[ ] 2. Chapter 6. = d = = Eq. (6-8): 1.58(1020) Eq. (6-20): kb. 6-2 (a) Table A-20: S ut = 80 kpsi. Eq. (6-8): S = 0.5(90) = 45 kpsi Ans.

Transcription

1 Chptr Eq. (-1): 3.4H 3.4(300) 100 MP Eq. (6-8): (100) 510 MP Tl 6-: 1.58, Eq. (6-19): k B (100) (10) Eq. (6-0): k d Eq. (6-18): kk (0.877)(0.969)(510) 433 MP As. 6- () Tl A-0: 80 kpsi Eq. (6-8): 0.5(80) 40 kpsi As. () Tl A-0: 90 kpsi Eq. (6-8): 0.5(90) 45 kpsi As. (c) Aluiu hs o durc liit. As. (d) Eq. (6-8): > 00 kpsi, 100 kpsi As. 10 kpsi, 70 kpsi 6-3 rv Fig. 6-18: 0.8 Eq. (6-8): 0.5(10) 60 kpsi Eq. (6-14): Eq. (6-15): [ ] ( ) 0.8(10) kpsi (10) log log / rv Eq. (6-16): N ccls As MP, 900 MP 6-4 rv Fig. 6-18: 1600 MP 3 kpsi. O th grph, so stit Eq. (6-8): Eq. (6-14): > 1400 MP, so 700 MP [ ] ( ) 0.77(1600) MP 700 higl s MED, 10 th ditio Chptr 6 olios, Pg 1/58

2 (1600) Eq. (6-15): log log / rv 900 Eq. (6-16): N ccls As kpsi, N ccls Fig. 6-18, poit is o th grph, so stit: 0.77 Eq. (6-8): > 00 kpsi, so 100 kpsi 1 Eq. (6-14): Eq. (6-15): [ ] ( ) 0.77(30) kpsi (30) log log Eq. (6-13): N 313.6( ) kpsi As MP 160 kpsi Fig. 6-18: 0.79 Eq. (6-8): 0.5(1100) 550 MP Eq. (6-14): Eq. (6-15): [ ] ( ) 0.79(1100) 1373 MP (1100) log log Eq. (6-13): N 1373( ) 64 MP As kpsi, 135 kpsi, N 500 ccls t Fig. 6-18: Fro Fig. 6-10, w ot tht low 10 3 ccls o th -N digr costits th lowccl rgio, i which Eq. (6-17) is pplicl. higl s MED, 10 th ditio Chptr 6 olios, Pg /58

3 Eq. (6-17): ( ) log /3 log /3 N As kpsi. Th tstig should do t copltl rvrsd strss o 1 kpsi, which is low th ild strgth, so it is possil. As. 6-8 Th grl qio or li o log - log N scl is N, which is Eq. (6-13). B tkig th log o oth sids, w c gt th qio o th li i slop-itrcpt or. log log N + log ustit th two kow poits to solv or ukows d. ustitig poit (1, ), log log(1) + log Fro which. ustitig poit 3 (10, ) d Fro which 3 log log10 + log 1/ 3 log N 1 N 10 (log )/ Rd ro grph: ( 10,90) d (10,50). Fro log log + log N 1 1 log log + log N N Fro which log log N log log N log log N / N log90log10 log50log log10 / log kpsi log50 / ( ) x 16 N 10 N 10 i kpsi As. higl s MED, 10 th ditio Chptr 6 olios, Pg 3/58

4 Chck: ( ) x 16(10 ) 90 kpsi ( ) x 16(10 ) 50 kpsi 6 10 Th d poits gr d 1.5 i, 110 kpsi Eq. (6-8): 0.5(110) 55 kpsi Tl 6-:.70, 0.65 Eq. (6-19): k (110) Eq. (6-0): k d (1.5) Eq. (6-18): k k 0.777(0.84)(55) 36.0 kpsi As For AII 4340 s-orgd stl, Eq. (6-8): 100 kpsi Tl 6-: 39.9, Eq. (6-19): k 39.9(60) Eq. (6-0): k Ech o th othr odiig ctors is uit (0.907)(100) 14.3 kpsi As. For AII 1040: 0.5(113) 56.5 kpsi k k (113) (s s 4340) Ech o th othr odiig ctors is uit 0.36(0.907)(56.5) 18.6 kpsi As. Not ol is AII 1040 stl cotdr, it hs suprior durc strgth. As. 6-1 D 1 i, d 0.8 i, T 1800 l i, 0.9, d ro Tl A-0 or AII 100 CD, 68 kpsi, d 57 kpsi. higl s MED, 10 th ditio Chptr 6 olios, Pg 4/58

5 () r 0.1 D 1 Fig. A-15-15: 0.15, 1.5, Kts 1.40 d 0.8 d 0.8 Gt th otch ssitivit ithr ro Fig. 6-1, or ro th curv-it Eqs. (6-34) d (6-35). Usig th qios, ( 3 ) ( 5 ) ( 8 )( 3 ) q s r 0.1 Eq. (6-3): K s 1 + q s (K ts 1) (1.40 1) 1.3 For purl rvrsig torqu o T 1800 l i, Tr K s16t 1.3(16)(1800) τ K s psi 3.6 kpsi J d 3 3 π π (0.8) Eq. (6-8): 0.5(68) 34 kpsi Eq. (6-19): k.70(68) Eq. (6-0): k 0.879(0.8) Eq. (6-6): k c 0.59 Eq. (6-18) (llig or shr): s 0.883(0.900)(0.59)(34) 15.9 kpsi For purl rvrsig torsio, us Eq. (6-54) or th ultit strgth i shr. Eq. (6-54): su (68) 45.6 kpsi Adjustig th tigu strgth qios or shr, [ ] su 0.9(45.6) Eq. (6-14): kpsi 15.9 s 1 su 1 0.9(45.6) Eq. (6-15): log log s τ Eq. (6-16): N 61.7( 10 ) ccls As o () For oprtig tprtur o 750 F, th tprtur odiictio ctor, ro Tl 6-4 is k d higl s MED, 10 th ditio Chptr 6 olios, Pg 5/58

6 s 0.883(0.900)(0.59)(0.9)(34) 14.3 kpsi ( ) [ 0.9(45.6) ] su kpsi 14.3 s 1 su 1 0.9(45.6) log log s τ N 40.9( 10 ) ccls As L F N (Tl A-0) 4 0.6, kn, 1.5, 10 ccls, 770 MP, 40 MP First vl th tigu strgth. 0.5(770) 385 MP k (770) ic th siz is ot t kow, ssu tpicl vlu o k 0.85 d chck ltr. All othr odiirs r qul to o. Eq. (6-18): 0.488(0.85)(385) 160 MP I kpsi, 770/ kpsi Fig. 6-18: 0.83 Eq. (6-14): Eq. (6-15): Eq. (6-13): ( ) [ 0.83(770) ] 553 MP (770) log log N 553(10 ) 403 MP Now vl th strss. M x (000 N)(0.6 ) 100 N Mc M ( / ) 6M 6( 100) 700 x P, with i I ( ) /1 Copr strgth to strss d solv or th cssr ( 10 ) / higl s MED, 10 th ditio Chptr 6 olios, Pg 6/58

7 0.099 lct 30. ic th siz ctor ws gussd, go ck d chck it ow. Eq. (6-5): d ( h) Eq. (6-0): k Our guss o 0.85 ws slightl cosrvtiv, so w will ccpt th rsult o 30. As. Chckig ild, ( 10 ) 67 MP x x Giv: w.5 i, t 3/8 i, d 0.5 i, d. Fro Tl A-0, or AII 100 CD, 68 kpsi d 57 kpsi. Eq. (6-8): 0.5(68) 34 kpsi 0.65 Tl 6-: k.70(68) 0.88 Eq. (6-1): k 1 (xil lodig) Eq. (6-6): k c 0.85 Eq. (6-18): 0.88(1)(0.85)(34) 5.4 kpsi Tl A-15-1: d / w 0.5 /.5 0., K t.5 Gt th otch ssitivit ithr ro Fig. 6-0, or ro th curv-it Eqs. (6-34) d (6-35). Th rltivl lrg rdius is o th grph o Fig. 6-0, so w will ssu th curvs cotiu ccordig to th s trd d us th qios to stit th otch ssitivit. ( 3 ) ( 5 ) ( 8 )( 3 ) q r 0.5 Eq. (6-3): K 1 + q( K 1) (.5 1).5 t F.5F K 3F A (3 / 8)(.5 0.5) higl s MED, 10 th ditio Chptr 6 olios, Pg 7/58

