材料力学第九章压杆稳定2013

1、 Mechanics of Materials crFF crFF crFF 过过度度对应的对应的压力压力yBFmmwBxylFcr)(xfw FwxM )(FwxMEIw )( （a)EIFk 202 wkw(b)(b)式的通解为式的通解为)(cossinckxBkxAw （A、B为积分常数为积分常数）mmxyBwFFwxM )(0 00 0 wx,0 0 wLx,0 00 01 10 00 00 00 0 BBABAcossin0 0 klAsin0 0 A0sin kl0 00 0 wA,.)3 , 2 , 1(0sin nnklkl mxmBxylFw,.)3 , 2 , 1 , 0(

2、2 nnklEIFk ,.)3 , 2 , 1 , 0(222 nlEInF 2 22 2lEIF crmxmBxylFw2 22 2lEIF cr2 22 27 70 0).(crlEIF Fcrl0.3l0.7l22cr)7 . 0 (lEIF C2 22 25 50 0).(crlEIF 2 22 22 2 )(crlEIF lFcr2l22cr)2( lEIF lFcrl/4l/4l/222cr)2/(lEIF l 2 22 2lEIF cr2 22 27 70 0).(crlEIF 2 22 25 50 0).(crlEIF 2 22 22 2 )(crlEIF 2 22 2)(cr

3、lEIF AlEIAF2 22 2)(crcr AIi 2 22 22 22 22 22 22 2)/()()(crcrilEilEAlEIAF il 2 22 2 E crcrcr AFPcr 2 22 2EPP EE 1 12 2令100100101020020010102062066 69 91 1 PEscr ba 。1 12 2 bas bas 2 21 1 12 2 2 22 2)(crlEIF ba crscr iL cr 22 Ecr P S 2 2 1 1scr bacraFF1.3 a F1. 6 adABCA杆先失稳杆先失稳aFF1.3 a F1. 6 adAal22 a

4、l3 . 11 aal12. 16 . 17 . 07 . 0 BC1001001 1 P E222244414)(64)(dDdDdDAIi 1004122 dDlilm6 . 11404. 005. 010022min lm2 . 143min ll122754 dDlil 575712121 12402403043042 2.sbbakN.)()(crcr5 51551554 42 22 2 dDbaAF stcrnFF stcrnFFn 86861 1 P E4dAIi 15 .62 ils243.2abMPacr301301 bacrcr478KNFA.stcrnFFn 5 51111pD活塞杆活塞杆活塞活塞dpD活塞杆活塞杆活塞活塞dN398042 pDF Nstcr2390023900 FnFAIi il 用试算法求直径用试算法求直径2 22 2)(crlEIF 2 24 42 22 22 26464)()(crldElEIF 2004 dlil 97971 1 P E惯性矩惯性矩 I 越大越大惯性半径惯性半径 i 越大越