材料力学 第九章 压杆稳定

1、maxmax AFN 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)(cossindkxBkxAw （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 nnklEIFk ,.

2、)3 , 2 , 1 , 0(222 nlEInF 2 22 2lEIF crmxmBxylFw kl22lEIFcr kxAwsin2 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

3、2)(crlEIF 2 22 2)(crlEIF zyxxzFFxyzy22126624)15622(2)622121(22412121233 zI2 21 12 22 21 12 21 11 1)()(crlEIlEIFzzz )(3 33 322226 612121 12 21212242412121 1 yI2 22 22 22 22 22 22 21 1)()(crlEIlEIFyyy ,mincrcrcr2 21 1FFF zy22126624 AlEIAF2 22 2)(crcr AIi 2 22 22 22 22 22 22 2)/()()(crcrilEilEAlEIAF il

4、 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 al3 . 11 aal12. 16 . 17 . 07 . 0 BC30mm20mmyz991 PE m0058. 002. 003. 0)02. 00

5、3. 0(1213 AIiyym0087. 0 AIizz15 . 0 zyuu30mm20mmyz11586 zzzyyyiluilu kN.crcr5 589892 22 2 zEAAF 1001001 1 P E222244414)(64)(dDdDdDAIi 1004122 dDlilm6 . 11404. 005. 010022min lm2 . 143min ll122754 dDlil5712. 1240304s2bakN.)()(crcr5 51551554 42 22 2 dDbaAF stcrnFF stcrnFFn 86861 1 P E4dAIi 15 .62 ilpD

6、活塞活塞杆杆活活塞塞d2 .43s2baMPacr301301 baMPacrcr478478 AF .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 N23900stcrFnFAIi 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 EABCF0.60.30.80 0 cm0 06 60 09 90 0 .sin.N FF8 . 06 . 08 . 0sin22 FF27272 2.N 991 PE 4dAIi ABCF0.60.30.8FN180 il572 bas 12 MPacr214214 bakNNcrcrFAF 268268 FFN27. 2 ABCF0.60.30.8直线平衡状态不变直线平衡状态不变平衡形式发生变化