# 3-D LUMPED MASS METHOD OF DYNAMIC ANALYSIS FOR HIGH-RISE BUILDING

### ZORIGT TUMURBAATAR, HARUYUKI YAMAMOTO

This study is related to decreasing size of stiffness matrix of high-rise building by using floor diaphragm constraints. The combined actions of horizontal structural members such as slab and beams produce structural response that is much stiffer than vertical elements such as columns. In structural analysis of high-rise building model, absolute rigid slab and vertical structure are working together for lumped mass method. Each lumped mass node has 6 degree of freedoms which is very suitable for high-rise building calculation. The lumped mass is consisted of slab and beams, on the other hand the system’s stiffness matrix is only assembly of columns and braces. High-rise building lumped mass model’s stiffness matrix size is n=6 x m (n; total size of stiffness matrix, m; total floor number). In the step by step calculation, total unknown number is decrease enough which means we can easily calculate high-rise building structures for dynamic analysis also nonlinear step by step calculation using simple personal computer. If building model has large span and short height, in this case rigid slab theory will not satisfied. This idea is more suitable for high-rise building calculation.

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