材料力學(xué)上課例題

1、lABxFmaxwmax 第七章 彎曲變形 上課例題xlwABxF( )() (1)M xF lx ( ) (2)EIwM xFlFx 21 (3)2FxEIwFlxC 2312(4)26FlxFxEIwxCC 21 (3)2FxEIwFlxC 2312(4)26FlxFxEIwxCC 0,0 0,0 xwxw120 0CC22FxEIwFlx 2326FlxFxEIw BwmaxmaxxlyAF（ ）222max|22x lFlFlFlEIEIEI max maxw（ ）3max|3x lPlwwEI max maxwABqRR2ABqlFFABqFRAFRBx2( )22qlqM xxx2

2、346qlqEIwxxC 222qlqEIwxx 341224qlqEIwxxCxD233(64)24qlxxlEI 233(2)24qxwlxxlEI 0w xABqFRAFRB A B3max24ABqlEI wmax4max25384lxqlwwEI ABFDabRAbFFlRBaFFlFRAFRBABFDab12xx1R(0)AbMFxFxxal2() ()bMFxF xaaxll11bFxEIwMl2112b xEIwFCl 31116b xEIwFC xDl22()bFxF xaEIwMl 2222()22bF xaxFEIwCl33222()66bF xaxFxEIwCDl12w

3、w12ww10w 20w 120DD2212()6FbCClbl ABFDabl12FRAFRB22211()36FbwlbxlEI 22216FbxlwbxlEI2222221()()23FblxawxlblEI b 33222() ()6FblxxawxlblEI b 10()|6AxFab lblEI 2()|6Bx lFab lalEImax()6BFab lalEI0w 10w22211()036FbwlbxlEI 221(2 )33lba abx1222 3max()0 06429 3x xFbPblw |lb.wEIlEI 222(34)0.062548CFbFblwlbEIEI

4、1222 3max()0 06429 3x xFbFbly |lb.wEIlEIABCABCq(a)BAMe(c)Aq(b)B)(qA )(qB ()Cqwe()BM e()MA e()CMwCe()(CCqMCwwwe)(AqMAA24e538416M lqlEIEI( )( )3e()243M lqlEIEI e)(BqMBB( )3e246M lqlEIEI ABCql/2ABCq/2CABq/2q/2ABCq/24415(2)5384768CqlqlwEIEI 3311(2)2448BAqlqlEIEI CABq/2q/2CABq/2q/2Bq/2ACq/23322( )( )2224

5、384ABqlqlEIEI 20Cw 4125768CCCqlwwwEI( )33312348384128AAAqlqlqlEIEIEI ( )33312748384384BBBqlqlqlEIEIEI ( )ABCDaa2a2qqABCDaa2a2qqBCDq2qa2BMqa2qAB2qa2BMqa2BMqa2qa2qaBCDq2BMqaqBCDBCD2BMqa()D qw()B q DBC 3)()(3BBqBMBqaEI 4()()24BDD qDMqawwwEI2qaBCDq2BMqa()BBM ()BD MwDBC2BMqa33)(243qBqlqaEIEI 32()33BBBMM

6、lqaEIEI 4455()38424D qqlqawEIEI 42()164BBDMMqalwEIEI2wA2qB2qa2BMqaAB1wBC2qaBDq2BMqa122BAwwwaw 22(2 )8qawEI44473412AqaqaqawEIEIEIl=400mmF2=2kNACa=0.1m200mmDF1=1kNBF2BCDA=+F2BCaF2BCDAM=+F1=1kNADCF2=2kNCABBl=400mmF2=2kNACa=0.1m200mmDF1=1kNB 21116BF lEI 211116CBF l awaEI 20B 3223CF awEI 2333BMllaFEIEI 2

7、2333CBF lawaEI +F2BC圖圖2圖圖3+F2BCDAM=圖圖1F1=1kNDC 212163BF lF laEIEI 2321221633CF l aF aF a lwEIEIEI44441284()643.14 (8040 ) 1064 188 10 mIDd F2=2kN=+圖圖1圖圖2l=400mmACa=0.1m200mmDF1=1kNBF1=1kNDBC圖圖3F2BDAMACCF2 23261225.19 10 m1633CF l aF aF a lwEIEIEI 212-40.4400200()163210 1880163 +0.423 10BF lF laEIEI

8、maxwwll 65max5.19 10 m10 mww 4max0.423 100.001a2aABCq2qDlCADBq2qAFNFNAwl ADBCq2qAwFNFNlBCq2qFNAwN()()AA qA FwwwN()()A qA Fwwl BCq2q()Aqw47()12A qqawEI N3N()A FF awEI CFNBN()AFwNF llEA 43NN712F aF lqaEIEIEA4N3712()AqaFIlAa ADBCq2qFNFNlA1Aw4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/mMB

