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Solution Manual for Finite Element Analysis Theory and Application with ANSYS, 4th Edition

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    (8) Using #we ‘elements rz 4 p Hd=orzs -oionss \ oJ EB A= 0.25 in hoz 0.187500" —— @) or Aszouzs in” R 3 : Ke. (Pwr hye 4 Zz 4 . 1000 lb 0-254 0.1875) (10-4 X10) K, = (025+ outgrs) (10-4x10) 455000 [hb 2 (5) ’ in : ¢ k, = (0:1875 14 04125) (10-4 X10) _ 3, e000 [b =o = 3 lo 2(5) nn 1 o yo uss u, o 3 ) 10] - 45 455+325 -325 ® ) 2 = o —3 - 25 328 u, | ooo Wi=o, U, = 0.002197 (n Uy = 0008274 in <= —_— Ee — (b) A =o025 wm" NES Z s1s247, A, = 0.234375 in . Te Tas” As= 0.1875 i” a] Agz 0111815 im ®) A, = 0/5625 mn La loo 1g Ag = 0.140425 nn Es Ag = 028m I~ StudyXY

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    Downloaded from StudyXY.com ® + StudyXY Sd Ye. o> \ | iF ’ pr E \ 3 S Stu dy Anything This ContentHas been Posted On StudyXY.com as supplementary learning material. StudyXY does not endrose any university, college or publisher. Allmaterials posted are under the liability of the contributors. wv 8) www.studyxy.com

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    [ Cont. Ki = 2015000 lb Kp 1985000 lb Kz I755000 te Ky = 162.5000 L Ks = 1475000 Le K¢ = 13¢ S000 L Kq = 1235000 lb Kg= losoeo lo in in i]. ° 2 0f8000 | 20 (Sebo) I i ug =) 7 i I I | ES RE . i 885008 | — 1755000) I] BS | —1755008| 1758000 | _j(2 5000 Uy Oo ASE. Lo WA USSU SU I I Ng HT us = | oo | _ nll — | ! a ! uy, ° Jlstmee A — { | —13(sues | 13¢5000% —inasvol Ug o § 3 i 123 See : J i A EE IORI Dv | - B °o | i | 123 oso prvi 1{oS00 0 Ug ] : ~t/oSea | 1105000 Ug {ooo i i | wy=o0, Us = 0-0004% 28 Uy= 0.00l0288, 4 <o.0olscs : Ug. = 0.0022 19, U, = 0.002 808, a= 0-00 3¢I34, u 20.00 44232 Ug 050053221 ih Edn) [exact defl_ | Two clone | Cont clmeit] ° oe Te Te 15 6.000 wes] 0. 00044028 7.5 0.003615Y 0-003¢13q 8-75 0.0044259 0.004232 [0-0 | oreo 0.005274 | 0-0053281 TE Fo — StudyXY

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    s00lh > NECA oo Au E \ + / L 14 10:5 412 ¢ “¢ K = Ks = (FE )EEae) [44 6 PZ Kk = Kg = 18,393,750 1b wm (o.5+1 Ya) (3-21 rs) 2:51 Y3)(3 Ky=Ky = —= "770 =1594 250 lb 3 ’ in 2 &) Ky= (X3)(3-27x10) _ 22,072, S00 1b. y n [1 ; s 19393760 - 18359750) | uy © BT Br Fon — 2 +1554iz50| 7TH) | | Ua ° CTS HiRs0 | T59H1250 | 2ao7i8ed le] - + 22072560 i u . — — 3 - -22072500; 22071500] Zisianse = o {+ 15941250] u [RSE EN id TT TT 4 i =1S94/250] 15991250 | _\g393950 i + 13313750] © | | TEEN || Us i J i | i | -18393150] 18393750 -5006 | | i i u | t i i i e 0 (Win -& ~ T= (%n-4iyg 27183 ¢ yl )E ~5.85483 x 1D - = fui SE PEA A RC | Cai) rT x16) psi C SEITEN mo )FRTXIO) py. ~ 12s Loe © 4 4 — ~0:39749 x40 [nae (=139744 41 1250) 10x (3-27 x43) TT = 148psic p: == as a Check: 0) (~gr2maxis ys 85483 )xio x ¢ PG) "500 . a. + (327x10) ec ol E2222 Jpepsi Cc I SE —— A (lestz NO) WO) igs parc cB. CSE angE a ad) _ [21 sic ES —— é TT 45 a cheeks EON (1 1258xi'h 8 1200 x109327016%) I ipc CL Eo522 9s py ¢ A xz) Qas a check: Lt Fomor AT (lesty3) z — StudyXY

