Energy Methods
The load-displacement relationship of an assembly of axial members (e.g., a truss) can be found using energy methods. The external work done by the applied force F is set equal to the internal elastic strain energy.
The work done by applied force F displacing by d is :
The internal forces (Pi) can be found in terms of the applied external force (F) using equilibrium. When the system is statically indeterminate, compatibility is generally used to determine the elongation of each axial member in the system (Di) in terms of the movement in the direction of the force d.
The internal elastic strain energy stored in one member is:
so the total elastic strain energy in the system is :
By setting the work W done to the energy stored U, movement d (or force F) can be determined:
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