[材料力学课件第十章压杆稳定.ppt

材料力学 （2）问题: 整个结构失稳是否与梁的弯曲刚度EI相关？ 答：无关。 F a a a l A B C D O1 O2 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例： 刚性桌面，大柔度柱EI 固连 求临界载荷Fcr。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解: 设 平面内失稳，长度因数 设立柱在 平面失稳， 故立柱在 平面失稳 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例： 上例将两立柱绕自身轴转90?安装， 求临界载荷Fcr。 故立柱在 平面失稳 解： 压杆在临界载荷较小平面内失稳。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例：求下列结构失稳临界载荷，OA，BC为大柔度杆， AB为刚性杆。 O A k l F EI (1) EI EI0 l O A B C F (2) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. O A k F ? k O A F 解（1）：（a）微干扰后，杆 OA 保持直线偏转 （b）微干扰后，杆OA变弯，A点水平位置不变 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. （b） 微干扰后，OA杆保持直线 偏转，A点水平位移 ? 解（2）:（a）微干扰后，OA杆弯曲失稳 EI EI0 l O A B C F (2) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例: 图示结构,AB 为刚性杆,BC 为弹性梁,在刚性杆顶端受铅垂载荷 F 作用,试确定临界载荷值.设BC抗弯刚度EI 为常数. F A B C a l Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 刚性杆微偏转时的临界状态 : F A B C Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 建立梁段的平衡方程 : 偏离力矩 恢复力矩 Me = M F M B C Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. §10-4 中、小柔度杆的临界应力 问题：欧拉公式适用范围？如何研究此范围之外的压杆的失效？ 欧拉公式一般表达式 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 一、 临界应力与柔度 ?l ——反映约束条件，与杆长度、约束条件有关， 与材料性质无关。 ——截面的惯性半径，只与截面形状相关。 ——压杆的柔度或长细比，无量