Modified Moment Distribution Method: Rapid Convergence Technique

ABSTRACT This paper introduces a modified version of the Moment Distribution Method (MMDM), aimed at significantly improving the convergence speed and computational efficiency in structural analysis. The Moment Distribution Method (MDM), a classical technique widely used in structural engineering for analyzing indeterminate structures, iteratively redistributes fixed‐end moments (FEMs) based on the stiffness of the structural elements. While effective, the traditional MDM suffers from slow convergence and high computational cost, particularly in large‐scale structures. The proposed method extends the concept of moment redistribution by employing generalized substructures, allowing for simultaneous redistribution across multiple nodes, thus accelerating convergence and reducing computational effort. This modification substantially enhances the accuracy and speed of the MDM, enabling rapid solutions for complex structures that would otherwise require time‐consuming manual calculations. The improvements presented in MMDM not only enhance the efficiency of structural analysis but also signify a conceptual and practical shift in the teaching and learning of this method. As MDM is widely used as an educational tool in structural engineering programs worldwide, these modifications have the potential to transform the pedagogical approach, offering students and instructors a more effective and faster way to analyze structural systems. Comparative studies with the conventional MDM and the widely used SAP2000 software demonstrate that the MMDM achieves faster convergence with fewer iterations, while maintaining high accuracy. This paper highlights the potential of MMDM in addressing the computational challenges associated with large‐scale structural analysis, offering an efficient and practical alternative to traditional methods. The results indicate that the proposed method can reduce both computational time and error in solving large indeterminate structures, thereby advancing the state of the art in structural analysis techniques and transforming the educational process for future engineers.