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Exact closed-form equations for internal forces functions of bridge-type structures
Mahmoud-Reza Hosseini-Tabatabaei,Mahmoud Reza Mollaeinia 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.80 No.2
Influence lines and internal forces functions are vital tools for designing and monitoring engineering structures. This research explored a static method to derive exact closed-form equations for internal forces functions of bridge-type structures, continuous beams, and bridge frames, considering the bending flexibility. For this aim, first, we achieved member-end moment functions by applying the moment-rotation relationships in conjunction with the rotation propagation method. Then, substituting these functions into the static equilibrium equations provided the desired functions in terms of both the unit load and intended cross-section positions all over the structure, subjected to concentrated loads. Finally, the authors solved three illustrative examples to clarify the dominance of their suggested method for constructing both influence line and internal forces diagrams of statically indeterminate structures.
Bridge-type structures analysis using RMP concept considering shear and bending flexibility
Mahmoud-Reza Hosseini-Tabatabaei,Mohmmad Rezaiee-Pajand,Mahmoud R. Mollaeinia 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.74 No.2
Researchers have elaborated several accurate methods to calculate member-end rotations or moments, directly, for bridge-type structures. Recently, the concept of rotation and moment propagation (RMP) has been presented considering bending flexibility, only. Through which, in spite of moment distribution method, all joints are free resulting in rotation and moment emit throughout the structure similar to wave motion. This paper proposes a new set of closed-form equations to calculate member-end rotation or moment, directly, comprising both shear and bending flexibility. Furthermore, the authors program the algorithm of Timoshenko beam theory cooperated with the finite element. Several numerical examples, conducted on the procedures, show that the method is superior in not only the dominant algorithm but also the preciseness of results.