材料力學(xué)第09章 超靜定結(jié)構(gòu)

1、中北大學(xué)理學(xué)院力學(xué)系中北大學(xué)理學(xué)院力學(xué)系第九章第九章 超靜定結(jié)構(gòu)超靜定結(jié)構(gòu)第一節(jié)第一節(jié) 概述概述第二節(jié)第二節(jié) 拉壓桿超靜定問(wèn)題拉壓桿超靜定問(wèn)題第三節(jié)第三節(jié) 簡(jiǎn)單超靜定梁的解法簡(jiǎn)單超靜定梁的解法變形比較法變形比較法第四節(jié)第四節(jié) 用力法解超靜定問(wèn)題用力法解超靜定問(wèn)題 第五節(jié)第五節(jié) 對(duì)稱性在超靜定分析中的應(yīng)用對(duì)稱性在超靜定分析中的應(yīng)用總結(jié)與討論總結(jié)與討論 . 輔助支撐輔助支撐跟跟刀刀架架頂頂尖尖 。 CABDF 1 12 23 3xyFA 2 21 10 0NNFFFx 0coscos03N2N1N FFFFFy ,MPa10021MPa603CABDF 1 12 23 3xyFA CABD 1 1

2、2 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 33 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 1cosNAEE

3、AFF 總結(jié)總結(jié):1.僅由靜力平衡方程不能求解僅由靜力平衡方程不能求解2.不僅與外力和幾何結(jié)構(gòu)有關(guān)不僅與外力和幾何結(jié)構(gòu)有關(guān),還與剛度有關(guān)還與剛度有關(guān)3.強(qiáng)度總有富余強(qiáng)度總有富余4.強(qiáng)度強(qiáng)度,剛度校核與靜定問(wèn)題相同剛度校核與靜定問(wèn)題相同4.補(bǔ)充方程實(shí)際上是變形體的平衡條件補(bǔ)充方程實(shí)際上是變形體的平衡條件ABCF3aal21ABCF3aal21FABC3aa21FN1FN2FN3F 0 xF0 xF 0 0yF03N2N1N FFFF 0 0BM0 02 22 21 1 aFaFNNABCF3aal21ABCl 3l 2l 1ABC3212 23 31 12 2 lll 1 11 11 11 1E

4、AlFlN EAlFl3 33 3N EAlFl2 22 2N 2 23 31 12 2NNNFFF ABCF3aal21ABCl 3l 2l 1ABC321N2N3N1FFF2 2 0 0 xF0 0 FFFFN3N2N102N2N1 aFaF6/53/6/N3N2N1FFFFFF 已知如圖，已知如圖，AB為剛性桿，求拉、壓桿為剛性桿，求拉、壓桿DE、CF 的內(nèi)力的內(nèi)力只寫(xiě)出變形協(xié)調(diào)關(guān)系只寫(xiě)出變形協(xié)調(diào)關(guān)系 AABCD 2 21 13 3l AABCD 2 21 13 3ll 3l 13 3l1l3l 1cosl cos1 13 3ll3 33 33 31 11 11 1AElFlAElFlN

5、3N1cos AABCD 2 21 13 3ll 3 l 1 2 21 11 13 33 3cosN1N3AElFAElF0coscos0sinsinN2N1N3N2N1 FFFFF ABC12aaB1A1C1l3C1Cl3C1CABC12B1C1A1ell 3 31 1aaxEAlFl1 11 1N1 3 33 33 3AElFlN3 AElFeAElFN1N3 3 33 3CAB0 0 N2N1N3FFFN2N1FF 蒸汽管道鋼軌接頭AB ABABB0 0 lABABAB0 0 FTlllEAlFlBFR lTllT EAlFlTBlR TEAFlBR TEAFlBTR BAB ABqlq

6、ABFRBABql0BwqABFRBR()()BBB qB FwwwR()()0BB qBFww ()B qwR()BBFwqAB 4()8BqqlwEI R3R()3BBBFFlwEIBAFRBqABFRB43R083BFlqlEIEIR38BFqlqABFRBFRAMAR58BFql218AMql()B qwR()BBFwqABBAFRB0A ABqlABqlMAa2aABCq2qDlCADBq2qAFNFNAwl ADBCq2qAwFNFNlBCq2qFNAwN()()AA qA FwwwN()()A qA Fwwl BCq2q()Aqw47()12A qqawEI N3N()AFF a

