Optimization method for design of anti-torsion cross-sections of beams shaped like'T'

Abstract

The invention discloses an optimization method for design of anti-torsion cross-sections of beams shaped like 'T'. Potential energy and kinetic energy of torsional deformation of the beams shaped like'T'are firstly obtained in the optimization method. Control differential equations and natural boundary conditions of torsional vibration of the structures shaped like'T'are obtained by utilizing an energy variation method.A calculation formula ofnatural frequency of the simply-support beamsshaped like'T'is obtained on the basis of the processes above. Eventually frequency values of the torsional vibration of the beams shaped like'T' are regarded as judgment basis. The higher the natural frequency value is, the lower the potential energy of the torsional deformation of the structures will be and the more excellent the sizes of the anti-torsion cross-sections of the beams shaped like 'T' will be. And the effectiveness of theoptimization methodfor design of anti-torsion cross-sections of beams shaped like 'T' is further proved by statics analysis of the structures. Because mechanicalanalysis is accurate in the optimization method, anti-torsion performance of the optimized structures shaped like'T'becomes better. And beam cracking which happens due to torsion, stiffness degradation, buckling and other adverse diseases can be avoided. The optimization method for design of anti-torsion cross-sections of beams shaped like 'T' is clear in mechanics concept, simple in calculation and good in application value, which can provide theoretical and technical support for the anti-torsion design of civil engineering structure or mechanical engineering.

Description

technical field [0001] The invention relates to an optimization method for the torsional section design of a T-shaped beam, and belongs to the technical field of structural engineering. Background technique [0002] Due to the good mechanical properties of the T-shaped structure, it is widely used in small and medium-span bridges, building structures and mechanical engineering, but this type of structure will be affected by torsion under eccentric load or curved beam state. Therefore, the selection of its reasonable torsional section size will make the T-shaped structure have good mechanical properties, which can not only reduce the amount of structural materials and maintenance costs, but also further improve the durability of this type of engineering structure. Therefore, the invention in this aspect has certain theoretical significance and engineering practical value. [0003] At the present stage, under the torsion state, many T-shaped civil engineering structures or ma...

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Problems solved by technology

[0003] At the present stage, under the torsion state, many T-shaped civil engineering structures or machinery in operation have suffered serious diseases, such as the reduction of the rigidity of civil structures, cracking of flanges and webs, and buckling failure of T-shaped beams in mechanical engineering. will seriously threaten the safety of the overall structure

However, due to the limitations of relevant design theories, the optimization of the torsional section size of the T-shaped structure has not been studied in depth at this stage, which will lead to unreasonable design of the section size of the T-shaped beam

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