材料力學(xué)課件第二章 拉伸壓縮、剪切

1、Mechanics of Materials Chapter2 Chapter2 鋼壓桿鋼壓桿 FFFFmmFFmmFFNmmFFmmFFmmFFNFNmmFFmmFFNmFmFNmFFmmFFNmFmxFNOCABD600300500400E40kN55kN 25kN20kNCABD600300500400E40kN55kN 25kN20kNCABDE40kN55kN 25kN20kNRkN1 10 00 02 20 02 25 55 55 54 40 00 0 RRFxCABDE40kN55kN 25kN20kN10 01 1 RFN)()(RF kNN10101 1 R40kNFN220

2、kNCABDE40kN55kN 25kNR20 04 40 02 2 RFN)()(RF kNN5 50 04 40 02 2FN320kN25kNCABDE40kN55kN 25kN20kNR30 02 20 02 25 53 3 NF)()kN(N 5 53 3F20kNFN440kN55kN 25kN20kNR4)()(F kNN20204 45010520+CABD600300500400E40kN55kN 25kN20kN)(FkNNmax5 50 0 FFabcdFFabcda b c d F FN AFN Fkk F coscos AFAFpFkkFp AFp cosAA FF

3、2coscospsinsin22p Fkk FFkkxn p Fkk FFkkxn p max2 2 max2 2 min0 00 0 ,2coscospsinsin22p xnFkk N AFmaxmaxmaxN FA NAFmax AFmaxN FABCFF3000400037024021 kNN50501 1 FFkNN1 15 50 03 32 2 FFFABCFF300040003702402150kN150kNMPa.N/m.2N8 87 70 01 10 08 87 70 02 24 40 02 24 40 05 50 00 00 00 06 61 11 11 1 AF MPa.

4、N/m.2N1 11 110101 11 137370 037370 01500001500006 62 22 22 2 AF max ABCF1mABCF1mFAxyFAxy0 030300 01 1 FFFysinN0 00 01 12 2 cos30NNFFFxFFFF7327321 12 22 21 1.NN 22mm6 62 26 61 11 10 02 28 86 60 02 21 14 43 30 01 10 02 21 17 72 22 21 10 08 86 6 AAAFmaxN FFFF7 73 32 21 12 22 21 1.NN kN.N2 24 43 36 69 9

5、1 11 1 AF kN.N2 20 04 48 86 62 22 2 AF kN.N6 61 18 84 42 21 11 1 FFkN.N7 72 28 80 07 73 32 21 12 22 2 FF2aaFABDC2aaFABDCCDFACBFFMNCDA2 23 30 0 MPa/N 1191194 42 23 32 2dFAFCDN AFCDCDF=33.5kN2aaFABDCCDFACB2 23 3FAFCD N N AFCDCD/N 2 23 3FFACD / 2 23 34 42 2Fd dl標(biāo)距標(biāo)距FOlefhabcddgfl0 p E p fOfhae p fOfhab

6、 e s bs b e p fOfhabce s b e p fOfhabce %1 10 00 01 1 lll %1001001 1 AAA abcefOgfhddpe abcdefOdgfhd 0.2 0.20.2% tg E2 20 0. oO /MPa/% dh0 03 35 51 1. dh sO O /MPa/% nu ns nb max max max max Kmax FFbh h1 lllll 1 1bbbbb 1 1 FFbhh1bbb AFN ll E EAlFlN F1F2F3l1l2l3ABCDF1F2F3l1l2l3ABCDF1FN1)(kNNN 20200 01

7、 11 11 1FFFF2F1FN2F1F2F3l1l2l3ABCD)(kNNN 15150 02 22 22 21 1FFFFRFN3)(kNNN 50500 03 33 3FRFFN2 =-15kN （-）FN1 =20kN （+）FN3 =- 50kN （-）15+-2050F1F2F3l1l2l3ABCDFN2 =-15kN ( - )FN1 =20kN （+）FN3 =- 50kN ( - )F1F2F3l1l2l3ABCD)(MPa.N 8 81761761 11 1AFAB )(MPa.N 6 674742 22 2AFBC )(MPa.N 5 51 11 10 03 33 3A

