This article is concerned with the analysis of continuous beams under static loading by the Boundary Element Method. The problem can be governed by the Euler–Bernoulli theory, also called classical beam theory, or by the Timoshenko theory; consequently, two different formulations arise. In order to obtain the analytical solutions for the Timoshenko continuous beams, an equivalent version of the three moments equation is presented. Two examples are included: the first consists of a two-span beam; the second, of a three-span beam. The results for the displacement, rotation, bending moment and shear force are always compared with the corresponding analytical solutions.

中文翻译：

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应用于欧拉-伯努利和铁木辛哥连续梁分析的边界元方法

本文涉及用边界元法分析静载荷下的连续梁。这个问题可以由欧拉-伯努利理论（也称为经典梁理论）或铁木辛哥理论来解决；因此，出现了两种不同的表述。为了获得 Timoshenko 连续梁的解析解，提出了三矩方程的等效版本。包括两个例子：第一个由两跨梁组成；第二，三跨梁。位移、旋转、弯矩和剪力的结果总是与相应的解析解进行比较。