No abstract

An RC frame school building was designed with lower fortification requirements than required. It collapsed in the 2008 Ms8.0 Wenchuan earthquake. This study evaluated the building’s deficiency and practiced a retrofit design based on traditional demand-capacity method but with a displacement-based (DB) procedure, in which target capacities were obtained from the equivalent single-degree-of-freedom (ESDOF) systems defined by target mode shapes of the MDOF system, and shear demands were assessed using an R- μ- T relationship to match different capacity levels. To make the DB procedure code-conforming, the retrofitting elements (BRBs) were simplified as bi-linear elements, with the two-phase parameters corresponding to the code’s two-stage requirements. Shear distribution to the MDOF building was also determined by displacement shapes. BRBs’ stiffness demands and sizes were from the difference of the required and available shear resistances. The effectiveness of the method was validated by time history analyses. Different earthquake level simulations showed that, the method realized the design goals but did not lead to over-retrofitting; the BRBs took most of the shear demand but would not induce other unexpected failures. So the method was suitable for retrofitting similar structures.

The difficulty in curved bridge design lies in the eccentricity. Eccentricities break the regularity and make it difficult to resist horizontal loads. However, relatively stable and robust performance can still be achieved through properly aligned eccentricity. This paper used the controllability-related concepts, the controllability Grammians and Hankel singular values (HSVs), to study the impact of eccentricities on the seismic performance of curved bridges. An analytical model was expressed by second order differential equations with rigid deck assumption. Six eccentricity cases: three different radii (resulting in different center of mass (CM)), three different bearing arrangements (resulting in different center of stiffness (CS)), and variable earthquake directions (resulting in different moment arms) were strategized for research. Analyses showed that effects of eccentricities (offsets of CS from CM) can be extensively interpreted by controllability indices. Proper eccentricity may “reach” and thus “control” the responses better and decrease the coupling effects, counteract the unfavorable excitation effects, and make the bridge less sensitive to excitation changes. In this sense, regularity or stability could be somewhat re-established through design. Time history analyses confirmed the results.

This study proposes a new arrangement-tuning method to maximize the potential of tuned mass dampers (TMDs) in decreasing the seismic responses of tall buildings. The method relies on a Grammian-based entropy index with the physical meaning of covariance responses to white noise without the involvement of external inputs. A twelve-story RC frame-shear wall building was used as an example to illustrate the method. Indices were computed for the building with TMDs placed on different stories and tuning to different modes and were compared with responses to white noise (colored) time histories. Results showed that greater index reduction cases agree well with greater story-drift reductions cases, despite the differences in the time step of the white noises and structural model types (pure shear vs. shear-bending), and the optimal TMD is not necessarily the traditional “roof—1st mode tuning” case. Comparisons were also made for the shear-bending building under seven earthquake excitations. It is found that, though TMDs are not full-band effective controllers, the index-selected TMDs still perform the best in three out of seven earthquakes. So, the proposed internal-property-based entropy index provides a good controller design for large-scale structures under unpredictable none-stationary excitations.