解：(1)整体编码。单元、结点和结点位移编码如图 (b)所示。[img=537x124]17a04a4601023ec.png[/img](2)计算各单元的单元刚度矩阵 [tex=28.714x5.214]wToKDUqBJEN4PlCmmLJYzdotCNY34UOXpSUkjZg1WEdM7kMrJ/Z8mvE+qlCxS81LxVAbrAKx+gM4rC9dY9mZkB4/jgIO6nz5m3VZlR4z4POo7p2NPmrnXZj+6GlX3YUuFlrdr2+4aqiKMZMCE0zh9W8zyXGb9BParXs2hPGCJCSEHemBYmr/9e4sE+lSeQoZPjUR8J2jqUFiYb+aUviips4GNSWhlYSO7uQbV3OFX8LcsI8TQxTfWfxfl77jQCR1UIVpTs0wMh0X9avsZTtW78djeJTGlQdiWxyiINNZsP+vzzdzxs1V/G5NOpN/yh6X639cZ+KzlPXCaqRFa4HelmvRY7ZheZUg3Cz3Z/pXq9vw77BmYRAB7nNd8qWG4nNI[/tex][tex=13.071x2.929]CwgTgdhu4bqnLEGqaJTx/wGF9aCGIl9NH4EbwDC5yNnypl+PlX4tz/qB0kBo40LhnVFTCd9hLVIeKPKcO79sSZ/rYt1Qul+wxUJTN2XRsy6O6/u4ZTNf1iBnnV3+zHmne2SCJDtg4btUHOAmYL/8Ao7kYTs50mpnwDh6balpnAA=[/tex](3)集成结构整体刚度矩阵。各单元杆端局部位移编码与结构结点位移编码的对应关系如表7-1所示。[img=1167x270]17a04a659f64a35.png[/img]将单元刚度矩阵中元素累加到结构刚度矩阵中，如单元②的单元刚度矩阵元素 [tex=1.286x1.286]F2HFiIK8SdnQc1a0aIr3Nw==[/tex]按上表关系应加在结构刚度矩阵中的[tex=1.643x1.286]HXhS5ANNiefZwA4whIlI1Q==[/tex]位置上。“对号入座”完成后，得结构刚度矩阵为[tex=20.0x4.214]Ij9Nw4owS22+xJlhtgNWqzBQhi5KINO27hVcKhHBiGn4DH3pTwlUCLQFBPMWOQvT3+Yz9TgfZcbEemWPYVdzLVE1Qm6N53EpweAR+o0LVG52OB5zWxDcQFzhd3VQk7i12BNItShuaQHmV/Z7kSrW3/UuMkbvNeCQqmfZwfrMhwQ64Nu+sC+aqK0Jlyl1ukKliC9M1vTrdCkAviqzEblkJGfPjKuvQYOHya+Zio/gXfU=[/tex](4)计算结构等效结点荷载向量①计算单元固端力[tex=10.929x2.786]3dAQxuyhCPULtjBXySRBUJjqR57gtyDLHUxpz7Znr7i4m8ZUoxjCo7/Ggtjywz9pYrlF50pCUsKkxyHvmLT0C9p9fF3R0kTbSmVRpnEhLa5diiKruHk91wQd5WRNx0FH/KHCjm0KS8o2ZDdy1gS1gQ==[/tex][tex=5.929x2.786]m6PU7DGqs2Y3CJpY9e5QOGRn9TQJMoulHXs80mq1GrL64bgBJNOcruxiaMaOsj5qpykZRR6q82y2tmGRTg6sjg==[/tex][tex=10.429x2.786]3u6QhD4ZZmYV50pnCZcLgo87mD37ScRXrRCJJ7oZ0oQh3wcsKobiJzjkhXAI6tEyKfvAEaldzjifLfYUWpkGpAysjf5kMOoL4xdNCzcB1TBP5JQdc7WntH