Performance-Based Economical Seismic Design of Multistory Reinforced Concrete Frame Buildings and Reliability Assessment

As the next generation of seismic design methodology, performance-based seismic design (PBSD) method requires a structure satisfy multiple preselected performance levels under different hazard levels. Optimal PBSD methods provide different strategies to design the numerous variables, including strength, stiffness and ductility of each structural component. The overall goal of this study is to develop a new optimal PBSD method for multi-story RC moment frames. This method is capable of overcoming the deficiencies of existing optimal PBSD methods and can be implemented by the U.S. design practice. The proposed method minimizes construction cost and takes the limit of member plastic rotation and optionally inter-story drift as optimization constraints. Other seismic design requirements reflecting successful design practice are also incorporated. Simplification is made by reducing design variables into two, one for the overall system stiffness and the other for the overall system strength. The optimization contains two stages, the determination of feasible region boundary in normalized strength and stiffness domain and optimization in the material consumption domain. Capacity spectrum method, which jointly considers nonlinear static analysis and inelastic design spectrum, is used to estimate the global and local deformation demands at the peak dynamic response. The proposed optimization approach is applied to the design of a six-story four-bay reinforced concrete frame. The optimal design results indicate that 30% of needed flexural strength and 26% of the cross-sectional area can be reduced from the initial strength-based design of this prototype structure. Nonlinear time-history analyses are conducted on the optimized structure using ten historical ground motions scaled to represent three levels of seismic hazard. In general, the average peak dynamic response meets the target performance requirements under the three levels of seismic hazard. Structural reliability analyses are applied on the optimal structure, the original structure and other 26 structures with different overall system stiffness and strength. The effects on nonperformance probability are determined based on the nonperformance contours, which is generated based on the reliability analyses results of all the 28 structures. To ensure the probabilities of nonperformance due to either plastic hinge or inter-story drift rotation is lower than the limits of all three preselected performance levels, the prototype structure should be design based on the relative overall system stiffness larger than 0.84 and the relative overall system strength larger than 0.4. To ensure that the probabilities of nonperformance only due to plastic hinge is lower than the limits of all three preselected performance levels, the prototype structure should be design based on two cases of relative strength and relative stiffness: (1) the relative overall system stiffness is larger than 0.75 and the relative overall system strength is larger than 0.4, and (2) the relative overall system stiffness is larger than 0.65 and the relative overall system strength is larger than 0.45. To ensure that the probabilities of nonperformance only due to inter-story drift rotation is lower than the limits of all three preselected performance levels, a structure should be design based on the relative overall system stiffness larger than 0.85 and the relative overall system strength larger than 0.6

Frequency response of space-based interferometric gravitational-wave detectors

Gravitational waves are perturbations of the metric of space-time. Six polarizations are possible, although general relativity predicts that only two such polarizations, tensor plus and tensor cross are present for gravitational waves. We give the analytical formulas for the antenna response functions for the six polarizations which are valid for any equal-arm interferometric gravitational-wave detectors without optical cavities in the arms.The response function averaged over the source direction and polarization angle decreases at high frequencies which deteriorates the signal-to-noise ratio registered in the detector. At high frequencies, the averaged response functions for the tensor and breathing modes fall of as $1/f^2$, the averaged response function for the longitudinal mode falls off as $1/f$ and the averaged response function for the vector mode falls off as $\ln(f)/f^2$.Comment: V3: minor corrections. PRD in pres

Source localizations with the network of space-based gravitational wave detectors

The sky localization of the gravitational wave (GW) source is an important scientific objective for GW observations. A network of space-based GW detectors dramatically improves the sky localization accuracy compared with an individual detector not only in the inspiral stage but also in the ringdown stage. It is interesting to explore what plays an important role in the improvement. We find that the angle between the detector planes dominates the improvement, and the time delay is the next important factor. A detector network can dramatically improve the source localization for short signals and long signals with most contributions to the signal-to-noise ratio (SNR) coming from a small part of the signal in a short time, and the more SNR contributed by smaller parts, the better improvement by the network. We also find the effects of the arm length in the transfer function and higher harmonics are negligible for source localization with the detector network.Comment: 14 pages, 8 figures, 2 tables. Phys. Rev. D accepted. Comments are welcome! arXiv admin note: text overlap with arXiv:2105.1127