中國(guó)石油大學(xué)工程力學(xué)答案合集PPT課件

1、2021-10-27Statics-Problems-1靜力學(xué)第1章作業(yè)/P23-1.1(g)*:第1頁(yè)/共96頁(yè)2021-10-27Statics-Problems-2靜力學(xué)第1章作業(yè)/P24-1.2(k):第2頁(yè)/共96頁(yè)2021-10-27Statics-Problems-3靜力學(xué)第1章作業(yè)/P27-1.3(c):第3頁(yè)/共96頁(yè)2021-10-27Statics-Problems-4靜力學(xué)第1章作業(yè)/P27-1.3(e)*:第4頁(yè)/共96頁(yè)2021-10-27Statics-Problems-5靜力學(xué)第2章作業(yè)/P58-2.3*:)(903060cos40coskNPRxSolutio

2、n:由此得到如下方程組：)( 060sin40sinkNPRy320sin100cosPP解得：)( 8 .105740kNP)( 1 .1953tan1第5頁(yè)/共96頁(yè)2021-10-27Statics-Problems-6靜力學(xué)第2章作業(yè)/P60-2.14*:Solution:按定義有:2211)(rFFrrFFrFMOSo, expressions (a), (d), (e) are valid.第6頁(yè)/共96頁(yè)2021-10-27Statics-Problems-7靜力學(xué)第2章作業(yè)/P61-2.20:Solution:(a)ar)(16. 04 . 048. 0mkjira)(6812

3、NkjiFjaIn vector form:)(96. 0)(mNjFMa)(96. 0010681216. 04 . 048. 0)(mNFrFMaaa第7頁(yè)/共96頁(yè)2021-10-27Statics-Problems-8)( 0100681216. 04 . 06 . 0)(mNFrFMzzzzr(b)(16. 04 . 06 . 0mkjirz)(6812NkjiFkzIn vector form:)( 0)(mNFMz第8頁(yè)/共96頁(yè)2021-10-27Statics-Problems-9+0 xxFRkNFRyy16161220mkNMM.36716485122200LRRLMy0

4、由)(25. 216360mRMLxySolution:靜力學(xué)第2章作業(yè)/P63-2.28*:第9頁(yè)/共96頁(yè)2021-10-27Statics-Problems-10與水平面夾角為，與水平面夾角為21TT1585 . 18 . 0tan178sin1715cos432 . 19 . 0tan53sin54cos0coscos21TTFX+0505 .142sinsin21TTFy)(1701NT )( 5 .1872NT （a)Solution:靜力學(xué)第2章作業(yè)/P63-2.30*:第10頁(yè)/共96頁(yè)2021-10-27Statics-Problems-11(b)+ARMC) 8 . 05

5、. 09 . 0(cos) 2 . 12 . 15 . 1 (sin22TT)2 . 15 . 1 (505 . 15 .142).( 0mN第11頁(yè)/共96頁(yè)2021-10-27Statics-Problems-12OOriginal forces and couple can be reduced to a force and a couple acting at point O:靜力學(xué)第2章作業(yè)/P64-2.32:RSolution:RC)(31030cos20NRx)(506030sin20kNRy)( 3 .23353212130sin205 . 030cos205 . 060mNC

6、R于是得到合力的大小、方向和作用線位置（如圖所示）：)( 9 .5272022NRRRyx)( 1 .1953tantan11yxRR)(441. 0mRCdR)(467. 0mRCdyRx)(348. 1mRCdxRyyddxd(或,或)yRRxR第12頁(yè)/共96頁(yè)2021-10-27Statics-Problems-13+0MCR0 xF0yF0zFNPx80NPy60NPz90kjiP906080mNM.392 . 0603 . 0900Solution:靜力學(xué)第2章作業(yè)/P64-2.34*:第13頁(yè)/共96頁(yè)2021-10-27Statics-Problems-14靜力學(xué)第3章作業(yè)/P

7、85-3.2*:Solution:RAyRByFrom the FBD of the beam in Fig:0BM+023129212AyR)( 0 kNRAyRBx3kN2m0 xF+)( 0 kNRBx0yF+032ByAyRR)( 1 kNRBy第14頁(yè)/共96頁(yè)2021-10-27Statics-Problems-15靜力學(xué)第3章作業(yè)/P86-3.11:Solution:GPGLStudying person and ladder, draw FBD(a) x=1.5m0AM+022BLPRGxGRBRAyRAx744.8(N)762gGxGRLPB0 xF+053AxBRR446.

