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Solution Manual For Applied Strength Of Materials, 5th Edition

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    CHAPTER 1 Basic Concepts in Strength of Materials WA 70 [o{S ANSWERS IN TEXT, . [16 Wem g = JBo0My 9.81 mfs> = 11658 hgmn/s*e/Z748 W=71744 147 ToTAL Wr = mg = ooo Rg 931 ans * *39,204N EAct Frowr whee: Fr =(E)(0.40(39.2000)= 785 Av EACH REN wien: Fy =()(0.40)( 39.200) = 4.7784 /-18 Loaciua = TOTAL FoRLE/ARA TOTAL FORCE = 680049 -9.8/m/s*=66.7 kN AREA = (5.0m) (3.8m)> / 2.5m ™ Lotome = $57RY so vu S351 A0fin¥ = 3.8400 LAT Fotce = WT= pngo= 25 kg 98 mmfkv=2us ns K = SPRING SCALG = YSVON Jom = F/B aL TEs BILL = 0.85Y5 m= SYS Ks Im STomen [22 wW=/2.9AN 212200 4/x 0.2248 L8/N =3980L8 1-23 Fe =785Ahn- 730 Nx 0.22Y8L8/n =/765 LB FR=1.7740+ //770/ 20, 2L¥8L6/w = 26¥6L8 12¥ Looms = 3MAAe = 3BINCN 0.229808 1a? == “ * 4 AN a = flele wet ER aye = TLL, 12S Fs29sw-0.229818/n = 55.4 La K= Ysvo NM » = ON 2.220800 Lo = 28520844 ef, SSece Abe eG ean LLM

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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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    /-2¢ - AT 28 gs; -s* [1-26 mm > en 5 LS, 8S8.YStves /-2 - ao J28008 st L227 om al Tor 398 L652 39850 ves [29 f= )200 ix 6.895 Rib fos = 827% Kpe : 1-30 OT = 2/600 pal XE.8IS KA f5 = 199000 Abn < 159 ith. 1230 Sus 17000 454% 6.995 Rin /P = 96, S00 kth < 96 SMP. Su= P6000pe x 6.895 Bfs/pei = 509 000 Aff. = SIMA 1-32 m= /ISDREV , ZR RAD. Jrisn _ J, —= Tw * Hey Ga = LE Raels 2 /= = JY. nF x 252, = 33 A= 00x Yon) = W900 * Warid Y= 0.08m x 285.Y29m/78 22.03 mm 1-35 Oimewsrons: 18 nx 2s. Yom fri= YS prom 12.100 % 285. Y omm Jon = 30Smm AREA = (18m\* = 32¢m* 3 aren = (51mm) = 209%/0% mm ® VYotvme =V = AREA »HigrenT V= 32¥m?y 72.1 =3888 14> V= 0.575 1oFT=2.25 Fr} V = (209818 mm) * 305 mm = 6,37 1/8 oni V= (0.9520 % 0.305 mm = 0.0637.m%= 6.37% on? 1-36. A= Nlo.sism)/Y= 0.200" A= O.200 wel 25mm)’ 129.mm? Nn —_— - = L= 22 3 = - 1-32 oo £ Zo fry 0.7 Mp0 = 0.7 Het — =L = 2040} - [38 of ToS = 86.9 Mp2 = bE Tm 0 [739 o=f.- Bois : _ # (0.40 /4y SB pet [40 of. Bswre_ i = a Ho 325mY/¥ L7s0pud