7、wEI CFNBN()AFwNF llEA 43NN712F aF lqaEIEIEA4N3712()AqaFIlAa ADBCq2qFNFNlA1Aw4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/mMBB B BB 3420 4243BBMEIEI 12804()243BMEIEI 3032(52)5653BBMEIEI 4253BMEIEI4m3m2mABDC30kN20kN/mDAB30kN20kN/mMBB B C128044252433BBMMEIEIEIEI31.80kN mBM 4m3m2mABDC30kND

8、AB30kN20kN/m20kN/mMBB B C4m3m2mABDC30kN20kN/m+-32.0547.9518.4011.64+-25.6831.8023.281.603m-+R32.05KNAF R66.35KNBF R11.6KNCF l0111 FXl11111XX l2)(2qxxM xxM )(EIqlxxqxEIlF8d)2(14021 lxxM )(xxM )(EIlxxxEIl3d13011 l0111 FXEIqlxxqxEIlF8d)2(14021 EIlxxxEIl3d13011 341038lqlXEIEIqlX831 l01111 FX 12 01111321

9、 FXXX1201111321 FXXX11111XX 21212XX 31313XX 01313212111 FXXX 02222321 FXXX1202222321 FXXX02323222121 FXXX 12121XX 22222XX 32323XX 03333232131 FXXX 01313212111 FXXX 02323222121 FXXX jiij )3 , 2 , 1,( ji 120002n21n12222212111212111 nFnnnFnnFnnXXXXXXXXX jiij 01111 FX xlxM1)( xlxM1)( 1)( xM1)( xMd(1)d)(

10、1002211 llxxlxEI xFxM2)( lFxM2)( FxxM )(1)( xM1)( xMxlxM1)( EIFlxFxxFlxlxFxEIl/ll/F2413 d1d12d212200201 EIl3411 FlX32131 01111 FX a=50mmq01111 FX xxM )(xxM )(axM )(0)( xMe)(MxM 2)(2eqxMxM 6811d)2(1d)(142e02e2/e1qaaMxaqaMEIxxMEIaaaF xa=50mmqa=50mmxxM )(axM )(xxM )(xxM )(xxM )(axM )(d dd102/2/011 aaaa

11、xaaxxxxxxEI 334a a=50mma=50mmx01111 FX 31134a 681142e1qaaMF 01111 FX 16.56kN)4(333214e1 qaaMaXa=50mmqa=50mmq)( 56kN.16R AyF)( 50kNR AxF m922kN AM0022221211212111 FFXXXX qqEIqaxaqxEIaF6d)21(1422201 EIqaxxqxEIaF8d)21(14222202 EIaxaxxEIaa34)ddEIaxxEIa3d13202222 EIaxaxEIa2d132022112 q 08320

12、62344231342313EIqaXEIaXEIaEIqaXEIaXEIa)(73)(28121 qaXqaXqqa73qa281qa742283qaqa281EIqaxaqxEIaF6d21402221 EIqaxxqxEIaF8d214022222 EIqaxqxEIaF6d121302223 EIaxaaxxxEIaa34dd1302110111 EIaxxxEIa3d13220222 EIaxxEIaa2d11d111021033 EIaxaxEIa2d132022112 EIaxaxxEIaa23d1d112021013113 EIaxxEIa2d1122023223 EIa343

13、11 EIa3322 EIa233 EIa232112 EIa2323113 EIa233223 000333323213123232221211313212111 FFFXXXXXXXXX232123212321312812312812938qaXaXaXqaXaXaXqaXaXaX 48167162321qaXqaXqaX aa01111 FX iFNiFNil1NNNXFFFiiFi iiilFFNNiiilFFNNF22 2 a2a2Fa22 a22a222/F2/F ) 222(NN FalFFiiialFFiii) 21 ( 4NN EAaEAlFFiiii)21(4NN11 EA

14、FaEAlFFiiiiF)222(NN1 1NNNXFFFiiFi 2)21(4)222(1111FaFaXF )4sin(0 FaMM)4(0 )24( sinaM 2Fa d)sin()4(sin1d241aaFaEIEIsMMsF EIaaaEIEIsMMs4d)sin(1d320211 0284313 EIFaXEIa01111 FX221FX EIFa283 sin)4sin(1aXFaM )24( 22Fa sin22sin1FaaXM )4(0 sin221)4(sin Fa000333323213123232221211313212111 FFFXXXXXXXXX0022221211212111 FFXXXX03333FX01111 FX 02127313 EIFaXEIaEIFaxaFxEIaF2d2)(232021 EIaxaxxEIaa127d)2(d232220012111 FX761 FFFByAy76RR FFFBxAx RRFaMMB