8、88(N)53BAxRR第15頁(yè)/共96頁(yè)2021-10-27Statics-Problems-160yF+054AyBLPRRGGGPGLRBRAyRAx344.96(N)517651521254gGGxGxGGGRLPLPLPAy(b) 051521LPAyGGxR)( 6 . 2215 . 2mGGxPL第16頁(yè)/共96頁(yè)2021-10-27Statics-Problems-17靜力學(xué)第3章作業(yè)/P87-3.18:Solution:300N0.5mRDRE(1) Studying entire structureFrom the FBD of entire structure in Fi

9、g:0DM+01 . 13006 . 1ER206.25(N)ER(2) Studying member ABFrom the FBD of member AB in Fig:RBxRByRAxRAy300N0.5m1.6m0BM+05 . 03006 . 1AyR93.75(N)AyR第17頁(yè)/共96頁(yè)2021-10-27Statics-Problems-18(N)00434AyEAxRRR(3) Studying member ACEFrom the FBD of member ACE in Fig:0.8mRERAxRAyAECRCxRCy0.8m0.6m0.6m0CM+06 . 08

10、. 08 . 0AxAyERRR0 xF+0CxAxRR)(400 NRRAxCx0yF+0ECyAyRRR-112.5(N)EAyECyRRRR.8(N)10422AyAxARRR.5(N)15422CyCxCRRR第18頁(yè)/共96頁(yè)2021-10-27Statics-Problems-19靜力學(xué)第3章作業(yè)/P90-3.28(f)*:Solution:(1) Studying member CDFrom the FBD of member CD in Fig:顯然，本題中在約束A、B、C、D處沒(méi)有水平方向的作用力RCRMRCR2qC3m1m0CM+0412DRMq42MqRD0DM+0324

11、MqRC423MqRC第19頁(yè)/共96頁(yè)2021-10-27Statics-Problems-20(2) Studying member ABCRARCRB2qAC1m2mRARCRB1mFrom the FBD of member CD in Fig:0AM+04322CBRqR26MqRB0BM+02122CARqR425MqRA第20頁(yè)/共96頁(yè)2021-10-27Statics-Problems-21靜力學(xué)第3章作業(yè)/P91-3.40:Solution:(1) From the FBD of joint A in Fig:APFABFAD1250 xF+052ADABFF0yF+051

12、ADFP)(5TensionPFAD)(2nCompressioPFAB第21頁(yè)/共96頁(yè)2021-10-27Statics-Problems-22(2) From the FBD of joint B in Fig:BPFBCFBDFAB0 xF+0BCABFF0yF+0BDFP)(2nCompressioPFBC)(TensionPFBD第22頁(yè)/共96頁(yè)2021-10-27Statics-Problems-23)(25nCompressioPFCD(3) From the FBD of joint D in Fig:DFBD0 xF+0525252DECDADFFF0yF+0515151

13、DECDADBDFFFF)(253TensionPFDEFDEFADFCD125125125第23頁(yè)/共96頁(yè)2021-10-27Statics-Problems-24(4) From the FBD of joint C in Fig:CRCFCEFBCFCD1250yF+051CECDFF)(21TensionPFCE第24頁(yè)/共96頁(yè)2021-10-27Statics-Problems-25)(413)(413nCompressioPFTensionPFGHCH靜力學(xué)第3章作業(yè)/P92-3.43*:Solution:(1) From the FBD of joint D in Fig:D

14、PFCDFDH0yF+0DHFPPFDH(1) From the FBD of joint in Fig:HFDHFGFC231323130 xF+0133133GHCHFF0yF+0132132DHGHCHFFF第25頁(yè)/共96頁(yè)2021-10-27Statics-Problems-26Solution:lbF54952 . 1合+060sin6 . 3290CDxFFM合04125BzAzyFFGM04125ByAyzFFFM合060sin0CDBzAzzFGFFF060cos0CDByAyyFFFFF合+)(33027lbFAy)(321527lbFBy)( 5 .612123lbFBz

15、)(51lbFAz)(340lbFCD靜力學(xué)第4章作業(yè)/P111-4.2*:第26頁(yè)/共96頁(yè)2021-10-27Statics-Problems-27靜力學(xué)第4章作業(yè)/P113-4.12*:Solution:RAzRAyRByRBxRCxRCzFrom the FBD of bent pipe and cable in Fig:0 xM04 . 08 . 0CzByAyRRR0yM08 . 04 . 08 . 0PRRBxAz0zM08 . 0CxAyRR0 xF0PRRCxBx0yF0PRRByAy0zF0CzAzRR第27頁(yè)/共96頁(yè)2021-10-27Statics-Problems-

