Chapter 6 Deflections of Beams梁变形.pptVIP

Chapter 6 Deflections of Beams梁的变形;Purpose of this chapter:;§1 Introduction 引言;? deflection curve 挠曲轴;? Deflection and slope 挠度与转角;§2 Differential equation of beam deflection 梁变形微分方程;Differential equation of deflection curve挠曲轴微分方程;? Approximate Differential equation of deflection curve挠曲轴近似微分方程;? Within linearly elastic range ;§3 Integration method to calculate deflections计算梁位移的积分法;Integration and boundary conditions of the differential equation挠曲轴微分方程的积分与边界条件;Pin or roller support(铰支座) : wC=0;? Integration method to calculate deflections of beam积分法求梁位移;? The constants of integration can be found by boundary conditions 利用边界条件确定积分常数;? Protraction of deflection curve 挠曲轴的绘制;? Examples 例题;求挠曲轴微分方程,列挠曲线的位移边界和连续条件;? Examples 例题;2. 确定积分常数;3. 截面 C 的挠度与转角;例：1.画剪力弯矩图 2.列挠曲线的位移和连续条件 3.画挠曲线大致形状(注明凹凸性与拐点);;§4 Macaulays method to calculate deflections计算梁位移的奇异函数法;? Singularity functions 奇异函数;? General equation of bending moment弯矩通用方程;? General equation of beam deflection梁位移通用方程;? 例题;2. 建立挠曲轴通用方程;例 4-2 计算截面 A 的挠度;例 4-3 建立通用挠曲轴微分方程，写出位移边界条件;§5 Method of superposition to calculate deflections计算梁位移的叠加法;? Method of superposition (I)叠加法;);? Method of superposition(II) 逐段变形效应叠加法;Known：EI=const常数;Known：EI=const常数;? 例题;例 6-8;例 求自由端位移d;?利用对称性求简支梁与悬臂梁的变形关系 ;;求C点挠度与转角 ;例: 求;用叠加法求AB梁上E处的挠度;刚化BC，CD为悬臂梁;Determine the slope and displacement of end D of the cantilevered beam subjected to two uniformly distributed loads. ;;位移与变形的相依关系 ;§6 Statically Indeterminate Beams静不定梁(超静定梁);Degree of statical indeterminacy and redundant confinement静不定度与多余约束;? Analytical method of simply statically indeterminate beams简单静不定梁分析方法;? 判断梁的静不定度;例 6-9 To find: Reactions;Discussion: ;例 6-11 直径为d 的圆截面梁,支座 B 下沉 d，smax=?;例 6-10 悬臂梁 AB，用短梁 DG 加固，试分析加固效果;例 试求杆 BC 的轴力;A;To find: deflection of point B(B点位移);习题6-24：已知弯曲刚度EI，梁单位长度重q，外伸长a,求拱起部分b。;§7 Stiffness analysis and design of beams梁的刚度条件与合理设计;? Stiffness analysis of beams梁的刚度条件;? Design of beams with consideration