材料力学第七章应力应变分析强度理论-正式

1、12345678 3 32 21 1 9 10Fl/2l/2Fl/2l/2S1121312aFzyzyFS13yxzAFWT34St2 zzxWM 1 1 t1WT t3WT zyFSzyzzxWM 3 3 14pDyzp 42DpF DA 442pDDDpAF l15直径平面直径平面p yFNFNd 0 0 yF20lplD 2 2pD 0sin2F20 dDplN16xyz17xyaea18xyaea19eaea0sin)sind(cos)sind( cos)cosd( sin)cosd(d0 AAAAAFyyxxxyn20eaea0cos)sind(sin)sind( sin)cosd(

2、cos)cosd(d0 AAAAAFyyxxxyt21 2cos2sin22sin2cos22xyyxxyyxyx xy yx 2cos121cos22cos121sin22sincossin222 2sin2cos22xyyxyxyx 9090 2sin2cos22)1802sin()1802cos(22902sin902cos220000900 xyyxyxxyyxyxxyyxyx）（）（23 2 22 22 22 22 22 22 2cossinsincosxyyxxyyxyx 02cos2sin2 2dd xyyx 02tan2xyxy 90900 00 0 24 2 22 22 22

3、 2sincosxyyxyx 2 22 22 22 2xyyxyx )(minmax25 02tan2xyxy 26 2 22 22 22 22 22 22 2cossinsincosxyyxxyyxyx 02sin2cos2 2dd xyyxxyyx 2 22 21 1 tan 90901 11 1 27 2 22 22 2cossinxyyx 2 22 22 2xyyx )(minmaxxyyx 2 22 21 1 tanyxxy 2 22 20 0tan1 10 02 21 12 2 tantan 28102tan12tan 即最大和最小切应力所在平面与主平面的夹角为即最大和最小切应力所

4、在平面与主平面的夹角为450。)2(2tan)2cot()2cot(2tan11111 因：因：4,2221010 比较得：比较得：29A alA50500 07070 xyyx ,30429. 10)70(50222tan0 yxxy 5 562625 527270 0. xA A MPaMPa)(minmax969626262 22 22 22 2xyyxyx MPa,MPa96960 026263 32 21 1 31n3030efMPa3 .58 )60sin()50()60cos(2604026040 2sin2cos2230 xyyxyxMPa3 .18)60cos()50( )6

5、0sin(260402cos2sin230 xyyx321 16060404050502 22 22 20 0 )(tanyxxy20 0 5 567675 522220 0. MPa7 .60MPa7 .80)2(222minmaxxyxyx MPa7 .60 0 MP7 .80321 133 yxxy 2 22 20 0tan 909090902 20 0 454545450 0 45 2 22 22 22 2xyyxyx)(minmax 134 cossin sincos 2 22 22 22 22 22 22 2xyyxxyyxyx 352 22 22 22

6、22 22 2xyyxyx )()(),(0 02 2yxC 2 22 22 2xyyxR )(36 xy37D xyO xA y yxDxy382 22 22 2xyyxR )(D xyO xA y yxD2)(21)(21yxOBOAOBOAOBOC 2 22 22 22 22 2xyyxADCACD )(2 2yx 39D xyO xA y yxDFxya40D xyO xA y yxDF)22cos(0 CEOCCFOCOF 2sin2sin2cos2cos00CDCDOC 2sin2cos22xyyxyx)22cos(0 CDOC 2sin2cosDACAOC41D xyO xA y

7、 yxDF 2sin2cos 2sin2cos2cos2sin )22sin()22sin(00CADACDCDCDCEFEoo 2cos2sin2xyyx42AB A431 12 22 21 11 12 22 2 max)(xyyxyxCAOCOA2 22 22 21 11 12 22 2 min)(xyyxyxCBOCOB 2D xyO xA y yxDFB1A144D xyO xA y yxD 2A1B1yxxyCADA 2 22 20 0)(tanyxxy 2 22 20 0tan()022arctanxyxy 45D xyO xA y yxD 2A1B1G1G2max)( 2 22

