用弯矩分量求三次样条插值函数的弯矩

The moment component for moment of cubic spline interpolation function

根据参考弯矩图解法原理,将相邻节点函数差和节点函数的导数变换为侧移分量和转角分量.利用各区间转角分量、侧移分量与函数的二阶导数形成弯矩-位移方程,以及连续梁支座相邻两跨转角方程,结合连续梁弯矩图的性质分析样条插值函数,做参考弯矩图;由此得到三次样条插值函数的支座弯矩.通过算例说明未知量参考弯矩图、荷载参考弯矩图、转角分量图和侧移分量图的使用方法.

According to theory ofreference bending moment, thedifferenceoffunctionatpointbetweenneighborpoints and derivative of function at node are translated into sideway component and angle component. The sideway component, angle component and the second derivative of the function assemble moment-deflection formula in each section. The mo- ment-deflection formula and the comer equation between adjacent span on continuous beam combined with reference ben- ding moment diagram are used for solving Cubic Spline Interpolation function. The example in article illustrates using methods of the load reference bending moment diagram, the unknown reference bending moment, the sideway component and the angle component diagram for solving.