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    /=%#/ Loo owSHece = Wang =/8Y0My-%.8/mpr = IBDN W/2 = 25 N ov EACH SIE Zt =0= 025) (boom) = Cy (200mm) er Cy=¥52 [3 €= ofan 25 ¥# L aks - o=f£_.C_ sw - 7% = RT 79.8mFa. 600 eso ~ =P _ ZoosLre : o=2L = L¥z TTR = 1393 pai -y3 o-=Lo= 29500 Le/3 Lis yw 7 2 = 8034 $y gL 350M Ak a 4 A (80mm = $Y. 2 mPa 1-Ys sm arog Panoky 98m =ypr2hn no ra 8y= AB 4in 3S ett ee | fod Bcy= BCainss® : Bey = BC Coa 55° i © Lgen SF =0= Ab ~8Cx al 0 = ABA 35° = BC .amSS’ . Bo AB= Bc =" = /Y288c pia hs = pry £Fy=0 = AB, +Bey 9/244 = AB cds FBC CaS ~ 2 MY 0= (L928 80) Ca3s® + BC Ca 85° ~Yh2 oN 2hv= BcL//7070.577] = 4793 8c Be = #28) 358 = 23,63 4K AB= 428 Bc = 33.)5hn STRESS IN RVD AB: Gym AE. B75un’y oe gr SIA < 101.9000 [4 23.63x4%/ Stress mw Pod Be: Ope =< "ey 05:2 Me , 80 _ Hl.2 0°. STRESS IN Rov BD: Opps =: Toomey Fy C4301 Mer

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    LHe F 2001007 1m Rn™= (0.00092(0.90)(0.60) (3000) * F= 2349s . A= TTC6m1m) Ji = 20) roy my + = £. Z3eww a a A 20) ran = YEH = z_ z /-%7 A=Bo mn) E= 900 smn For pas z= (10 ~4ora)he =/2hy G= Sano pox = le? MPa TEWSIONV A 900 mm» "mt Fok Be: £, = po -90 = 7040 _ FA 3 : Gwe LN 028m TENSIW RR CO: F< itohn F, 3 PA ad Lox, QUO = 122 AP TENS I0W LI pecs: #0; ne 12s tom C0; A= mURYH= 200 mm ™ FoR AB: Fg = 94S ~/2.32 +495 = J1.52. Aw Fas _ —/7.5270% Ong © = LLIN NH _ 5, . ‘as © ry Tween 35.7 Mba ComiR. FoR BL: Fp= -9.45 12.32 527.9240 = Foe _ =2.92300°N Og © =e LILY yy A TT get 4.7m come. FoRco: F,=-9.65 Ry , Fo = Feo o ~165 NEN =H. 0Mb_ Lome, Ae 20/ mm L482 A= allie) 00" Yr = 0.999 102 (13 ui Pree-hre. A42) FoR: Tg» L£Bb= DSob1e _ ; Td Deans S029 P5/ redsnw FoR AB: Fp = 2500 +2(8000 Crease’) =/4 35004 Tas = Lae. Loos, =20 #11 AT rewsrow

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    [50 EM. =0= 280005) ~F, (35 N TT Fp= Y200 Le 2 oss Foo Y2008 - . 9s 8" A Buna SA fr ol | TENN Fe = 280018 1-37 5 Jonr 8 B0=/0.5hN 8 2) J AB Bc 0.54 10.54 S.¢5k0 / 14 528 Joint A ? AD an 30° = 5:25 AN “ Ao = n.shv =co A A6 AC =A0Coa20°= 9.09 hv = 8c s.2.5k0 Stresses: s As ac: Fy= i. = FOIA ozs npn. TERHY (4 2X30) pem™ Bo: Go= Loa = Jo —— Botan = LL. revs AO, Edt A =(30) (20) = So0mm* - 3 Bo Teo = LOSXLON_ 2), opts. Comnmession $Y 0 my ——————

