Beam Deflection: Integrating Loads to Deformation

This lecture delves into how reaction forces deform beams, transitioning from load equations to final beam shapes through integration methods. The instructor highlights the versatility of beam deflection in measuring forces, introducing atomic force microscopy applications in nanoscale biology. The lecture covers the derivation of differential equations linking loads, shears, moments, angles, and deflections, emphasizing the importance of boundary conditions in solving beam deflection problems. The superposition principle is introduced as an alternative method to solve complex loading situations. A practical example involving thermal expansion in a constrained system is presented, showcasing the application of stiffness calculations and stress analysis in determining maximum stress points in beams.