[物理]第7章 應力和應變分析 強度理論ppt課件

1、3 32 21 1 三、應力形狀的分類Fl/2l/2Fl/2l/2S平面平面213aFzyzyFSyxzAFWT34St2 zzxWM 1 1 t1WT t3WT zyFSzyzzxWM 3 3 xyzxyaeaxyaeaeaea0sin)sind(cos)sind( cos)cosd( sin)cosd(d0 AAAAAFyyxxxyn 2cos2sin22sin2cos22xyyxxyyxyx 0cos)sind(sin)sind( sin)cosd(cos)cosd(d0 AAAAAFyyxxxytyx 9 90 0yxxy 2 22 22 22 22 22 22 2cossinsinc

2、osxyyxxyyxyx 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 )(minmaxxyyx 2 22 21 1 tanyxxy 2 22 20 0tan1 10 02 21 12 2 tantan

3、 42220101A alA50MPa0,70MPa,xyyx429. 10)70(50222tan0 yxxy 5 562625 527270 0. xA A MPaMPa)(minmax9 96 62 26 62 22 22 22 2xyyxyx MPa,MPa9 96 60 02 26 63 32 21 1 n3030efMPa3 .58 )60sin()50()60cos(2604026040 2sin2cos2230 xyyxyx18.3MPa)6050)cos( )60sin(26040cos2sin22xyyx301 16 60 04 40 05 50 02 22 22 20 0

4、 )(tanyxxy20 0 5 567675 522220 0. MPa7 .60MPa7 .80)2(222minmaxxyxyx MPa MPa7 .6007 .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 2xyyxyx )()(),(0 02 2yxC 2 22 22 2xyyxR )( xyD xyO xy x

5、A 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 2cossinxyyxAB A1 12 22 21 11 12 22

6、 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)ADC BD12015152709z250kN1.6m2mAB

7、C+200kN50kN+80kNm250KN1.6m2mABCzIMy 4633mm1088 1227011112300120 zImm135 aydISFzz*S 3 32560002560005 57 71501501515120120mm).(* zaS12015152709zMPa5 .122 azCayIM MPa.*S6 66 64 4 dISFzzaa a CAB(122.5 , 64.6)D(0 , - 64.6)A1 1 3A2MPa27MPa1502211 OAOA 4520 5 .220 MPa MPa22 27 70 01 15 50 03 31 1 5 52 22 2

8、0 0. a12015152709zMPa5 .136 bzCbyIM 0 b mm150 byb 0,MPa5 .136321 b(.5 , 0)D(0 , 0)xyzxzyExx Eyx Ezx xy y)(1zyxxE )(1xzyyE )(1xyzzE Gyzyz Gxyxy Gzxzx zyx,zxyzxy,Gyzyz Gxyxy Gzxzx )(1zyxxE )(1xzyyE )(1xyzzE Gxyxy )(1yxxE )(1xyyE )(xyzE xyz x xy y x y y yx x x y xy y yx x)(13211E )(11322E )(12133E )(12

9、11E )(1122E )(123E 3213213211 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 bhzb=50mmh=100mmaAF1F2F2lMPa202 AFMPa3023S AF A x = 20MPa4 .21MPa4 .41)2(222minmax xyxyxM

10、Pa4411. 02 MPa4213. 4311104 . 2)(1 E5312103)( E 4133107 . 1)(1 E020 zyx410 Exx5103 xyE5103 xzE2221221v()1 1223312v ()222123122331122v EdVvvv(a) 1 2 3(b) m m m=( 1+ 2+ 3)/3()()()aadaVvvv()()bbVvv()()()()()222222bbmmmmmm2m21231223 122126Vvv EEE ()()()aadaVvvv()()bbVvv()()abVVvv)(21321E ()2221231223311

11、22v E ()()()2ab123126VVvvE ()()() d22212233116VvvvE (a) 1 2 3maxNmaxAF maxmaxWMz S AFtmaxmax WT*maxmaxSmax bISFzz 1. 最大拉應力實際第一強度實際最大拉應力實際第一強度實際 Maximum-normal-stress criterionEb1 )(13211E )(321 2smax s3131max)(21 31 ()()() 222d1223312s16126vEE 2ds126vE )()()(21213232221 )()()(21)(2132322214r313r3212r11r r b 140 MPa 110 MPac70 MPa140 MPa80 MPad50MPaaMPa120)0120()120120()1200(212224r 01 MPa12032 MPa120)120(0313r MPa128)140(1103021MPa1402224r313r 1140MPa110MPa2 03 a 140 MPa 110 MPa180MPa-70MPa2 -3140MPa28. 572.9440)23070(2307022minmax MPa72941. MPa2853. MPa502 zMPa2203r MPa1954r MPa44893r. MP