8 ic iit li ws ot tiod, w ll ssu iiit li is dsird, so th copltl rvrsd strss ust st low th durc liit F F 4.3 kips As Giv: D i, d 1.8 i, r 0.1 i, M x l i, M i 0. Fro Tl A-0, or AII 1095 HR, 10 kpsi d 66 kpsi kpsi Eq. (6-8): Eq. (6-19): k (10) 0.76 Eq. (6-4): d 0.370d 0.370(1.8) i Eq. (6-0): Eq. (6-6): k c 1 k d (0.666) 0.9 Eq. (6-18): k k k (0.76)(0.9)(1)(60) 4.0 kpsi c Fig. A-15-14: D / d / , r / d 0.1/ K t Gt th otch ssitivit ithr ro Fig. 6-0, or ro th curv-it Eqs. (6-34) d (6-35). Usig th qios, ( 3 ) ( 5 ) ( 8 )( 3 ) q r 0.1 Eq. (6-3): K 1 + q( K 1) (.1 1) 1.96 t I ( π / 64) d ( π / 64)(1.8) i x i Mc 5 000(1.8 / ) psi 43.7 kpsi I Eq. (6-36): x i K kpsi higl s MED, 10 th ditio Chptr 6 olios, Pg 8/58

9 ( ) x i K kpsi Eq. (6-46): As. A ctor o st lss th uit idicts iit li. Chck or ildig. It is ot cssr to iclud th strss coctrtio or sttic ildig o ductil tril As. x Fro r-od digr lsis, th rig rctio orcs r oud to.1 kn t th lt rig d 3.9 kn t th right rig. Th criticl loctio will t th shouldr illt tw th 35 d th 50 ditrs, whr th dig ot is lrg, th ditr is sllr, d th strss coctrtio xists. Th dig ot t this poit is M.1(00) 40 kn. With rottig sht, th dig strss will copltl rvrsd. Mc 40 (35 / ) I ( π / 64)(35) rv kn/ 99.8 MP This strss is r low th ild strgth o 390 MP, so ildig is ot prdictd. Fid th strss coctrtio ctor or th tigu lsis. Fig. A-15-9: r/d 3/ , D/d 50/ , K t 1.7 Gt th otch ssitivit ithr ro Fig. 6-0, or ro th curv-it Eqs. (6-34) d (6-35). Usig th qios, with 470 MP 68. kpsi d r i, q r Eq. (6-3): K 1 + q( K 1) (1.7 1) 1.55 Eq. (6-8): Eq. (6-19): Eq. (6-4): k ' t (470) 35 MP (470) (35) 0.85 k d higl s MED, 10 th ditio Chptr 6 olios, Pg 9/58

10 Eq. (6-6): k c 1 ' Eq. (6-18): k k k (0.88)(0.85)(1)(35) 176 MP c Iiit li is prdictd. As. K rv 6-17 Fro r-od digr lsis, th rig rctio orcs r oud to R A 000 l d R B 1500 l. Th shrorc d dig-ot digrs r show. Th criticl loctio will t th shouldr illt tw th 1-5/8 i d th 1-7/8 i ditrs, whr th dig ot is lrg, th ditr is sllr, d th strss coctrtio xists. M (.5) l i With rottig sht, th dig strss will copltl rvrsd. Mc (1.65 / ) rv 35.0 kpsi 4 I ( π / 64)(1.65) This strss is r low th ild strgth o 71 kpsi, so ildig is ot prdictd. Fig. A-15-9: r/d 0.065/ , D/d 1.875/ , K t 1.95 Gt th otch ssitivit ithr ro Fig. 6-0, or ro th curv-it Eqs. (6-34) d (6-35). Usig th qios, q r Eq. (6-3): K 1 + q( K 1) (1.95 1) 1.7 t Eq. (6-8): Eq. (6-19): Eq. (6-0): k ' Eq. (6-6): k c (85) 4.5 kpsi (85) (1.65) k d higl s MED, 10 th ditio Chptr 6 olios, Pg 10/58

11 Eq. (6-18): k k k (0.83)(0.835)(1)(4.5) 9.5 kpsi ' c As. K rv Iiit li is ot prdictd. Us th -N digr to stit th li. Fig. 6-18: ( ) [ 0.867(85) ] Eq. (6-14): (85) Eq. (6-15): log log K rv (1.7)(35.0) Eq. (6-16): N 4611 ccls N 4600 ccls As Fro r-od digr lsis, th rig rctio orcs r oud to R A 1600 l d R B 000 l. Th shr-orc d dig-ot digrs r show. Th criticl loctio will t th shouldr illt tw th 1-5/8 i d th 1-7/8 i ditrs, whr th dig ot is lrg, th ditr is sllr, d th strss coctrtio xists. M (.5) l i With rottig sht, th dig strss will copltl rvrsd. Mc (1.65 / ) rv 3.8 kpsi 4 I ( π / 64)(1.65) This strss is r low th ild strgth o 71 kpsi, so ildig is ot prdictd. Fig. A-15-9: r/d 0.065/ , D/d 1.875/ , K t 1.95 Gt th otch ssitivit ithr ro Fig. 6-0, or ro th curv-it Eqs. (6-34) d (6-35). Usigth qios, higl s MED, 10 th ditio Chptr 6 olios, Pg 11/58

12 q r Eq. (6-3): K 1 + q( K 1) (1.95 1) 1.7 t Eq. (6-8): Eq. (6-19): Eq. (6-0): k ' (85) 4.5 kpsi (85) (1.65) k d Eq. (6-6): k c 1 ' Eq. (6-18): k k k (0.83)(0.835)(1)(4.5) 9.5 kpsi c As. K rv 1.7( 3.8) Iiit li is ot prdictd. Us th -N digr to stit th li. Fig. 6-18: ( ) [ 0.867(85) ] Eq. (6-14): (85) Eq. (6-15): log log K rv (1.7)(3.8) Eq. (6-16): N 757 ccls N 7500 ccls As Tl A-0: 10 kpsi, 66 kpsi N (950 rv/i)(10 hr)(60 i/hr) ccls O pproch is to guss ditr d solv th prol s itrtiv lsis prol. Altrtivl, w c stit th w odiig prtrs tht r dpdt o th ditr d solv th strss qio or th ditr, th itrt to chck th stits. W ll us th scod pproch sic it should rquir ol o itrtio, sic th stits o th odiig prtrs should prtt clos. First, w will vl th strss. Fro r-od digr lsis, th rctio orcs t th rigs r R 1 kips d R 6 kips. Th criticl strss loctio is i th iddl o th sp t th shouldr, whr th dig ot is high, th sht ditr is sllr, d strss coctrtio ctor xists. I th criticl loctio is ot ovious, higl s MED, 10 th ditio Chptr 6 olios, Pg 1/58

13 prpr coplt dig ot digr d vl t pottill criticl loctios. Evlig t th criticl shouldr, M kip( 10 i) 0 kip i Mc M ( d / ) M 3( 0) kpsi I π d / 64 π d π d d rv Now w will gt th otch ssitivit d strss coctrtio ctor. Th otch ssitivit dpds o th illt rdius, which dpds o th ukow ditr. For ow, lt us stit vlu o q 0.85 ro osrvtio o Fig. 6-0, d chck it ltr. Fig. A-15-9: D / d 1.4 d / d 1.4, r / d 0.1 d / d 0.1, K t 1.65 Eq. (6-3): K 1 + q( K 1) (1.65 1) 1.55 Now, vl th tigu strgth. t k ' 0.5(10) 60 kpsi (10) 0.76 ic th ditr is ot t kow, ssu tpicl vlu o k 0.85 d chck ltr. All othr odiirs r qul to o. (0.76)(0.85)(60) 38.8 kpsi Dtri th dsird tigu strgth ro th -N digr. Fig. 6-18: 0.8 ( ) [ 0.8(10) ] Eq. (6-14): (10) Eq. (6-15): log log Eq. (6-13): N 49.6( ) 41.9 kpsi Copr strgth to strss d solv or th cssr d K rv d.9 i 3 ( 1.55)( 03.7 / d ) higl s MED, 10 th ditio Chptr 6 olios, Pg 13/58

