Abstract
Trusses are among the basic components of large-span bridges and large-space structures. A method is proposed to conduct a comprehensive deformation analysis of a truss in terms of the basic rigid body displacements and the tension and compression deformation based on complete mathematical orthogonality and mechanical equilibrium. The correctness of the proposed method is verified by comparison with a traditional strain analysis. Furthermore, a relative deformation decomposition of the mode shape is proposed to analyse in detail its relative displacement and deformation. The correctness and superiority of the proposed method are verified by comparison with the modal mass participation coefficient method and the animation from observation method. Additionally, the relative deformation decomposition of a plane truss structure is realized under any load conditions based on the superposition of mode shapes. The quantitative analysis of the basic deformation performance of a plane truss structure can also be conducted by countable mode shapes, which do not involve load conditions. Finally, the number of mode shapes that must be considered differs when using the maximum displacement and the tension and compression deformation analysis indicators.
Highlights
A method is proposed to conduct a comprehensive deformation analysis of a truss in terms of the basic rigid body displacements and the tension and compression deformation based on complete mathematical orthogonality and mechanical equilibrium
The relative error in the maximum relative tension and compression deformation of the rod element is less than 5% considering the superposition of the first five mode shapes under the N-H wave, and the relative error is less than 5%
When the acceleration response is maximum under the N-H wave, the relative error of the maximum displacement of the node is less than 5% considering the superposition of the first four mode shapes, and the relative error of the maximum tension and compression deformation of the rod element is less than 5% considering the superposition of the first five mode shapes
Summary
The rod element is the basic element of truss, and rotations are permitted at ends 1 and 2 such that the rod element is subjected only to axial force [33]
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