Analysis of Plane Multi-Span Frames with the Analytical Method of Force-Displacement Combination

Document Type : Article

Authors

Faculty of Engineering and Technology, University of Mazandaran, Mazandaran, Iran.

Abstract

This paper investigates the effectiveness of the mixed forced-displacement method for solving indeterminate plane frames that combine force and displacement relations based on the beam’s axial and bending deformation behavior simultaneously. In this method, the differential equations of all structural members are determined based on the general theory of the Bernoulli beam by considering the axial effects. In the following, with the help of an analytical solution and application of boundary conditions, the integral constants of the equations related to the uniaxial frames of the structure are obtained. For the effectiveness of the proposed method, three examples of common frames have been analyzed and validated with the finite element method. The results show that the answers determined by the two methods are completely consistent. One of the advantages of the combined displacement-force method is determining the parametric solution as well as the high accuracy of this method. In addition, it does not need post-processing to find the quantity of kinematic and static responses. Therefore, this method can be used as an alternative approach to the finite element method in solving multi-axial plane frames. Moreover, its capability to handle intricate loading and various boundary condition configurations highlights the method's efficiency. Furthermore, the method simplifies the simultaneous influences of material and geometric nonlinearities in the analysis process. Material nonlinearities, such as yielding and hardening, are accommodated by adjusting the stiffness matrix. In contrast, geometric nonlinearities arising from significant displacements are addressed through iterative updates of the displacement field until convergence is achieved. In summary, the mixed displacement-force method is a comprehensive and efficient tool for 2D frame analysis. The ability to provide accurate results without the need for complex numerical simulations increases the importance of this method in the range of structural analysis techniques. Future research efforts could examine developing the process to three-dimensional frames and investigating its application in the performance-based design and analysis areas.

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References

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