Applied Solid Mechanics Lecture Notes, Lecture notes of Applied Solid Mechanics

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6Yiald point AB- Ela hteeg'n^ htht^ aicvial $tres/shain (^) Cuevt. LyuTSC^ UItimate tole (^) Sty).

Sroin is Measued In V4s ( t n i t t u n ) Yictd oint laih the mit. l ashe mit of tht natial) for Jam Motu b E F O R M A T I D N the and with t o n s t r u c h e n . l a s t l r o n A t w m i n i om the More th lhein o m a t a n i o T o r s i o n al b i t t l e M a t s i a l s D o n t havt ( B r i t H l e at (Sudden enid). S r e s s neh anital P r o h u t i e Jbbutidd^ P u i n t 3Mild S4cul (ogneeing t h e n ( u t r a i n tarv) Anothot type is tiue šen /shraia torv. ln true S llios S e r h o n al)

Stahtallytndtexmant shochue

Ue tonnet ind ih joritO athag isidt he shothur oth one tquahon ( C a l u l a t t v 3hes M o d u l u N a t e n i a l 300mm 900m A P u 5 D K N a S t r e s s e s d v o l o b d bn the eol and tho tobe Est 20 DG Po t C u = l D GO Pa dlao dsc 3 0 0 m m l a0mm dia 2 0 0 K N {m A=s mm 1 2 5 K N Im D H r m i n th ow she e at sta dt oach t o m p o n e n t R A e t R s c 200 KN R e B

R g c 25kN AE P u 9 0 0 t b o Y I o ( 1 0

) Pst Pu P a t x 3OD B r a s s 25KN Bran C a l u l a t e S h r e s s e s in Pods Ast 00 mn mm P a x n S 0

Th euma S h r e (han s ge ta t e m þ e u a f u l At leihal lengh o} m a t z x i a l = t. .dt = xl dt a dtxt (nihal lngth) and dla dt( han ge ln ten) di

dt S y h a i n e= dt

tbluent epanion. o themal T 0 0 m m ( 1 0 6 0 m m 600 mm 3 0 0 m r n 6= xo 6 bx ( 0 6

2 1 ) . 3 9 7 8 0 x 1 0 Est 20 0 G P a EM= 1 s G P a t h o t m a l S h e s s x p a n s r o n bung Modul luu ad te change 0 A

rod Dm ong is ied al boh end b| +e turmal sheus t not to ex cued Tb: MPa, a f e u l a t e thi t e m p e r & t u e t h i o u g t othith o rod s h o u l d be heot ed. N I 7 1 0 k a v i r t = 2 m hut due to tht hang Lo t emp 6 = HPo =16S and f i n d i n g thrmal Ihun dut to this ehqne And G (an be SzEX dt 10ond Out a u u a l . u s e s t e d t 6961 N fmmt ach oth is t u u a l stvas / a v a l a A 1 s o d l 4 L dst z A 1

N A Lst t Atd l = 1 1 ( 1 6 7 v I o 6 0 0 2 3

4 x | 0 vgo0) this tonp nien

0

2 9 8 m m in duu to {re d e o m a h o n An qmout o At but to At ahd by orte reqto pvo nt A L . A n d ' d u o t h i s t o r c e isha Est

6a

Elasheonstanb ut a0d bo Ms. hr Nuts a t h h i n t u t ht t o m þ r e a s T o e foad on tuh is SOKN. S o t e v m i n t Ahe t e n b e v a t w e the Sh( 35QA |n the vod and tube when SOr ( n d a t i y a i n RuRw = T h e r mal P< Aiat P o s o n Raio =- l a t u a l s h n Pot Pu 3Pst 2Pu Pst 20KN and Pot

Pu= S 1 2 u o x s 0 0 0 = 6 3

6 9 KN 6 C u = 3 0 1 0 3 I(uo20= 0 0 0 1 8

: 7 = 0 : 2 7 1 8 mm ( A t ( M u -at). 118 0 = 6 s t . 6 8 0 0 S 6 u Posos Ratio Shnss duto M a i o r i d t o n d i n g V o t u m t r i Strain oh aial oru I n i t i a l V o l u m e = V lbt: final olume = (t A 1 ) , ( b

A 5 ) , (t- at). thang' ( l b t

b 4 t t A l

4 A b L ) tbt = (bt+ & l b t

A b l t

At b )

l b t AN m

E!as He o n s t a n b per p d i a u l a w ero AN c i a l V e l L i t a l o t V 4 S i m i l a u fov o thy ho o 0 7 1 9 e 4 T h u e a l t w A d d i i o n . thag in volomt o He blotl ohsne t L 0 0 6 P a , me i0/8, 83 E (^9004) Pa 20010 N / m n ? 2 5 0 0 Y 2 D 0 2 5 O D A 0 0 r 1 0 9 5 0 0 v 2 0 0 v

2 5 0 0 a 0 0 x 1 0

2 0 0 6 (tad snal) 2 5 0 0 200 9 s 0 0 v 2 o 0 2 5 0 0 2 0 O , 2 S 0 0 x Q 0 0 1 0 10 Shatn inm dir d to toad KN (w) Bulk M o d u l u s K= D i v t t SN N o u m e h i C S h a i n Shah ME 6 4 d. d d i o n c . In hrec divs S r a u , thr tuoo ao n, dv 3 d dv

$tain taergt strs and S6rr dont ot m o i m u m " a l o g H n Are ondu tht s h i e 3

h a i n torv s t r a i n ststd tn a bt åy daing oot. s o t d n l y Ptid to l#. E 2 0 0 h o a . wheo an aia lod A e g A S 0 _ 2 5 K 2 Sama m i l s 1 (28A At t tt Aveag Lode ped PoP 2 Asthe apptibem o load ts dont ado ally . the toad is c o n u i d u e d vbagt all tht imu. & 1 J u d d e n = | 6 2