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    LLLLLL GN rss i [Ul K K= AE a i £2 o 2 K = Ko GoReooe((BAX0) = Ry = 0.025 © q Ky K, =Ky=1.32288% 10 N wu 2 3 K, = (0:02)(0-00L)(48-9510) © Ky o.l q 4 y K, = 0.08208 x10 MN 800K m 1 ° pe - . heres ~+3198 ‘| o Jol Disme ussamiectnte 29 o8re¥ Ya o | . 0.092469 o.0gaeByl ings hin Ye _1-32298 32208 I 1800 | 40556 —0.0%26% os \\Ye © \ ~ 0.08268 1.40556 sag LU NF AC -] [<] 1-328 L32288\ (Uy goons | n Ie } <= w= 1.300 BX10 m u, 2z.33135 xm W, = 2.449202 x 5m eee — te a) U,-4 3 1 3c0clgxiD-6) FUL E Yam (epanie) (1230088 XI0 TR) 3950000 = 3.75 MRL 1 Y oons ZL = as a check: Vl FE - 18% = 3.95 MPa . A (0-08)(0-006) TT 3 -6 FE Ug-ty | rpaad)( asain eUEXy 1s MPa < yi ol as a cheek ¢®_ \30oN = 1SMR, (0:02)(6.006> c -u 9 R RW COE WY pqy a) oT RION0, 5 gs mp, y 0028 - — StudyXY

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    3 K, = K, = (4) (er9@2x15) > 44 3 2 K, K, K = Ky = 7x0 A in . Kp= KyzKqzKs= lo-625)(s)EEN2) kd fru, ) = Grrgakurits 8 i . «4K, kz = 27343g Lo i . (COMER Soo 1b K. = (4)(273438) = ( 2)" (4)(273438) 113750 Lb i _® le o pd “ . pit 7 x10% 1093750 — 1093750 Ua ° . B - 1023750 1093750 47x10 - 7x10 "| o ( Go 3 =7x10 7x1 | Ly. od 8093750 — 1093750 [2] TP I b A | uy = -10937506 2093750 Tae | \s | [+ 7x10" 7x10 | WM Soc } -5 -y 4 Uy = 7.042857 x 10° in U, = 5.285714 X10 in U. = X10 in — Le A — | — . -T. eV gy Math )- Lgs (ZT 2) toes to. J 2 CT as a check , FE. Serotec lb A ()0a25) in 4 _s £a E(t) sand ((S2ETRNEAC | ole, = £ Ce i aso check. No) So wee le (25)(0-125) int 4 4 CE FE ULL) NE Zz’ 2 To — StudyXY |

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    1 B Ki = 7x10 la 2 {1a} Ka = 1093750 lb m 34 [3 : Ky= 7x10 fo mn jl P=500(b (I node 1: I R-K, (Ua-ty)=0 Ky (ua-up) . K)(da-4,) nedez: 4] Ky (tat) - Ka (U3-U)=0 | x (uy, Ka (Uz-uz) nodes: | Ko (ds- tz y= Ky (Uy-U3) =o Ky (Uq=Us) K3 (uy-u3) node y: 34-4) sce | Ks(#y-Us) - P=o P In matrix form: Ky =k Uy (-R7 -K, Kit Ka ~Ky, u, ) 0 \ “ka Kaw -kg Nu [Yo Ks KX; | [uy P