14 ic th siz ctor d otch ssitivit wr gussd, go ck d chck th ow Eq. (6-0): k 0.91d Fro Fig. 6-0 with r d/ i, w r o th grph, it pprs our guss or q o 0.85 is low. Assuig th trd o th grph cotius, w ll choos q 0.91 d itrt th prol with th w vlus o k d q. Itrdit rsults r 36.5 kpsi, 39.6 kpsi, d K This givs K d.36 i rv 3 ( 1.59)( 03.7 / d ) As. A quick chck o k d q show tht our stits r still rsol or this ditr kpsi, 60 kpsi, 80 kpsi, τ 15 kpsi, 5 kpsi, τ 0 Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi ( 3 ) ( ) 3( ) 1/ x x + τ x + + τ + τ kpsi As x () Modiid Good, Tl As. (5.00 / 40) + (5.98 / 80) () Grr, Tl (5.98)(40) As (5.00) (c) AME-Elliptic, Tl As. (5.00 / 40) + (5.98 / 60) higl s MED, 10 th ditio Chptr 6 olios, Pg 14/58

15 kpsi, 60 kpsi, 80 kpsi, τ 0 kpsi, 10 kpsi, τ 0 Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi ( 3 ) ( ) 3( ) 1/ x x + τ x + + τ + τ kpsi As x () Modiid Good, Tl As. (10.00 / 40) + (34.64 / 80) () Grr, Tl (34.64)(40) As (10.00) (c) AME-Elliptic, Tl As. (10.00 / 40) + (34.64 / 60) 6-40 kpsi, 60 kpsi, 80 kpsi, τ 10 kpsi, τ 15 kpsi, 1 kpsi, 0 Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi ( 3 ) ( ) 3( ) 1/ x x + τ x + + τ + τ kpsi As x () Modiid Good, Tl 6-6 higl s MED, 10 th ditio Chptr 6 olios, Pg 15/58

16 As. (1.07 / 40) + (5.98 / 80) () Grr, Tl (5.98)(40) As (1.07) (c) AME-Elliptic, Tl As. (1.07 / 40) + (5.98 / 60) kpsi, 60 kpsi, 80 kpsi, τ 30 kpsi, τ 0 Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi ( 3 ) 0 kpsi ( 3 ) ( ) 3( ) + τ kpsi As / x x + τ x + + τ + τ x () Modiid Good, Tl As. (51.96 / 40) () Grr critrio o Tl 6-7 is ol vlid or > 0; thror us Eq. (6-47) As (c) AME-Elliptic, Tl As. (51.96 / 40) ic iiit li is ot prdictd, stit li ro th -N digr. ic ' 0, th strss stt is copltl rvrsd d th -N digr is pplicl or '. Fig. 6-18: higl s MED, 10 th ditio Chptr 6 olios, Pg 16/58

17 [ ] ( ) 0.875(80) Eq. (6-14): (80) Eq. (6-15): log log / rv Eq. (6-16): N ccls As kpsi, 60 kpsi, 80 kpsi, τ 15 kpsi, 15 kpsi, τ 0 Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi 1 ( 3 ) ( ) 3( ) 1/ x x + τ x + + τ + τ kpsi As. 30 x () Modiid Good, Tl As. (5.98 / 40) + (15.00 / 80) () Grr, Tl (15.00)(40) As (5.98) (c) AME-Elliptic, Tl As. (5.98 / 40) + (15.00 / 60) 6-5 Giv: Fx 8 kn, Fi 8 kn. Fro Tl A-0, or AII 1040 CD, 590 MP, 490 MP, Chck or ildig higl s MED, 10 th ditio Chptr 6 olios, Pg 17/58

18 F A (5 6) x x N/ MP As. x Dtri th tigu ctor o st sd o iiit li Eq. (6-8): Eq. (6-19): Eq. (6-1): 0.5(590) 95 MP k ' k 1 (xil) (590) 0.83 Eq. (6-6): k c 0.85 ' Eq. (6-18): k k k (0.83)(1)(0.85)(95) 08.6 MP c Fig. 6-0: q 0.83 Fig. A-15-1: d / w 0.4, K.44 K t 1 + q( K 1) (.44 1).0 F t F MP A (10)(5 6) x i K Fx + Fi K 0 A Not, sic 0, th strss is copltl rvrsig, d As. 34. ic iiit li is ot prdictd, stit th li ro th -N digr. With 0, th strss stt is copltl rvrsd, d th -N digr is pplicl or. 590/ kpsi Fig. 6-18: 0.87 Eq. (6-14): Eq. (6-15): [ ] ( ) 0.87(590) (590) log log / Eq. (6-16): rv 34. N ccls N ccls As. higl s MED, 10 th ditio Chptr 6 olios, Pg 18/58

19 6-6 Fx Fi 590 MP, 490 MP, 8 kn, 1 kn Chck or ildig F A 10(5 6) As x x N/ MP x Dtri th tigu ctor o st sd o iiit li. Fro Pro. 6-5: 08.6 MP, K. Modiid Good critri: F x F i K MP A (10)(5 6) Fx + Fi K.31.6 MP A (10)(5 6) As. Grr critri: (31.6)(08.6) (9.63) 1.49 As. AME-Elliptic critri: 1 1 ( / ) + ( / ) (9.63 / 08.6) + (31.6 / 490) 1.54 As. Th rsults r cosistt with Fig. 6-7, whr or strss tht is o hl o th ild strgth, th Modiid Good li should prdict ilur sigiictl or th othr two. higl s MED, 10 th ditio Chptr 6 olios, Pg 19/58

20 MP, 490 MP () Fx 8 kn, F 0 kn i Chck or ildig F A (5 6) x x N/ MP As x Fro Pro. 6-5: 08.6 MP, K. F x i K F MP A (10)(5 6) Fx + Fi K MP A (10)(5 6) For th odiid Good critri, As. ic iiit li is ot prdictd, stit li ro th -N digr. First, id quivlt copltl rvrsd strss. For th odiid Good critri, s Ex rv Fig. 6-18: 0.87 Eq. (6-14): Eq. (6-15): Eq. (6-16): MP 1 ( / ) 1 (16.1/ 590) [ ] ( ) 0.87(590) (590) log log / rv 3.5 N ccls As. 163 F () x 8 kn, F 1 kn i Th xiu lod is th s s i prt (), so MP x higl s MED, 10 th ditio Chptr 6 olios, Pg 0/58

21 3.3 As. Fctor o st sd o iiit li: F F MP A (10)(5 6) x i K Fx + Fi K.31.6 MP A (10)(5 6) As. (c) Fx 1 kn, F 8 kn i Th coprssiv lod is th lrgst, so chck it or ildig. i F A (5 6) i MP c As i Fctor o st sd o iiit li: F F MP A (10)(5 6) x i K F + F MP A (10)(5 6) x i K 08.6 For < 0, 0.90 As ic iiit li is ot prdictd, stit li ro th -N digr. For gtiv strss, w shll ssu th quivlt copltl rvrsd strss is th s s th ctul ltrtig strss. Gt d ro prt (). 1/ rv 31.6 Eq. (6-16): N ccls As Eq. (-1): 0.5(400) 00 kpsi Eq. (6-8): 0.5(00) 100 kpsi ' higl s MED, 10 th ditio Chptr 6 olios, Pg 1/58