16、2808 . 00011100008 . 00004 . 08 . 00014 . 0008 . 0010010001001100100PRRRRRRCxCzByBxAzAy無(wú)解??？第28頁(yè)/共96頁(yè)2021-10-27Statics-Problems-290 xM0yM0zM04030CBTT0300210DzCFT030090DyBFT0yF0zF0BDyAyTFF0CDzAzTFF)(60 NTC)(56 NFAy)(18 NFAz)(24 NFDy)(42 NFDzSolution:靜力學(xué)第4章作業(yè)/P113-4.13*:第29頁(yè)/共96頁(yè)2021-10-27Statics-Probl

17、ems-30靜力學(xué)第4章作業(yè)/P114-4.14(b):Solution:S令形心坐標(biāo)為(xc, yc), 按定義有:SScdSxdSxSScdSydSy)(51624023410402341ftdxxdydxdSxS)(76434023410402341ftdxxxdyxdxxdSxS)(23234030402341ftdxxydydxydSxS)(720ftdSxdSxSSc)(85ftdSydSySSc第30頁(yè)/共96頁(yè)2021-10-27Statics-Problems-31靜力學(xué)第4章作業(yè)/P115-4.24:Solution:已知crucible的密度rc=2000kg/m3, 外

18、徑R=0.28m, 內(nèi)徑r=0.2m; iron的密度ri=7200kg/m3OStudying crucible，Drawing FBD in Fig.WiWcGiGcFyFx0ABM+0sincosccOGWOCFtanOCOGWFccgVWcccrROCcccVrRVrrRROG44334132833283第31頁(yè)/共96頁(yè)2021-10-27Statics-Problems-32)(tan250tan4tan141tan4444NRrRgRVrRgVOCOGWFccccccrrgVWcccrROCcccVrRVrrRROG44334132833283OWiWcGiGcFyFx第32頁(yè)/

19、共96頁(yè)2021-10-27Statics-Problems-33Solution:端圓心為原點(diǎn)：軸如課本所示，木柄底、軸，以木柄軸線為yxz)/(1033. 8)225(3040304521304090/(919. 0362mmkgvmsssteelr)(8167. 0)904030(1kgmsteelr)(1227. 0)225(30(22kgmsteelr)(2250. 0)454030(3kgmsteelr)(151mmy)(02mmy)(453mmy )(1953mmz )(1952mmz )(1951mmz x=0 )(088. 2432144332211mmmmmmymymymy

20、my)(099.04kgm)( 04mmy )(1054mmz )(25.186432144332211mmmmmmzmzmzmzmz靜力學(xué)第4章作業(yè)/P116-4.27*:第33頁(yè)/共96頁(yè)2021-10-27Statics-Problems-34xyO2xyO1靜力學(xué)第5章作業(yè)/P131-5.2:解：3075. 0s75. 0s36lb20lb18in假設(shè)系統(tǒng)是靜力平衡的先研究圓柱，有030sin00011111fGPXrfMOP1G1G2N1N2f2f1P1得1121GP 再研究方塊，有030cos0030sin022221NGYfGPX得)(28)(21212lbGGf而)(4 .23

21、232222max2lbGNfmax22ff 因，所以系統(tǒng)不能保持靜力平衡第34頁(yè)/共96頁(yè)2021-10-27Statics-Problems-35Discussion:1. 方塊會(huì)不會(huì)先翻倒?3075. 0s75. 0s36lb20lb18in2. 如果圓柱和方塊的接觸面不光滑,會(huì)怎樣?xyO2G2N2f2P1x2x2=?第35頁(yè)/共96頁(yè)2021-10-27Statics-Problems-36Solution:總體分析: 0CAff分析木條 :0 xF0yF0AM0SinNCosffBBA02GSinfCosNNBBA025 . 15 . 012GCosNB圓盤分析 :0OM03 .

22、03 . 0CBff解之得： ASAANfBSBBNfCSCCNfNNA64.39NNB27.150NNC27.390NfffCBA.22.0655. 0AS15. 0BS056. 0CS0AM025 . 15 . 01121CosGGNC0CM01)25 . 15 . 01 (2ANCosG0 xF達(dá)到最大靜摩擦力時(shí) :解之得： 靜力學(xué)第5章作業(yè)/P132-5.10*:第36頁(yè)/共96頁(yè)2021-10-27Statics-Problems-379000N/mBCDBCD靜力學(xué)第5章作業(yè)/P132-5.12:解：P假設(shè)系統(tǒng)是靜力平衡的先研究樁子CBD，有NBNBNAfAfBRxRy)(9000

