# HW7_soln - m For the given state of stress, determine the...

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Unformatted text preview: m For the given state of stress, determine the safety factor against yielding by (a) the maximum shear stress yield criterion, and (b) the octahedral shear stress yield criterion. First calculate principal normal stresses, and then use these to obtain the effective stress and safety factor for each method. Or for (b), the alternate form can be applied without ﬁrst calculating principal stresses. 2 ———]Z+Txy=613i’c3, 63:62 034511), XS =Go/53 , '62 —631, _ 1 _ 0H =51/(01 ‘02)2 +(62 “03)2 +(03 ‘01)29' XH =50/6H Or use alternate form for 6H ,_ 1 6H = 7—2—1/(6x —o'y)2 +(oy —csz)2 +(0'Z — x)2 +60% +13% +155) 6S = MAXUGI — 02 Stresses in MPa AISI 1020 steel (Table 4.2) 6x Cy CZ Txy 513 T3 01 62 (53 —100.00 40.00 _ 0.00 -50.00 -30.00 86.02 56.02 -116.02 0.00 Max Shear Oct Shear Go XS 6H XH 260 172.05 1.51 151.99 1.71 — ‘ (2440} 7.20 Soh‘d circuicw shaf—‘t wander Pe::)¢;§ am +5 "0’34 Fwd dsﬂczwxm MJT) usmg 5, r5: , (9:) EH. q>o) 62 < 0 0‘3 30;, O‘UCTZ give. Tm.” 7 2 2 o4 0‘ )-— 031/2 i ﬂog/2) +779, H 2 " __ :UI‘_0- E‘s-:Maxﬂcn—m, [cg-(r3), 10} 0H) 2 7‘ ‘ d 5‘5: 2 Marx/22+ 7k): — (Yo/X0 _ 32M d2) _ M(d/2) 2 N ﬁzMé/ _ 77014/64- 1M3 LT 67/2) _ 7(4/2) 2 , (70:73“ "' ’I'Td4/32 .mde CT ’4’” 2 “)2: 323V/M1+T2:.>_<2 53:2 + m3 rm 0 (“7.20, pnz) ‘ / d= _ ‘ () b a; = if; (01*03z)2+(0}'”6§)2+(0§‘62)2+ 6075+ 7;: +721) air—'EMV/zojf + £33} : 612+ 37x? 3 z (32M)2+ 3 léT 2 r J_.6 4M2+3T2=E§ H ’TTda 7Td3 7rd? 0 1/3 dz, (16xO ‘ TOT: , _ ' 0—2 =~Oz <-—-—-——' (UEJO; bo-H/g megah‘ue) ‘ Vzo w2a/ was W=a5h 9;: A0 M25 A75 00 6;, YeSJ‘bV/y effech m0 Vicioh‘mg 1+,(ory15‘l‘. VO/H’WIQ because: 741814 0“: 0‘ :0?) whip}; [s Sf’WI/J/a hydkosf'aﬁc COWkeSS/bm, ‘ (b) Ocz‘ahedral shear agrié— /(U:-0“z)1+<Uz-03)2+<0‘3-07)2 = 0; (7,23) [7.2) — -_1__ v52. 2 "_ F2? 2 0H _\r§\/2(crz— W) _ P? G; 0:, 0‘}: (To (1‘13?) (saw/Ia as (m) ‘ CC) AIS] mm 5mg]: <33: 2.50 Mpg) 7,5012% {Taé/es 492, 5:2). Assume 02,:—250MF52.:“MC. 0; = (‘260/‘4'0‘0 (“Li—773233) =—+4+ MP4 - ‘ 771/75 sagas/Lamf/‘ﬂ/fy 270266/5 CE. ——7'31 Solid circular shaH , L:/,0’m) M = [0) 72 L5 k/V'm} X0 = 20. (a) I1: AISI mo STEEL) jams! 015m. (b) (alibi/m? .0") am for o‘err wa‘I‘eH‘a/s Mao/Med. CC) CWZ/ for AISI /02[J/ CWFQ for ALE} Cam: 3 1CD? AIS]: 4140. COM/Oakﬁi Ve/aﬂ'l/e 5051: (d) Selecf a Wma‘f‘erial, (a) AISI ,/020: 0793260 MP2) 9:: 7.37 g/cm3 (Tables 4.2) 3,1) ‘" 4 +1BL+G743MMU I: E) kzd/E _, I 0’4 “T -1: :1. 7“ a"? 32 0 +0 0 —0 61,62: x2y_[x2 y]z+1:§y, 03—0220 ‘65 =MAX(|01 —Gzl,|62 —03 , 0'3 —O'1|), XOS =GO/BS 2 2 2 0117:72- (ox—oy) +_(6y—O'z)2+(GZ-Gx) +6(tw+r§2+’c;) Camb/‘WJ/‘Mg Hoe aboya 52014172944: gives express/am: {or Hm Vegm'red 0/ as Ciel/fixed 1'44 Prob. 7,20 solut‘fom. -~ 1/3 ' ‘ d5 = (ffg'D MZ+ T2) (35) max shear) (exp '2 27/3 — _ dH=(qTO; 4M +3T (UH) oat shear) d 2 (W32 (2-0) ‘/(IDXI06)Z+(L5XIO")2 IV-mm>i/3 5 m2 eoMPa.) d5 : 52.09 771111 I /3 ‘ \ __ _32 (2.0) é 2 , | r. 2) om- 40.0200) +3(15x;o) dH 250.45 mm ‘ Mass: use 01H) mote g/C’MB: Wig/7:73 “0'21. qjvzpl/zlo "4 _ ‘ M2 5.9. 