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

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

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}, ...
View Full Document

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).

Page1 / 13

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

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online