Fundamental Systems: Displacement Calculations in Structural Analysis

This lecture discusses the fundamental system in structural analysis, focusing on the essential definitions and calculations of displacements associated with unknown forces. The instructor explains that the fundamental system is the initial structure made isostatic by allowing all freedoms under kinematic conditions without external loads. The lecture emphasizes the importance of accurately defining the fundamental system, especially when dealing with complex structures involving springs. The calculation of displacements A0 and A1 is detailed, where A0 represents the displacement under external loads when the unknown variable x equals zero, and A1 represents the displacement when x equals one. The instructor illustrates how to calculate these displacements using the virtual work theorem and the integral of real moments. The significance of signs in displacement calculations is also highlighted, ensuring clarity in determining the direction of forces and reactions. The lecture concludes with a systematic approach to resolving the final system of equations to find the unknowns in structural analysis.