用积分法求下图所示梁得挠曲线方程及自由端得挠度和转角。设EI为常数。[p=align:center][img=346x133]17aa414556877e6.png[/img]
选取如图 [tex=1.714x1.357]pNF/M/+GMfTPpwPioTcGRtWOXMerIDMukQUSU9cvnMA=[/tex] 所示的坐标系。弯矩方程、挠曲线微分方程及其积分为A C 段[p=align:center][tex=23.929x3.357]jJaNDagHB00aCFtgCc+zxNcH4pbFKJw5a3SgLzhfJ2CdoFtzx1YElYKY8lcqYRbCradF5XjYA5oD+GCuA/V5P2sFNmnFtWGb+6o+CU4k5jQz6Cdheg0NqlBMXWWqBPPDh3by3PZjtTUheNSux+figHBQBvHAHveHZHroVQVNiZe7Zsy30hHAbjnAfWFE2VirYzIOZCG05cI+Z3YCc5+P+GRhUFlv9w6JA6guCouVSeOvL9ybdTLq6wjR9Oh9PpNd[/tex][p=align:center][tex=16.286x3.357]ND3iRy1ZEG/oHKJnFY0YnMcAj4X0tbNJfMpSDyQAzI9VRiiwHHbpDkXcbe2EUT8AWGCZZNQdUHa5ul4k7tADvOaNnH8/pcsxMtz2AHk0n+e8rz/PLarU99RO6a1jhqXu0idzq+wJF8/kWIr8dD655u67OiMaV45b9P1iyBea8Sw=[/tex][p=align:center][tex=16.714x2.929]ND3iRy1ZEG/oHKJnFY0YnHUqJY9GE8AbAU9MWLm2bMgkHV1B6FJuw1vycL9Xs3U6ej05CJERN3hkWgYOlwVo7DL+YqM1uicPtgto5uWCReVaxb8XQGxUdjn95M0g+5ZUaePxBUiywEf4tA1BoaEH1qmjLsMZHtk56tfyk8HQGXU=[/tex][p=align:center][tex=22.214x3.357]kAY1ExHd/6FFXrWdMvtvQSGC/IRBNEpPkLolthUypjOVGHpYX6kgM+qnCMV00PQovM4qoimENViBIU8TYUEk7A4Uoy31epc9/ojBL2SVzsp7Bc4J4YZWXiPYa7X4PnXTbesVjtFBvW2sLR9ITb6B33sGlpGL1+VYmbeFO+skGkkSTmpgv6CyYd6k5W7MIlGt[/tex]C B 段 [tex=18.0x2.786]ZjSM7me3EWPAO4KDzWOjkWqOIOnmBV8+4xjTfNV07e0tVzhaQVNUKj42T+TdNFQBdR5lgkwWiQ4aoU6YCFst/+a5xIovzurIJI9xVLBNsxii7dJSx3mrOz0nqKuPBxMQ6z4FihOgsuuwFq/HbosyYAWJG9GFC2Taqo7kPvrIf8g=[/tex][p=align:center][tex=8.714x2.357]DT13RsYLSxbIV2rhsx58CGYDpGfIaUysncMLJgDToayzbRUL8y70WcGr7GbnoqHzpuSrE5u0LDsGdjN/7pDDyBGtb+5LJ+/HmajmnipoC9k=[/tex][p=align:center][tex=10.143x2.357]DT13RsYLSxbIV2rhsx58CBrMU9hBKwE/h+XAep0RC4sEtRr7pIvb+3lS70W/5u4jP1bLmWE6yowxRFz12ZWBUrolnD9T3qJ2VOGRYwnJvio=[/tex][p=align:center][tex=14.357x2.357]gQs/FVtA0kny+F3MSUejPPRRvbk5pZ3lEVxF50MNyagHXUSLPlwZMyJ/s1grATzYWoAffx166JaCyjt3ngXJR7vszs2pTkE+ZDUQ+qNcmbc=[/tex]由边界条件和连续性条件确定积分常数:由 [tex=4.929x1.429]WC+iBY7Ik1qzn3RmoNS1w78vkToXdix7bc6kZ9+jmIo=[/tex], 得 [tex=6.357x2.357]Yr+E8Qs0anvhUzVA8/Otb7w63nI058GcfD67K6BNjhpQDZ2l6W/1d7KdPdtRHuJR[/tex][br][/br]由 [tex=5.0x1.214]9sOHQN0e+5ixjmRLUqFmTUZxBhPiLkLqYStGFl0d9vo=[/tex], 得 [tex=6.214x2.357]OMqCGtgNCaHGSNyDDb7sufA5SXTKMETAZV9mO7Dejv2RxB4XU8P32R0FfkRyqHrk[/tex]由 [tex=7.643x2.429]ujY5uIsUXz57CzGo/etYGK69oyHlfT+lQwd7vlrcVKrBoBBeO8D6ZF006iPbzTG2501EvbX+rzRfjKMMqvVaTw==[/tex], 得 [tex=6.357x2.357]xRuAPmjag6en8thBWtvx2rZ6dXqS9V13zcPXLFpbCjDJo+sekq8R+AcEIG4p74TJ[/tex] 由[tex=7.857x2.429]ujY5uIsUXz57CzGo/etYGD0D3AsG4TxAzjN4Gr63Z0NUMzgqeHlfyGKegGi5z24X[/tex], 得 [tex=6.214x2.357]V7abJMb2tvCrWZBzzGaCsStYiKrdw9+AINg/qAPoMEzPf/wHNiF+GZfn/v3e763w[/tex]各段挠曲线方程和转角方桿[p=align:center][tex=24.929x15.643]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[/tex]自由端的挠度和转角[p=align:center][tex=23.571x2.5]c215sWa9HCEiK3hB4/70i+IejKXTtBA3TXkD5n8nRiZKOexKsLKiLjyai3biW4Wz9EjWe1ZMsXa+bNyhY5U42wN+VFnc/XBsNlcEnotQBEn0eFpYtUE/ddS+hy4SpWkpGwQM36zR9UeOc1fwtB6XYfKcGfg60Xou1CcTddqxiaEXpVwtIhnsS/mHFIYbpFm97f8Yl7Asaw4uBkoPHV3/v929ExHOGIqPuJonasSIXTm1qYqewBFtbF9TBYcR94Lv[/tex][p=align:center][img=418x175]17aa417f7c65926.png[/img]
举一反三
- 用积分法求下图所示各梁得挠曲线方程、端截面转角[tex=1.0x1.214]p6BR3A6t1+Yf6pbN+g9hHQ==[/tex] 和 [tex=1.0x1.214]SbhUNMPFi/QvYVXqMn7vjA==[/tex]、跨度中点的挠度和最大挠度。设EI为常量。[p=align:center][img=361x115]17aa4871f00f20e.png[/img]
- 用积分法求下图所示各梁得挠曲线方程、端截面转角[tex=1.0x1.214]p6BR3A6t1+Yf6pbN+g9hHQ==[/tex] 和 [tex=1.0x1.214]SbhUNMPFi/QvYVXqMn7vjA==[/tex]、跨度中点的挠度和最大挠度。设EI为常量。[p=align:center][img=337x130]17aa43fad972cc4.png[/img][br][/br]
- 用积分法求下图所示各梁得挠曲线方程、端截面转角[tex=1.0x1.214]p6BR3A6t1+Yf6pbN+g9hHQ==[/tex] 和 [tex=1.0x1.214]SbhUNMPFi/QvYVXqMn7vjA==[/tex]、跨度中点的挠度和最大挠度。设EI为常量。
- 求图所示超静定梁。设EI为常数[p=align:center][img=358x139]17af28d86d68237.png[/img]
- 作下图所示各梁的剪力图和弯矩图。设EI=常数。[p=align:center][img=316x151]17b0b0a99d7cd52.png[/img]
内容
- 0
求下图所示纵横弯曲问题的最大挠度及弯矩。设杆件的抗弯刚度EI为已知。[p=align:center][img=334x129]17ac357dd9ede3f.png[/img]
- 1
图示各梁,抗弯刚度EI为常量,试利用积分法求自由端的挠度与转角。[img=585x316]179e99ec10e4268.png[/img]
- 2
积分法求梁的挠度、转角方程时,用边界条件、连续条件确定积分常数。
- 3
作下图所示各梁的剪力图和弯矩图。求出最大剪力和最大弯矩。[p=align:center][img=346x133]17a7bd11e60fcc2.png[/img]
- 4
试用积分法求图示各梁的挠曲线方程、转角方程、最大挠度和最大转角。梁的抗弯刚度 [tex=1.071x1.0]d8Cds5UqM8uqH8U+QXpHKg==[/tex] 为常数。[img=465x190]17a676b86994716.png[/img]