8、21 12 2xyyxCGmin)( 2 22 22 22 2xyyxCG2 22 21 1 minmax46 ACB(-1,-0.2)DD(-0.4,0.2)47ADC BD4849 1 3 1 2 2 2 150 1 2 3 3 2 151 A 1O 2BC 352 1 2 1 2 353 A 1O 2BC 31 1 max54 A 1O 2BC 3)(2131max 55MPa20 z 40MPaxyz20MPa20MPa20MPaMPaMPaMPa MPa2020202020204040 yxyxyx 56MPaMPaMPa MPa2020202020204040 yxyxyx A1A

9、2 O C 1 3MPa36231max 57xyzz58xzyExx Eyx Ezx xy yzz59)(1zyxxE )(1xzyyE )(1xyzzE Gyzyz Gxyxy Gzxzx 60zyx,zxyzxy,Gyzyz Gxyxy Gzxzx )(1zyxxE )(1xzyyE )(1xyzzE 61 Gxyxy )(1yxxE )(1xyyE )(xyzE xyz xy x y yx x y xy yx62)(13211E )(11322E )(12133E )(1211E )(1122E )(123E , , , ,63123123643213213211 dddddd)1(d

10、dd dddddd)1(d)1(d)1(d zyxzyxzyxzyxzyxzyxVVV )(21321E )(13211E )(11322E )(12133E 653321m Km )(21321E )21(3 EKm 66xy 3102 0 3321m mmmm321)(21 EE m m m)(21321E 67m321E m m m 1 2 3dxdydz mmmm321211EE )(21321E 168)(21zyxE 69MPa301 . 010300233 AFaaaF0)(13211 E0)(13122 Ezyx 1 2 37015.5MPa )30(0.34-10.34)0.

11、34(1 1)1(23221 MPa25. 7)(2131max 433211095. 1)3025 .15(1010034. 021)(E21 MPa303 MPa51521. 71MeMeA45x72yxyx 22minmax)2(2 02tan2xy EE1)(1311 3210450 451 11 EGPa2 .802121)1(2te11 WMEG 1 373bhzb=50mmh=100mmaAF1F2F2l74MPa202 AFMPa3023S AF A x = 20MPa4 .21MPa4 .41)2(222minmax xyxyx4 .411 02 4 .213 bISFzzS

12、 754311104 . 2)(1 E5312103)( E 4133107 . 1)(1 E020 zyx410 Exx5103 xyE5103 xzE76222221EEv 77()1 1223312v ()222123122331122v EdVvvv)(13211E 78mEE 321)(21321(a) 1 2 3 (b) m m m=( 1+ 2+ 3)/379()()()()()222222bbmmmmmm2m21231223 122126Vvv EEE ()()()aadaVvvv()()bbVvv()()abVVvv)(21321E ()222123122331122v E8

13、0()222123122331122v E ()()()2ab123126VVvvE ()()() d22212233116VvvvE (a) 1 2 3即：即：81maxNmaxAF maxmaxWMz S AFtmaxmax WT*maxmaxSmax bISFzz828384858687 88Eb1 )(13211E )(321 892smax 31 s 31）（31max21 902ds126vE )()()(21213232221 21323222161 Ed s 2132322212191)()()(21)(2132322214r313r3212r11r r 929394（a）Dy

14、z（b）95MPa904 pDMPa90MPa18021 MPa156 )()()(212132322214r MPa1802 pD 03 9610903010909090MPar803 MPar1003 MPar903 最危险最危险972214212 2234212 223134r 2221323222143 21）（r982)(31 2 993 3)()- (-0()0(21222 6 . 0577. 03 100 作业(1)：7-2(a.c)/4(b.c)/5 作业（2）：7-16/1810112015152709z250kN1.6m2mABC102+200kN50kN+80kNm250KN1.6m2mABCzIMy 4633mm1088 1227011112300120 zIdISFzz*S 1033 32560002560005 57 71501501515120120mm).(* zaS12015152709zMPa5 .122 azCayIM MPa.*S6 66464 dISFzzaa amm135 ay104 CAB(1