同济大学结构力学习题答案朱慈勉

朱慈勉结构力学第2章课后答案全解22试求出图示体系的计算自由度，并分析体系的几何构造。ABW5342610几何可变CD23试分析图示体系的几何构造。AW3322410可变体系B24试分析图示体系的几何构造。ABW4332510几何可变体系CDEFGH25试从两种不同的角度分析图示体系的几何构造。AB同济大学朱慈勉结构力学第3章习题答案32试作图示多跨静定梁的弯矩图和剪力图。A4PFA2PFA2PFA4PF34PF2PFBABCAAAAAFPADEFFP2M6M2M4M2MABCD10KN2KN/MC21018018040M1560704040QD3M2M2MABCEF15KN3M3M4M20KN/MD3M2M2M2M2M2M2MABCDEFGH6KNM4KNM4KN2M33试作图示刚架的内力图。AB4KNM3M3M6M1KN/M2KNACBD6M10KN3M3M40KNMABCDCD3M3M2KN/M6KN6M4KNABCD2KN6M2M2M2KN4KNMACBDEMQNEF4M4MABC4M1KN/MD4M4KNABC2M3M4M2KN/M34试找出下列各弯矩图形的错误之处，并加以改正。ABCDMEF35试按图示梁的BC跨跨中截面的弯矩与截面B和C的弯矩绝对值都相等的条件，确定E、F两铰的位置。BCEFXDAQLXBCEFDA28QLM2221222116121618CBCBCCQQLMLXXQXXMMMMQLQLXQLXLQ中FD2QLX36试作图示刚架的弯矩和剪力图。A2B20945364505209459405,135453135,05209900520990FFEECFCDBARRMRMMM对点求矩B575111MQ4254242135150252575A724252505C42052442535,02557521,2442537525EKBBBBAAEFKMMRRHHVHQQ左对点求矩对点求矩22937542521C8016016016010060401680/38030MQ8080380,616033302023304/2120612010304202113203803DAEDCCBBAMMHFVAVVV对点求矩对点求矩D43543520358841423341614284444142638,03DABBBBAAMAVVCHHHV对点求矩对点求矩E02,020322222,24,0CBPEBFBPHPFHPFPDPDMVFMHVMFAAFAVAHFVFHFVF88利用对称性进一步简化BHBVIHIV884,44,4,42810BBIIAHKNVKNHKNVKNMNM可知88888844444444GQA2AAAAAAAABCGHFJDEIQQ22QA232QA2QA22QA2QA232QA232QA22QA2QAQA2QA15QA15QA2222152150150,15CCAADGFGHHQAQAHAHQAQAAHAHQAHMQAMQA对点求矩对F点求矩同济大学朱慈勉结构力学第5章习题答案51试回答用单位荷载法计算结构位移时有何前提条件单位荷载法是否可用于超静定结构的位移计算AAFPFPBCAAAADENCDNCENBENADNBCNACDEFF0,FF2FFFABPPPPRRFF由对称性分析知道122221121212122222NNP12222F1268322PPPCXPFAFALFAFAEAEAEAEAEA54已知桁架各杆截面相同，横截面面积A30CM2，E206106N/CM2，FP981KN。试求C点竖向位移YC。5PF5PF5PF5PF54PF54PF54PF2PF2PF25544PPPPFFFFNADNAENECNEF由节点法知对A节点F5F对E节点FF1151225162441146NNPYCPPPFFLFFFEAEACMNADNAE由节点法知5对A节点FF2555255已知桁架各杆的EA相同，求AB、BC两杆之间的相对转角BQ。42424242424214214214141428141424111242NNPBFFLEAEAQ56试用积分法计算图示结构的位移（A）YB；（B）YC；（C）BQ；（D）XB。A211232113421YC1004142B1261112611130120PLLPQQQXXQLQQMXQXXLMXXQQMXMXDQXXDXEIEILQLQLEI以点为原点，向左为正方向建立坐标。显然，B22QL254QLPML74LM222413153251315127324244342243416YCQLQLLQLLQLLLLLLQLEIEIABQ2Q1LEIL3L4ABCQLEI常数C22201SIN121COS21111SIN121COS283142EIEIBMRRRRRDEIPJJJQJJJP逆时针DJQQDSQRDQ20SIN1COSMQRDRQRJJQJQJ2240SIN1111COSSIN2XBMRMMDSQRRRDQREIEIEIPJJJJJJ57试用图乘法计算图示梁和刚架的位移（A）YC；（B）YD；（C）XC；（D）XE；（E）DQ；（F）YE。