Capacity design and topology optimization of rocking spine systems for nonlinear earthquake response

Rocking spine systems are innovative earthquake-resistant structural systems that dampen seismic shaking through uplift at the base and confine damage to energy-dissipating fuses, thereby significantly reducing the potential of building downtime. Currently, United States building codes and standards provide very limited design guidelines for such systems. This thesis focuses on developing procedures and algorithms for design and optimization of rocking spine systems under nonlinear earthquake response. A new capacity design procedure, the modified modal superposition (MMS) method, is developed for the seismic design of rocking spine systems. The methodology uses an efficient elastic response spectrum analysis to approximate the nonlinear earthquake response through (1) modified boundary conditions to simulate rocking at maximum considered earthquake (MCE) level and (2) a first mode inelastic reduction factor. The methodology is extended to coupled and stacked rocking braced frames, as well as strongback systems, with various hysteretic and viscous dampers. Using nonlinear dynamic analyses on a set of seven archetype frames ranging from 6 to 18 stories, the MMS procedure is shown to accurately capture higher modes effects and estimate axial brace and column forces. A reliability analysis conducted supports applying a load amplification factor of 1.3 for scaling the MMS seismic forces to design the steel braced frame as force-controlled components. A new dynamic topology optimization methodology, called the sum of modal compliances (SMC), is introduced for seismic loading. Recently developed dynamic topology optimization procedures for linear elastic response in the frequency domain are compared and contrasted. The novel procedure is applied to the design of lateral bracing system of high-rise buildings for various earthquake hazards and yields important considerations of the influence of higher modes on the overall dynamic response of the system. The efficiency of the SMC optimization algorithm is demonstrated on a 3D high-rise building with over one million degrees of freedom. Using the modified modal superposition as inspiration, the dynamic topology optimization procedure is extended to design of the elastic spine in rocking braced frames for nonlinear earthquake response. The extruded optimized bracing pattern is compared to a conventional X-bracing system using nonlinear dynamic analyses. An optimization framework is proposed for selecting the number, location and properties of nonlinear dampers in stacked rocking systems, where the total overturning moment in the spine is minimized, subjected to interstory drift and hinge rotation constraints. A ground motion selection routine is developed to facilitate the optimization by estimating the median dynamic response under earthquakes. Algorithmic procedures are developed to solve the structural optimization problem using both modified sequential linear programming (SLP) method and particle swarm optimization (PSO). On a 20-story dual rocking hinge case study, the SLP algorithm is shown to converge to the optimum with less than 40 nonlinear dynamic analyses compared to over 4,000 for an exhaustive search. For a 20-story stacked rocking system with N arbitrary hinges, the SLP optimization yields three rocking joints, whereby the total overturning moment in the spine is reduced by half compared to the initial design, while maintaining drift limits below 2.5% at MCE level. Overall, this thesis introduces design and optimization procedures for both the rocking spine and nonlinear articulated hinges. This research project demonstrates the advantages of rocking spine systems for improved seismic performance and introduces novel optimization algorithms for structural design under earthquake loading

Advisor: Deierlein Gregory G. (Gregory Gerard)
Baker Jack W. 
Paulino G. H.