23、05 . 1) 331()9000321(0NNNMBBC再研究桿AB，有000008 . 08 . 20PffYNNXPfMBABABA)(450075)(225072maxmaxNNfPfNNfPfAAsAABBsBB5 . 0s25. 0sP9000N/m1.5m2m3m0.8mABCDABfBAB第37頁(yè)/共96頁(yè)2021-10-27Statics-Problems-38只有當(dāng)fAfAmax或fBfBmax時(shí)，桿AB才能移動(dòng)，由以上計(jì)算結(jié)果可知，當(dāng)P6300(N)，桿AB在A點(diǎn)處開(kāi)始移動(dòng)第38頁(yè)/共96頁(yè)2021-10-27Statics-Problems-39靜力學(xué)第5章作業(yè)/P13

24、3-5.18*:Solution:0601CosPN0601SinPmgN0 xF0yFNP8 .550105 . 0311601322mgSinPmg0OMNP9 .1032NP9 .103因此 :第39頁(yè)/共96頁(yè)2021-10-27Statics-Problems-40Solution:020GSinfP020GCosNNf 05 . 0208 . 020PhGCosGSinNP3 .374木塊翻轉(zhuǎn)臨界時(shí)：滑動(dòng)時(shí)：mh192. 1靜力學(xué)第5章作業(yè)/P133-5.19*:第40頁(yè)/共96頁(yè)2021-10-27Statics-Problems-41BANN BAff AANf當(dāng)P=600 l

25、b時(shí)： 0yF06005 . 7cos5 . 7cos5 . 7sin5 . 7sin0000BABAffNNBBNf當(dāng)P=200 lb時(shí)： 0yF02005 . 7cos5 . 7cos5 . 7sin5 . 7sin0000BABAffNN2633. 0Solution:靜力學(xué)第5章作業(yè)/P134-5.22*:第41頁(yè)/共96頁(yè)2021-10-27MOM-Problems-42第六次作業(yè)/P34-1.1(b):SolutionPPPP332211PPPPPPPPPPPPN1N2N3N1=PN2=0N3=PNPP001PNFx001PPNFx001PPPNFx第42頁(yè)/共96頁(yè)2021-10

26、-27MOM-Problems-43第六次作業(yè)/P34-1.6:SolutionPpd1DPpp6Pb研究活塞桿，有)(4212dDpP 12114dP )( 1 .181211MPadDp研究右擋蓋，有)(46212dDpPb 2224dPb )(50. 6621222MPadDdp得)(50. 6maxMPap第43頁(yè)/共96頁(yè)2021-10-27MOM-Problems-44第六次作業(yè)/P34-1.7*:SolutionPBPsPwBSteelWoodP30AC研究節(jié)點(diǎn)B，有030sin0030cos0PPYPPXswsPPPPws3,2研究桿BC，有 )(0 .48212222222k

27、NAPAPAPs研究桿AB，有 )(4 .40313111111kNAPAPAPw取)(4 .40kNP 第44頁(yè)/共96頁(yè)2021-10-27MOM-Problems-45第六次作業(yè)/P35-1.13*:SolutionBPPCASteelAluminumL1L21m)(4 . 0)(405. 01021075. 010110222931mmmAEPLs根據(jù)題意列出方程組：解得)(25. 0)(75. 021mEEELmEEELassassAEPLAEPLLLas21211總伸長(zhǎng)為第45頁(yè)/共96頁(yè)2021-10-27MOM-Problems-46dxx第六次作業(yè)/P37-1.14*:Sol

28、utionLBCAc(1) A formula for the downward displacement C of point CxPLxLWPPEAPdxcL0cdxEALxLWcL0dxEALWxLcEALcLW222(2) The elongation B of the entire barBEALLW2022EAWL2第46頁(yè)/共96頁(yè)2021-10-27MOM-Problems-47(3) The ratio r of the elongation of the upper half of the bar to the elongation of the lower half of

29、 the barThe elongation of the upper half of the barufEALLLW2222EAWL83lfEAWLufB8The elongation of the lower half of the barSo3lfufr第47頁(yè)/共96頁(yè)2021-10-27MOM-Problems-48第六次作業(yè)/P37-1.21:SolutionE1E2eebbPPP1P1P2P2(1) 靜力平衡方程：研究右擋板，有PebPbPMPPPXo22002121(2) 變形協(xié)調(diào)方程：PeP1P2O2211221121EPEPAELPAELPLL(3) 求解方程組：21212