2AGumVPa8gQ18cuLQbRg3vgTl5YxzpLQ==[/tex]②计算单元等效结点荷载[tex=14.0x2.786]A55syoU6Q9Q838Jnn/t+lKezE3tDCVnnZ3OBHx/IdIfzBBJZg0Ag1Nvt3cb4t29Ub6ONrDC8MAb14d3BRaXFd9863RpXkxYPUmY9uNGUIRL4YyPmWOJKT+cd33W1PJD3m9GjfttdO2yeJPjYGHZxmojchrsveLflXQXouSnlMzA=[/tex][tex=13.5x2.786]IN/u+OlLPnLNGW1cvuRa9SHvCyvD0lr5lmp0fkiZWJe8QpXSgQ/KsEofSDU/gHlgKqX3pYY9dfrSe+FHuhJ9BXsE61ZztMQBes84CC+c8Af0zhmflPP/t7ijq3faJ7R26TEd8RMCI83U0gwQLc40ruJW3ffWswHTEPA9XPXjki0=[/tex]③“对号入座”集成结构等效结点荷载将单元等效结点荷载按表7-1中的单元局部位移编码与结构结点编码对应关系累加到结构等效荷载矩阵中，得结构等效荷载矩阵为[tex=10.429x3.929]bdDwWbcpM1+ksd/yReN+Tcfz4dXWxTU4hpyNyYjw8F9dxjBKuGmWBWCo/5mlTmQLcJcXC2rjJV3nZzj1sMYhLEBlG9T76tNHjNW3zr7VmlEDpLBKffcXSGQWE4iMUKUKAZfMbBS+2VLDXm1q1vdFeJTORrwm4j0mdOHEMf6h4mw=[/tex](5)计算结构综合结点荷载。结构直接结点荷载矩阵为[tex=8.571x3.643]yV/X6x1etwV1RBl+2H4Uw9E3Eh8Z2zPwxZfgUYH+xZkb3BXRNYw/ai6Y2Q0F2GceHKgbAXogP/g/QhtCGcSOIyHwskD3Opg7tkC8A1wMqdM=[/tex]结构综合结点荷载为 [tex=30.714x3.929]fPt7xiib1jabZ7jhAMltL6B2iZDPYhvJ1WCup1iBTN2sXWt8fOLmzp5JCusvDvxuCXaNBEWReZMlHPrxcPgMbl225T11luywMIKGVF1Y9dZIC9Hu3y+xVT88cg8vPu/a9WSwHGcpocuT5uv5a3BETDrBoGq0hXSfu7oSBnZ3p8tFlzZBPmDgPybDxtv+RIlnVSNDd6HipfkQ+nBFGiTiYHonnVvmf84h5cUmA3bq7LShfeP6IKWLsZwd76xuXF6ELhM86f5oFOsil4Nl0/3bpC1gvWdt2cKR84GTLB0XlApiBM2MKpwHYEHyAaXicdXSPpSW1GZUYS773Reu2qg01b/HG6tv0SCRF9JSFrzzH8I/dFpVOt1kW6znke7bXaU2TBuHTOi0iGJgavfzJa+a1wTELLwuA+f441KVqovgxVY=[/tex](6) 形成结构整体刚度方程,并求解[tex=31.5x4.214]5SDDTVXzEoQstAgRYtbdacikw5UpBp8pT4V57yCtdb4SDWe9bPCbfp3w0arti/do0AaNo7ubL1A91WI0dMXa4QjvCqBoEYPhYJz3dYmDtiJKG7Ev9L8TakRSjvisz45iBzh9IlJBAbkRiFd6qjLeCrJJQlUYAzFbfZk717eq0otpwx4g0NvoUV2ppl08D3kE16hQHK4WkVAr4n/qN+5tZQr+BPKTHzRS6Wd0KO5xHA9u0Q1Hsq55PxYdz5fNYdLqJ9BAnPd+CuPzcOTh5umE0C6OYU3drBarde0so9vfpvmNDzL2087PK37sHvZjIKOqks85uNC0m4VBotM5q9KqC+Q/rQt1Uon8pEyqdvUk5fmf4bm5Oz/y3HLw5BUVE1fl2KjuGzU9Qe8f15M3fn/QVhx9b0znLtsXlcrvUg0jAVGoPY+OA4WxEHpXJGODEnOQWqtX9fROVzWVZ+7vfH/OwJi9mAgh6IbGtQeqi5WJ4xY=[/tex]解方程,得结点位移为[tex=14.929x4.5]075gCzZzsMRb6HYXYk9X94T84v+9QFVmEO+RT3+KGsZKuVa5nYfpU9Uu3IGKgNHtkNta0tMmJ0n9zqFkgNyq1GlVbJpt7bIt3dUJpT5zbgmPo1q6JSNQ9+/2962sUdRr89clCNWILn5Uu9ZJn7mTaBp6fBoFy/FvRV9P8cvTy3yNogSV+Fes6B34u9Pe8N0qN63/btvBtNE6WZ62GXxZ/kjvf1ex2LyRG/pN/ko5G+sxoOfja3qrvQz9Gl7k1AroOm7hhsYuHPBvyovK3EZHws+21RQGHFPr9eYSRLvZrW4=[/tex](7)计算单元杆端力根据表7-1对应关系和结构结点位移可知各单元杆端位移为[tex=12.143x2.929]vKrPzcD/yg7XkGl3L7c3RjXUhB4x8p34K9opc0O+5XY/plm8yK4YkcD419VTc+FveVOGNne9Yp1YBMPQUE9gCls9bkqKyFIXBlCsRuI2KpfvZkajc8QILOQsyDy6ZVzajiOk8XlmLbw3oeFI+I9DGFy514BaRvbtmbjZq/4v1ZU=[/tex]; [tex=12.143x2.929]j9ebQ1hNR1/i1MAmf5ar8VYHGo0dWnq6xPOvAPVNUZ94/0BlEagZ7a6jMBG1YT5xXEWSIcUxILKqQRr9AYX5VnYjpmHcrgmDvbEIcOTKQ8oM6ULXoTXh7jwVUIf7vZI4IpC9M5nnNU75XVWiQR/nvlRFCrjcx6P+iQnSDZ8hx6E=[/tex];[tex=12.143x2.929]qnvLcA7SCUAiN/h6c8fv6BEnNT7KbhzcCLrmHKs4SfCQcGP4nJvJKdsH+kWv1K2T+dXK5dRPCiOccK/0WmQuY1Tsg6lkiqIOm1Yh4Mfw+dP1HuG/EdcmJYURYmfo8XcfafJL1sUSY90tnHwCHyNqWu4DIkJY6Ua/imbNCkigM2A=[/tex]由单元刚度方程计算各单元杆端力[tex=7.429x1.429]OQvtBJ+gRZoy0iEdxSAdYpn6jH+CGM8/1rW2KE+bJEw2QnK5cmoTSo2jgnN+q4ddGAiWpkqa+9bDpeDJorU07TAu4MkejCvJ/Aia2y2TFDiLjY0VGFeG8OavK4qigq72[/tex][tex=33.214x2.929]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[/tex][tex=8.929x2.786]CMIhUyI8bpw2/d9UIDux4ucERuKeO0w7TUaZD0oNlaRE5EYWrIXhM8M2MeUj25EKdVoSQQhQKdxHQUmJU1wgIuag4cgpmTqkyUinsIeKcYt1BhGwIPGoAlFshcigo6r5[/tex];[tex=7.429x1.429]OQvtBJ+gRZoy0iEdxSAdYgnMBM4e/Y7Spwouj3mTlvLGv1Q9LkYQgzkTOyxA