Analysis of MDOF Pseudo-Dynamic Test Design of High Flexible Structure

In order to point out the main factors in MDOF pseudo-dynamic test design of high-rise flexible, the key points in pseudo-dynamic test design using equivalent MDOF system were analyzed based on the theoretic derivation and numerical simulation, and the problems to notice in test design were pointed out, the pseudo-dynamic test results validity of high piers based on equivalent SDOF system was discussed, and the impact of high mode to the earthquake response of high-rise flexible structure was acquired. The results of numerical simulation of lumped-mass model prove that the contribution of high mode to the displacement of high flexible structure is little, and the displacement is mainly provided by the first-order mode, which is nothing to do with the selection of seismic waves. However, the high mode have great influence on seismic base shear and base moment of high flexible structure, and the influence level is associated with the properties of seismic wave spectrum. Under one specific earthquake wave, the second-order vibration may play a main contribution to seismic base shear and base moment of high-rise flexible structure. Therefore, it is proper to use equivalent two-degree of freedom system in pseudo-dynamic test of high piers. However, if using equivalent SDOF system, the structural displacement response is correct while the strain data and experimental phenomenon may be untrue. The conclusion proposed is significant in guiding the pseudo dynamic test design of high-rise flexible structure and ensuring the rationality of test.

Static Pushover Analysis Based on an Energy-Equivalent SDOF System

In this paper, a new energy-based pushover procedure is presented in order to achieve an approximate estimation of structural performance under strong earthquakes. The steps of the proposed methodology are quite similar to those of the well-known displacement modification method. However, the determination of the characteristics of the equivalent single-degree-of-freedom (E-SDOF) system is based on a different rational concept. Its main idea is to determine the E-SDOF system by equating the external work of the lateral loads acting on the multi-degree-of-freedom (MDOF) system under consideration to the strain energy of the E-SDOF system. After a brief outline of the theoretical background, a representative numerical example is given. Finally, the accuracy of the proposed method is evaluated by an extensive parametric study which shows that, in general, it provides better results compared to those produced by other similar procedures.

Evaluation of Seismic Damage of Multi-Storey RC Frames with Damage-Based Inelastic Spectra

In the context of performance-based design, structural damage as a comprehensive measure of the seismic demand against the available capacity may be used as an effective performance indicator. Accurate methods of damage estimation usually require sophisticated dynamic response analysis and yet they do not necessarily yield the best results due to the great uncertainties involved in the seismic input. A simple and rational method based on well-constructed response spectra could be more desirable, especially in a design environment. In this paper, a methodology is developed to estimate the seismic damage of multi-storey reinforced concrete (RC) frames in terms of both the overall (global) damage and the damage distribution. The multi-storey frame is first transformed into an equivalent SDOF system, so that the damage in the equivalent SDOF system can be found from the damage-based inelastic spectra for a specified seismic intensity. Numerical investigation on a series of generic frames under a selection of real ground motions indicates that the SDOF damage and the overall damage of the actual frame correlates in a consistent manner, thus the conversion from the established SDOF damage back to the overall frame damage is rather straightforward. Two alternative methods are proposed for the prediction of the distribution of damage along the frame height, one using the modal pushover analysis, and the other based on the structural characterization using a storey capacity factor.

Investigation into the Effects of Foundation Uplift on Simplified Seismic Design Procedures

Uplifting of and yielding below shallow foundations supporting rigid lateral force–resisting elements can provide additional nonlinearity into a system's overall force-deformation behavior. While this nonlinearity may be advantageous, potentially reducing seismic demands, displacement compatibility may result in overstress of lateral and/or gravity-resisting elements. Incorporating this balance of benefit versus consequence in structural design is one goal of performance-based earthquake engineering (PBEE). There are a variety of approaches in design codes for estimating seismic demands and incorporating “performance” as a design goal. Such methods generally account for the displacement of an equivalent SDOF system by reducing the design strength, however, not explicitly for the case of foundation uplift. To address this shortcoming, this paper investigates the relationship between the strength ratio R and the displacement ratio C1 using the beam on nonlinear Winkler foundation (BNWF) concept. Numerical models were constructed considering a range of soil-structure natural periods and a range of design R values. Nineteen ground motions with a broad range of characteristics are used to conduct nonlinear time-history analyses. Results from these simulations indicate that current suggestions for C1- R relations are highly unconservative when uplifting foundations are anticipated. Revised C1- R relations for uplifting foundations are presented and an example numerical comparison provided.