The force method algorithm in the form of a loop resultant method
https://doi.org/10.33979/2073-7416-2024-114-4-42-55
Abstract
The object of research is the behavior of statically indeterminate frames under the influence of temperature. The purpose of this work is to suggest a simple algorithm for the analysis of framed structures by using the original idea of the loop resultant method. This basic loop is generated by splitting the given structure into statically indeterminate loops instead of the conventional approach of treating the redundant forces in the whole structure. The current approach allows to simplify the calculation, thanks for using the loop compatibility conditions and by dealing with the primary unknowns for each basic loop. The advantage of this presented approach is in simple structure of a system flexibility matrix: the location of zero and non-zero blocks depend only on the numbering of loops. Different types of flexibility matrices of the element-rods are established; it is shown how to build the compatibility matrix for any loops with or without hinges; and the simple algorithm of the loop resultant method is developed. Some numerical examples are performed to describe the presented algorithm in more detail.
About the Authors
V. V. Lalin
Peter the Great Saint Petersburg Polytechnic University
Russian Federation
Russian Federation
Vladimir Vladimirovich L., doctor of technical sciences, professor of the Higher School of Industrial, Civil and Road Construction of the Institute of Civil Engineering
Saint Petersburg
I. I. Lalina
Peter the Great Saint Petersburg Polytechnic University
Russian Federation
Russian Federation
Irina Igorevna L., senior lecturer of the Higher School of Industrial, Civil and Road Construction of the Institute of Civil Engineering
Saint Petersburg
H. H. Ngo
Peter the Great Saint Petersburg Polytechnic University
Russian Federation
Russian Federation
Huu Hieu N., post-graduate student of the Higher School of Industrial, Civil and Road Construction of the Institute of Civil Engineering
Saint Petersburg
T. M. D. Le
University of Science and Technology - The University of Da Nang (DUT-UD)
Viet Nam
Viet Nam
Tran Minh Dat L., PhD of the department of Hydraulic Structures Construction
Danang
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Review
For citations:
Lalin V.V., Lalina I.I., Ngo H.H., Le T. The force method algorithm in the form of a loop resultant method. Building and Reconstruction. 2024;(4):42-55. https://doi.org/10.33979/2073-7416-2024-114-4-42-55
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