A Closed-form solution to the buckling of cracked beams on elastic foundation using equivalent moment technique

Document Type : Original Research

Authors
T. Makaremi
V. Akrami
Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran
10.22034/25.2.101
Abstract
Beams placed on elastic foundations are widely used in simulating a main portion of mechanical and civil structures. The buckling behavior of these beams, including the load and the shape of the buckling mode, is different from normal beams due to the loads imposed by the elastic foundation that is proportional to the beam deflection. Due to their functional modality, these types of beams are generally subjected to repetitive loads (such as railway tracks) and extreme environmental conditions (such as piles and buried pipelines), making them susceptible to damage such as cracks. The presence of these flaws along the members can lead to premature failure of these structural elements due to buckling in the damaged area. Evaluating the stability of such structures considering structural flaws is essential for ensuring their safety. In this context, this paper presents a new method for calculating the closed-form solution to the buckling of cracked beams on elastic foundations. In the proposed method, a concentrated moment is used to model the crack and apply the slope difference caused by the crack at the damage location. Then, the governing differential equations for pin-ended beams are derived, and by using Fourier expansion and calculating the value of applied moment, a closed-form solution is presented to calculate the buckling of beams on elastic foundations. Using this technique for crack modeling makes it easier to solve beam differential equations and achieve a closed-form solution for calculating beam buckling load. Finally, the effects of different parameters such as the bending stiffness of the beam, length of the beam, crack depth, and stiffness of the bed on the buckling load of the beam can be studied. To verify the proposed solution, the results of solving closed-form equations are compared with the exact solutions of simplified problems and the results from finite element models, which confirms the accuracy of the performed calculations. As the current solutions to the buckling of cracked beams on an elastic foundation are mainly based on numerical or finite element methods, the presented closed-form solution in this study can significantly contribute to enhancing the accuracy and facility of calculations in the design and analysis process for such structures.

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Modares Civil Engineering journal
Volume 25, Issue 2 - Serial Number 82
May and June 2025
Pages 101-114