Solution of Internal Forces in Statically Indeterminate Structures Under Localized Distributed Moments

Classical methods for manually solving internal forces in statically indeterminate structures mainly include force and displacement methods. While the force method involves substantial work when solving the internal forces of structures with higher degrees of indeterminacy, the displacement method offers a fixed and easily understood approach. However, the displacement method requires prior knowledge of load constant formulas. Common methods for deriving load constant formulas include the force method, virtual beam method, and energy method. Nevertheless, deriving load constant formulas for localized distributed moments using these methods proves to be highly challenging. This study aims to derive load constant formulas for localized distributed moments. Firstly, the load constant formula for a single concentrated moment is derived using the formula for a single concentrated force. Then, the load constant formulas for localized uniform moments and localized linearly distributed moments are derived via the integral method, leveraging the load constant formula for a single concentrated moment. This approach addresses the problem of solving internal forces in statically indeterminate structures under distributed moments via the displacement method. Finally, the proposed approach is verified using three typical examples. The promotion of the research results in this article in teaching can deepen students' understanding of load constants and the displacement method, enrich teaching content, and have certain engineering applications and teaching practical significance.