22 Eq. (6-19): k (00) 0.31 Eq. (6-5): d 0.37d 0.37(0.375) i Eq. (6-0): k d (0.1388) 1.09 ic w hv usd th quivlt ditr thod to gt th siz ctor, d i doig so itroducd grtr ucrtitis, w will choos ot to us siz ctor grtr th o. Lt k 1. Eq. (6-18): (0.31)(1)(100) 3.1 kpsi F 10 l F 30 l 3M 3(10)(1) 3.18 kpsi 3 3 π d π (0.375) 3M 3(30)(1) kpsi 3 3 π d π (0.375) () Modiid Good critrio As. ic iiit li is ot prdictd, stit li ro th -N digr. First, id quivlt copltl rvrsd strss ( Ex. 6-1). rv Fig. 6-18: Eq. (6-14): Eq. (6-15): Eq. (6-16): kpsi 1 ( / ) 1 (69.54 / 00) [ ] ( ) 0.775(00) (00) log log / rv N ccls As () Grr critrio, Tl 6-7 higl s MED, 10 th ditio Chptr 6 olios, Pg /58

23 (69.54)(3.1) (3.18) 1.16 Iiit li is prdictd As. 6-9 E 07.0 GP () I (0)(4 ) Fl 3EI F 3 3EI l (07)(10 )(106.7)(10 )()(10 ) Fi 48.3 N As (10 ) F (07)(10 )(106.7)(10 )(6)(10 ) x N As. 140 (10 ) () Gt th tigu strgth iortio. Eq. (-1): 3.4H B 3.4(490) 1666 MP Fro prol sttt: (1666) 1499 MP Eq. (6-8): 700 MP Eq. (6-19): k 1.58(1666) Eq. (6-5): d 0.808[0(4)] 7.3 Eq. (6-0): k 1.4(7.3) Eq. (6-18): 0.84(1)(700) 588 MP This is rltivl thick curvd, so us th thod i ct to id th strsss. Th xiu dig ot will to th ctroid o th sctio s show. M 14F N, A 4(0) 80, h 4, r i 4, r o r i + h 8, r c r i + h/ 6 Tl 3-4: h 4 r l( r / r ) l(8 / 4) o i higl s MED, 10 th ditio Chptr 6 olios, Pg 3/58

24 r r c ci r ri co ro r Gt th strsss t th ir d or surcs ro Eq. (3-65) with th xil strsss ddd. Th sigs hv st to ccout or tsio d coprssio s pproprit. Mci F (14 F)(1.7708) F i F MP Ar A 80(0.9)(4) 80 i Mco F (14 F)(.9) F o.145 F MP Ar A 80(0.9)(8) 80 i x i x o ( ) 3.441(144.9) MP i ( ) 3.441(48.3) 166. MP i ( ).145(48.3) MP o ( ).145(144.9) MP o ( i ) 166. MP ( i ) 33.4 MP ( o ) MP ( o ) 07. MP To chck or ildig, w ot tht th lrgst strss is MP (coprssio) o th ir rdius. This is cosidrl lss th th stitd ild strgth o 1499 MP, so ildig is ot prdictd. Chck or tigu o oth ir d or rdii sic o hs coprssiv strss d th othr hs tsil strss. Ir rdius: 588 ic < 0, Or rdius: ic > 0, usig th Modiid Good li, / higl s MED, 10 th ditio Chptr 6 olios, Pg 4/58

25 Iiit li is prdictd t oth ir d or rdii. Th or rdius is criticl, with tigu ctor o st o As Fro Tl A-0, or AII 1018 CD, 64 kpsi, 54 kpsi Eq. (6-8): Eq. (6-19): Eq. (6-0): 0.5(64) 3 kpsi ' k (64) k 1 (xil) Eq. (6-6): k c 0.85 Eq. (6-18): (0.897)(1)(0.85)(3) 4.4 kpsi Fillt: Fig. A-15-5: D / d 3.5 / , r / d 0.5 / , K t 1.85 Us Fig. 6-0 or Eqs. (6-34) d (6-35) or q. Estit littl high sic it is o th grph. q 0.85 K 1 + q( K 1) (1.85 1) 1.7 t x x wh 3.0(0.5) i F kpsi kpsi 3.0(0.5) 3.33 ( 10.67) kpsi x i K K ( 10.67) kpsi x i Dos ot ild i ic th idrg strss is gtiv, Hol: Fig. A-15-1: d / w1 0.4 / K t.68 Us Fig. 6-0 or Eqs. (6-34) d (6-35) or q. Estit littl high sic it is o th grph, q 0.85 higl s MED, 10 th ditio Chptr 6 olios, Pg 5/58

26 K (.68 1).43 F x x h( w1 d ) 0.5( ) F i i h( w1 d ) 0.5( ) kpsi 10.3 kpsi 3.6 ( 10.3) kpsi x i K ( 10.3) kpsi x i K dos ot ild 10.3 i ic th idrg strss is gtiv, Thus th dsig is cotrolld th thrt o tigu t th hol with iiu ctor o st o As kpsi, 54 kpsi Eq. (6-8): Eq. (6-19): Eq. (6-0): 0.5(64) 3 kpsi ' k (64) k 1 (xil) Eq. (6-6): k c 0.85 Eq. (6-18): (0.897)(1)(0.85)(3) 4.4 kpsi Fillt: Fig. A-15-5: D / d.5 / , r / d 0.5 / , K t.1 Us Fig. 6-0 or Eqs. (6-34) d (6-35) or q. Estit littl high sic it is o th grph. q 0.85 K 1 + q( K 1) (.1 1) 1.94 t x x wh 1.5(0.5) i F kpsi 1.5(0.5) 1.3 kpsi higl s MED, 10 th ditio Chptr 6 olios, Pg 6/58

27 K 1.3 ( 5.33) kpsi x i K ( 5.33) kpsi x i Dos ot ild. 1.3 x Usig Modiid Good critri, Hol: Fig. A-15-1: d / w1 0.4 / K t.55 Us Fig. 6-0 or Eqs. (6-34) d (6-35) or q. Estit littl high sic it is o th grph. q 0.85 K (.55 1).3 F 16 x x h( w1 d ) 0.5(.5 0.4) F 4 i i h( w1 d ) 0.5(.5 0.4) 15. kpsi 3.81 kpsi x i 15. ( 3.81) K.3.1 kpsi x + i ( 3.81) K kpsi Dos ot ild. 15. x Usig Modiid Good critri Thus th dsig is cotrolld th thrt o tigu t th illt with iiu ctor o st o 0.77 As. higl s MED, 10 th ditio Chptr 6 olios, Pg 7/58

28 kpsi, 54 kpsi Fro Pro. 6-30, th tigu ctor o st t th hol is To tch this t th illt, kpsi 1.48 whr is uchgd ro Pro Th ol spct o tht is ctd th illt rdius is th tigu strss coctrtio ctor. Otiig i trs o K, x i 3.33 ( 10.67) K K 7.00K Eqig to th dsird strss, d solvig or K, 7.00K 16.5 K.36 Assu sic w r xpctig to gt sllr illt rdius th th origil, tht q will ck o th grph o Fig. 6-0, so w will stit q 0.8. K ( K 1).36 K.7 t t Fro Fig. A-15-5, with D / d 3.5/ d K t.6, id r / d. Choosig r / d 0.03, d with d w 3.0, r 0.03w i At this sll rdius, our stit or q is too high. Fro Fig. 6-0, with r 0.09, q should o Itrtig, w gt K t.8. This is t diicult rg o Fig. A-15-5 to rd th grph with coidc, w ll stit r / d 0.0, givig r 0.06 i. This is vr rough stit, it clrl dostrts tht th illt rdius c rltivl shrp to tch th tigu ctor o st o th hol. As kpsi, 110 kpsi Ir ir whr r 3 / 4 i c 3 3 ro () 3 3 ri Tl 3-4, p. 135, h 3 /16 r i ro l l r i higl s MED, 10 th ditio Chptr 6 olios, Pg 8/58

29 Eq. (3-65), p. 133, r r i c c r r i i 3 3 A i Mci T ( ) i 993.3T Ar ( )(0.0039)(0.6565) whr T is i l i d i is i psi. ' Eq. (6-8): Eq. (6-19): i 1 ( 993.3) T T 496.7T kpsi k (110) Eq. (6-5): d /16 3 / i Eq. (6-0): k (roud to 1) Eq. (6-19): (0.777)(1)(55) 4.7 kpsi For coprssiv idrg copot, /. Thus, Or ir whr T 3 T 8.7 l i r c.5 i 3 ro ri /16 r l i co i Mco T (0.0949) o T psi Ar ( )( )(.59375) o 1 (889.7 T ) T psi higl s MED, 10 th ditio Chptr 6 olios, Pg 9/58