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    6000 12000 Ey =0= booo(§) +1200072) ~Re (4) ok Le Rr = 10000 Le \ 2M =0 = ]2000 (5) +6000 02) -R, 08) 9 . 8 Raw 8ooo Ls Ae Ay e Oo 2 O = id ° € ALC Ao £ 8 Ie a= 8ovots Ra = AB ao = A600) AB = R, Jo = 8000/0.8 =/0000L8 (sms, 300 AP= AB cra0= /0008(0.6)= 6080 LE TEMS. Ao | DE =AP= 6000L8 2 bo00L6 BE 2/40 16000 ~AB 48 =O Be = A8sin0 boro J0000(D/E) ~4ooe 259015 70s, —£ 8¢ PN = o.8 ° JINe BCS ABLon® + BE cose = 10000(0.4) + 250(0/) = Be B8C= 7500 Ls Come. Ab= gp=o 2000 LB BC= CF Con® o CF = BC [eos = 2500 /0.6° [2590 Ls Comp. 6 ce CE 2 12000 = CF 2m © = /2000-/2 S90(0.8) = 200018 < ee cE Fz 120 Le EF = CF eno = 2500 (0:8) = SV0L8 rEWS, oN F ’ STResses: , EF Tio = Ope = 6000/0.968 = 6/95 pai Re ®/0000L6 Ter = 7500/p.968 =*]778 pi po =0 Reps oF memsees : (her, As, 86) | oie =250/0.0ty "574.5 psd AO, 08, EF = 2098) = 0.968.m*| Tre =20m fp, ypy = tg poi 8D, ke, cE~ 0%Ym™ Ope = ~P00/s.p = = $132 ped Ay Be, CF = 20/2) = 2.8m The = =7%0/2,42% = 3049 pri Mote: ComPRessIon MEMBERS musT BE Ote = “RSVO2.¥2 = ~ 5/65 poi CHE tren Fog Coromwm Bockiiné + StudyXxy

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    /-5% en ae ’ TH =0= (25X40 ~-AB(25) SEL BW Ab= 20 Rn ’ Coe 2000 | bor 12.545 Co) mmr —— - 15% A= moss) VY =0. 200m o-= Flas 12600L8/p,50 += 63000p8 L258 pe 26s Av0) + 2LbyMo.YCE)] = Yat mY o= Fs (Stevo tory uy 0) = /) 79/ Poi /~56 - L/P + === 4=(80)(10) ~(60)(/$) + IT (40) /¥= 3ST 7. mm a= fps SOKO A cr > = VI /-57 DIRECT SHEAR —~ SINGLE SHEAR Ags [12.004] men = 113 summ™ = Fags IeSXOWY,) ron = 146 mp Fs ssw /-58 " Br === IFyzo= $I) =F (45) Ps Fo= 1727 ¥ As= MOO) = 0.07 mm™ 100 ys T= Fo = 178s rman = 25.1 en, _ Pw a Sire sxeae L559 Fpom Pos V6: F=23495 & As 220mm HM] = 157 mm™ DovBie Sree T= Fjps 2369S 0) mm S151 MPa

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    /-60 As=B.oX35I/0.Sm* P= Fase G8oo rel so.cimX 17/28) Ll As = (2039) +1150) = #957 omm® T= FlAs= 30.6 x0°N / Y757 mm >= 8) HE I in V2 6% = 0.72) m. — As= L20460) + 1(0.8)/2 +2(0.720] 0.09 y/ N M Rs= L/¥m* 4 4 T= Flas= YS00008/).1990>=3932¢ #57 of [- £3 rape - Fon T/R= ISN. 05mm Ss Bs A po =5V29 4st, As= bt = (o)(22) = 220 amwm™ T= Ffgy= NEC C7 29.780Pa L6Y Fie Ths Boniamy,,, -moce Asc 5.2 2lo.so)z.28)= frst T= Fol, = 8o00i8 ys spre Ip pid Lb aw Dove shone) Aes AUTO R)= 0.393 40> 7= hs 20000087, 355 22 & 9S0s5/ ColLag srem coin FRom Cowwerror Bony Ag = Tt = T(082)(0/875) = Ors SY Iu ™ = = 20000 Lp Sym =38 300 #5) LE yp E00080)-8,(8) nk J = le B,= BocoLe B= By Jeers =893(8 6, As=2(mo325) 4) som vr Gate . 77% 8/4 = 85/3L8/) 05, + = _385V0 PS) Le As = H0)(12) = Y80. mam © 7% Fly o 8BAI® NJyp mt =. 183 MP LEB 452 Grodir20) = 4800 man 7'= Flgs= 88.2 xn J 9800 smas® = 18:4 HP

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    L288 pce wrot=mUN(BY2I0L6 mm Toe Fly = 22.300 J301,6 apa = 13. 92000 490. g,« 202] =226.2mm Two RIETS=SINGLE SHEAR T= Ffas= B23 [33 2 goun® = 15:/MP2c dT) pyr wor) HT = 452.Y mmm Two RIGTI- BebLE SHEAR T= Faas PRAWN [ys2.4 ma” =22.55mbn

