A new seismic structural design methodology which is based on optimal control theory is developed for inelastic shear buildings. The methodology is aimed at minimizing the maximum absolute accelerations by changing the floor masses and horizontal story stiffnesses only. The design approach utilizes a modified H ∞ -synthesis algorithm tailored to structural design variables and uniquely adapted to a closed-loop system of structured controller. This resembles to minimizing the Square Root of the Sum of the Squares (SRSS) of the Magnitude of Absolute Acceleration Gains (MAAGs), while subjected to dynamic equilibrium and structural constraints. The free-parameter of the structured controller (i.e., design variables) are the floor and roof masses and horizontal story stiffnesses. The modified H ∞ -synthesis algorithm addresses linear systems, but when inelastic shear buildings are concerned the methodology resorts to the two newly developed iterative equivalent linearization procedures. The first procedure, referred to as the inelastic-to-elastic procedure, employs the direct-displacement-based-design (DDBD) approach in calculating the effective story stiffness coefficients of an equivalent linearly-elastic building. The second procedure, referred to as the elastic-to-inelastic procedure, reverses the DDBD approach and transforms the linearly-elastic building (after being upgraded by the modified H∞-synthesis) back into the redesigned inelastic building. A five-story inelastic shear building is analyzed and redesigned in the case-study of this paper. The H ∞ -synthesis solution is thoroughly examined concerning changing the algorithm variables, and the two DDBD based procedures are tested regarding peak response and modal properties. The redesigned building shows significant improvement in absolute story accelerations. The design methodology developed achieves optimal changes that depend on the assigned side-constraints only in four distinct steps. This in itself is a novel approach to the utilization of H ∞ based algorithms.
ASJC Scopus subject areas
- Civil and Structural Engineering