1BhtPAUxGZSNzXImQSRTCZucR01ctqrhTN2ffLNoGJh5drtF0PcqSkl45TLDhuIEdhbs[/tex][tex=24.143x2.929]MQCrta+if/82r87YQV4KqCbXWolfZi+JXEA6F5WCo7JybmtE8Nsg5Ig4j2BjDgLlcQ1ZOwByG+Y1T5zz29LJzMJnQYToAH7giLztEUgfxB5fl9PA2hXdXh8fiprNLpNAd4Sg2zsq9E/yTnHUGgk44tJxotEOoEn0GDVw/r1rMT3AkKUNbnVfSgD8ppTWw9C02K1kYiZpwuHO3BMcvYuQsmhYmm7/xViMVgIcrKQzV3pk6coXroNpqjgzOUe/7eet+PkY39xiDYJKLZ5Rg4U3ri22OmDd4sAaSGNeraTCEREmS44Tn/4VgUTbM5ekPeFHCv3XcgG3IIL4pIl+7rjJKQEgFv8VV9yHcy0X27AUu6jCJI6TU8sr1iYFog/3Z52c[/tex][tex=8.143x2.786]CMIhUyI8bpw2/d9UIDux4quUaLRox1uY07jn5YG744Dvmnkn8/4SFPNIw9sWyOAHH4UuaI6gqbCxuyfvoVEbKeZWEVqRR42+xm2QJwsDSXuVbmIz4XNnSTmQAQH/wb1+1DhLTktK2rU7FKrMQbLzzFJeIGJCKN1/p/sqQCFtHA0=[/tex];[tex=7.429x1.429]OQvtBJ+gRZoy0iEdxSAdYhajGoX3+Ju3OUG3KyTI5atazCDIdmBsNAydYbNxN2Y//Mn66W2jOJ4nx38qAz3wkv9WFAm/ZugP/X6qeDjT0TDLgCOlRIS8AQ8NS9kPcul9[/tex][tex=30.714x2.929]MQCrta+if/82r87YQV4KqCbXWolfZi+JXEA6F5WCo7JKFFgqIreP6tXOELKjYQYD+IHZGBkz9Yn/7ofqy4GJPLETM0E+jIV6vsxSJDuE/g2Sd/XdEl+SPYQMJoFf987LjODOkYB/Ebt/AN+tJ5B9Xlg12443zToJj6ZzZAq8L/86vkUA2Izwv5dkKh1NDI68SzMAOXuf7JRf5vvQMKscqcjECZ4r5fN3AncmUuEjob5DUzNJBEYuagwJadRvzVt5oOs7sp85xY9DBH8Jd8eFw1f/nk8EQma+GwOxchf/lCB26rAoZ8qZ9Lk8UMxPtpW7GyUaOZTprZwXJbIvqKdXiVdsFUguqkg+6oYBlJQy/BYmvYDdKzyPkb8kLqkqzj5yIBbpWkNATsqR0YVA9Cm5KbAW+z63MAWyQp8OUHOmHEO/oBIYN0UPl6RAOpMg5/vFM+x8K10tDRvXyydLeMqv4iP45rLLraFtLLvzJKwocZA=[/tex][tex=8.429x2.786]CMIhUyI8bpw2/d9UIDux4opuHDRyNtvT4mcLPeVSNiKxz8L2JxmnjtWV6SRPEwk9A+wrF7UkJtGX0Rw3SwmLaDSZrMuPcnvs5zPG8XzBQz51P8eWjbI6BUdhubJlcRP5BbE0p2fgoVojYvox/jyCXH74Q3FIRYJDy9XBTkZLrmo=[/tex](8)作弯矩图作弯矩图时需注意内力符号的规定，本章规定杆端弯矩绕杆端逆时针转为正，弯矩图要画在杆件受拉侧。作出的弯矩图如图 (c)所示。[img=582x182]17a04aaff08c5fb.png[/img]