4 H P a A tlors dont -loadv d i s p l a u m e o t 2x 2 0 0 I 0 gadual e sudden 2€. 62V 6 2 A l = = P x C L P load abud with Im þact. A- Area o}0s Se then o bat bat G 2 P / A , (oad Alo tdorb done c F o r t e d i n p l o m a n t P(htd Al 2€ sA p h

P o l = {a d A E A E Al PhE Pt t a u a d r a t i e s l }

ridy ottahrd to votial oigbt jalle to IDmm on a tell bat Ume long end 600min stthm.t the movimum n s t o n t a n c o y & An un Knewn tdtsin is nm,find out the lut e eke tün ougt and t o r r u o n d i n g thes Take fc kPa. A600m f 200Pa 20bon Priouhal skUS ond strain u E S O F 90 MKS J U P E | A plan whove only ormal shs oct and the sheaH stresu at zeHO Obtihur plant

flant at ony angt M pnpuing P ( w i d t t 1 ) PL fn is the normal lo ad h t h e o b l l q e t blang MN ! . P o = M N G MN n MN). Strain ents fov Shta shain =62Sin 2€ (^) 62V P U o l o t M N 6MO Cos= HN DD P/e ADx = / a l o ( v i ) x AD MN for 9g=^ þinupa 0, 1 8 0 ° , 9 6 0 ° =uso ( a a r m u m ) y sind =135° (Mini mum) stng

R n u t o n t ond angle o v e s u t 4 a n t

o and Po ?

THNCOos ON Cos M 0 s i n e MN MN for srintibal Jhoy:i- 2 L S i n 2 e

• Cos2¢. 2 2 40e bui thut v a l a t s i n Co then tR shtss o c h e i v e d oiu se prioupa t .tan 20 2 ay : i n 2 0

2 y 6m 2 B i a i a l and Shea G r n 6(

frinupal dhs N e t h o d (Nohr cir de M e t h b d ) OxQi v e h r e s e n b N o v m a l Jhe Y ais v e p r u t n h Shar Jhus oAsign all n e r m a l s h sta at X aù aith vohect to O. B i s e c d 0 Pat & Taking fetat h radiw 28 om & fn t l o c k w i s e d i v z h o n to o boint Drad a p e p i n d i ular MN on o) ( 6 n , t ) M M 6

M & l e s 20 (So,^ N 0 ) ( 0 ) (Gn- ) P ( G m , 0 ) 3- fro ukut to

f make a p e r b n d i u l u equal h the l u n g t h o sh shes ty ).

from O a^ makt LUay s) hith r o p r u g n b th é n p t i m n i y t h t a h y As on ho i o n t a l lant the n o v m a l Jt is Zno 5 Join Sand u h i c h b i s e r t s y at T , N O w A S 0 T and arAf aut stmt la M ( G n e ) . N 6 (0,o (6noT

Torsion lkint ol difteai h ehith the i no th ongy in di ante e lngh -kAd M a l o u d h a l t i s u n i g o v m hrov ah out T o v s i o n a l stus and s t r a i n : S h e a y s h a i n t = D { 6 D 84 JO stel Shaht hu to hans mit k^100 at 1 6 0 r þ m takig ll o u a b l z siar shs as 10MPq ind the S u i t a b l e diq o the s h a l t . T h e Nan tor qut t h a n m t e d In eah v a v e l o h n o v t t i b t h t mtan by C i r u t r s h a t

• Shear o t v e s s at vadiu noiu be R &rto dht e l e m e n t = 2rad At a diu, she au s tresy t ( 2 r n d ) ( t ) heeu fovtt at he e l e m e n t he tDv qut v o d U c t d by ht e l e m e n t at m d i s t a n c e 60 T = 5 . 9 6 x I n s o l s h at ( 5

9 6 = T xD = A 22 (8o id s h a ) . t l 1 9 2 ) T o r s i b n eau ahm and T= R Torquc p u e d o u d by tht ohelu shaft 32 Polox H r d u l u o } t o r s i o n 39 27R 4 16

4Sod f h e s t o 200 mm dia has 0 3ame ro 3ech on aa as o hollo Hnd te ratio o shelt o th s amt m a t e u i a l wt lnside dio o isomm t y a n m i t t e d by oth shalt als ame an (Q00) ( o

i s 0 y D=ulu ia o holl ow 250 mm that Voy tus uken c o m p a r e d to Hte dolome o Df Tha t h i c k n s must belug than Ys or yacth oh b d i a m e t e n P h o l l o w D ( D 0 0 ) " 2 ( 2 5 0 4 1 S 0 4 ) 2 Torai on t h t e e ' s n o chan ge in shabe but dsplo tumcat o oin Ahuc 0 i r w n j e r e n t i a l Shus (o) hou Ht m a l o n a l is b m u i n g t h u t too sho) <. lo Dus hsht o ength qnd at m d i s d a n t t = t h i c k n u s diamotoy=d^ =t^ S h r e s s t ruit d i h o f m a h e n = 61 Total hore athog oo u i r w n j t v e n t t = P(01) fayide ao tensid ened a R r t f o n f l t 4c Roshng tove (s tueto thuq shipu oh tonnrdsvom) tytinu togtodna Shres (62) = Prnd? 4 Reoting toru = 2 6 t l 2t the d i e m t o 4t 5 w i u w e t K to th ang l a o q t h