第七章 應(yīng)力應(yīng)變分析 強(qiáng)度理論

1、Chapter7 3 32 21 1 Fl/2l/2Fl/2l/2S213mm zaFzyzyFSyzAFWT34St2 zzxWM 1 1 t1WT t3WT zyFSzyzzxWM 3 3 xyzxyaeaxyaeaeaea0sin)sind(cos)sind( cos)cosd( sin)cosd(d0 AAAAAFyyxxxyn0cos)sind(sin)sind( sin)cosd(cos)cosd(d0 AAAAAFyyxxxyt 2cos2sin22sin2cos22xyyxxyyxyx yx 9 90 002cos2sin2 2dd xyyx 02tan2xyxy 90900

2、00 0 2 22 22 22 2sincosxyyxyx 2 22 22 22 2xyyxyx )(minmax ）02sin2cos2 2dd xyyxxyyx 2 22 21 1 tan 90901 11 1 2 22 22 2cossinxyyx 2 22 22 2xyyx )(minmaxxyyx 2 22 21 1 tanyxxy 2 22 20 0tan1 10 02 21 12 2 tantan ,22201 02tan2xyxy 2 22 22 22 2xyyxyx )(minmaxxyyx 2 22 21 1 tan2 22 22 2xyyx )(minmax401 A a

3、lA50500 07070 xyyx ,429. 10)70(50222tan0 yxxy 5 562625 527270 0. xA A MPaMPa)(minmax9 96 62 26 62 22 22 22 2xyyxyx MPa,MPa96960 026263 32 21 1 n3030efMPa3 .58 )60sin()50()60cos(2604026040 2sin2cos2230 xyyxyxMPa3 .18)60cos()50( )60sin(260402cos2sin230 xyyx1 16 60 04 40 05 50 02 22 22 20 0 )(tanyxxy 1

4、3513545452 20 0 5 567675 522220 0. MPa7 .60MPa7 .80)2(222minmaxxyxyx MPa7 .60 0 MP7 .80321 150,60,40 xyyx yxxy 2 22 20 0tan 909090902 20 0 454545450 0 45 2 22 22 22 2xyyxyx)(minmax 1 cossin sincos 2 22 22 22 22 22 22 2xyyxxyyxyx 2cos2sin22sin2cos22xyyxxyyxyx 2 22 22 22 22 22 2xyyxyx )()(),(0 02 2yxC

5、 2 22 22 2xyyxR )( xyD xyO xy xA y yxD2 22 22 2xyyxR )(D xyO xA y yxD2 22 21 12 21 1yxOBOAOBOAOBOC )()(2 22 22 22 22 2xyyxADCACD )(2 2yx D xyO xA y yxDFxya )22cos(0 CEOCCFOCOF 2 22 22 22 20 00 0sinsincoscosCDCDOC 2 22 22 22 2sincosxyyxyx 2 22 22 22 22 22 20 00 0sincoscossin)sin(CDCDCEFEo 2 22 22 2co

6、ssinxyyxAB A1 12 22 21 11 12 22 2 max)(xyyxyxCAOCOA2 22 22 21 11 12 22 2 min)(xyyxyxCBOCOB 2D xyO xA y yxDFB1A1D xyO xA y yxD 2A1B1yxxyCADA 2 22 20 0)(tanyxxy 2 22 20 0tan()022arctanxyxy D xyO xA y yxD 2A1B1G1G2max)( 2 22 21 12 2xyyxCGmin)( 2 22 22 22 2xyyxCG2 22 21 1 minmax ACB(-1,-0.2)DD(-0.4,0.2)

7、ADC BD12015152709z250kN1.6m2mABC+200kN50kN+80kNm250KN1.6m2mABCzIMy 4633mm1088 1227011112300120 zImm135 aydISFzz*S 3 32560002560005 57 71501501515120120mm).(* zaS12015152709zMPa5 .122 azCayIM MPa.*S6 66464 dISFzzaa a CAB(122.5 , 64.6)D(0 , - 64.6)A1 A2MPa27MPa1502211 OAOA 4520 5 .220 MPa MPa227270 01

8、501503 31 1 5 522220 0. a12015152709zMPa5 .136 bzCbyIM 0 b mm150 byb 0,MPa5 .136321 b(136.5 , 0)D(0 , 0) 1 3 1 2 2 2 1 2 1 1 2 3 3 zxy A 1O 2BC 3 2 12D 1 2 1 2 3 A 1O 2BC 31 1 max A 1O 2BC 3)(2131max MPa20 z 40MPaxyz20MPa20MPa20MPaMPaMPaMPa MPa2020202020204040 yxyxyx A1A2 O C 1 3MPamax3 36 6 yOxyOyx

9、xyOyx sindcosddyxxOP ABdxdydxABdxdyxyOyxxPPAAxd DOPDP cosdcosxPPDPx 2coscosdcosd1xxxxOPDP APABdxdyxyOyxyPPBByd OP sindsinyPPDPy D 2sinsindsind2yyyyOPDP PBABdxdyxyOyxyPPBBxyd OP cosdcosyPPDPxy cossinsindcosd3xyxyyyOPDP 321 cossinsincos22xyyx )sincos(cossin)(222 xyyx 2sin212cos22xyyxyx 2cos212sin22xyy