77(0.05o+e>2<1.o>m? 474: I574 kg ' 4 Cb) Simiiar calcula‘h‘oms +0? Him aﬂqek Warts, give values as im tame. om max-1; page, (DAlso calculate C7“??? Vaiués as a; weasum I a; reia‘h‘I/e <0ch of H43 wafer/a! 1'77 each shaft ‘ Folycakbomafe 103A 024: 7/: 0.33 {Eb/e 52) 21.2 054:: 62 MPQ E :2 2‘4 Gina _ . Q};- a‘f’ yiﬁldfmgg Shaw b/bzzr/LQ/ Eggs: pi” A 2 + 2 (LZXéZ maﬁa +70%) :2 2x\.27\42 0330*?2‘2’27‘ + /2.4{/+W)0‘2, ~4g/2,€-=o 0. 76M— Jf + /7,//2 a; —- 4-6 12,3 = o ’ Sc)er quadrmﬁc 65244,: O; : €7.31 “8‘27 Mpg 0‘2: “99.7 M1001 [—- 1/007“ as COWPI’ESSIU‘W) 4 m m = 300, 015: -—I 000 , (Ti =. ——500 MA; (0.) Mod. Mom,» failure. \ocus for 6" v5. 0; (b) Emvelope om 0" US. \$7! _ + . Kw): W _—_ 0.250 (ﬂaxOLL) loam—03+ + 01 rm : \$144 (I), (1): I448” ﬂ :— tam ¢ : 0.258 _ 7, , /l+7rr lGuc’I fl—Wn G— 227: -:——— -———— I‘MCI ( l_,),},) 3 I]: a 1+7” 4 100 O [—0.250 ‘ 2 \/ [+0250 3 7 {TH/aux”)? NIH-0.2580: 337 MPCL 4 GE TEMP C17,, at 'm‘w 6C MPaW Mch KYH rmrm (I) -/@ 42 700 (looms Us (2) we /60 4—80 0.0354 35.3L —__—'—.. The shag! is much Wash: 600 ‘l'aleramT of {Haws Cit-i 'Hﬁe higher few/gera‘fure (2). 4 E For ear/1 metal I‘m Table. 8.! , :é/cu/afe ai 0440’ p/oz‘ 07) log scale Us. 02,, __l___(KIc)2—_—_ J.(W)z ’lT 6‘: 1T 540MP61. 52f: +.75></0'3,m = 4.75 07147: (for AISI H44- \$+ee£ J o-Hners s/xmi/ar/y) 61E: Kit: 60 13! ch 0'0 at MPa mo'5 MPa mm MPa mc"5 MPa mm (a) Steels (b) Aluminum Alloys 66 540 4.75 24 415 1.06 60 620 2.98 34 - 325 3.48 187 760 19.27 36 350 3.37 110 1090 3.24 29 505 1.05 123 1310 2.81 52 435 4.55 176 1290 5.93 (0) Titanium Alloy 152 1070 6.42 66 925 1.62 65 1740 0.44 100 0 Steel I El Al A Ti 10 ahmm 0.1 . 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Go , MPa (9. 3, p. 2) Al+hawgh +heke is COMS/‘derab/e Staffer; z'z‘ appears Hag-t 0% decreases («u/7% Murms— [m9 0'3 740% sfee/s. A/Mm/mu/m a//0ys Shaw 0‘! s/mm'ﬂw' 7914403 baﬂ‘ Luff/4 07f Swal/er *ham for sfee/s of 51m»: flak s-fremg-H/L 3-7 F, =+abmicﬁed waives / (X = Cit/b I Z “050‘ +032“ F13, 9mm 8’5: [FET— 2 "m (193 Pg: Hedi; (C) Er: ﬁ'tQ/ME (’ITGl/Z m Vadz‘ams) For eac/v 01 :01; a1) 0.2 0,9) Cé’I/[M/Qfe F2.) F3?) (2419’ F4) @4421 411.59 +148 l/af/os 5/5} a’nd a = a/b Tada Fig. 8.12a Secant Tangent Fig. 8.12a Secant Tangent F1 F2 F3 F4 F2/F1 F3IF1 F4/F1 0 1 ‘ 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.1 1.006 1.0048 1.0062 1.0041 0.9988 1.0002 0.9982 0.2 1.025 1.0208 1.0254 1.0170 0.9959 1.0004 0.9922 0.3 1.058 1.0510 1.0594 1.0398 0.9934 1.0013 0.9828 0.4 1.109 1.1001 1.1118 1.0753 0.9920 1.0025 0.9696 0.5 1.187 1.1759 1.1892 1.1284 0.9907 1.0019 0.9506 0.6_ 1.303 1.2924 1.3043 1.2085 0.9918 1.0010 0.9274 0.7 1.488 1.4784 1.4841 1.3360 0.9935 0.9974 0.8979 0.8 1.816 1.8082 1.7989 1.5650 0.9957 0.9906 0.8618 0.9 2.578 2.5743 2.5283 2.1133 0.9986 0.9807 0.8197 (01) F; is wn‘Jr-Aim 1% {or (X f: 0.9 03) E3 is Wi‘H’lf’H 2 for 0K .4; 0.51 (C3 F4, [5 LON-Infra Z’Z +0V WK :4; 0.3) 5°70 for O’x £03) amd I870 (9-H: 4 art 04 = 0.5}, ...
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## This note was uploaded on 04/26/2008 for the course M&AE 212 taught by Professor Miller during the Spring '07 term at Cornell University (Engineering School).

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HW7_soln - m For the given state of stress, determine the...

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