Beam Deflection | Double Integration Method Step-by-Step | Cantilever with Partial UDL example

Learn how to calculate beam slope and deflection using the double integration method for a cantilever beam carrying a partial uniformly distributed load (UDL). 📐🏗️ In this tutorial, we work step-by-step through a beam where the loading only covers part of the span. This requires a piecewise analysis, where separate bending moment, slope, and deflection equations must be derived for different regions of the beam. The example demonstrates how discontinuous loading changes the mathematical formulation and how boundary conditions and continuity conditions are applied to solve for the constants of integration. 📌 In this tutorial, we: ✅ Sketch the expected elastic curve for a cantilever beam ✅ Divide the beam into regions due to the partial loading ✅ Derive bending moment expressions for each region ✅ Apply the double integration method to obtain slope and deflection equations ✅ Apply boundary conditions at the fixed support ✅ Apply continuity of slope and deflection between regions ✅ Determine the slope and displacement at the transition point This example is ideal for students who want to build confidence solving piecewise beam deflection problems, especially where loading does not extend over the full span. 👷‍♀️ Delivered by Dr Margi Vilnay – Senior Lecturer in Structural Engineering, Chartered Engineer, and Senior Fellow of the Higher Education Academy. 🔎 Want the full learning experience? 📚 Check out the complete Beam Deflection playlist: https://bit.ly/49Ai2BD 👉 Subscribe for more tutorials like this! #BeamDeflection #DoubleIntegration #CantileverBeam #PartialUDL #StructuralEngineering #EngineeringMechanics #CivilEngineering #EngineeringStudents #EngineeringTutorial #EngineeringEducation #EngineeringTheCurriculum