AOAB1KN/M2KNR2M4MBORAQEI常数3212121AX以为原点，向右为正方向建立坐标26YC0510X32133X6281MXXXXMXXMXMXDXEIEIB6M2M2M2KN/M6KNABCDE1MEI常数PMM611211236236238431132162366222561262YDEIEIEIEIEIC2KN2KN2EI6MADCBEIEI2KN/M3M3M3M2323611PM6M2321822182230423018423042366436630626122691823666338XCEIEIEIEIEEIABCEIDK4KN2KN/M6MM1812111012312121261214111311101622641613532632486227316PDPMMDSFFEIKEIEIEEIEIKEIKQ顺时针59图示结构材料的线膨胀系数为，各杆横截面均为矩形，截面高度为H。试求结构在温度变化作用下的位移（A）设HL/10，求XB；（B）设H05M，求CD（C、D点距离变化）。（A）LAB3525CDL252511LLM1N1202102226030TTT1022T1013012230102/23010NKTTTTCCTFDSMDSHLLLHLLLLAAAAAAAOOBABCD0000000TTT4M4M4M3M3434545411111N图055451511243243422545NKTTTFDSMDSTHTTTHAAAAAAM图510试求图示结构在支座位移作用下的位移（A）CQ；（B）YC，CQ。AHADCEDCEBBA2L2LBCQ1H1H1RCAFCAHHQ方向与图示一致BC1ABCDBCAA2A2ADC2C3CQRF图122113312222RYCFCCCCC34A54A12A123213351531442442CCCCCCCAAAAAAQ习题61试确定图示结构的超静定次数。ABCDEFG所有结点均为全铰结点2次超静定6次超静定4次超静定3次超静定II去掉复铰，可减去2（41）6个约束，沿II截面断开，减去三个约束，故为9次超静定沿图示各截面断开，为21次超静定III刚片I与大地组成静定结构，刚片II只需通过一根链杆和一个铰与I连接即可，故为4次超静定H62试回答结构的超静定次数与力法基本结构的选择是否有关力法方程有何物理意义63试用力法计算图示超静定梁，并绘出M、FQ图。A解上图L1MPM01111PXD其中EILLLLLLLEILLLLEI8114232332623232333211311DEILFLLFLLFEILPPPP81733232226323108178114313EILFXEILPPFX211PMXMM11LFP61LFP61FPA2L3L3B2EIEIC题目有错误，为可变体系。PFPLF32X11M图PQXQQ11PF21PF21B解基本结构为L1M3LL2MLFP21PMLFP310022221211212111PPXXXXDDDDPMXMXMM2211PQXQXQQ221164试用力法计算图示结构，并绘其内力图。AL2L2L2LABCDEI常数FPL2EFQ图FPX1X2FP解基本结构为1MPM01111PXDPMXMM11B解基本结构为EI常数QACEDB4A2A4A4A20KN/M3M6M6MAEI175EIBCD20KN/MX1166810810计算1M，由对称性知，可考虑半结构。A211M计算PM荷载分为对称和反对称。对称荷载时AQ22Q2QA2QA26QA26QA26QA反对称荷载时AQ22QA2Q2QA2QA28QA28QA28QA22QA214QA22QAX11122PM01111PXDPMXMM1165试用力法计算图示结构，并绘出M图。A解基本结构为1M2MPM用图乘法求出PP21221211,DDD0022221211212111PPXXXXDDDDB6M6M3M3MABCEI2EIEID11KNX1X211KN1121663311KN33解基本结构为1M2MPMMEIEI1086623323326611D03323326612EIDEIEI1086623323326622DEIEIP27003231806212362081632323180621121EIEIP5403231806212362081632323180621122EI常数6M6M6MEDACB20KN/MX1X120KN/MX2X236336111118090150301505250540108027001082111XXEIXEIEIXEIMKNMCA9035253180MKNMCB12035253180MKNMCD3056C解基本结构为1N1MPMEIIEEI5558293299233256633263111DEIIEP144210310910923102566101111PXD2911XMKNMAC6111029196M3M5III10KNM10KNMEACABD5I12M10KNM10KNMX110KNM11933910KNM10KNM1010MKNMDA136102913MKNMDC8732913MD解基本结构为1M2MPMEIIEEI6111293299233256623326311D6M3