【2017年整理】材料力学9.ppt

第九章 压杆稳定 压杆稳定的概念 两端铰支细长压杆的临界压力 其他支座条件下细长压杆的临界压力 欧拉公式的适用范围 经验公式 压杆的稳定校核 提高压杆稳定性的措施 * 纵横弯曲的概念 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. §9.1 压杆稳定的概念 平衡的稳定性 a）稳定平衡 b）随遇平衡 c）不稳平衡 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2. 弹性平衡的稳定性： 弹性体保持初始平衡状态的能力。 本课程只讨论压杆的稳定性 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. §9.2 两端铰支细长压杆的临界压力 临界压力：使压杆保持微弯平衡的最小压力。 M=-Fv 令： BC: x = 0, x = l 时 w = 0 B = 0 sinkl=0 ? kl = n? k = n?/l w l x y F F ―欧拉公式 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. §9.3 其他支座条件下细长压杆的临界压力 一端固定： y F x a BC：x = 0 时，w = 0 ? = 0 B=- a A = 0 x = l 时，w = a kl=(n+1/2)? 令： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2l ?=2 ?=1 ?=0.7 ?=0.5 0.5l 0.7l l F F F F ?=1 2. 长度系数? Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. F F F F F 1.5l 2l 4l 5l 3l ?l 3l 2l 2.8l 2.5l 1.5l (1) (2) (3) (4) (5) 截面材料相同，确定失稳次序。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 图示托架中AB杆的直径d=40mm,长度l=800mm，两端可视为铰支，材料为A3钢，E=200GPa, ?s=240MPa。试求托架的临界载荷Qcr 。 ?=1 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. §9.4 欧拉公式的适用范围 经验公式 欧拉公式的适用范围： ?：柔度（长细比）; ?1：是材料参数。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2. 临界应力总图 ?s ?p ?2 ?1 ? ?cr ?cr=a-b? ?cr=?s 局部削弱对稳定无影响！ Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0