear. Planar CASE. (2D). A y OY or ob Shear- bhress.—-» Shear Strain. A(T) SD H Shear strain. measures. ditorbion th. aye ne i a Shear. $trln.,... oA ea | a ee pe it Pitas i ° i ici . : _ ° HD _ ealived Shear: ShressSkrin. , _—Piagram— | Biter wa We) Se 17 © _ _ - — _— K Sandwiched... - ; between two Comparison. between. Axial 2a Shear (TysT)] en, (SO | Consilr. an_tntentesmal... _ _ | clement at, dy, cle. 28. Shown... “The-general state cp. stress. and strain, ale.syattesized... ~-4 r tig. the print ch ipepai & . 2 Sx cpaliat, ‘veered B? oe. 7 Gener val_State of Shes. OMe i tas. Generalized olds Law... _an_tnhnitesmal clement... ee a an. lake onl, oe bx Jomagenenus aul. skobaple. wabnial.. Elastic, w ni a oem. on - we ee te meee geen emee nee, | let é. Mederial. rogin - eriginal shape aher_unloading,.. i . Shress.and, Stale ave. proporbionst..;, Haz. ov tees vate yess = ml emagenieas. Matevisl: » Watevial. Popetet- se te amet al. points. _ —_ ae ee ne Of the. body... senescent nen q pila Material 2. Makevial having same. ve_prpectes ta. all. dictions. aba. — i ve . LSame.. Stress _sholn. relationship taall directions at. a potdt..) ll Ssatrepic PAL EVAV co cece vi van vv nce eee mii oe a a aan rap erm pee nts ee iy ne neg ee ne en me a —: Cee iL Same. 0-6 elahionship, th K¥5- and. ciactions. ee coe Examples. en cece inet ee enna nnn wl Steel Homogeneous and.tobropit.-' _ { ——— ane Wadd... Nan. home gentous._dnd._ Anisotropic... pe __ Concrete. a (Cor. Non.. Pomegenents»- _ m7 shoul, be. robed. bot. any. “body can be. heated 10s a_homogeneouts — al the scale..dt. which the. analysis. 15 conducted is made. sufficiently —— ofp large (naked. eye level, gas Jevel... atomic level, or crystal.size.level.).. 1 é,--V Zz ik. Oe €,-% . | Due fo...triacal. loading » Ox, Oy, and. 03, and. by super poston’: . C Linear elashe., Homogeneous, and. tsolropic. Material). 2... | Axial Strains .... [Due te. 0% +04, Op]. e.-&_ yO _ v& fa... = = = ab & = = Sy _ vy % Oi uv Oe. E E i) Gps Be ye vy 31. | E £ £ . the cee te teen ten _ _ ceo coe i + Shear Sbains... yer + Canby Dye Tayl ne 2; Ee - en (ee QL, Gs and VY.ar. physical. properties oh t the. Mhdeoral. ma Dieta ad. Bulk. Myduluss | ai TRE sides dey dy, cond. de Q the snPiovtesna dement considered. i before... become... C1. Hex Ydx.,. C14 Ey), ly. ond _ MA». 2). dd: epee a . pa Flere. straining. eens ae eee de. yd. pede nee) sg ——EO™ eee neuen teutevene eg eG bz. pee nnn ok. dy da. L 1p Ex. eye Ged ne b eo Mk. dy. dz. ieeyeter Ex, y- ree ae Sabon . 7 ae ¥; La dhesdy. Fe oo i nS ae AY = _YV; a En sbyy€a) dpdgde og ps Ul, DI and. BI. enn on | — be eer Gp e= _( 1.20) Lop + Sy 0%]. i _ | Eivan. elastic bay sade snr ike te shtessens , Os 20y=03=—~P— —— | sucha bodes jerk ine ‘pies Pe pleura. ent ten ne nn = =e. 3-29) .p a ee <n eye P---—---= OMS sage ses). _ Guibrt & G=Ex€é) ; Example. - ts Subject. Aydrostatic pressure. | Delermine. ehange. {u.. dimensions. Let the cube, and compute its bulk “tnodalvs. A 50mm - cube alle of bbeel., F=.200GFR ,.V= 0.25, of uniform. cnbensi ps 200 MR. Cpu VF v Geo CL. 2v) = = - 200" man 24025). E = E& ~—_F-- 200%107 cece eeney ete sug mutt ot gy tne nin sie watunareete ee aaweweseanieemaes wate ewes _=-0:0005. Yam —= we 005%... az& x= Oy =Dz = Exel =. =O. 0 an S0.-mm..... — 0.025: OL Tf ae ee 2 Reduckion Jt COONS IAL... Ee 1 (0540 a). 200 MR et ee A= Grr 64+ 62s BEng 3.Co0S”) = OAS Lee 0001S. PP or > _O= Oe ee _ oe ke En © 133233,33 MIR. = 1333348 e -a.00IS" IR “simply, ke £ = 200GR. 8 133.33 GP. a 30-29) 3 C- 2 (0. 2s)) | Beoal es Oe . | LC). Plane. Shress, « AU shnsses, Cantal x shear). relabed. B... th EU’ are qual. 13. Zero, ee te ee ne a>. OF eal TL. ne Oe — GE 1 ®) 2) ane Shan : AL shrains “Conte shear). ‘relaked. 42 ZEOKIS 7 ae cpual & Zero - EE re ws Ena he-Byo= 0 (Ho) Pes Sisfoce. ” (From ya ‘[T3])_ Reaction ore COx 40) ve CEES [ll Plane Shain. CE Gol Fake D Dams... f i ee m "Preesuve Vessels, 8 ~P “Generalized ~~ ee See ae