M5IIIEADABE2I5ICEA10KN/MFG38738761361316116110KN/MX1X21339966140545EIIE2256396256612DEIIEIE45066226666256622DEIEIIEEIP251721645632519454053405924532566433453311102P6983917045022502517212256111212121XXXEIXEIEIXEIXEIMKNMAD4924839179405MKNMBF37104391796986MKNMFE175239173MKNMCG145269861752M4924837104145266试用力法求解图示超静定桁架，并计算1、2杆的内力。设各杆的EA均相同。AB题66图67试用力法计算图示组合结构，求出链杆轴力并绘出M图。AAFPFPAAA1215M2M2M1230KN解基本结构为PFL2LFPPF1MPMEILLKLLLEILEAL272222262311QDEILFLKLFLLFLLFEILPPPPP2222631Q01111PXDPFX721LFLFLFMPPPA73272LFP73LFP72MBLLLEIABCFPK12EILEA2EIL2AAAAABCDEFGQQAEAEI常数EAEI/A21168试利用对称性计算图示结构，并绘出M图。A解原结构中无弯矩。取半结构基本结构为1MPMEIEI22433299921211DPPPFEIFEI22433292992111PPFXX41011111D6M6M9MABCEAFP2EIEIEIDEFEA2PF2PF2PF2PF2PF2PFX112PFPF2999M图整体结构M图BC解根据对称性，考虑1/4结构Q基本结构为Q1X128LQ11MPMEILLEI2121111DEIQLQLLQLLEIP121821823112221LLABCDEI常数QQ3M4M5M4M60KNABCDEI常数PF49PF49PF49PF49PF2901111PXD1221QLXPMXMM11242QL242QL242QL122QL242QL242QLMD解取1/4结构Q基本结构为QX2X11L111M12MPMLLLDEABEI常数QQCF122QL122QL22LQEILLLEI332213211DEILLEI212112212DEILLLEI2311112122DEIQLLQLLEIP8432311421EIQLQLLEIP612311322221321242213361125062320823QLXQLXEIQLXEILXEILEIQLXEILXEIL362QL362QL362QL362QL362QLME9MABC50KNIDEF6M6MI2I2III92QL92QL92QLFBEH杆弯曲刚度为2EI，其余各杆为EI取1/2结构中弯矩为0。考虑反对称荷载作用下，取半结构如下中无弯矩。考虑弯矩图如下AAA2A2AA4FPGDEFABCHIPF2PF2PFPFPFPFPFPFPFPFPFPF2PF2PF2PF2PF2PF2PF2PF2PF2PF2PF2PFAFP2AFP2AFP2AFP2AFP2AFP2AFP2AFP2AFP2AFP2AFPAFPAFPG解原结构弯矩为0。反对称荷载下基本结构为X112A1MPMEIAAAAEI3832222211311DFPAAAAEI常数ADK3EI4A3KBGCEF2PF2PF2PF2PF2PF2PF2PFAFP2EIAFAFAAFAEIAPPPP1252222631PPPFXXEIAAEIFXEIAKXX485341253811331311111DM图如下H69试回答用力法求解超静定结构时应如何恰当地选取基本结构610试绘出图示结构因支座移动产生的弯矩图。设各杆EI相同。AB题610图611试绘出图示结构因温度变化产生的M图。已知各杆截面为矩形，EI常数，截面高度HL/10，材料线膨胀系数为。ABLLLABCD151510151554A4A4A3AABDBEI常数CDLLABC251510D2L2L2LABDELCDEI常数4FPLHLLLACEBDFI2I2I2IIIIIIAFP485AFP485AFP247AFP247题611图612图示平面链杆系各杆L及EA均相同，杆AB的制作长度短了D，现将其拉伸（在弹性范围内）拼装就位，试求该杆轴力和长度。题612图题613图613刚架各杆正交于结点，荷载垂直于结构平面，各杆为相同圆形截面，G04E，试作弯矩图和扭矩图。614试求题611A所示结构铰B处两截面间的相对转角BQ。615试判断下列超静定结构的弯矩图形是否正确，并说明理由。ABCD题615图616试求图示等截面半圆形两铰拱的支座水平推力，并画出M图。设EI常数，并只考虑弯曲变形对位移的影响。题616图ABLBACDFPFPQFPQFPRRFPRABC同济大学朱慈勉结构力学第7章位移法习题答案71试确定图示结构的位移法基本未知量数目，并绘出基本结构。