30、12121212221112EEAPAPEEEEbeEEPEPEEPEP第48頁(yè)/共96頁(yè)2021-10-27MOM-Problems-49abLAyRP1N2NAxR第六次作業(yè)/P37-1.23*:SolutionPhh2B1A2CDabL(1) Equation of equilibrium BACDPLbNaN21(2) Equation of compatibility ba21(3) Force-displacement relations EAhN11EAhN222得補(bǔ)充方程baNN212第49頁(yè)/共96頁(yè)2021-10-27MOM-Problems-50PLbNaN21baNN2

31、12解得有22122baPLaN2222baPLbN22222112222baEAPhLbaPLaEAhaLEAhNaLaLB第50頁(yè)/共96頁(yè)2021-10-27MOM-Problems-51第六次作業(yè)/P37-1.24*:Solution2a2a 變形過(guò)程中3根桿的長(zhǎng)度始終滿足下面的關(guān)系：223212241)LL(21La)LL(31L)L2LL2L(21L2L312331122而3根桿的長(zhǎng)度變化滿足下面的關(guān)系：(1) 靜力平衡方程：研究節(jié)點(diǎn)A，有132P3030APAP1P3P2030sin30sin0030cos30cos031321PPPYPPPX(2) 變形協(xié)調(diào)方程：第51頁(yè)/共9

32、6頁(yè)2021-10-27MOM-Problems-5202320323213311332211PAAAAA(3) 求解方程組：)(30cos31)(31331122333111222APAPAPEALPEALPEALPMPaPAAAAAAAAMPaPAAAAAAAAMPaPAAAAAAAA6 .8633224338 .26332232328 .1263322334133221213133221132133221321030sin30sin0030cos30cos031321PPPYPPPX第52頁(yè)/共96頁(yè)2021-10-27MOM-Problems-53F F30ABC30D123xyP P

33、A1P2P3PxyAAxy將將A A點(diǎn)的位移分量向各桿點(diǎn)的位移分量向各桿投影投影. .得得cossin1xylxl2cossin3xylcos2213lll變形關(guān)系為變形關(guān)系為 2133 lll(4) 討論：3根桿長(zhǎng)度變化關(guān)系的另一種求法：第53頁(yè)/共96頁(yè)2021-10-27MOM-Problems-54RBRA第六次作業(yè)/P37-1.26:SolutionA1A2aa(1) Equation of equilibrium 0BARR(2) Equation of compatibility A1A2RB0TTA1A2TT0RTA1A2RBR(3) Force-displacement re

34、lations TaTaTaT2212111AAEaREAaREAaRBBBR得補(bǔ)充方程011221AAEaRTaB第54頁(yè)/共96頁(yè)2021-10-27MOM-Problems-55解得21112AATERBMPaAATEARB667. 010511020020105 .12212982111MPaAATEARB333. 051011020020105 .12212981222第55頁(yè)/共96頁(yè)2021-10-27MOM-Problems-56T2T1材料力學(xué)第2章作業(yè)/P58-2.1(b) :Solutionm3mmm3mmmm23T2T2mmm1T001mTMx0302mmTMx第56頁(yè)

35、/共96頁(yè)2021-10-27MOM-Problems-57材料力學(xué)第2章作業(yè)/P59-2.11:Solution123ABC400500N1N2N3(1) 123ABCm1m2m3)(214. 45003007024N7024m)(810. 25002007024N7024m)(024. 75005007024N7024m332211mkNnmkNnmkNn)(214. 4T)(024. 7T3BC1ABmkNmmkNm對(duì)于AB段， )(0 .801616/33maxmmTddTWTABABABABtABAB由強(qiáng)度條件得 )(6 .843218032/1801804242maxmmGTddG

36、TGITABABABABPABAB由剛度條件得 第57頁(yè)/共96頁(yè)2021-10-27MOM-Problems-58)(85 mmdAB取 )(4 .671616/33maxmmTddTWTBCBCBCBCtBCBC由強(qiáng)度條件得 )(5 .743218032/1801804242maxmmGTddGTGITCBBCBCBCPBCBC由剛度條件得 對(duì)于BC段，)(75 mmdAB取(2) )(85 mmdAB取(3) 齒輪1安放在齒輪2、3中間。123ABC400500N1N2N3123ABCm1m2m3第58頁(yè)/共96頁(yè)2021-10-27MOM-Problems-59材料力學(xué)第2章作業(yè)/P5

37、9-2.14:Solution方法一（傳統(tǒng)法）：L/4L/4L/2AB3T0T01. 解除某些約束，施加相應(yīng)約束反力，使之成為靜定基；2. 扭矩與變形協(xié)調(diào)方程：04/32/00PPPBGILTGILTGILT得TB=5T0/43. 外扭矩3T0和T0作用處的轉(zhuǎn)角分別為：PPPPPBPPPPBGILTGILTGILTGILTGILTGILTGILTGILTGILT1611854/32/2116114/3212/4101max000200013T03T0T0TBT0TB=第59頁(yè)/共96頁(yè)2021-10-27MOM-Problems-60材料力學(xué)第2章作業(yè)/P59-2.14:Solution方法二