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    CHAPTER 2 Design Properties of Materials ONLY THOSE PROBLEMS REQUIRING NUMERICAL PATH ACE Show. EM Sun Goksi (62min); Sy = Oh (H11 MM), 25% crowd, BetAvse Yo ELowsATIon >So, IT 1S DicTiLE. (per. #14) 2/5 Joo HE: 36% Eons ATIIN - GREATER DutnLiry 1040 HR: 25% sowintion (App, 4-1) 296 Ais; NY OOT 700: Hin Sve rue AtLsy STEEL wini o4% CARBON , QuewcHeED 4 OIL , TEMPER Ar 700'F. (APP, 4-17) ZS) VES. Sys [72 kei@d OOTI00 Sy = 129 4% @ 0OT 90 BY WrERfoLATION Sy 2/0 Mt ® O0rd00, (APs AY) 2B E-= 3pu or) f 20260) Fok ALL crCBow Aw Aris Sreecs. 24 wrs Dew sry « VoLumss =(0,.283L84,3 H Le B 2-2 (Are. 4-1) PA La Wiortvamnl re wr) a reins flac Lemar = FC) x 29 = 49093050003 ASS = 7680 hy 4.909 v165 peran® pony? . (APra-1)=""am XT SR 5.07 Ay wry = Mg = 3.714g. 9.8 an/s *e 3 98 hgrmfst = 6.98 va 2-2 MAGNESIVM wovLo BECAUSE IT HAS 4 Lowe £, EL Guz USGI Epp = 19GRa] Ti 8 siFER, (APP.A-IS) 2:23 AlLoY or Atrium WITH Sivilon AND MAKNESIVA HeAT TREATED TO T6 rempPeR. 2-2¢ Sa sy £ ENS ITY {ee #16) bosr-0 JB wi Bkst loxwCFsi 0.410 L8/sn3 bobt-TY 3SKs/ UKs) bobr-re Ysks/ Hfousi “ 2-29 I. - / ) === Sue = YOks/ | Swe = Yo ks) (APP AI, L231 Bevo 03= tysogsi; Tewsiow 05 8508S; Cont ooo 15 PAMMUA. To GAN, 38S FSi Pet Pew dicutan To 6h 3 SHER 15 = 95° #5/ (are. 4-19) 4-32 2000 10 1000 #5; (Secon 2/0)

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    2-44 Graphite fibers. 2-45 S-glass, quanz fibers, tungsten fibers coated with silicon carbide. 2-51 Material Specific strength Ratio to (in) AISI 1020 Graphite/Epoxy (High Strength) 4.86x106 25.0 Aramid/Epoxy Composite 4.00x106 20.6 Boron/Epoxy Composite 3.60x106 18.5 Graphite/Epoxy (Ultra-hi mod) 2.76x106 14.2 Glass/Epoxy Composite 1.87x106 9.63 Titanium Ti-6Al-4V 1.00x106 5.15 AISI 5160 OQT 700 Steel 0.929x106 4.78 Aluminum 7075-T6 0.822x106 4.23 ) Aluminum 6061-T6 0.459x106 2.36 AISI 1020 HR Steel 0.194x106 1.00 2-52 Material Specific modulus Ratio to (in) AISI 1020 Graphite/Epoxy (Ultra-hi mod) 8.28x108 7.81 Boron/Epoxy Composite 4.00x108 3.77 Graphite/Epoxy (High Strength) 3.45x108 3.25 Aramid/Epoxy Composite 2.20x108 2.07 AISI 1020 HR Steel 1.06x108 1.00 AISI 5160 OQT 700 Steel 1.06x108 1.00 Titanium Ti-6Al-4V 1.03x108 0.97 Aluminum 6061-T6 1.02x108 0.96 Aluminum 7075-T6 0.99x108 0.93 Glass/Epoxy Composite 0.66x108 0.62 2-60 Vm=1-Vf=1.0-060 = 0.40 2-61 See Equation (24). 2-62 See Equations (2.I), (242, (23), (2-H) + StudyXY