ABCEIEIEI2EI2EI1个角位移3个角位移，1个线位移4个角位移，3个线位移DEFEI1EAEIEI13个角位移，1个线位移2个线位移3个角位移，2个线位移GHIK一个角位移，一个线位移一个角位移，一个线位移三个角位移，一个线位移72试回答位移法基本未知量选取的原则是什么为何将这些基本未知位移称为关键位移是否可以将静定部分的结点位移也选作位移法未知量73试说出位移法方程的物理意义，并说明位移法中是如何运用变形协调条件的。74试回答若考虑刚架杆件的轴向变形，位移法基本未知量的数目有无变化如何变化75试用位移法计算图示结构，并绘出其内力图。ALLLABCDIIIQ解（1）确定基本未知量和基本结构有一个角位移未知量，基本结构见图。11R11Z3I4I2III1M图1PR213QL216QLPM图（2）位移法典型方程1110PRZR（3）确定系数并解方程IQLZQLIZQLRIRP24031831,821212111（4）画M图2724QL2524QLM图218QL216QLB解（1）确定基本未知量1个角位移未知量，各弯矩图如下4M4M4MACDB10KNEI2EI25KN/MEI11R11Z1M图32EIEI12EI590PM图（2）位移法典型方程1110PRZR（3）确定系数并解方程1115,352PREIR153502EIZ114ZEI（4）画M图KNMM图2640147C解（1）确定基本未知量一个线位移未知量，各种M图如下6M6M9MABCEAFP2EIEIEIDEFEA11R1M图11Z27EI227EI27EI1243EI2243EI1243EIPM图PF1PR（2）位移法典型方程1110PRZR（3）确定系数并解方程1114,243PPREIRF140243PEIZF12434ZEI（4）画M图94PF94PF92PFD解（1）确定基本未知量一个线位移未知量，各种M图如下A2AA2AAEAEAABCDEFFPFPEI111Z2/25EAA4/25EAA11R1M图25EA11R1M图2/25EAA2/25EAA简化1PRPFPF45A35A15APM（2）位移法典型方程1110PRZR（3）确定系数并解方程11126/,55PPREAARF126055PEAZFA13AZEA（4）画M图M06PFAPFA12PF06PFELLEAABCDEAEAFP解（1）确定基本未知量两个线位移未知量，各种M图如下图11Z11R21R112121424EARLEARL1M2EALEAL21Z12R22R22214EARL2M2EALEAL120PPPRFRPM1PRPF（2）位移法典型方程11122121122200PPRZRZRRZRZR（3）确定系数并解方程112212212221,44214,0PPPEAEARRRLLEARLRFR代入，解得121222121212PPLZFEALZFEA（4）画M图图M122212PF2212PF1212PF76试用位移法计算图示结构，并绘出M图。A解（1）确定基本未知量两个角位移未知量，各种M图如下23EI13EI23EI23EI13EI1121213REIREI1M10KN/MACBEDF6M6M6M6MEI常数23EI23EI13EI22116REI2M13EI13EI11300PPRRPM（2）位移法典型方程11122121122200PPRZRZRRZRZR（3）确定系数并解方程11221221212,311630,0PPREIRREIREIRR代入，解得121547,281ZZ（4）画最终弯矩图3516图M19699381031327187140B解（1）确定基本未知量两个位移未知量，各种M图如下ACEDEI常数6M6M6MB10KN/M11R21R1MIII12R22R图2MI/21PR2PR图PM3030（2）位移法典型方程11122121122200PPRZRZRRZRZR（3）确定系数并解方程11221221211,03430,30PPRIRRIRRKNRKN代入，解得123011,4011ZZII（4）画最终弯矩图MC解（1）确定基本未知量两个位移未知量，各种M图如下图21RI4I2I3I3I1M11R图22R2M12R32I32I1PR30KN2PR图PM（2）位移法典型方程11122121122200PPRZRZRRZRZR（3）确定系数并解方程ACBEDF30KNEI常数2M2M2M2M2M112212212311,2640,30PPIRIRRIRRRKN代入，解得12631646316,ZZEIEI（4）求最终弯矩图图M42125261263632947D解（1）确定基本未知量两个位移未知量，各种M图如下11R1Z4EIL2EIL3EIL3EIL3EIL21R图1MABEDFEI常数LLLLCGQ2LQL12R21Z23EIL23EIL22R2M26EIL26EIL1PR218QL2PRPM2116QL（2）位移法典型方程11122121122200PPRZRZRRZRZR（3）确定系数并解方程112212222212133,181,16PPEIEIRRRLLEIRLRQLRQL代入，解得34126211,3603600QLQLZZEIEI（4）求最终弯矩图20125QLM20176QL20008QL20315QL20231QL20278QL20055QLE8M4M4M4MABCD50KNM80KNM20KN4M10KNM2EIEIEI解（1）确定基本未知量两个角位移未知量，各种M图如下11R21R11Z34EI12EI14EI1M12R22R21Z38EI12EI14EI2M图PM图50252020202525（2）位移法典型方程11122121122200PPRZRZRRZRZR（3）确定系数并解方程11221221251,447845,0PPREIRREIREIRKNMR代入，解得123818,1091ZZ（4）求最终弯矩图M77试分析以下结构内力的特点，并说明原因。