材料力学：第二章 拉伸压缩、剪切

1、Chapter2 2Chapter23 456 FFFF7mmFF8mmFFNmmFF9mmFFmmFFN10FNmmFFmmFFNmFm11FNmFFmmFFNmFm12xFNO13CABD600300500400E40kN55kN 25kN20kN14CABD600300500400E40kN55kN 25kN20kNCABDE40kN55kN 25kN20kNFRAkN100202555400RR AAxFFF15CABDE40kN55kN 25kN20kN10R1N AFF)()kN(10R1N AFF16 F40kNFN220kNCABDE40kN55kN 25kNF2040R2N

2、AFF)()kN(5040R2N AFF17FN320kN25kNCABDE40kN55kN 25kN20kNF30 0202025253 3 NF)()kN(53N F1820kNFN440kN55kN 25kN20kNF4)(kN)204N F195010520+CABD600300500400E40kN55kN 25kN20kN(kN)50Nmax F20FFabcd21FFabcda b c d 22 F FN23AFN 24Fkk F coscos AFAFpFkkFp AFp cosAA FF 25 2coscosp sinsin22p Fkk FFkkxn p26 Fkk FFk

3、kxn p27 max2 2 max2 2 min0 00 0 ,2coscospsinsin22p xnFkk 28Nmaxmax AFNmax FA NmaxAF AFmaxN 29FABCFF3000400037024021kNN50501 1 FFkNN1501503 32 2 FF30FABCFF300040003702402150kN150kNMPa.N/m.2N87870 0101087870 024240 024240 050000500006 61 11 11 1 AF MPa.N/m.2N1 11 110101 11 137370 037370 01500001500006

4、 62 22 22 2 AF max 31ABCF1m32ABCF1mFAxy33FAxy0 030300 01 1 FFFysinN0 00 01 12 2 cos30NNFFFxFFFF7327321 12 22 21 1.NN 242241m1028692345.14Am102172286.10A34AFmaxN FFFF732. 122N1N kN.N24243693691 11 1 AF kNN73.48722AFkNN62.184211FFkNN59.281732. 122FF352aaFABDC362aaFABDCCDFACBFFMCDA230N /N232119MPa4CDFF

5、Ad N AFCDCD37F=33.5kN2aaFABDCCDFACB2 23 3FAFCD N N AFCDCD/N 2 23 3FFACD / 2324dF 38 3940 dl标距标距41FOlefhabcddgfl042 p E p fOfha43e p fOfhab es 44 s b b e p fOfhabce45 s b e p fOfhabce46 %1001001 1 lll %1001001 1 AAA 47 abcefOgfhdd48pe abcdefOdgfhd49 50 0.2 0.20.2% tan E2 20 0. oO /MPa/% 5152dh0 03 35

6、 51 1. dh53 sO 54O /% 55nu ssn bbn 56max max 57 max K max max 5859 FFbh h1 lllll 1 160bbbbb 1 1 FFbhh1 bbb 161 AFN ll E EAlFlN 62 F1F2F3l1l2l3ABCD63F1F2F3l1l2l3ABCDF1FN1)(kN2001N1N1 FFF64F2F1FN2F1F2F3l1l2l3ABCD)(kN1502N2N21 FFFFFFN3)(kN5003NR3N FFFD65FN2 =-15kN （-）FN1 =20kN （+）FN3 =- 50kN （-）15+-205

7、0F1F2F3l1l2l3ABCD66FN2 =-15kN ( - )FN1 =20kN （+）FN3 =- 50kN ( - )F1F2F3l1l2l3ABCD)(MPa.N 8 81761761 11 1AFAB )(MPa.N 6 674742 22 2AFBC )(MPa.N 5 51101103 33 3AFDC 67F1F2F3l1l2l3ABCDm102.534-N 1 11 11 1EAlFlABm101.424-N 2 22 22 2EAlFlBCm101.584-N 3 33 33 3EAlFlCD-0.3mm BCCDBllumllllCDBCABAD41047. 0 6