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    2-63 Given: Vr = 0.50; Fibers are high strength carbon-PAN; Matrix is Epoxy See Table 2-s'for data. Vm =1- Vf=1 0 - 0.50 = 0.50 Use Equation (2.4): suc = Suf Vf + om' Vm Strain at which fibers would fail: & = suf /Ef = (820x 103 psi)/(40x106 psi) €f = 0.0205 Stress in matrix at this strain: om' = Em € = (0.56x106 psi)(0.0205) = 11 480 psi Then: suc = (820x 103 psi)(0.50) + (11 480 psi)(0.50) = 415x103 psi Modulus of elasticity: Ec = Ef Vf + Em vm = (40x106)(0.5) + (0.56x106)(0.50) Ec = 20.3x106 psi Specific weight: yc = yf Vf + ym vm = (0.065)(0.50) + (0.047)(0.50) yc = 0.056 Ib/in3 2-64 Given: Vf= 0.50; Fibers are high modulus carbon; Matrix is Epoxy See Table 2-/5for data. Vm =1- Vr=10 - 0.50 = 0.50 Use Equation (2-1): suc = Suf VF + om' Vm Strain at which fibers would fail: ef = suf /Ef = (325% 103 psi)/(100x106 psi) &f = 0.00325 Stress in matrix at this strain: om = Em € = (0.56x106 psi)(0.00325) = 1820 psi Then: suc = (325x 103 psi)(0.50) + (1820 psi)(0.50) = 163x103 psi Modulus of elasticity: ~~ Ec = Ef Vf + Em vm = (100x106)(0.5) + (0.56x106)(0.50) Ec = 50.3x106 psi Specific weight: yc = yf Vf + ym vm = (0.078)(0.50) + (0.047)(0.50) yc = 0.0625 Ib/in3 2-65 Given: Vr = 0.50; Fibers are aramid; Matrix is Epoxy See Table 2-5for data. Vm =1- Vf=1 0 - 0.50 = 0.50 Use Equation (2-4): Suc = suf Vf + om' Vm Strain at which fibers would fail: €f = sur /Ef = (500x 103 psi)/(19x106 psi) &f = 0.0263 Stress in matrix at this strain: om' = Em € = (0.56x106 psi)(0.0263) = 14 740 psi Then: suc = (500x 103 psi)(0.50) + (14 740 psi)(0.50) = 257x103 psi Modulus of elasticity: Ec = Ef Vf + Em vm = (19x106)(0.5) + (0.56x106)(0.50) Ec = 9.78x106 psi Specific weight: yc = yf Vf + ym vm = (0.052)(0.50) + (0.047)(0.50) ye = 0.0495 Ib/in3 + StudyXxy

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    Solutions to Problems 2-66 to 2-67: Some data approximated from Figure P2-66. Most accurate values are for Ultimate strength (b.)and % elongation (f). Elastic limit (d.) estimated between proportional limit (c.) and yield strength (a.) Modulus of elasticity (e.) computed from (A stress / A strain). Data are approximated Materials found from Appendixes A-13 through A-17 matching s,,, s,, % Elongation, and E 2-66 a. sy = 73 ksi- Offset 2-67 a. s,=173 ksi Yield point b. s,= 83 ksi b. s, = 187 ksi c. s,=60ksi c. p= 162 ksi d. Sq =67ksi d. sq =168 ksi e. E=10.0x10° psi e. E=20.0x10° psi f. 11% Elongation f. 15% Elongation g. Ductile g. Ductile h. Aluminum h. Steel I. 7075-T6 1. AISI 4140 OQT 900 2-68 a. s,= 62 ksi Offset 269 a. s,=49 ksi - Yield point b. s,=75Kksi b. s,=65ksi c. s,=50ksi Cc. s,= 4B ksi d. Sq = 56 ksi d. Sq=48 ksi e. E=16.7x10° psi e. E=26.5x10° psi f. 15% Elongation f. 36% Elongation g. Ductile g. Ductile h. Copper Alloy h. Steel I. G54400 Bronze-hard I. AIS] 1020 CD 2.70 a. Nos,- Brittle 2-71 a. s,= 53 ksi - Offset b. s,=55ksi b. s,= 59 ksi c. Ss, =50ksi c. Sp=31ksi d. Sy=53ksi d. Sq =42ksi e. E=20.0x10° psi e. E=12.0x10° psi f. 0.5% Elongation f. 5.0% Elongation g. Brittle g. Borderline Brittle/Ductile h. Cast Iron h. Zinc I. ASTM A48 Grade 60 I. Cast ZA-12 2-72 a. s,=35ksi- Yield point 2-73 a. s,= 19 ksi- Offset b. s,= 57 ksi b. sy =40ksi c. Sp=30ksi c. sp=14ksi d. Sq =27ksi d. Sq =17 ksi e. E=26x10° psi e. E=6x10° psi f. 21% Elongation f. 5% Elongation g. Ductile g. Borderline Brittle/Ductile h. Structural Steel h. Magnesium I. ASTM A36 I. ASTM AZ 63A-T6