30 () Usig Eq. (6-46), or odiid Good, w hv T T T 3.0 l i As. () Grr, Eq. (6-47), t th or ir, + 1 3( T ) 3( T) T 8. l i As. (c) To gurd gist ild, us T o prt () d th ir strss As. i (8.) 6-34 Fro Pro. 6-33, 4.7 kpsi, 60 kpsi, d 110 kpsi () Assuig th is stright, Mc M h / 6M 6T x 910.T 3 3 I h /1 h (3 /16) Good: T T T.5 l i As. () Grr: 3( T ) 3( T ) T 7.6 l i As. 60 (c).39 As. x 0.910(7.6) higl s MED, 10 th ditio Chptr 6 olios, Pg 30/58

31 6-35 K,d K,xil K,tors 1.4, 1.1,.0, 300 MP, 400 MP, 00 MP Bdig: 0, 60 MP Axil: 0 MP, 0 Torsio: τ 5 MP, τ 5 MP Eqs. (6-55) d (6-56): [ ] [ ] 1.4(60) (5) 10.6 MP [ ] [ ] (0) + 3.0(5) MP Usig Modiid Good, Eq. (6-46), As. Chck or ildig, usig th cosrvtiv x +, As K,d K,tors 1.4,.0, 300 MP, 400 MP, 00 MP Bdig: x 150 MP, i 40 MP, 55 MP, 95 MP Torsio: τ 90 MP, τ 9 MP Eqs. (6-55) d (6-56): Usig Modiid Good, [ ] [ ] 1.4(95) + 3.0(9) MP [ ] [ ] 1.4(55) + 3.0(90) 31.1 MP As. Chck or ildig, usig th cosrvtiv x +, As higl s MED, 10 th ditio Chptr 6 olios, Pg 31/58

32 ic th cosrvtiv ild chck idicts ildig, w will chck or crull with x otid dirctl ro th xiu strsss, usig th distortio rg ilur thor, witho strss coctrtios. Not tht this is xctl th thod usd or sttic ilur i Ch. 5. x x x + 3 τ MP As. x 7.8 ic ildig is ot prdictd, d iiit li is ot prdictd, w would lik to stit li ro th -N digr. First, id quivlt copltl rvrsd strss ( Ex. 6-1) rv 69.5 MP 1 ( / ) 1 (31.1/ 400) This strss is uch highr th th ultit strgth, rdrig it iprcticl or th -N digr. W ust coclud tht th strsss ro th coitio lodig, wh icrsd th strss coctrtio ctors, produc such high idrg strss tht th quivlt copltl rvrsd strss thod is ot prcticl to us. Witho tstig, w r ul to prdict li Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-68, th criticl strss lt xprics 15.3 kpsi d τ 4.43 kpsi. Th dig is copltl rvrsd du to th rottio, d th torsio is std, givig 15.3 kpsi, 0 kpsi, τ 0 kpsi, τ 4.43 kpsi. Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi 1/ x x x kpsi Chck or ildig, usig th distortio rg ilur thor x Oti th odiig ctors d durc liit kpsi Eq. (6-8): Eq. (6-19): Eq. (6-0): k k (64) (1.5) 0.86 higl s MED, 10 th ditio Chptr 6 olios, Pg 3/58

33 Eq. (6-18): 0.90(0.86)(3) 4.8 kpsi Usig Modiid Good, As Tl A-0: 440 MP, 370 MP Fro Pro. 3-69, th criticl strss lt xprics 63 MP d τ 57.7 MP. Th dig is copltl rvrsd du to th rottio, d th torsio is std, givig 63 MP, 0, τ 0 MP, τ 57.7 MP. Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ MP 1/ MP 1/ x x x MP Chck or ildig, usig th distortio rg ilur thor x 81 Oti th odiig ctors d durc liit MP Eq. (6-8): Eq. (6-19): Eq. (6-0): k k (440) (30) 0.86 Eq. (6-18): 0.90(0.86)(0) 170 MP Usig Modiid Good, Iiit li is ot prdictd. As Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-70, th criticl strss lt xprics 1.5 kpsi d τ 5.09 kpsi. Th dig is copltl rvrsd du to th rottio, d th torsio is std, givig higl s MED, 10 th ditio Chptr 6 olios, Pg 33/58

34 1.5 kpsi, 0 kpsi, τ 0 kpsi, τ 5.09 kpsi. Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi 1/ x x x kpsi Chck or ildig, usig th distortio rg ilur thor x Oti th odiig ctors d durc liit (64) 0.90 k k (1) (0.88)(0.5)(64) 5.3 kpsi Usig Modiid Good, As Tl A-0: 440 MP, 370 MP Fro Pro. 3-71, th criticl strss lt xprics 7.9 MP d τ 0.3 MP. Th dig is copltl rvrsd du to th rottio, d th torsio is std, givig 7.9 MP, 0 MP, τ 0 MP, τ 0.3 MP. Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ MP 1/ MP 1/ x x x MP Chck or ildig, usig th distortio rg ilur thor x higl s MED, 10 th ditio Chptr 6 olios, Pg 34/58

35 Oti th odiig ctors d durc liit MP Eq. (6-8): Eq. (6-19): Eq. (6-0): k k (440) (0) 0.90 Eq. (6-18): 0.90(0.90)(0) 178. MP Usig Modiid Good, As Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-7, th criticl strss lt xprics 35. kpsi d τ 7.35 kpsi. Th dig is copltl rvrsd du to th rottio, d th torsio is std, givig 35. kpsi, 0 kpsi, τ 0 kpsi, τ 7.35 kpsi. Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi 1/ x x x kpsi Chck or ildig, usig th distortio rg ilur thor x Oti th odiig ctors d durc liit. Eq. (6-8): 0.5(64) 3 kpsi Eq. (6-19): (64) 0.90 Eq. (6-0): k k (1.5) 0.86 Eq. (6-18): 0.90(0.86)(3) 4.8 kpsi Usig Modiid Good, higl s MED, 10 th ditio Chptr 6 olios, Pg 35/58

36 Iiit li is ot prdictd. As. 6-4 Tl A-0: 440 MP, 370 MP Fro Pro. 3-73, th criticl strss lt xprics MP d τ 16.3 MP. Th dig is copltl rvrsd du to th rottio, d th torsio is std, givig MP, 0 MP, τ 0 MP, τ 16.3 MP. Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ MP 1/ MP 1/ x x x MP Chck or ildig, usig th distortio rg ilur thor x Th spl ils ildig, iiit li is ot prdictd. As. Th tigu lsis will cotiud ol to oti th rqustd tigu ctor o st, though th ildig ilur will dictt th li. Oti th odiig ctors d durc liit. Eq. (6-8): 0.5(440) 0 MP Eq. (6-19): (440) 0.90 Eq. (6-0): k k (50) 0.8 Eq. (6-18): 0.90(0.8)(0) 16.4 MP Usig Modiid Good, Iiit li is ot prdictd. As. higl s MED, 10 th ditio Chptr 6 olios, Pg 36/58

37 6-43 Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-74, th criticl strss lt xprics copltl rvrsd dig strss du to th rottio, d std torsiol d xil strsss.,d,xil kpsi, 0 kpsi,xil,d 0 kpsi, 0.36 kpsi τ 0 kpsi, τ kpsi Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi 1/ x x x kpsi Chck or ildig, usig th distortio rg ilur thor x Oti th odiig ctors d durc liit. Eq. (6-8): 0.5(64) 3 kpsi Eq. (6-19): (64) 0.90 Eq. (6-0): k k (1.13) 0.87 Eq. (6-18): 0.90(0.87)(3) 5.1 kpsi Usig Modiid Good, As Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-76, th criticl strss lt xprics copltl rvrsd dig strss du to th rottio, d std torsiol d xil strsss. higl s MED, 10 th ditio Chptr 6 olios, Pg 37/58