38、（船長(zhǎng)法）：L/4L/4L/2AB3T0T03T0T0TATB1. 解除約束，施加約束反力；2. 扭矩與變形協(xié)調(diào)方程：右起第一段：TB右起第二段：TB- T0右起第二段：TB- 4T004/)4(4/)(2/00PBPBPBGILTTGILTTGILT得TB=5T0/43. 可見(jiàn)，右起第一段和第二段的扭矩都大于0，最大轉(zhuǎn)角發(fā)生在外扭矩3T0作用處：PPBPBGILTGILTTGILT16114/)(2/00max第60頁(yè)/共96頁(yè)2021-10-27MOM-Problems-61材料力學(xué)第3章作業(yè)/P72-3.1(c):BqaqACaaqa21122Solutionqaqqa2V1M12112

39、321,2qaaqaaqaMqaqaqaV對(duì)于1-1截面，有qaqqa2V2M222222121,2qaaqaaqaqaMqaqaqaV對(duì)于2-2截面，有第61頁(yè)/共96頁(yè)2021-10-27MOM-Problems-62qa補(bǔ)充：內(nèi)力圖BqaqACaaqa2Vqa2x-221qa223qa225qax第62頁(yè)/共96頁(yè)2021-10-27MOM-Problems-63(1) Shear-Force and Bending-Moment Equations 材料力學(xué)第3章作業(yè)/P73-3.2(a):Solution2PBACaaPa2PBACPaxxaaVM020PVYPV20)(20Paxa

40、PMMOPaPxM2ax02PBACPaxxa2VMax000VY0V00PaMMOPaM axa2axa2第63頁(yè)/共96頁(yè)2021-10-27MOM-Problems-64(2) Shear-Force and Bending-Moment Diagrams PV2PaPxM2ax00VPaM axa22PBACaaPaxxVP2-PaPa(3) Maximum Shear Forces and Bending MomentsPV2maxPaMmax第64頁(yè)/共96頁(yè)2021-10-27MOM-Problems-65材料力學(xué)第3章作業(yè)/P73-3.3(b)*:qABCL/2L/2Solut

41、ionxVMVM) 2/0(,31312/21,2/2132LxxLqxLqxxMxLqLqxxV,2424)2(21)2()232(221,4)2(22122xqxqLqLLxLxqLxqLMqxqLqLxqLV)2/(LxLxxM242qL2472qL控制截面法？V4qL43qL第65頁(yè)/共96頁(yè)2021-10-27MOM-Problems-66Solution材料力學(xué)第4章作業(yè)/P90-4.6*:PPACDB2m2m2mNo20a1. 求約束反力2. 求彎矩作出彎矩圖RARB0006420BAABRRPPYRPPMPRPRBA313103223220BBDACAMPRMPRMM3. 求許

42、用載荷MP32P32 )(88.5610160102373266maxmaxkNPPWM由強(qiáng)度條件得危險(xiǎn)截面在C或D，有,32maxPM查表得),(2373cmW 第66頁(yè)/共96頁(yè)2021-10-27MOM-Problems-67材料力學(xué)第4章作業(yè)/P91-4.8:SolutionA T-beam made of cast iron in pure bending. Knowing the ratio of tensile allowable stress to compressive allowable stress is t/c=1/4. Determine the reasonable

43、 width b of the flange. bzC3060400MMz3403060230340303060bbycy)(1703910030mmbb tzctcIMy310 czcccIyM310400 4400tcccyymmyc80801703910030bbmmb510第67頁(yè)/共96頁(yè)2021-10-27MOM-Problems-68材料力學(xué)第4章作業(yè)/P91-4.13:Solution1. 求剪力和彎矩PMMPVABAB0作出剪力圖和彎矩圖PV2. 根據(jù)膠合面強(qiáng)度條件求P1mPAB505050100G整個(gè)截面都是危險(xiǎn)截面，考慮剪應(yīng)力互等定理，有 )(825. 31034. 00

