DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Mathematical calculation model for geometrical parameters of timber mesh design with orthogonal grid

Вестник МГСУ 12/2014
  • Loktev Dmitriy Aleksandrovich - Siberian Federal University (SibFU) engineer, Department of Building Structures and Control Systems, Civil Engineering Institute, Siberian Federal University (SibFU), 79 pr. Svobodnyy, Krasnoyarsk, 660041, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Inzhutov Ivan Semenovich - Siberian Federal University (SibFU) Doctor of Technical Sciences, Professor, Department of Building Structures and Control Systems, Director, Civil Engineering Institute, Siberian Federal University (SibFU), 79 pr. Svobodnyy, Krasnoyarsk, 660041, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Lyakh Nikolay Ivanovich - Siberian Federal University (SibFU) Candidate of Technical Sciences, Associate Professor, Department of Building Structures and Control Systems, Civil Engineering Institute, Siberian Federal University (SibFU), 79 pr. Svobodnyy, Krasnoyarsk, 660041, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Zhadanov Viktor Ivanovich - Orenburg State University” (OSU) Doctor of Technical Sciences, Professor, Chair, Department of Building Structures, Orenburg State University” (OSU), 13 prospekt Pobedy, Orenburg, 460018, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Ermolin Vladimir Nikolaevich - Siberian State Technological University (SibGTU) Doctor of Technical Sciences, Professor, Chair, Department of Composite Materials Technology and Wood Science, Siberian State Technological University (SibGTU), 82 prospect Mira, Krasnoyarsk, 660049, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 60-69

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.

DOI: 10.22227/1997-0935.2014.12.60-69

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