38 ,d,xil kpsi, 0 kpsi,xil,d 0 kpsi, kpsi τ 0 kpsi, τ kpsi Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi 1/ x x x kpsi Chck or ildig, usig th distortio rg ilur thor x Oti th odiig ctors d durc liit. Eq. (6-8): 0.5(64) 3 kpsi Eq. (6-19): (64) 0.90 Eq. (6-0): k k (0.88) 0.89 Eq. (6-18): 0.90(0.89)(3) 5.6 kpsi Usig Modiid Good, Iiit li is ot prdictd. As Tl A-0: 440 MP, 370 MP Fro Pro. 3-77, th criticl strss lt xprics 68.6 MP d τ 37.7 MP. Th dig is copltl rvrsd du to th rottio, d th torsio is std, givig 68.6 MP, 0 MP, τ 0 MP, τ 37.7 MP. Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ MP 1/ MP 1/ x x x MP higl s MED, 10 th ditio Chptr 6 olios, Pg 38/58

39 Chck or ildig, usig th distortio rg ilur thor x Oti th odiig ctors d durc liit. Eq. (6-8): 0.5(440) 0 MP Eq. (6-19): (440) 0.90 Eq. (6-0): k k (30) 0.86 Eq. (6-18): 0.90(0.86)(0) 170 MP Usig Modiid Good, As Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-79, th criticl strss lt xprics 3.46 kpsi d τ 0.88 kpsi. Th dig is copltl rvrsd du to th rottio, d th torsio is std, givig 3.46 kpsi, 0, τ 0 kpsi, τ 0.88 kpsi. Oti vo Miss strsss or th ltrtig, id-rg, d xiu strsss. 1/ kpsi 1/ kpsi 1/ x x x kpsi Chck or ildig, usig th distortio rg ilur thor x Oti th odiig ctors d durc liit. Eq. (6-8): 0.5(64) 3 kpsi Eq. (6-19): (64) 0.90 Eq. (6-0): k k (1.375) 0.85 higl s MED, 10 th ditio Chptr 6 olios, Pg 39/58

40 Eq. (6-18): 0.90(0.85)(3) 4.5 kpsi Usig Modiid Good, As Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-80, th criticl strss lt xprics 16.3 kpsi d τ 5.09 kpsi. ic th lod is pplid d rlsd rptdl, this givs x 16.3 kpsi, i 0 kpsi, τ x 5.09 kpsi, τ i 0 kpsi. Cosqutl, 8.15 kpsi, τ τ.55 kpsi. For dig, ro Eqs. (6-34) d (6-35), q r 0.1 Eq. (6-3): K 1 + q( K 1) (1.5 1) 1.38 For torsio, ro Eqs. (6-34) d (6-35), t q r 0.1 Eq. (6-3): K 1 + q ( K 1) (.1 1) 1.88 s s ts Oti vo Miss strsss or th ltrtig d id-rg strsss ro Eqs. (6-55) d (6-56). { } kpsi kpsi Chck or ildig, usig th cosrvtiv x +, higl s MED, 10 th ditio Chptr 6 olios, Pg 40/58

41 Oti th odiig ctors d durc liit. Eq. (6-8): 0.5(64) 3 kpsi 0.65 Eq. (6-19): k.70(64) 0.90 Eq. (6-4): d d Eq. (6-0): i k d (0.370) 0.98 Eq. (6-18): (0.90)(0.98)(3) 8. kpsi Usig Modiid Good, As Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-81, th criticl strss lt xprics 16.4 kpsi d τ 4.46 kpsi. ic th lod is pplid d rlsd rptdl, this givs x 16.4 kpsi, i 0 kpsi, τ x 4.46 kpsi, τ i 0 kpsi. Cosqutl, 8.0 kpsi, τ τ.3 kpsi. For dig, ro Eqs. (6-34) d (6-35), q r 0.1 Eq. (6-3): K 1 + q( K 1) (1.5 1) 1.38 t For torsio, ro Eqs. (6-34) d (6-35), q r 0.1 Eq. (6-3): K 1 + q ( K 1) (.1 1) 1.88 s s ts Oti vo Miss strsss or th ltrtig d id-rg strsss ro Eqs. (6-55) d (6-56). higl s MED, 10 th ditio Chptr 6 olios, Pg 41/58

42 { } kpsi kpsi Chck or ildig, usig th cosrvtiv x +, Oti th odiig ctors d durc liit. Eq. (6-8): 0.5(64) 3 kpsi 0.65 Eq. (6-19): k.70(64) 0.90 Eq. (6-4): d 0.370d 0.370(1) i Eq. (6-0): k d (0.370) 0.98 Eq. (6-18): (0.90)(0.98)(3) 8. kpsi Usig Modiid Good, As Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-8, th criticl strss lt xprics rptdl pplid dig, xil, d torsiol strsss o x,d 0. kpsi, x,xil 0.1 kpsi, d τ 5.09 kpsi.. ic th xil strss is prcticll gligil coprd to th dig strss, w will sipl coi th two d ot trt th xil strss sprtl or strss coctrtio ctor d lod ctor. This givs x 0.3 kpsi, i 0 kpsi, τ x 5.09 kpsi, τ i 0 kpsi. Cosqutl, kpsi, τ τ.55 kpsi. For dig, ro Eqs. (6-34) d (6-35), q r 0.1 Eq. (6-3): K 1 + q( K 1) (1.5 1) 1.38 t For torsio, ro Eqs. (6-34) d (6-35), higl s MED, 10 th ditio Chptr 6 olios, Pg 4/58

43 q r 0.1 Eq. (6-3): K 1 + q ( K 1) (.1 1) 1.88 s s ts Oti vo Miss strsss or th ltrtig d id-rg strsss ro Eqs. (6-55) d (6-56). { } kpsi 16.8 kpsi Chck or ildig, usig th cosrvtiv x +, Oti th odiig ctors d durc liit. Eq. (6-8): 0.5(64) 3 kpsi 0.65 Eq. (6-19): k.70(64) 0.90 Eq. (6-4): d 0.370d 0.370(1) i Eq. (6-0): k d (0.370) 0.98 Eq. (6-18): (0.90)(0.98)(3) 8. kpsi Usig Modiid Good, As Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-83, th criticl strss lt o th rl xis i th iddl o th logst sid o th rctgulr cross sctio xprics rptdl pplid shr strss o τ x 14.3 kpsi, τ i 0 kpsi. Thus, τ τ 7.15 kpsi. ic th strss is tirl shr, it is covit to chck or ildig usig th stdrd Mxiu hr trss thor. / 54 / 1.89 τ 14.3 x higl s MED, 10 th ditio Chptr 6 olios, Pg 43/58

44 Fid th odiirs d durc liit. Eq. (6-8): 0.5(64) 3 kpsi 0.65 Eq. (6-19): k.70(64) 0.90 Th siz ctor or rctgulr cross sctio lodd i torsio is ot rdil vill. Followig th procdur o p. 97, w d quivlt ditr sd o th 95 prct strss r. Howvr, th strss sitio i this cs is olir, s dscrid o p Notig tht th xiu strss occurs t th iddl o th logst sid, or with rdius ro th ctr o th cross sctio qul to hl o th shortst sid, w will sipl choos quivlt ditr qul to th lgth o th shortst sid. Eq. (6-0): d 0.5 i k d (0.5) 1.0 W will roud dow to k 1. Eq. (6-6): k c 0.59 Eq. (6-18): s 0.9(1)(0.59)(3) 17.0 kpsi ic th strss is tirl shr, w choos to us lod ctor k c 0.59, d covrt th ultit strgth to shr vlu rthr th usig th coitio lodig thod o c Fro Eq. (6-54), su 0.67 u 0.67 (64) 4.9 kpsi. Usig Modiid Good, As. ( τ / s ) + ( τ / su ) (7.15 /17.0) + (7.15 / 4.9) 6-51 Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-84, th criticl strss lt xprics 8.0 kpsi d τ 15.3 kpsi. ic th lod is pplid d rlsd rptdl, this givs x 8.0 kpsi, i 0 kpsi, τ x 15.3 kpsi, τ i 0 kpsi. Cosqutl, 14.0 kpsi, τ τ 7.65 kpsi. Fro Tl A-15-8 d A-15-9, D / d 1.5 /1 1.5, r / d 0.15 / K t,d 1.60, K 1.39 t,tors Eqs. (6-34) d (6-35), or Figs. 6-0 d 6-1: q d 0.78, q tors 0.8 Eq. (6-3): higl s MED, 10 th ditio Chptr 6 olios, Pg 44/58

