(2011), "Shear and bending flexibility in closed-form moment solutions for continuous beams and bridge structures", Eng. (2009), "Closed-form moment solution for continuous beams and bridge structures", Eng. (2002), "Kinematic method for constructing influence line and theorem of reciprocal reactiondisplacement", Mech. (2003), The Influence Line Approach to the Analysis of Rigid Frames, Kluwer Academic Publishers, New York, USA. (1997), "Basic influence line equations of continuous beams and rigid frames", J. (2005), Structural Analysis, 2nd Edition, Vikas Publishing House, New Delhi, India. Finally, three representative examples for constructing force influence lines of statically indeterminate beams and frame illustrate the superiority of the proposed method. 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. 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. 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. 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. Constructing the influence lines of forces of statically indeterminate structures is a traditional issue in structural engineering and mechanics.
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