1、Chapter7 3 32 21 1 Fl/2l/2Fl/2l/2S213aFzyzyFSyxzAFWT34St2 zzxWM 1 1 t1WT t3WT zyFSzyzzxWM 3 3 pDyzp 42DpF DA 442pDDDpAF lp yFNFNd 0 0 yF20lplD 2 2pD plDDpl dsin20 xyzxyaeaxyaeaeaea0sin)sind(cos)sind( cos)cosd( sin)cosd(d0 AAAAAFyyxxxyn 2cos2sin22sin2cos22xyyxxyyxyx 0cos)sind(sin)sind( sin)cosd(cos)c

2、osd(d0 AAAAAFyyxxxytyx 9090 2 22 22 22 22 22 22 2cossinsincosxyyxxyyxyx 02cos2sin2 2dd xyyx 02tan2xyxy 90900 00 0 2 22 22 22 2sincosxyyxyx 2 22 22 22 2xyyxyx )(minmax 2 22 22 22 22 22 22 2cossinsincosxyyxxyyxyx ）02sin2cos2 2dd xyyxxyyx 2 22 21 1 tan 90901 11 1 2 22 22 2cossinxyyx 2 22 22 2xyyx )(min

3、maxxyyx 2 22 21 1 tanyxxy 2 22 20 0tan1 10 02 21 12 2 tantan 4,2220101 A alA50500 07070 xyyx ,429. 10)70(50222tan0 yxxy 5 562625 527270 0. xA A MPaMPa)(minmax969626262 22 22 22 2xyyxyx MPa,MPa96960 026263 32 21 1 n3030efMPa3 .58 )60sin()50()60cos(2604026040 2sin2cos2230 xyyxyxMPa3 .18)60cos()50( )60

4、sin(260402cos2sin230 xyyx1 16060404050502 22 22 20 0 )(tanyxxy20 0 5 567675 522220 0. MPa7 .60MPa7 .80)2(222minmaxxyxyx MPa7 .60 0 MP7 .80321 1 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 2 22 22 22 22 22 2xy

5、yxyx )()(),(0 02 2yxC 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(

6、CDCDCEFEo 2 22 22 2cossinxyyxAB 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

7、(-1,-0.2)DD(-0.4,0.2)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 A2MPa27MPa1502311OAOA4520 5 .2

8、20 MPa MPa227270 01501503 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 1 2 3 3 2 1 A 1O 2BC 3 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 3MPamax3636

9、yOxyOyxxyOyx sindcosddyxxOP ABdxdydxABdxdyxyOyxxPPAAxd DOPDP cosdcosxPPDPx 2coscosdcosd1xxxxOPDP APABdxdyxyOyxyPPBByd OP sindsinyPPDPy D 2sinsindsind2yyyyOPDP PBABdxdyxyOyxyPPBBxyd OP cosdcosyPPDPxy cossinsindcosd3xyxyyyOPDP 321 cossinsincos22xyyx )sincos(cossin)(222 xyyx 2sin212cos22xyyxyx 2cos212s

10、in22xyyx 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 )(12

11、3E , , , , 1231233213213211 dddddd)1(ddd dddddd)1(d)1(d)1(d zyxzyxzyxzyxzyxzyxVVV )(21321E )(13211E )(11322E )(12133E xy 3102 0 3321m mmmm321)(21 EE m m mm321E m m m 1 2 3dxdydz mmmm321211EE )(21321E )(21zyxE MPa301 . 01030023yAFaaaFzyx z x y0)(1zyxxE0)(1yxzzE15.5MPa )30(0.34-10.34)0.34(1 1)1 (2y2zx

12、MPa25.7)(2131max 433211095. 1)3025 .15(1010034. 021)(E21 MPa303 MPa51521. MeMeA45xyxyx 22minmax)2(2 02tan2xy EE1)(1311 3210450 451 11 EGPa2 .802121)1 ( 2te11WMEG 1 3D yMeK450900 x0 zD yMeK450900 xMPa80max1 yMPa80max3 xxyk 1 3 max max4maxmaxmax102 . 5)1()(1)(1 EEEyxx 41102 . 5 x 0)()(maxmax EEyxz 0)(

13、 zE bhzb=50mmh=100mmaAF1F2F2lMPa202 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 E0

14、90 MPa2 .9490sin90cos2245 xxxMPa3 .43270sin270cos22135 xxx613545010536)(1 E 0.5F0.50.25A04590h/4 A = 50.8222221EEv ()1 1223312v ()222123122331122v EdVvvv(a) 1 2 3(b) m m m=( 1+ 2+ 3)/3()()()()()222222bbmmmmmm2m21231223 122126Vvv EEE ()()()aadaVvvv()()bbVvv()()abVVvv)(21321E ()222123122331122v E ()()

15、()2ab123126VVvvE ()()() 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),18351918O2OO1O3FN22222222c3123t311331c231t1OOOO

16、FONO 231321OOOOFONO t3ct1 （a）Dyz（b）MPa904 tpDMPa90MPa18021 MPa155 )()()(212132322214r MPa1802 tpD 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 MPa12032 MPa120)120(0313r MPa128)140(1103021MPa1402224r313r 1140MPa110MPa2 03 （a） 180MPa-7

17、0MPa2 -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 0.42CDAB0.421.662.500.42CDAB0.421.662.50maxmax