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    2-74 a. s,=155 ksi - Offset 2.75 a. S,= 40 ksi - Offset b. s,=170ksi b. s,=45ksi c. sp=142ksi c. sp =30ksi d. Se =149 ksi d. Se =35ksi e. E=16.5x10° psi e. E=10.0x10° psi f. 8% Elongation f. 17% Elongation g. Ductile g. Ductile h. Titanium h. Aluminum 1. 6Al4V l. 6061-T6 2-76 a. s,=80ksi- Offset 2-77 a. s,=80ksi- Offset b. s,=90ksi b. s, = 95 ksi c. sp=62ksi c. sp=55ksi d. Sg=T71ksi d. Sq=68ksi e. E=26x10°psi e. E=26x10° psi f. 15% Elongation f. 2.0% Elongation g. Ductile g. Brittle, but does yield h. Stainless Steel h. Malleable Iron 1. AISI 430 full hard 1. ASTM A220 Grade 80002

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    CHAPTER 3 Design of Members Under Direct Stresses = & 2.501’ 2, 31 o-= el SB te =x 35 2 Reod _Sy= 2 = 2/08) * 2b sla. ALvenum 201Y-TY HAS Sys 290mb (APPewpry A168) 32 = he 200x0°N 22 oA, = 66.747" 05 = Sug REGO Sy = & T5° 8L66.2MF0)5 533 (1a. AWS Goow DucaLiTY AISI 115) ANNEALED HAS Sus 600M) 26% Ecavsaminy, (A-1d) 33 o=8= /720 LOL orn)? = PISVA5) = 0 = Su fg ReGD Su= 8 a = 8(/0750)® BE000FS] Pus Govo Ducnuiry AI3)D WOT Boo WAS 5, = 81Aei 332% sroncarnn (A-19) I4 o=he 180s = i. , == Hessremy fered = Ga so.0 sy (ASC) Reoo Sy= 03/p.co 167054) 40 =27900 per. ASTM A36 STRICVRAL STEEL MAS Sy=36c00ms (A-/6) 28 oho SL0Lte 95h pai 100 Hibwy Gui SSE (A419) (A-4) _Sesm ee) 3-6 “W0./ GRADE DovGLAS FIR HAS Gaueon= /050PS (A-19) © T0 USE No.2 GRAVE SovTHERW FINE: O@uion® TSP ReoD Aten Lo, 520088 gpg 2 ra rym Le] 3 USE 2X8 or ¥xY of Two 2xY. 37 =a) A-e_ _ evoore IS =C PATE. T2000 yn © 2.533 rs TOVY Reoo 0=V7775 <Y¥las33:0") pr = 0:88 14 SPECIFY Yom (0.875w) 02 1.00 4. D/A. 38 TTA MASE = JISO + 6350 = Woy 1815 Ry owenck sre. F=meg wil 1SAg GU m/s¥e IW NC Read A=_P__ (8394 2 = BIL 2263 mem = (wr X 8 pum) Re®Dd wr= 263 ann’/8 pum = 32.8 ammm SELEY r= 35.0 ows + StudyXxy

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