45 ,d d,d,tors tors,tors ( t ) ( t ) K 1+ q K K 1+ q K Oti vo Miss strsss or th ltrtig d id-rg strsss ro Eqs. (6-55) d (6-56). { } kpsi 7.0 kpsi Chck or ildig, usig th cosrvtiv x +, ic strss coctrtios r icludd i this quick ild chck, th low ctor o st is ccptl. Eq. (6-8): 0.5(64) 3 kpsi 0.65 Eq. (6-19): k.70(64) Eq. (6-4): d d Eq. (6-0): i k d (0.370) Eq. (6-18): (0.897)(0.978)(0.5)(64) 8.1 kpsi Usig Modiid Good, As. ic iiit li is ot prdictd, stit li ro th -N digr. First, id quivlt copltl rvrsd strss ( Ex. 6-1). rv Fig. 6-18: 0.9 Eq. (6-14): Eq. (6-15): kpsi 1 ( / ) 1 (7.0 / 64) [ ] ( ) 0.9(64) (64) log log higl s MED, 10 th ditio Chptr 6 olios, Pg 45/58

46 1/ rv 46.7 Eq. (6-16): N 7534 ccls 7500 ccls As Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-85, th criticl strss lt xprics x,d 46.1 kpsi, x,xil 0.38 kpsi d τ 15.3 kpsi. Th xil lod is prcticll gligil, w ll iclud it to dostrt th procss. ic th lod is pplid d rlsd rptdl, this givs x,d 46.1 kpsi, i,d 0 kpsi, x,xil 0.38 kpsi, i,xil 0 kpsi, τ x 15.3 kpsi, τ i 0 kpsi. Cosqutl,,d,d 3.05 kpsi,,xil,xil kpsi, τ τ 7.65 kpsi. Fro Tl A-15-7, A-15-8 d A-15-9, D / d 1.5 /1 1.5, r / d 0.15 / K 1.60, K 1.39, K 1.75 t,d t,tors t,xil Eqs. (6-34) d (6-35), or Figs. 6-0 d 6-1: q d q xil 0.78, q tors 0.8 Eq. (6-3): K 1+ q K ,d d,d,xil xil,xil,tors tors,tors ( t ) ( t ) ( t ) K 1+ q K K 1+ q K Oti vo Miss strsss or th ltrtig d id-rg strsss ro Eqs. (6-55) d (6-56) ( 1.3)( 7.65) kpsi 0.85 { } kpsi Chck or ildig, usig th cosrvtiv x +, ic th cosrvtiv ild chck idicts ildig, w will chck or crull with with x otid dirctl ro th xiu strsss, usig th distortio rg ilur thor, witho strss coctrtios. Not tht this is xctl th thod usd or sttic ilur i Ch. 5. higl s MED, 10 th ditio Chptr 6 olios, Pg 46/58

47 x x,d x,xil x x τ kpsi As This shows tht ildig is iit, d urthr lsis o tigu li should ot itrprtd s gurt o or th o ccl o li. Eq. (6-8): 0.5(64) 3 kpsi 0.65 Eq. (6-19): k.70(64) Eq. (6-4): d d Eq. (6-0): i k d (0.370) Eq. (6-18): (0.897)(0.978)(0.5)(64) 8.1 kpsi Usig Modiid Good, As. ic iiit li is ot prdictd, stit li ro th -N digr. First, id quivlt copltl rvrsd strss ( Ex. 6-1). rv kpsi 1 ( / ) 1 (38.40 / 64) This strss is uch highr th th ultit strgth, rdrig it iprcticl or th -N digr. W ust coclud tht th luctig strsss ro th coitio lodig, wh icrsd th strss coctrtio ctors, r so r ro th Good li tht th quivlt copltl rvrsd strss thod is ot prcticl to us. Witho tstig, w r ul to prdict li Tl A-0: 64 kpsi, 54 kpsi Fro Pro. 3-86, th criticl strss lt xprics x,d 55.5 kpsi, x,xil 0.38 kpsi d τ 15.3 kpsi. Th xil lod is prcticll gligil, w ll iclud it to dostrt th procss. ic th lod is pplid d rlsd rptdl, this givs x,d 55.5 kpsi, i,d 0 kpsi, x,xil 0.38 kpsi, i,xil 0 kpsi, τ x 15.3 kpsi, τ i 0 kpsi. Cosqutl,,d,d 7.75 kpsi,,xil,xil kpsi, τ τ 7.65 kpsi. Fro Tl A-15-7, A-15-8 d A-15-9, higl s MED, 10 th ditio Chptr 6 olios, Pg 47/58

48 D / d 1.5 /1 1.5, r / d 0.15 / K 1.60, K 1.39, K 1.75 t,d t,tors t,xil Eqs. (6-34) d (6-35), or Figs. 6-0 d 6-1: q d q xil 0.78, q tors 0.8 Eq. (6-3): K 1+ q K ,d d,d,xil xil,xil,tors tors,tors ( t ) ( t ) ( t ) K 1+ q K K 1+ q K Oti vo Miss strsss or th ltrtig d id-rg strsss ro Eqs. (6-55) d (6-56) ( 1.3)( 7.65) kpsi 0.85 { } kpsi ic ths strsss r rltivl high coprd to th ild strgth, w will go hd d chck or ildig usig th distortio rg ilur thor. x x,d x,xil x x τ kpsi As This shows tht ildig is prdictd. Furthr lsis o tigu li is just to l to rport th tigu ctor o st, though th li will dicttd th sttic ildig ilur, i.. N ccl. As kpsi Eq. (6-8): Eq. (6-19): k (64) Eq. (6-4): d d Eq. (6-0): i k d (0.370) Eq. (6-18): (0.897)(0.978)(0.5)(64) 8.1 kpsi Usig Modiid Good, As. higl s MED, 10 th ditio Chptr 6 olios, Pg 48/58

49 6-54 Fro Tl A-0, or AII 1040 CD, 85 kpsi d 71 kpsi. Fro th solio to Pro w id th copltl rvrsd strss t th criticl shouldr illt to rv 35.0 kpsi, producig 35.0 kpsi d 0 kpsi. This prol dds std torqu which crts torsiol strsss o Tr / τ 967 psi.97 kpsi, τ 0 kpsi J π 1.65 / 3 4 Fro Tl A-15-8 d A-15-9, r/d 0.065/ , D/d 1.875/ , K t,d 1.95, K t,tors 1.60 Eqs. (6-34) d (6-35), or Figs. 6-0 d 6-1: q d 0.76, q tors 0.81 Eq. (6-3): K 1+ q K ,d d,d,tors tors,tors ( t ) ( t ) K 1+ q K Oti vo Miss strsss or th ltrtig d id-rg strsss ro Eqs. (6-55) d (6-56). { } { } kpsi kpsi Chck or ildig, usig th cosrvtiv x +, Fro th solio to Pro. 6-17, 9.5 kpsi. Usig Modiid Good, As. ic iiit li is ot prdictd, stit li ro th -N digr. First, id quivlt copltl rvrsd strss ( Ex. 6-1). rv kpsi 1 ( / ) 1 (7.66 / 85) Fig. 6-18: higl s MED, 10 th ditio Chptr 6 olios, Pg 49/58

