三铰拱结构设计（26页）PPT

1、第四章 Chapter IV,铰 拱 Three-hinged arches,拱 (arches) 一、简介Introduction,曲梁curved beam,杆轴线为曲线在竖向荷载作用下不 产生水平反力。 The centroidal axis of an arch is a curved line. Horizontal thrusts wont be developed at the supports under the action of vertical loads,FP,三铰拱 Three-hinged arch,拱-杆轴线为曲线，在竖向荷载作用下会产生 水平推力的结构。 The

2、 centroidal axis of an arch is a curved line. Horizontal thrusts will be developed at the supports under the action of vertical loads,拱的有关名称,跨度span,拱趾铰 Foot support,拱趾铰 Foot support,顶铰top hinge,矢高rise,斜拱inclined arch,拉杆拱 Tied arch,平拱horizontal arch,三铰拱Three-hinged arch,两铰拱two- hinged arch,无铰拱nonhing

3、ed arch,静定拱statically determinate arch,超静定拱statically indeterminate arch,超静定拱statically indeterminate arch,二、三铰拱的解法 calculation method,FAH,FBH,FAy0,FBy0,FBy=FBy0,FAy=FAy0,FH= MC0 / f,等代梁,请大家想：由上述公式 可得哪些结论,反力计算,列平衡方程可得 From equilibrium Equations we obtain,三铰拱的反力只与荷载及三个铰的位置有关，与拱轴线形状无关 The reactions ar

4、e related to the locations of the hinges and loads, but have no relationship with the form of the axial line of arch. 荷载与跨度一定时，水平推力与 矢高成反比 Given loads and span, thrust is inversely proportional to rise 1/f,等代梁,内力计算 the determination of internal forces,请大家对上述 公式进行分析,由于推力的存在，拱的弯矩比相应简支梁的弯矩要小。Because of

5、 the horizontal thrust, the moment of arch is less than that of the corresponding simple beam,三铰拱在竖向荷载作用下轴向受压.Under the action of vertical loads, the arch is axially compressed,Example. Construct the internal force diagrams of the following arch,Solution,截面2为集中力作用处，其两侧的剪力将发生突变,斜拱如何求解？How to solve th

6、e inclined arches,三、三铰拱的合理拱轴线 (Rational axial lines of arches,使拱在给定荷载下只产生轴力的拱轴线，被称 为与该荷载对应的合理拱轴。 Under the action of Stationary loads the axial line of an arch that will induce the bending moment on the sections to vanish is referred to as rational or optimal axial line or centre line of the arch,只限

7、于三铰平拱受竖向荷载作用。合理轴线 横截面上,在竖向荷载作用下，三铰拱的合理拱 轴线的纵坐标与相应简支梁弯矩图的 竖标成正比。Under the action of Vertical loads, the ordinates of optimal centre line is directly proportional to those of the bending moment diagram of the simple beam,试求图示对称三铰拱在均布荷载作用下的合理拱轴线 determine the rational axis of the arch under the action

8、of uniformly distributed load,MC0=ql2/8,FH=ql2/8f,M0=qlx/2-qx2 /2 =qx(l-x)/2,y=4fx(l-x)/l2,抛物线,试求三铰拱在垂直于拱轴线的均布荷载作用下的合理拱轴线。Find the optimal centre line of the arch under the the uniformly distributed load vertical to the centre line of the arch,返 章,园,所以拱的合理轴线为园,在同样荷载作用下铰的相互位置不同，其合理轴线也不同，这是因为支座反力不同。 R

9、ational axial lines of arches will not be the same if the positions of hinges are different even under the action of the same loads,左图顶铰位置不同，合理轴线不同,小 结Summary 1.三铰拱与粱的区别 The differences between three-hinged arches and beams 几何方面in geometry:几何形状不同the geometrical configuration is different 受力方面in stat

10、ic aspect:三铰拱脚有水平力horizontal thrust will be developed in supports； 2.水平推力依赖于何种因素The factors influencing horizontal thrust 三铰拱的反力只与荷载及三个铰的位置有关，与拱轴线形状无关 The reactions are related to the locations of the hinges, but have no relationship with the form of the axial line of arch. 荷载与跨度一定时，水平推力与 矢高成反比,3.内力

11、依赖于何种因素The factors influencing internal forces 三铰拱的内力不但与荷载及三个铰的位置有关，而且与拱轴线的形状有关。The internal forces are not only dependent of loads and the positions of hinges, but also of the form of centroidal axis . 4.粱与三铰拱内力分布的不同The difference of the internal force distribution in beams and three-hinged arches；

12、 由于推力的存在，拱的弯矩比相应简支梁的弯矩要小。Because of the horizontal thrust, the moment of arch is less than that of the corresponding simple beam. 三铰拱在竖向荷载作用下轴向受压.Under the action of vertical loads, the arch is axially compressed. 5.三铰拱的合理轴线Rational axial lines of arches,词汇Vocabulary,1.拱 (arches) 2.水平反力Horizontal thrusts 3.三铰拱 Three-