10、x 22 2 )()(2122minmaxxyyxyx yxxy 02tan 2cos2sin22sin2cos22xyyxxyyxyxxyzzxzyExx Eyx Ezx xy yzz)(1zyxxE )(1xzyyE )(1xyzzE Gyzyz Gxyxy Gzxzx zyx,zxyzxy,Gyzyz Gxyxy Gzxzx )(1zyxxE )(1xzyyE )(1xyzzE Gxyxy )(1yxxE )(1xyyE )(xyzE xyz xy x y yx x y xy yx)(13211E )(11322E )(12133E )(1211E )(1122E )(123E , ,

11、, , 1231233213213211 dddddd)1(ddd dddddd)1(d)1(d)1(d zyxzyxzyxzyxzyxzyxVVV )(21321E )(13211E )(11322E )(12133E xy 3102 0 m m mKEEm 3)()21(3)(21321321，平均應(yīng)力，平均應(yīng)力體積彈性模量體積彈性模量3,)21(3321 mEKKEm 3)()21(3321MPa301 . 010300233 AFaaaFzyx z x y0)(13211 E0)(13122 E15.5MPa )30(0.34-10.34 1321 MPa25.7)(2131max 4

12、33211095. 1)3025 .15(1010034. 021)(E21 MPa303 MPa51521. MeMeA45xyxyx 22minmax)2(2 02tan2xy EE1)(1311 3210450 451 11 Ete112121)1(2WMEG 1 3MPa2 .80 Dd dyMeK450900 x0 zDd dyMeK450900 xMPa80max1 yMPa80max3 xxyk 1 3 max max4maxmaxmax102 . 5)1()(1)(1 EEEyxx 45.2 10yx 0)()(maxmax EEyxz 0)( zE bhzb=50mmh=10

13、0mmaAF1F2F2lMPa202 AFMPa3023S AF A x = 20MPa4 .21MPa4 .41)2(222minmax xyxyx4 .411 02 4 .213 4311104 . 2)(1 E5312103)( E 4133107 . 1)(1 E020 zyx410 Exx5103 xyE5103 xzE0.50.50.25FA0459090450,h/425. 02 FMAMPa8 .50 AzAAyIM)(MPa8 .68*S dISFzzAAA *zASzAh/42SFFA A = 50.88 .500 A090 yE00 E090 MPa2 .9490sin9

14、0cos2245 xxxMPa3 .43270sin270cos22135 xxx6135454510536)(1 E 0.5F0.50.25A04590h/4 A = 50.8222221EEv ()1 1223312v ()222123122331122v E dVvvv(a) 1 2 3(b) m m m=( 1+ 2+ 3)/3()()()aadaVvvv()()bbVvv()()()()()222222bbmmmmmm2m21231223 122126Vvv EEE ()()abVVvv3)()21(3321EKm ()222123122331122v E ()()()2ab1231

15、26VVvvE ()()() d22212233116VvvvE (a) 1 2 3maxNmaxAF maxmaxWMz S AFtmaxmax WT*maxmaxSmax bISFzz Eb1 )(13211E )(321 2smax s3131max)(21 31 ()()() 222d1223312s16126vEE 2ds126vE )()()(21213232221 )()()(21)(2132322214r313r3212r11r r 阿托阿托莫爾莫爾(O.Mohr),18351918O2O1O1231321OOOOFONO FNO22222222c3123t311331c231

16、t1OOOOFONO t3ct1 O331rM ct （a）Dyz（b）pDyzp 42DpF d dDA d dd d 442pDDDpAF lp yFNFNd 0 0 yF20lplD d dd d 2 2pD plDDpl dsin20MPa904 d dpDMPa90MPa18021 MPa155 )()()(212132322214r MPa1802 d dpD 2)(31 2 3 3)()0()0(21222 6 . 0577. 03 （b） （c）70 MPa140 MPa80 MPa（d）50MPa（a）MPa120)0120()120120()1200(212224r 01

17、MPa12032 MPa120)120(0313r MPa128)140(1103021MPa1402224r313r 1140MPa110MPa2 03 （a） 180MPa-70MPa2 -3140MPa28. 572.9440)23070(2307022minmax MPa72941. MPa2853. MPa502 zMPa2203r MPa1954r MPa44893r. MPa5 .774r 140 MPa80 MPa（c）70 MPa（d）50MPaFFMPa7 .351 . 0700016MPa37. 6101 . 05043t32N WTAF32397 .35)237. 6(237. 6)2(22222minmax MPa32, 0,MPa39321 1 MPa4 .9410)37. 73 . 088. 1(3 . 011 . 2 )(1722 yxxE xyAA003r7 . 71701701 .183 MPa1 .18310)88. 13 . 037. 7(3 . 011 . 2)(1722 xyyE 0,MPa4 .94,MPa1 .183321 MPa1 .183313r 0.42CDAB0.421.662.500.42CDAB0.421.662.50ma