若考虑杆件的轴向变形，结构内力有何变化ABCFPFPFPDEF78试计算图示具有牵连位移关系的结构，并绘出M图。A解（1）画出PMMM,21图11R11Z21R29EI29EI29EI11R481EI43EI21R43EI由图可得112211124,813REIRREI21R21Z22R29EI12EI22R43EI12EI16EI16EI32EI16EI2M16EI118EI由图可知22149REIQEI1EI对称轴FPFPM20KN8M8M6M3MACDEBFGEI1EI13EI3EI3EIEI1PR2PRPM12200PPRKNR（2）列方程及解方程组12121124200813414039EIZEIZEIZEIZ解得12118338,7147ZZEIEI（3）最终弯矩图B解C点绕D点转动，由CY1知，45,43CDXCC知4M6M8M4M10KN10KNBCADEI常数EIEIEIRREIEIEIREIEIEIRREIRREIR16027403323,1098410412833231289,4,3223221331211211KNRRMKNRPPP256,0,10321求33R0DM知EIEIEIEIEIEIR055081481289128912834031602733EIZEIZEIZEIZZEIZEIZZEIZEIEIZZEIEIZ/6285/558/91702560550160271283016027109401012834321321321321C解（1）作出各M图O瞬心2264EIEIAA2262EIEIAA210EIA242EIA242EIA29EIA1M图FPEI1EIEIDCBAA2A2AA01133113918029218EIEIMRAAAAAEIRAO瞬心图PM1PR14PAP0110022PPAMPRAPR（2）列出位移法方程1110PRZR解得3129218PAZEI（3）最终M图59218PA49218PA59218PA5229218PA14PA229218PAD解基本结构选取如图所示。作出1M及PM图如下。L2L2LCABDEI1EIK4EIL3Q11R11Z210EIL28EIL292EIL1M图2112QL2112QL218QLPM图3222211292/2910810LEILLEILEILLEILEIRQLLQLQLRP127/1212121由位移法方程得出EIQLZRZRP34870411111作出最终M图241348QL285348QL25768QLM图218QL79试不经计算迅速画出图示结构的弯矩图形。AB题79图710试计算图示有剪力静定杆的刚架，并绘出M图。ACABACBDYBBBFADCQAAGEQQQAAAAEI常数解（1）画出PMMM,21图11R21R11Z1M图12R22R21Z2M图3II3IIPM图218QL218QL212QL212QL2QL2QL由图可知，得到各系数222122211211813,858,7QARQARIRIRRIRPP求解得5512,4405321ZZ（2）求解最终弯矩图M图2159440QL2104440QL2263440QL2177440QL2238440QL23655QL24355QL26755QL711试利用对称性计算图示刚架，并绘出M图。A解（1）利用对称性得6M6M6M6MCABDEFGEI常数6M20KN/M11Z11R23EI23EI13EI13EI1M图PM图1PR（2）由图可知MKNREIRP300,341110300341EIZ可得EIEIZ225433001（3）求最终弯矩图M图B解（1）利用对称性，可得EIEI10KN11R1Z125EI45EI4EI1M图PM（2）由图可知，各系数分别为02020212020215441111EIZMKNREIEIEIRP20KNEIBAC4M3M4MEIEI解得EIZ214001（3）求最终弯矩图如下76215242476M图C解（1）在D下面加一支座，向上作用1个单位位移，由于BD杆会在压力作用下缩短，所以先分析上半部分，如下图。2125EINLPM图15X1PR45NPLP18PLD点向上作用1个单位，设B向上移动X个单位，则XLEIXLEI112333，得54X个单位。（2）同理可求出MP图。