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Deflections using Energy Methods - Purdue University

Deflections using Energy MethodsConservation of Work and EnergyWork done by external forces on a material point or a structure is converted to internal work and internal stored : ( spring )(Ref Chapter 9)Example: (Trusses)(for conservative systems)(for linearspring)There are multiple (infinitely many) "paths" that the external load can be applied along built up from 0 to P1, P2, P3(as long as all paths satisfy equilibrium at all points on each path).For conservative system of forces, total work done is path independent depends only on the initial and final : (for linear material behavior of truss elements) WorkEnergyMethods Page 1 Example: (Beams)(for linear moment0curvature relationship)Note: External work done by a single forceor a single momenton a linearsystem:Note: External Work done by a force or moment in the presence of another existing force or moment: WorkEnergyMethods Page 2 Internal strain0energy storedAxial(for truss members): Bending For General 3D problems:(for li)

Example : (Spring) (Ref Chapter 9) Example : (Trusses) (for conservative systems) (for linear spring) • There are multiple (infinitely many) "paths" that the external load can be applied along i.e. built up from 0 to P 1, P 2, P 3(as long as all paths …

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