均布荷载作用下榫卯连接木梁的解析解

ANALYTICAL SOLUTION FOR MORTISE-TENON END WOODEN BEAM SUBJECTED TO UNIFORM LOAD

基于弹性力学的半逆解法,在均布荷载作用下的简支木梁、铰接木梁和固接木梁解答的基础之上,结合中国古建筑榫卯节点半刚性连接的特点,通过引入两个表示半刚性的参数,得到了榫卯连接木梁内应力分布的多项式解答。通过对一个随梁实例的计算,分析了两个半刚性参数对梁内应力分布的影响,又通过比较榫卯梁和简支梁、铰接梁及固接梁内应力分布的特点,发现剪应力对于木梁尤其是榫卯木梁的影响不能被忽略。该文最后指出,榫卯节点的刚度随荷载的增大是在不断变化的,并给出了变荷载作用下半刚性参数的确定方法。

In order to solve the stress distribution of mortise-tenon end wooden beams subjected to uniform loads in traditional Chinese architecture, the analytical solution for a simply supported wooden beam, hinged wooden beam and fixed-end wooden beam were first developed by employing the half-inverse method. Based on the above results, the stress distribution for mortise-tenon end wooden beams was derived by introducing two parameters characterizing the semi-rigid nature of the joints. These two parameters were analyzed later using a simple example to assess their influence on the distribution of bending stress within the beam. The stress distribution of mortise-tenon end beams was also compared with beams with other boundary conditions. Results show that the shear stress within the wooden beam, especially for beam in mortise-tenon end, should not be neglected. Lastly, it was pointed out that the stiffness of the mortise-tenon joint changes with increasing load and a method for determining semi-rigid parameters under this condition was given as well.