8、FDC (F1F2F3l1l2l3ABCDm102.534-N 1 11 11 1EAlFlABm101.424-N 2 22 22 2EAlFlBCm101.584-N 3 33 33 3EAlFlCD-0.3mm BCCDBllumm10-0.474- CDBCABADllllABC12 ABC12 FyA12 x0 00 00 00 02 21 11 12 2 FFFFFFFyx coscossinsinNNNN cosNN2 22 21 1FFF AABC12 ABC12 （伸長）（伸長） cosNEAFlEAlFll2 21 11 12 21 1 ABC12 A A2 2A1Al 1

9、 12AAAAA )(mm.coscos 2 29 93 31 12 22 21 1 EAFllAAAF FA12x300yA1 1l 12mABCF3001 12 2FFFFNN7327321 12 22 21 1. A2 2l 2mm.mm.NN7657650 01981981 12 22 22 22 22 21 11 11 11 11 1 EAlFlAAEAlFlAA30300 0AA1A2l 1l 2A300 0AA3 為所求為所求A點(diǎn)的位移點(diǎn)的位移A1 1l 12mABCF3001 12 2A2 2l 2A30 01 12 22 22 23030cosllAAAAAA 0 01 10

10、 02 22 23 32 23 30 03 30 0sintgtg300llAAAA mm.)()(7 78 83 32 23 32 22 22 23 3 AAAAAA CABDF 1 12 23 3xyFA 2 21 10 0NNFFFx 0 00 03 32 21 1 FFFFFyNNNcoscos CABDF 1 12 23 3xyFA CABD 1 12 23 33 3l A1 12 23 3 CABDF 1 12 23 3CABD 1 12 23 31 1l cos3 31 1ll 1 11 11 11 1EAlFlN 3 33 33 33 3AElFl cosN 2 23 33 3

11、3 31 1cosNNAEEAFF CABDF 1 12 23 33 3l A1 12 23 3 1 1l 2 23 33 32 21 12 21 1coscosNNAEAEFFF 2 21 1NNFF 0 03 32 21 1 FFFFNNNcoscos 2 23 33 33 31 1cosNNAEEAFF 2 23 33 33 32 21 1cosNAEEAFF ABCF3aal21ABCF3aal21FABC3aa21FN1FN2FN3Fx 0 0 xF0 0 xF 0 0yF0 03 32 21 1 FFFFNNN 0 0BM0 02 22 21 1 aFaFNNABCF3aal21A

12、BCl 3l 2l 1ABC3212 23 31 12 2 lll 1 11 11 11 1EAlFlN EAlFl3 33 3N EAlFl2 22 2N 2 23 31 12 2NNNFFF ABCF3aal21ABCl 3l 2l 1ABC321N2N3N1FFF2 2 0 0 xF0 0 FFFFN3N2N10 02 2 aFaFN2N16 65 53 36 6FFFFFF N3N2N1 AABCD 2 21 13 3l AABCD 2 21 13 3ll 3l 13 3l1 1l 3 3l cos1 1l cos1 13 3ll3 33 33 31 11 11 1AElFlAElFl

13、N3N1cos AABCD 2 21 13 3ll 3 l 1 2 21 11 13 33 3cosN1N3AElFAElF0 00 0 coscossinsinN2N1N2N2N1FFFFF ABC12aaB1A1C1l3C1Cl3C1CABC12B1C1A1ell 3 31 1aaxEAlFl1 11 1N1 3 33 33 3AElFlN3 AElFeAElFN1N3 3 33 3CAB0 0 N2N1N3FFFN2N1FF AB ABABB0 0 lABABAB0 0 FTlllEAlFlBFR lTltT EAlFlTRt TEAFtBR TEAFR BAB(FFFFFFmFFABt

14、dt1t1nnFFnnFFmmF剪切面剪切面FS FFmm0 00 0 FFFSxFFS AFS mmF剪切面剪切面FFmm AFSnu u FFFFFF bsbsbs AFAFbsbs hhdAbs bsbs FA bsbs AFS AFbsbs SFA u bhlMeFMeeMdF 2 2kNe5 57 71 10 07 70 01 10 02 22 22 23 33 3 dMF MPa.6 6282810101001002020101057576 63 3blFAFSFFS bsbsbsMPa. 3 39 95 51 10 06 61 10 00 01 10 05 57 72 26 63 3hlFAFMeFbhlt1FFAtt1Bdt1FFAtt1Bdd2F2FF剪切面剪切面d2F2FFF2 2FFS 4 42 2dA MPa5151AFS1 12 2tt bsbsbsMPa 150150tdFAF