Abstract

Mathematical models are presented for calculating the stress–strain state (SSS) of structures under seismic impacts. The general mathematical formulation for determining the SSS is considered. For linear models, two methods are presented for calculating the SSS characteristics by decomposition of the eigenvectors: a method that integrates the time equations for given accelerograms of the base and a method that uses standard seismic spectra. In calculating seismic spectra, various methods for summing the tones of oscillations of structures are proposed to evaluate the structural response. In order to assess the forces and moments of interaction between a structure and the foundation supports and to test the calculation programs, mathematical models of structures are presented in the form of simple mechanical analogs: angular oscillators. These calculation methods take into account building code requirements and have been adapted to modern software packages that use the finite element method.

中文翻译：

---

估算建筑结构的地震荷载

摘要

提出了用于计算地震作用下结构的应力-应变状态（SSS）的数学模型。考虑用于确定SSS的通用数学公式。对于线性模型，提出了两种通过特征向量分解来计算SSS特性的方法：一种将给定加速度图的时间方程式积分的方法，另一种是使用标准地震谱的方法。在计算地震频谱时，提出了各种方法来对结构振动的音调求和，以评估结构响应。为了评估结构与基础支座之间相互作用的力和力矩并测试计算程序，以简单的机械类似物（即角振子）的形式给出了结构的数学模型。