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Structural Engineering and Mechanics Volume 54, Number 4, May25 2015 , pages 793-807 DOI: https://doi.org/10.12989/sem.2015.54.4.793 |
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Direct kinematic method for exactly constructing influence lines of forces of statically indeterminate structures |
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Dixiong Yang, Guohai Chen and Zongliang Du
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| Abstract | ||
| Constructing the influence lines of forces of statically indeterminate structures is a traditional issue in structural engineering and mechanics. However, the existing kinematic method for establishing these force influence lines is an indirect or mixed approach by combining the force method with the theorem of reciprocal displacements, which is yet inconsistent with the kinematic method for statically determinate structure. This paper proposes the direct kinematic method in conjunction with the load-displacement differential relation for exactly constructing influence lines of reaction and internal forces of indeterminate structures. Firstly, through applying the principle of virtual displacement, the formula for influence lines of reaction and internal forces of indeterminate structure via direct kinematic method is derived based on the released structure. Then, a computational approach with a clear concept and unified procedure as well as wide applicability based on the load-displacement differential relation of beam is suggested to achieve conveniently the closed-form expression of force influence lines, and exactly draw them. Finally, three representative examples for constructing force influence lines of statically indeterminate beams and frame illustrate the superiority of the proposed method. | ||
| Key Words | ||
| statically indeterminate structure; influence lines of reaction and internal forces; closed-form solution; direct kinematic method; principle of virtual displacement | ||
| Address | ||
| Dixiong Yang: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China; State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi\'an University of Technology, Xi\'an 710048, China Guohai Chen and Zongliang Du: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China | ||