44、1125. 0)025. 0415. 0(1215. 01 . 026223kNPPPgGMP第68頁(yè)/共96頁(yè)2021-10-27MOM-Problems-69PV1mPAB505050100GMP3. 根據(jù)截面剪應(yīng)力強(qiáng)度條件求P整個(gè)截面都是危險(xiǎn)截面，有 )(1010101. 015. 01 . 0236maxkNPPP4. 根據(jù)截面正應(yīng)力強(qiáng)度條件求PA截面是危險(xiǎn)截面，有 )(75. 31010000375. 0615. 01 . 062maxkNPPP5. 綜上所述，取)(75. 3kNP 第69頁(yè)/共96頁(yè)2021-10-27MOM-Problems-70 xLq0q0LBAyx材料力學(xué)

45、第5章作業(yè)/P110-5.3(c)*:Solution1. 求約束反力03221003121000LRLLqMLRLLqMBAABRARBLqRLqRBA0031612. 求彎矩方程OARAV Mx)1(613121)(300 xLLxqxxxLqxRxMA第70頁(yè)/共96頁(yè)2021-10-27MOM-Problems-713. 求撓曲線方程：2150301402030012036241266)(CxCxLqxLqEIvCxLqxLqvEIxLqxLqxMvEI 代入邊界條件：000vLxvx時(shí)，時(shí)，得：360703012LqCC)3107(3604230 xLLxLEIxqv最大撓度：兩端轉(zhuǎn)

46、角：LLx51933. 015810EILqLv7685)21(40中間撓度：)15307(3604230 xLLxLEIqvEILqA360730EILqB4530EILqxvv76801. 5)(400max0)(0 xv取合理解第71頁(yè)/共96頁(yè)2021-10-27MOM-Problems-72材料力學(xué)第5章作業(yè)/P111-5.8:SolutionThe cantilever beam shown in the figure has moments of inertia I1 and I2 in parts AC and CB, respectively. (a) Using the m

47、ethod of superposition, determine the deflection B at the free end due to the load P. (b) Determine the ratio r of the deflection B to the deflection 1 at the free end of the prismatic cantilever beam with moment of inertia I1 carrying the same load. BAL/2L/22I1ICxy(a)PB2/2LCBCxyA1B2C第72頁(yè)/共96頁(yè)2021-1

48、0-27MOM-Problems-73BAL/2L/22I1ICxyPBA2I1ICPB1IC2/PLPB2/2LCBCxyA1B2C232223248522/2/32/EIPLEILPLEILPC222222832/2/22/EIPLEILPLEILPC131312432/EIPLEILPB2113132223712424283485IIEIPLEIPLLEIPLEIPLB第73頁(yè)/共96頁(yè)2021-10-27MOM-Problems-74BAL/2L/22I1ICxyP2113132223712424283485IIEIPLEIPLLEIPLEIPLB(b)BAL1IxyP1313EIPL

49、87137124211321131IIEIPLIIEIPLrB第74頁(yè)/共96頁(yè)2021-10-27MOM-Problems-75BAL/2L/22I1ICxyPDiscussionUse energy methodLxPxM)(Lx0LLLEIdxxMEIdxxMU2/122/0222)(2)(LLLdxLxdxLxIIEIP2/22/0221122242472332112LLIIEIP211327148IIEILPWPB2121137124IIEIPLB第75頁(yè)/共96頁(yè)2021-10-27MOM-Problems-76材料力學(xué)第5章作業(yè)/P111-5.9:SolutionBAqL/2L/

50、2BAq1. 解除某些約束，施加相應(yīng)約束反力，使之成為靜定基；2. 變形協(xié)調(diào)方程：RB=BAqBARBfBufBdBdBuff查表得EILRfBBu33EIqLLEILqEILqLffCCBd384726282243412873847343qLREIqLEILRBB第76頁(yè)/共96頁(yè)2021-10-27MOM-Problems-773. 求其它約束反力：1287qLRBBAqRBRAMA0200420BABAARRLqYLRLLqMML/2L/212891287128572qLMqLRqLRABA第77頁(yè)/共96頁(yè)2021-10-27MOM-Problems-78材料力學(xué)第5章作業(yè)/P112-

51、5.13*:SolutionThe bars 1 and 2 have the same tensile rigidity EA. (1) If the beam AB is considered as rigid, determine the internal forces in the two bars. (2) If the beam AB is considered as deformable with bending rigidity EI, determine the internal forces in the two bars. (1) the beam AB is consi

52、dered as rigidPLaAB21CaaAyRP1N2NAxRBACa(a) Equation of equilibrium PaaNaN221(b) Equation of compatibility 2121PNN21212第78頁(yè)/共96頁(yè)2021-10-27MOM-Problems-79(1) the beam AB is considered as rigidPLaAB21CaaAyRP1N2NAxRBACa(a) Equation of equilibrium (b) Equation of compatibility 2121PNN21212(c) Force-displ