PLRLEILEIXLEIRP54,5132512121332311可得3331PLZ（3）求最终弯矩图LLLFPA12IL2EIEIEIEAABCDE图811NPL311PL211PL211PL211PLMDE解（1）利用对称性，取左半结构ADBCADBEIEI2EI2EIEIEI10KN4M4M4M4M4M3M50KNEIABCDBA3M3M3M3MEIEIEIEIECEI1EI1EIEI1M图11R11Z21R43EI23EI43EI23EI2M图12R21Z22R29EI23EI23EI49EI49EI89EI2PR25KN1PR图PM（2）由图可知KNRREIREIRREIRPP25,02720,94,382122122111解得EIZEIZ375,42521（3）求得最终弯矩图50350312561256125622562256503503253253M图F解由于不产生弯矩，故不予考虑。只需考虑（）所示情况。对（）又可采用半结构来计算。如下图所示。10KN10KNEI常数ABCDEF2M2M2M2M5KN5KN2Z1Z1M图21R11Z11R2M图22R21Z12R112PR1PR712试计算图示结构在支座位移作用下的弯矩，并绘出M图。ALLLABCDEIEIEIDB解（1）求PMMMM,321图。11R21R4I12I6I2I31R1M图12R22R4I12I6I2I32R2M图13R23R33R3M图6IL6IL6IL6IL（2）由图可知LIRIRRLIRIRLIRRIRRIRPPPFF18,8,024,16,6,6,1632133223223211211代入典型方程，得LZZZ7630,3740,4260321（3）求最终弯矩图M图287EILF193EILF373EILF467EILF713试用位移法求作下列结构由于温度变化产生的M图。已知杆件截面高度H04M，EI2104KNM2，1105。解（1）画出TTTMMM,1图。3EILADCBLEIEIJLJ6M4MABC200200题713图11R4EIL4EIL2EIL2EIL1M图1TR203EIA1TM图453EIA1TRTM图10EIA（2）求解各系数，得，0,695,35111TTREIREIRA典型方程0695351AEIEIZ解得A2191Z（3）求最终弯矩图M图714试用混合法作图示刚架M图。FPFELADCBLEI常数LL题714图同济大学朱慈勉结构力学第8章矩阵位移法习题答案81试说出单元刚度矩阵的物理意义及其性质与特点。82试说出空间桁架和刚架单元刚度矩阵的阶数。83试分别采用后处理法和先处理法列出图示梁的结构刚度矩阵。A解（A）用后处理法计算（1）结构标识YX1234单元局部坐标系（JI）杆长ACOSASIN各杆EI21L102EI32L10EI43L10EI（2）建立结点位移向量，结点力向量T44332211QNQNQNQNTYMFMFMFMFF4Y43Y32Y211Q（3）计算单元刚度矩阵2222322211211462661261226466126122EI21LLLLLLLLLLLLLKKKKK2222333322322233363632336362EI21LLLLLLLLLLLLLKKKKKLLLABCDEIEI2EI2222344433433233363632336362EI21LLLLLLLLLLLLLKKKKK（4）总刚度矩阵22222222223444334333332232222211211233000036360000340300360123600003632600363186120000264600006126122EI00000043214321LLLLLLLLLLLLLLLLLLLLLLLLLLLLLKKKKKKKKKKKKKQ（5）建立结构刚度矩阵支座位移边界条件00004311将总刚度矩阵中对应上述边界位移行列删除，得刚度结构矩阵。2222222320043063033182EILLLLLLLLLLLLKQB用先处理法计算（1）结构标识YX12345单元局部坐标系（JI）杆长ACOSASIN各杆EI21L012EI32L01EI43L01EI（2）建立结点位移向量，结点力向量TT00005411NNQN故T54322QQQQN（3）计算单元刚度矩阵2322466122EILLLLKQN222234324262466612EILLLLLLLLLKQQN222235444EILLLLLKQQ（4）建立结构刚度矩阵（按对号入座的方法）2222222235432220004030203000460336182EILLLLLLLLLLLLLLLKQQQQQNB84试分别采用后处理法和先处理法分析图示桁架，并将内力表示在图上。设各杆的EA相同。