50 ( ) [ 0.867(85) ] Eq. (6-14): (85) Eq. (6-15): log log Eq. (6-16): 1/ rv 66. N 51 ccls N 300 ccls As Fro th solio to Pro w id th copltl rvrsd strss t th criticl shouldr illt to rv 3.8 kpsi, producig 3.8 kpsi d 0 kpsi. This prol dds std torqu which crts torsiol strsss o Tr / τ 611 psi.61 kpsi, τ 0 kpsi J π 1.65 / 3 4 Fro Tl A-15-8 d A-15-9, r/d 0.065/ , D/d 1.875/ , K t,d 1.95, K t,tors 1.60 Eqs. (6-34) d (6-35), or Figs. 6-0 d 6-1: q d 0.76, q tors 0.81 Eq. (6-3): K 1+ q K ,d d,d,tors tors,tors ( t ) ( t ) K 1+ q K Oti vo Miss strsss or th ltrtig d id-rg strsss ro Eqs. (6-55) d (6-56) kpsi { } { } kpsi Chck or ildig, usig th cosrvtiv x +, Fro th solio to Pro. 6-18, 9.5 kpsi. Usig Modiid Good, higl s MED, 10 th ditio Chptr 6 olios, Pg 50/58

51 0.50 As. ic iiit li is ot prdictd, stit li ro th -N digr. First, id quivlt copltl rvrsd strss ( Ex. 6-1). rv kpsi 1 ( / ) 1 (6.74 / 85) Fig. 6-18: ( ) [ 0.867(85) ] Eq. (6-14): (85) Eq. (6-15): log log Eq. (6-16): 1/ rv 61.3 N 40 ccls N 4000 ccls As Kts L Fi Fx 55 kpsi, 30 kpsi, 1.6, t, 150 l, 500 l Eqs. (6-34) d (6-35), or Fig. 6-1: q s 0.80 K 1+ q K Eq. (6-3): s s ts T x 500() 1000 l i, T 150() 300 l i i 16K stx 16(1.48)(1000) τ x psi 11.5 kpsi 3 3 π d π (0.875) 16K sti 16(1.48)(300) τ i 3375 psi 3.38 kpsi 3 3 π d π (0.875) τ x + τ i τ 7.3 kpsi τ x τ i τ 3.94 kpsi ic th strss is tirl shr, it is covit to chck or ildig usig th stdrd Mxiu hr trss thor. / 30 / 1.33 τ 11.5 x Fid th odiirs d durc liit. higl s MED, 10 th ditio Chptr 6 olios, Pg 51/58

52 Eq. (6-8): 0.5(55) 7.5 kpsi Eq. (6-19): (55) 0.81 k Eq. (6-4): d 0.370(0.875) 0.34 i Eq. (6-0): (0.34) 0.99 k Eq. (6-6): k c 0.59 Eq. (6-18): s 0.81(0.99)(0.59)(7.5) 13.0 kpsi ic th strss is tirl shr, w will us lod ctor k c 0.59, d covrt th ultit strgth to shr vlu rthr th usig th coitio lodig thod o c Fro Eq. (6-54), su 0.67 u 0.67 (55) 36.9 kpsi. () Modiid Good, Tl As. ( τ / ) + ( τ / ) (3.94 /13.0) + (7.3 / 36.9) s su () Grr, Tl su τ τ s τ s suτ (7.3)(13.0) (3.94).49 As kpsi, 10 kpsi Fro Eqs. (6-34) d (6-35), or Fig. 6-0, with otch rdius o 0.1 i, q 0.9. Thus, with K t 3 ro th prol sttt, K 1 + q( K 1) (3 1).80 t 4P.80(4)( P) x K.476P π d π (1.) 1 (.476 P ) 1.38 P P ( D + d ) 0.3P ( ) Tx 0.54P 4 4 Fro Eqs. (6-34) d (6-35), or Fig. 6-1, with otch rdius o 0.1 i, q s 0.9. with K ts 1.8 ro th prol sttt, Thus, higl s MED, 10 th ditio Chptr 6 olios, Pg 5/58

53 K 1 + q ( K 1) (1.8 1) 1.74 s s ts 16K st 16(1.74)(0.54 P) τ x.769p 3 3 πd π (1.) τ x.769p τ τ 1.385P Eqs. (6-55) d (6-56): + τ P + P P 1/ [( / 0.85) 3 ] [(1.38 / 0.85) 3(1.385 ) ].81 + τ P + P P 1/ [ 3 ] [( 1.38 ) 3(1.385 ) ].70 Eq. (6-8): 0.5(145) 7.5 kpsi Eq. (6-19): (145) 0.7 Eq. (6-0): k k (1.) 0.86 Eq. (6-18): (0.7)(0.86)(7.5) 45.1 kpsi Modiid Good: 1.81P.70P P 4.1 kips As. 10 Yild (cosrvtiv): 5.9 As. + (.81)(4.1) + (.70)(4.1) 6-58 Fro Pro. 6-57, K.80, K 1.74, 45.1 kpsi s 4Px 4(18) x K kpsi π d π (1. ) 4Pi 4(4.5) i K kpsi π d π (1.) D + d Tx Px 0.3(18) 9.7 kip i 4 4 D + d Ti Pi 0.3(4.5).43 kip i Tx 16(9.7) τ x K s kpsi 3 3 π d π (1.) 16Ti 16(.43) τ i K s kpsi 3 3 π d π (1.) ( 11.14) kpsi higl s MED, 10 th ditio Chptr 6 olios, Pg 53/58

54 τ τ Eqs. (6-55) d (6-56): ( 11.14) 7.85 kpsi kpsi kpsi + τ + 1/ [( / 0.85) 3 ] [(16.71/ 0.85) 3(18.70) ] kpsi + τ + 1/ [ 3 ] [( 7.85) 3(31.16) ] kpsi Modiid Good: ic iiit li is ot prdictd, stit li ro th -N digr. First, id quivlt copltl rvrsd strss ( Ex. 6-1). rv kpsi 1 ( / ) 1 (60.73 /145) Fig. 6-18: 0.8 ( ) [ 0.8(145) ] Eq. (6-14): (145) Eq. (6-15): log log Eq. (6-16): 1/ rv 65. N ccls 98. N ccls As For AII 100 CD, Fro Tl A-0, 390 MP, 470 MP. Giv: 175 MP First Lodig: ( ) 60 MP, ( ) 100 MP 1 1 higl s MED, 10 th ditio Chptr 6 olios, Pg 54/58

55 Good: ( ) 1 cod lodig: ( ) MP iit li 1 / 1 60 / 470 > MP ( 470 log ) / N ccls ( 00) 30 ( 00) 60 MP, ( ) 60 MP MP 1 60 / 470 () Mir s thod: N 1/ ccls ccls As. N N () Mso s thod: Th ur o ccls riig tr th irst lodig N riig ccls Two dt poits: 0.9(470) MP, 10 3 ccls 3.8 MP, ccls 3 ( 10 ) ( 65 90) log log MP / ccls As Giv: 50 kpsi, 140 kpsi, 0.8. Usig Mir s thod, higl s MED, 10 th ditio Chptr 6 olios, Pg 55/58

56 kpsi ( 140 log ) / kpsi, N ccls / kpsi, N ccls / kpsi, N ccls N 0.5N 0.3N N ccls As Giv: 530 MP, 10 MP, d 0.9. () Mir s thod MP ( 530 log ) / MP, N ccls / MP, N ccls / MP, N ccls N1 N N ccls As () Mso s thod: Th li riig tr th irst sris o cclig is N R ccls. Th two dt poits rquird to di,1 r [0.9(530), 10 3 ] d (350, 8550). higl s MED, 10 th ditio Chptr 6 olios, Pg 56/58

57 3 ( 10 ) N N ( 8550) R log log MP 1/ ccls ccls 3 3 ( 10 ) log , MP log / N ccls As Giv: 45 kpsi, 85 kpsi, 0.86, d 35 kpsi d 30 kpsi or 1 (10 3 ) ccls. 35 Grr quivlt rvrsig strss: kpsi rv 1 / 1 30 / 85 () Mir s thod: rv <. Accordig to th thod, this s tht th durc liit hs ot rducd d th w durc liit is 45 kpsi. As. () Mso s thod: Agi, rv <. Accordig to th thod, this s tht th tril hs ot dgd d th durc liit hs ot rducd. Thus, th w durc liit is 45 kpsi. As Giv: 45 kpsi, 85 kpsi, 0.86, d 35 kpsi d 30 kpsi or 1 (10 3 ) ccls. 35 Good quivlt rvrsig strss: rv kpsi 1 / 1 30 / 85 Iitil cclig higl s MED, 10 th ditio Chptr 6 olios, Pg 57/58