9、B B BB 3420 4243BBMEIEI 12804()243BMEIEI 3032(52)5653BBMEIEI 4253BMEIEI4m3m2mABDC30kN20kN/mDAB30kN20kN/mMBB B C4m3m2mABDC30kN20kN/m+-32.0547.9518.4011.64+-25.6831.8023.281.603m-+R32.05KNAF R66.35KNBF R11.6KNCF pDyzp 42DpF DA 442pDDDpAF l第八章：應(yīng)力狀態(tài)分析和強(qiáng)度理論p yFNFNd 0 0 yF20lplD 2 2pD plDDpl dsin20A alA50

10、500 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( )60sin(260402cos2sin230 xyyx1 16060404050502 22 22 20 0 )(tanyxxy20

11、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 ACB(-1,-0.2)DD(-0.4,0.2)ADC BD12015152709z250kN1.6m2mABC+200kN50kN+80kNm250kN1.6m2mABCzIMy 4633mm1088 1227011112300120 zImm135 aydISFzz*S CAB(12

12、2.5 , 64.6)D(0 , - 64.6)A1 A2MPa27MPa1502211 OAOA 4520 5 .220 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)MPa20 z 40MPaxyz20MPa20MPa20MPaMPaMPaMPa MPa2020202020204040 yxyxyx A1A2 O C 1 3MPamax3636 MPa301 . 010300233 AFaaaFzy

13、x z x y)(13211E )(12133E MeMeA45xD yMeK450900 x0 zD yMeK450900 xMPa80max1 yMPa80max3 xxyk 1 3 max max4maxmaxmax102 . 5)1()(1)(1 EEEyxx 41102 . 5 x 0)()(maxmax EEyxz 0)( zE bhzb=50mmh=100mmaAF1F2F2lMPa202 AFMPa3023S AF A x = 20MPa4 .21MPa4 .41)2(222minmax xyxyx4 .411 02 4 .213 4311104 . 2)(1 E5312103

14、)( E 4133107 . 1)(1 E020 zyx410 Exx5103 xyE5103 xzE5FA0459090450,h/425. 02 FMAMPa8 .50 AzAAyIM)(MPa8 .68*S dISFzzAAA *zASzAh/42SFFA A = 50.88 .500 A090 yE00 E090 MPa2 .9490sin90cos2245 xxxMPa3 .43270sin270cos22135 xxx6135454510536)(1E0.5F0.50.25A04590h/4 A = 50.8（a）Dyz（b）MPa904pDMPa90MPa180

15、21 MPa155 )()()(212132322214r MPa1802 pD 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-70MPa2 -3140MPa28. 572.9440)23070(2307022minmax MPa72941.

16、MPa2853. MPa502 zMPa2203r MPa1954r MPa44893r. MPa5 .774r 140 MPa80 MPa（c）70 MPa（d）50MPaFFMPa7 .351 . 0700016MPa37. 6101 . 05043t32N WTAFMPa32397 .35)237. 6(237. 6)2(22222minmaxMPa32, 0,MPa39321 1 MPa4 .9410)37. 73 . 088. 1(3 . 011 . 2 )(1722 yxxE xyAA003r7 . 71701701 .183 MPa1 .18310)88. 13 . 037. 7

17、(3 . 011 . 2)(1722 xyyE 0,MPa4 .94,MPa1 .183321 MPa1 .183313r 0.42CDAB0.421.662.500.42CDAB0.421.662.50maxmaxWMz 36maxm10494 MWz m1062.24m1085. 0m1071142*248 SIdIzzMPa5 .95maxS*maxmaxSmax dSIFdISFzz 122 13.7126.32808.5 126.3 )(MPa1 .149max zAAIyM36*m10223)27 .133 .126(7 .13122 ASMPa8 .73*maxS dISFzAA

18、 122 13.7126.32808.5 126.3MPa197)()()(212132322214r 221)2(2 02 223)2(2 %9 .15%1004r .FACD1.2m1.2mB30FFRAyFRAxFyxFNCB3002 . 14 . 230sin 0NFFMCBAFFCBNFFFFFFAyyAxx5 . 00866. 00RR 第九章：組合變形AFAFAx866. 0R zzAyWFWF6 . 02 . 1Rmax MPa37.946 . 0866. 0maxc zWFAFFACD1.2m1.2m30BFFRAyFRAxFyxFNAB30yzz0z150501501503

19、50FFyzz0z15050150150350FFnnFNMyyFFMFFy22N105 .4210)5 . 735( yzz0Pa15NFAF nnFNMyyzz0z15050150)(MPa53105 . 74250maxt FIzMyy )(MPa53105 .124251maxc FIzMyy 5050150150yzz0z1拉拉nnFNMy53105 . 742515tmaxtmaxt FF5050150150yzz0z1拉拉壓壓nnFNMy53105 .12425cmaxcmaxc FAF5050150150yzz0z1拉拉壓壓nnFNMyaaaa1122

