Application of an Energy Theorem to Derive a Scaling law for Structural Behaviors

A general procedure for deriving a scaling law for structural behaviors from a principle of conselation of energy was proposed. This method provides clear scaling results of a full-sized structure, since the whole members are scaled simultaneously rather than considered separately. The concept of this method is that a total potential energy of a similar scaled model has to be proportionate to that of a full-size structure and satisfy the principle of conservation of energy. An applicability of this procedure was demonstrated by deriving scaling factors for static deflection of a beam and plate under various load cases and support conditions. Moreover, the procedure was applied to a dynamic problem, i.e. the scaling factor for frequency response of a plate. All of the derived scaling factors were validated by comparing the scaling solutions of the prototype's behaviors using similitude theory to those computed from closed-form solutions. The derived scaling factors for all cases considered predict the exact results ofthe prototype's behaviors.