解（1）结构标识如图LLLABCDEIEI2EILLFP1234XYEA常数单元局部坐标系（JI）杆长ACOSASIN21L1043L1031L0142L0132L2222241L22222（2）建立结点位移向量，结点力向量T44332211NMNMNMNMTYXPYXFFFFFF0003311（3）计算单元刚度矩阵000001010000010121LEAK同理000001010000010143LEAKK101000001010000031LEAK同理101000001010000042LEAKK21212121212121212121212121212121232LEAK同理21212121212121212121212121212121241LEAKK（4）形成刚度矩阵，刚度方程424420010424242424010042420042442424210014242442420010424242442000042424242401424210004244242420001424244321LEAKQ刚架总刚度矩阵方程TYXPYXTFFFFFK000331144332211NMNMNMNM（5）建立结构刚度矩阵，结构刚度方程制作位移边界条件为0000331121NMNM将刚度矩阵中对应上述边界位移的行、列删除，即得结构刚度矩阵，相应结构刚度方程为00042442104242400104244200424244422PFLEANMNM（6）计算节点位移，得692810442221354557800004244210424240010424420042424114422PFLEANMNM（7）计算各杆内力278880788807888078880001354255780212121212121212121212121212121212325PPFEALFLEAF07888007888027888078880788807888011001100001100112255PPPFFFFTF同时可得其他杆内力。（B）采用先处理法（1）步与后处理法相同。（2）建立结点位移向量，结点力向量T4422NMNMTPFF000FPPF55780PF44220PF44220PF06253PF7888000012LEAK00014LEAKK101000001010000042LEAK2121212124LEAK2121212124LEAK（4）形成总刚度矩阵，结构刚度方程00042442104242400104244200424244422PFLEANMNM（5）结点位移及内力计算同上。85试列出图示刚架的结构刚度方程。设杆件的E、A、I均相同，结点3有水平支座位移S，弹簧刚度系数为K。解（1）结构标识单元局部坐标系（JI）杆长ACOSASIN2120132223212MK30KNM20KN1MS3M33YX21E、A、I常数3YX21（2）建立结点位移向量，结点力向量T3222QQNMTF003002（3）建立单元刚度矩阵（L2M）LEILEILEALEILEIK406006012233222QNMLEILEILEILEILEILEILEALEILEILEALEILEALEILEILEILEILEALEILEALEILEAK432333034331243343004333000941243000034322232332233333222QNQNMKK（4）建立结构刚度方程（对号入座的原则写出保留支座位移3N在内的刚度方程）030020432333034331243343008333000945124300001543333222222323322333XFKNKNLEILEILEILEILEILEILEALEILEILEALEILEALEILEILEILEILEALEILEAKLEILEAQNQNM由已知，支座位移C3N，将以上刚度矩阵3N的行删除，并将3N与刚度矩阵第4列乘积移至方程右端与荷载向量合并。EICEICMKNCEIEACEIEAEIEIEIEIEIEIEIEIEIEIEIEAEIEAEIEIEIEAKEIEA434330432328383243343443343433433898523243434323243815833222QQNM86试采用先处理法列出图示刚架的结构刚度方程，并写出CG杆杆端力的矩阵表达式。设各杆的EI常数，忽略杆件的轴向变形。5147解（1）结构标识如上图。单元局部坐标系（JI）杆长ACOSASIN3254/53/553610766012130134601（2）建立结点位移向量，结点力向量T65322QQQQNTF00001015（3）建立单元刚度矩阵（考虑杆件及两端点无相对水平位移，故水平位移可以不考虑）LEILEILEILEIK422432QQ其中L5M6M6M4M3M15KN10KN50KN50KNADBCFGEI常数236LEILEILEILEIK422453QQ其中L6MLEILEILEILEIK4661222362QN其中L6MLEILEILEILEIK4661222322QN其中L3MLEILEILEILEIK4661222332QN其中L6M（4）建立结构刚度方程（按对号入座的方式）000025320006103231000311532526100521532326106132956532265322QQQQNQQQQNEIEIEIEIEIEIEIEIEIEIEIEIEIEIEI方程中已省去单位解得EI152209008113125068265322QQQQN（5）写出CG杆杆端力的矩阵表达式000522000682320613106100000061018161018131061320610000006101816101810005220006821406620660000006603612660361220664066000000660