8、8ABC12 69ABC12 , ,FyA12 x0coscos00sinsin02N1N1N2N FFFFFFFyx cos22N1NFFF 70AABC12 ABC12 cosNEAFlEAlFll2 21 11 12 21 1 71ABC12 A A2 2A1Al 1 12AAAAA )(mm293. 1cos2cos21 EAFllAAA72F FA12x30yA1 1l 12mABCF301 12 2FFFF732. 122N1N A2 2l 2mm.mm.NN765019712222211111EAlFlAAEAlFlAA733030AA1A2l 1l 2A30A1 1l 12mA

9、BCF301 12 2A2 2l 2A330cos1222llAAAAAA 30sin30tantan3012232llAAAA mm.)()(7973232223AAAAAA74五、应变能五、应变能 (strain energy) 应变能应变能弹性体受力而变形时所积蓄的能弹性体受力而变形时所积蓄的能量。量。 V W， V = W。 J（1J=1Nm）。）。 75 或或EAlFEAlFFlFV221212NNNN EAlFEAFlFlFV221212 外力外力F所作功所作功： lFW21 WV 杆内杆内应变能应变能：lFV 2176亦可写作亦可写作 22)(22llEAEAlFV 2121 A

10、llFVVvEv22 22 Ev 或或或或应变能密度应变能密度 v 单位体积内的应变能单位体积内的应变能。 应变能密度的单位为应变能密度的单位为 J/m3。77fxxF )(NEAxxFV2d)(d2N llEAxxFVV02N2d)(dlxf沿杆长沿杆长均匀分均匀分布的荷载集度布的荷载集度为为 ffl轴轴力图力图)(xxffxxx微段的分离体微段的分离体78 (V=W ) A。 已知：已知：P = 100 kN， l = 2 m， d = 25 mm， = 30，E=210 GPa。79 V=W PP，A Ax=0， Ay ， A= Ay1/2 P A = V求求 A 。80J67.64mN

11、67.64)m1025(4)Pa10210()m2()30cos2N10100()cos2(2223923221N EAlPEAlFV FN1= FN2 = P/2cos 81)(mm293. 1m10293. 1N10100mN67.642233 PVA21VPA 82838485860coscos03N2N1N FFFFFy 2 21 10 0NNFFFx CABDF 1 12 23 3xyFA 87CABDF 1 12 23 3xyFA CABD 1 12 23 3883 3l A1 12 23 3 CABDF 1 12 23 3CABD 1 12 23 31 1l cos3 31 1l

12、l 1 11 11 11 1EAlFlN 3 33 33 33 3AElFl cosN 2 23 33 33 31 1cosNNAEEAFF 89CABDF 1 12 23 33 3l A1 12 23 3 1 1l23321coscos2AEAEFFF NN2 21 1NNFF 0 03 32 21 1 FFFFNNNcoscos 2 23 33 33 31 1cosNNAEEAFF 3333cos21AEEAFF N90ABCF3aal2191ABCF3aal21FABC3aa21FN1FN2FN3F 0 xF0 xF 0 0yF03N2N1N FFFF 0 0BM0 02 22 21 1

13、 aFaFNN92ABCF3aal21ABCl 3l 2l 1ABC3212 23 31 12 2 lll 1 11 11 11 1EAlFlN EAlFl3 33 3N EAlFl2 22 2N 2 23 31 12 2NNNFFF 93ABCF3aal21ABCl 3l 2l 1ABC321N2N3N1FFF2 2 0 0 xF0 0 FFFFN3N2N102N2N1 aFaF6/53/6/N3N2N1FFFFFF 94 AABCD 2 21 13 3l95 AABCD 2 21 13 3ll 3l 13 3l1l3l 1cosl cos1 13 3ll3 33 33 31 11 11 1AElFlAElFlN3N1cos 96 AABCD 2 21 13 3ll 3 l 1 2 21 11 13 33 3cosN1N3AElFAElF0coscos0sinsinN2N1N3N2N1 FFFFF 9798