20、N14)2(aFaFAFAF aa22N222612/2aFaaFaaaFWMAF 8 84 42 22 22 2 aFaF/yzebhmmyze2 21 1FFF eFMz 221FFF eFMz 2AFFAF21N 6/22bheFWMzz 06/2221 bheFAFF 6/ )(2212bhFAFFe yzeOdA 11,2zyada422diizy ,82162121dddaiyyzF 0121 zyFaiz1d/8bBCDyzO12121222232hibhbhbAIizyy 112zyaha62122211hhhaiyyzF 0121 zyFaiz 1BO12346 60 02

21、22 2bzyFF ,)0,6(h),(6 60 0b hbABCDyzO2341 0 10202 yiyzizzFyF0122 FzBFyByiyziz313 324hb ABCD1.4m0.6m15kN10kN0.8mABFemkN15 6 . 0104 . 115e MkN25 FABFMe+15kNm-20kNmmkN20max MmkN15 T)1(3243 DWMPa26.157223r WTMzxyABl/2l/2MeMeMeCF=3F2e221e22)(MDFDFFMCkN3202 FkN20 F+T=1kNm+1kNm1223r TMW323dW mm83.44dmkN1 T

22、mkN1max MMeMeCF=3F2BACDyz5kN10kN300mm300mm100mmx1.82kN3.64kNBACDyz5kN10kN300mm300mm100mmx1.82kN3.64kNxyzACBD5kN1kNm1.82kN3.64kN10kN1kNm1CT 圖圖-My圖圖0.57CB0.36Mz圖圖0.2271CBxyzACBD5kN1kNm1.82kN3.64kN10kN1kNmmkN36. 0mkN57. 0 yByCMMmkN1mkN227. 0 zBzCMMmkN227. 0mkN57. 0 zCyCMMCT圖圖-My圖圖0.57kNmCB0.36kNmMz圖圖0.

23、2271CBmkN1mkN36. 0 zByBMMmkN1 CBTTmkN063. 122 zByBBMMMmkN36. 022 zCyCCMMM WWTMBB137275. 0224r323dW .3632 137251 9mm100 10d 400400400400mkN4 . 0kN1e2 MFmkN4 . 0mkN8 . 04 . 08 . 0max21max TFFM WTM2max2max3rmm5 .38 d400400400mkN4 . 0mkN8 . 04 . 08 . 0max21max TFFMkN203N FF400400400MPa143Nmaxmax AFWMz M

24、Pa8 .31tmaxmax WT MPa1574223rlFcr2l()2cr22EIFl Fcrl0.3l0.7l( . )2cr20 7EIFl Fcrl2cr2EIFl l 22cr)(lEIF lFcrl/4l/4l/2( / )2cr22EIFl l第九章：組合變形 22crlEIF 22cr)7 . 0(lEIF 22cr)5 . 0(lEIF 22cr)2(lEIF 22cr)(lEIF x8801000yzyxz880FFlxz880 x8801000yzykN6 .134)11(105 . 6101 . 214. 3)(2811222cr lEIF x8801000yzyk

25、N4 .406)88. 05 . 0(108 . 3101 . 214. 3)(2811222cr lEIF FFlxz880dF1.3 a BF1.6 aCaFAal22 al3 . 11 aal12. 16 . 17 . 07 . 0 dF1.3 a BF1.6 aCaFA30mm20mmyz1p99E m0058. 002. 003. 0)02. 003. 0(1213 AIiyym0087. 0 AIizz15 . 0 zy 30mm20mmyz11586 zzzyyyilil kN5 .8922crcr zEAAF 1p100E 222244414)(64)(dDdDdDAIi 10

26、04122 dDlilm6 . 11404. 005. 010022min lm2 . 143min ll122754 dDlil 5712. 1240304s2bakN5 .155)(4)(22crcr dDbaAF stcrnFF stcrnFFn 1p86E 4dAIi 15 .62 il 2 .43s2baMPa301cr baMPa478crcr AF.stcrnFFn 5 51111pD活塞桿活塞桿活塞活塞dN398042 pDFN23900stcr FnFAIi il pD活塞桿活塞桿活塞活塞d24222cr)(64)(ldElEIF 2004 dlil 97P1 E ABCF0

27、.60.30.80 CM0 06 60 09 90 0 .sin.N FF8 . 06 . 08 . 0sin22 FF27272 2.N 1P99E 4dAIi ABCF180 ils257ab 12 MPa214cr bakN268NcrcrFAF FF27. 2N ABCFFF tzAtry sintIrMIyM sint 1 2 3 4 1O第十二章：交變應(yīng)力.maxmax24 58300561MPa0 0115FA .minmin24 55800537 2MPa0 0115FA MPa1225375612minmaxa MPa54925375612minmaxm 957. 0561537maxmin rf f50f f40r=525. 14050dD125