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    ' [0] Kz 80 Ki =5 Wn wy kezto lb 3 Tol; rs IME) peel © Kky=20& —q © 5 “) Size of the global matrix: 5x5 oo © ®@ @ o 5 -$5T70 ® rg -gle [x] = [5 Je [k] = [% HH @ @ @ a 5s -57@ <3" 20 RA ® TT sje [rn os @ @ Ko io 5 Fe) (¢) 2 -2071@ KJ = [ HA x] = [= 20 © 5 -5 ® ~-5 5+845+20 —- 8-5 ~20 [x= -8-s 8:5 -10 —-20 —-10 20410420 -2.0 -10 20 applying BCs and leads, wi zu;zo F=f FE =io 1b 38-13-20 (us © -13 23 io Uh =40 —20 -10 50 Uy 1) Uy =0-942 mn CUy= 0.874 in Uy = 0:7501n <= node: R, << Ki(Uy-wy) R= § (0962-0) = 4.8 lb node 5 < /3 ——rga fs Rs = 20 (0-760-0)= 15.2 1b Kdq-us) note also as a check, Ri3Rs= TE 4.94152 10410

  9. Page 9
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    1 so 0 | i T Io S887 55] ] | Y Co 5ggt —2.agl [EE To o ~5-88 3.27 | ; | i oo IP py 10 | | T ° — ——— I-10 [10¢ass)|-0.581 | | Ta [4 150 | i i | ose Ell | (TE) e . LS EN [nm SR TT | joes a. T. o | -ogl |e 2.22 . EE EE EE BE nl T ° | | | HR SELLA E— | I EN EN ER | ! [= i | dl pd Te “8 : | i o |i nn 150 10 12-04 17-31 » T= °F | 18.51 <= 39-12 §q.4¢ 59. 85 ég 4 = UAAT = (047)(I50)(48-5785) = [gop Bi f ¢ he ==] or as another example: —_—— i 3 = (e78N(156)(54- 46-3012) = 1 goo gh er (150) 2-10) = = [00 Bl ¥= A (T= Tos) © oUt odq ola + 12810451 org he 2 Resistance

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    oo 5 -5 | T 20 123 a an Ty © o [TT [ole Na ©0653 _ es 1653 | SE = | { oess] 0.0534 _.4,] T [o] 1 de] | n.22] "222% 15 I ——E ARE — SS i. i i | | | 1 rel T ce o 7/1 iso L0 20:37 22.0% UE 2-95 °F ¢ 45.57 ¢¢.54 6g { = UA LT as oan example: $= (-941)¢s0) (68-4c. §4) = 320 Blu he or a Fs SE A RLU i PE PY TT . > Revision, © 171 © R14 1:32 +15 + 0-451 6.63 he

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    with dhe help of a WE Psychometac chart, using a dry bub Temp of £2 and dodo; we identify PB 5 Condensation femperature Ho 71 boll Temp be 42°F Thus condensation will occur between Surfaces 4 and 5. ) Koo ° ! 147” 7 | T [1s I | -1. [47+ | ~ 0.053 T | o ACA Te hte I I 000 | —oes3 ogsst 2.22 7 N o —~2.22] 2.224] _p.g | TE Ei ad HE ° | Va A Ts | 70 | i i to an loos 150 16-81 ° $18 dso q9h F <= c9.19 70 = VA AT AS an example: § = (147) (1000) 70-68-19) = 2cco BAW he or — <= § =(147) (eve) (1-01-15) = zcéo BIL — StudyXY

  12. Page 12
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    ' + o 22.5 > oe SE Ir 20 -5.88 5-88+2-5¢ -2.5¢ T. ° 22-5 . -2.5¢ 2.564147 —1.47 5 l. “ea ATT 70 “0 JL 22.5 20 {tr} = 26.95 °F 42-59 70 7 = YAALT = (5.88 )(22-5) (2645-20) = To Bhs op as another example: ~ —n = VLALT= (2.50) (22-S)(4 251" 26:85) = 900 eo <= —_— or E— (T-Toa)= _ (22+5)(70-20) : 1 TS Pesistanee ’ (0114 6-394 0: £8) {= 70 Bx I _ hr

