Перевод названия: Mathematical calculation model for geometrical parameters of timber mesh design with orthogonal grid
Тип публикации: статья из журнала
Год издания: 2014
Ключевые слова: деревянные сетчатые своды, геометрическая схема, timber mesh cover design, geometrical calculation, Geometric layout, geometrical parameters, Transcendental equation, mathematical model, Orthogonal grid, геометрический расчет, геометрические параметры, трансцендентные уравнения, математическая модель, ортогональная сетка
Аннотация: Разработаны математические модели в виде трансцендентных уравнений для поиска требуемых геометрических параметров деревянных сетчатых сводов с ортогональной сеткой. Полученные трансцендентные уравнения, являющиеся основой математической модели, описывают геометрические параметры любой марки свода с ортогональной сеткой при требуемыПоказать полностьюх исходных данных. Mesh cover design, a multi-element design, which ensures the correct geometrical arrangement of the elements, is a very important task. The purpose of the given article is the development of a mathematical model for selecting the geometric parameters of wooden arches with mesh orthogonal grid with different input data. In this article three variants of design were observed. The main differences between them are in the relative position of longitudinal and transverse components. When performing static calculations of such designs in order to achieve their subsequent correct assembly, the following location conditions were observed: all the items must strictly match with each other without a gap and without overlap. However, these conditions must be met for any ratio of height to the arch span, the number of longitudinal members and the thickness of longitudinal members. Inverse problems also take place. In this case, the geometric calculation is not possible to vary the cross-section elements, and the stress-strain state of the cover is provided by varying the pitch of the transverse arches of the elements, on which the geometric calculation has no influence. All this determines the need for universal mathematical models describing any geometrical parameter of the designs needed for their geometrical calculation. The basic approach for the development of such models is the use of the known trigonometric formulas, giving a complete description of the desired geometry of the arch. Finally three transcendental equations were obtained, the solution algorithm of which using Newton’s method is presented in the MathCAD. The complexity of solving such equations using the proposed algorithm in the MathCAD is reduced to a minimum.
Журнал: Вестник МГСУ
Выпуск журнала: № 12
Номера страниц: 60-69
ISSN журнала: 19970935
Место издания: Москва
Издатель: Федеральное государственное бюджетное образовательное учреждение высшего образования Национальный исследовательский Московский государственный строительный университет