The Similarity of Deformations in High-rise Buildings

摘要

For A column shape high-rise building which the shape and the structure of every layer are the same and the number of the story is more enough, Author proved that the interaction between the upper structure and the foundation can be estimated simply by means of chain model and the theory of matrix continued fraction. That is, the subsidence u_1 of the first story can be divided into many special patterns y_j. Namely it is u_1 = ∑a_jy_j. Every pattern obeys an index decay from story to story, or say, the subsidence of the i-th story will becomes u_i = ∑a_j d_j~(i-1) y_j(‖d_j‖ ＜ 1). The most patterns will be almost zero and only a pattern u_i ≈ a_1 d_1~(i-1) y_1(i＞＞1) after several stories in the most stories high enough, except the several stories very near the foundation. Here the y_j or d_j is just the eigenvectors or the eigenvalues of a matrix decided only by the structure of a standard layer respectively. The y_1 often takes the shape like a dish or a bowl. The phenomenon mentioned in this paper is well known by engineers, but the theory explanation is given up only in these years. This result will be commonly used in the urban constructions.