53、acement relations EALN11EALN22得補(bǔ)充方程2121NN解得PN511PN522第79頁(yè)/共96頁(yè)2021-10-27MOM-Problems-8012(2) the beam AB is considered as deformablePLaAB21CaaAyRP1N2NAxRBACa(a) Equation of equilibrium (b) Equation of compatibility PNN212C2121C(c) Force-displacement relations EALN11EALN22EIaNPC48231得補(bǔ)充方程EALNEIaNPEAL

54、N231121482解得33121523AaILPAaILN322156AaILILPN第80頁(yè)/共96頁(yè)2021-10-27MOM-Problems-811. 危險(xiǎn)點(diǎn)位于圓軸固定端橫截面的最上處和最下處（A點(diǎn)和B點(diǎn)）材料力學(xué)第6章作業(yè)/P135-6.1(d):mPLdmTMPLSolution:忽略橫力彎曲剪力的影響2. 用單元體表示危險(xiǎn)點(diǎn)的應(yīng)力狀態(tài)VP3. 用應(yīng)力圓表示危險(xiǎn)點(diǎn)的應(yīng)力狀態(tài)(,)(-,)(0,-,-)B點(diǎn)點(diǎn)A點(diǎn)點(diǎn)AB332dPLWM316dmWTtA點(diǎn)：或B點(diǎn)：或第81頁(yè)/共96頁(yè)2021-10-27MOM-Problems-82材料力學(xué)第6章作業(yè)/P135-6.3(d):40

55、2040如右圖所示單元體，畫出對(duì)應(yīng)的應(yīng)力圓Solution maxmax(-40,-40)(-20,40)1. 主應(yīng)力和主方向 3 3 1 102023.7123.1140220402204022231MPaMPa42040)40(222tan0yxxy)(02.52,04.1042)(98.37,96.75210030011.2371.232. 如圖所示在單元體上畫出主平面方向52.023. 最大剪應(yīng)力23.41231max第82頁(yè)/共96頁(yè)2021-10-27MOM-Problems-83材料力學(xué)第6章作業(yè)/P135-6.4(b)*:30305020如右圖所示單元體，畫出對(duì)應(yīng)的應(yīng)力圓Sol

56、ution 1 1 2 2 maxmax(30,-20)(50,20)60MPa32.5260sin)20(60cos2503025030MPa66.1860cos)20(60sin25030(52.32,-18.66) =30第83頁(yè)/共96頁(yè)2021-10-27MOM-Problems-84材料力學(xué)第6章作業(yè)/P136-6.7*:Solution30如右下圖所示，在A點(diǎn)取單元體并進(jìn)行應(yīng)力狀態(tài)分析MPadP21.61002. 0052. 010203MPadTdT63.70002. 0052. 0600222/222 =120 2222222222rddddAddAdAIWAdAddAdpt

57、A test of thin walled tube is shown in the figure. If the loads are a concentrated force P=20kN and a torque T=600Nm. The diameter of the tube is d=50mm, thickness is =2mm. (1) Determine the normal and shear stresses on the inclined section at point A. (2) Determine the magnitude and orientation of

58、the principal stresses at point A. (Draw stress element.) 第84頁(yè)/共96頁(yè)2021-10-27MOM-Problems-85(2)038.4659.10763.70221.61221.6122231MPaMPa308. 221.61)63.70(222tan0yxxy)(71.56,43.1132)(29.33,57.662300100 (61.21,-70.63)(0,70.63) 3 3 1 166.5733.29(1)MPa86.451202sin)63.70(1202cos221.61221.61MPa81. 81202cos

59、)63.70(1202sin221.61第85頁(yè)/共96頁(yè)2021-10-27MOM-Problems-86材料力學(xué)第6章作業(yè)/P136-6.11:SolutionxxyyWhen a train pass through a steel bridge, the strains tested by instrument are ex=0.0004, ey=-0.00012 at point A. Find the normal stresses in directions x and y at point A. (E=200GPa, =0.3) yxxEe1xyyEe10z)(1zyxxE e

60、 e )(1xzyyE e e yxxEee21xyyEee21MPa800第86頁(yè)/共96頁(yè)2021-10-27MOM-Problems-87材料力學(xué)第6章作業(yè)/P137-6.17*:Solution薄壁上任意一點(diǎn)都是危險(xiǎn)點(diǎn)，在薄壁上任一點(diǎn)A取單元體并進(jìn)行應(yīng)力狀態(tài)分析A MPattDPtptD6 .10015. 0185. 010200015. 04104185. 0436MPatptD7 .2403. 0104185. 026 A thin-walled tube shown in the figure is made of cast iron. Knowing its outside d