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    2 2 (A)=(y= (222:5)3)- 1 (0.5) = 33.11 in Ki K 2 i 2 2 (A)=(A4y (10-544) (3)-3 (0-5) = 28.660 in [3 (3 2 (Ay = (13) - 30 (0s): 26.41 in" < ‘ (K), = () « (3:14)(327618) 1g p72, 795 Lb (4 m £ ¢ (Ky) = (K ) o (gw@)(3:23x10) _ 15 £20,245 1b 2) S\N, ET 7 in (Ky) = GANG) | 4) 590992 1b c y n 2 ¢ DE) 0-5) 2 (K), - (6)s=(K,), =(K,),= GIG) -S) are) 2,947 068 bb ¢ in 2 3 (k ) = GE)os)tzaxid) _ 4,270,602 lo 3; re = n The Combined st ffnesses: Ki = Kgs = 18072745 + 2,847, 008= 20719213 Ky= Kg = 156202454 2,897,009 = |g 447,313 Ky = 24570 992 4 4,270, 402 = 25861574 1 © 26 YA 3 | ~20419 [ o yi ois ur IS EO PE Ee Ee i wl fo - XY TT hE SE Ca i id NY WN DCN UO -25 gu, SY NR I 271 rs SB ° — = ef [TR REE cong | | Ye © i | ai | | ms 20403 | | Ug ~(s00 | J Ui=o Wa =~. 79016 515° in 4 z-ronas) xp? in SEE LRT RR LT BCRP FE Ce —_— A — StudyXY

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    112 oo Cont. LE (uw) - Benn SYA Ts gw 261 Concrete I = EE = Sie Foy = E (Yast) = z31 1b ¢ £ n> as a check: 6) - | ALE 6A), = (6) (si) +2306) Eos) = oe 1B t -4 -5 Te E(t) GAmDCE TE CTC) gy 2) 4 ¢ . in T= 23 1b ¢ fi , in* . 2, tA check; a A) + %.), = Go)(as¢1) + (231k) )(o-5) = (060 il (3 3) 4 -q 0. = Fo LB) (3-27 x18 )(=1- 04/8 x10 + 1-0 Lasix (0 ) sa c 4 in 3) 4 Fo A 67% 0) pag) (orton ave) agp . A 4 it Check: i chy = odin) 4 (229)(3) (1) (0.6) == [000 Ib : 3) A), = BEE) ae) + 0 = Ae ug-u (3 27 11 FTE gx (04 Lo C15 X10) em Be (Mente) = (Siam x lr Je elk “) 4 ¢ int 0; = 23) 1b C int . 4 pos (lcs) (3:27x10)(-2- 9354 age) Kio 20h ‘ A ‘ in (5) —_— 0's 231 NL, h* a) (5) @) I note 0 =F and b= ct as expected.

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    ©) 2 N = A... E (Wy - U5) ad )l ) 3 dy ) Moy - Ko Ns KOR [0 5) = 2 A = A = A de Ee (Lig =U) + (A), E. (Uier=47) 24 2] JAE tA) El (gmt) & 24 4, 30 * ¢ ny A [Ets a1xe)s Ges) CL) gtpoiens)= 0.024 Ib.jn or) GI) 2 y Ae L ~ Jeornaer eta] o.024 E (2) A A ACERT | af ¢ 2 3 2. i = [(CRD010) 3 20D) EI) Is tae drm) 0.027 or 20¢) a v AM = [ ” Jer: 94TLEy 1 qoeIR)nD 3: 0.027 Ae Bh), E+ BE (uyuy) 24 3 > ¢ = NE [Ceniemad)s RODEN 10 aocroy ort] 204) = 0.019 lb.in A = GY) o-024) 4 o.o\q 2(0-027)= 2.42) \boain <= hod —_—

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    , P=3slb ee hr 9 Ry ” Lr sr weet, I. @ &xM =o (-€1b)(5iny + (35b)(Lin)y+F (Bin) =o £= 30 16 f= Kx 30 lb= Co x X= 0-5 ihn <= ee 801 ® — ol T drt. > 2 © m = 2 AC oS Fu. = Sw; dw; a du; z =e So (Lkyy- 3 (59K) $F G0) Cgxy =o Kx - SIE). ()(5) =o po GGG) to X= 0-5 in <=

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