Time-history analysis

Perhaps the most commonly overlooked, aspect of using SDOF approximations is the determination of the dynamic reactions for the actual member. The spring force r) in the SDOF system is not equal to the support reaction. In order to determine the dynamic reactions, the distribution of the inertia force within the member must be considered (Biggs 1964, Chapter 5). The basic approach as illustrated in Figure 6.8 is to express the dynamic forces acting on the member, or a segment of the member, in terms of the displacement and acceleration at the control point. This displacement, y(t) is determined in the solution of the time history analysis of the equivalent SDOF system,... 

For primary members (external walls, roof slabs, etc.), the load computation is performed in accordance with Chapter 3. Loads on supporting, or interior members, are determined either by I. the tributary area method or 2, from a computed dynamic reaction. In the tributary area method, external blast pressures are multiplied by the exterior surface area tributary to a support location. The resulting force is then applied to the next member. Dynamic reactions result from a numerical time history analysis (refer to Section 6.5.3) and provide a more accurate time-varying load on the supporting member. 

Selected entries from Methods in Enzymology [vol, page(s)] Background literature, 210, 638 in biological data, 210, 648 definition, 210, 665 identification in biochemical reactions, 210, 651 related terminology, 210, 655 for time scaling in biochemical networks, 210, 636 noise scaling, 210, 643 time history analysis, 210, 643. 

Yj, and Y, including an appropriate d3mamic load factor, are used unless a time-history analysis is performed to justify otherwise. 

The theory of elasto-plastic time history analysis based on section fiber model has been rapid developed in recent years, especially in seismic technology developed country such as American and Japan (D Ambrisi Filippou 1999, Spacone et al. 1999). In this paper, Shenzhen Nanshan Bridge is taken as the engineering background. Time history method based on section fiber model is used to analyze the nonlinear seismic responses of the bridge under rare earthquake. 

Time history analysis under seismic waves with different peak accelerations... 

Qin, C.L. Zhang, A.H. 2004. Nonlinear time history analysis based on section fiber model. Journal of Zhejiang University (Engineering Science) 39(7) 1003-1008. 

The dynamic methods used are a modal analysis with a spectrum as an input and a space-time history analysis which needs one or more accelerograms for inputs. Analyses of the first type are the most common ones the second type is used in particular cases or for the accurate study of the response of a plant component placed at a specific place in a structure. 

Liu Hanlong, Fei ICang, Gao Yufeng. Time History Analysis Method of Slope Seismic Stability [J]. Rock and Soil Mechanics, 2003, 24(4) 553 556. 

Preparation of 3D dynamic models suitable for a time history analysis of the racks which includes the assemblage of all racks in the SFP, all fluid coupling interactions, and mechanical couplings appropriate for a nonlinear simulation. 

Figure 9 presents the deformed sub-structure shapes for the reference building during a response time history analysis (THA). The shapes illustrate the synchronized seismic responses of two core walls and the frame as well as the flexibility of the floor and shear deformations in the wall. 

This brief overview deals mainly with the nonlinear procedures in ECS. Other seismic codes contain similar approaches (ATC 40, 1996 EEMA 356, 2000). Two nonlinear methods of analysis are considered in ECS the nonlinear pushover analysis (NPO) and the nonlinear time history analysis (NTH). 

The nonlinear time-history analysis is the most general nonlinear method of analysis. It is deemed unpractical by some becanse of the compntational length of the analysis, but as computer speeds increase, NTH becomes increasingly feasible. Time-history analysis is a general dynamic method of analysis and there are no compntational peculiarities related to earthquake engineering analysis. The inpnt force is the inpnt ground motion, expressed in the form of one or more accelerograms. The dynamic equations of motion are ... 

Assuming that the parent (i.e. uneontrolled) frame remains elastie during the seismic event, a linear time history analysis using the Newmark... 

Time-History Analysis Forthe earthquake time-history analysis of bridge models, three analysis tools are available. Among them, the approach (a) is adopted universally. 

The design or evaluation for global structural damage may be performed by one of three methods energy balance, force-time history analysis or missile-target interaction analysis. 

Nonlinear dynamic analysis Nonlinear response history analysis Time history analysis... 

A novel solution proposed by Han et al. (2012) used a GPU to accelerate urban seismic damage prediction based on refined building models and nonlinear time-history analysis (THA). Figure 2 shows the flow chart of the Han s program in which the CPU reads the data, copies the data into the GPU, and assigns the computational tasks to each GPU core, whereas the GPU implements the nonlinear THA for individual buildings and copies the results back to the host memory for output. 

Fan (1998) investigated the behavior of nonductile reinforced concrete frame buildings with viscoelastic dampers. He derived an equivalent elastic-viscous model based on the complex stiffness and energy dissipation of the viscoelastic system and proposed a simplified design procedure for a stmcture with viscoelastic dampers. Lee et al. (2005, 2009) applied this method to structures with elastomeric dampers and validated the simplified design procedure by comparing the design demand with the results from nonlinear time-history analysis. 

Performance-Based Design Procedure for Structures with Magneto-Rheological Dampers, Table 5 Median and standard deviation of maximum and residual story drift from nonlinear time history analysis... 

The simplified analysis procedure enables the design demand to be determined without performing a nonlinear time-history analysis by linearizing the structure and utilizing the response spectrum analysis method. 

Response spectrum analysis (RSA) is a method widely used for the design of buildings. Conceptually the method is a simplification of modal analysis, i.e., response history (or time history) analysis (RHA) using modal decomposition, that benefits from the properties of the response spectrum concept. The purpose of the method is to provide quick estimates of the peak response without the need to carry out response history analysis. This is very important because response spectrum analysis (RSA) is based on a series of quick and simple calculations, while time history analysis requires the solution of the differential equation of motion over time. Despite its approximate nature, the method is very useful since it allows the use of response spectrum, a very convenient way to describe seismic hazard. 

The approximation of Taylor series expansion enables the avoidance of iterative response analyses such as time-history analysis for evaluating the objective function. However, the computation of full elements of the Hessian matrix requires a huge computational load when N is large, especially for numerical sensitivity analysis, i.e., the finite difference analysis using gradient vectors. A simpler approach has therefore been proposed by Chen et al. (2009) where the non-diagonal elements of the Hessian matrix are neglected. 

For a nonlinear earthquake analysis (time-history analysis), the general equation of motion in the incremental form... 

Seismic Analysis of Steel and Composite Bridges Numerical Modeling, Fig. 27 Time history analysis of 2 X 34 m long span plate girder bridge with a 3D beam model... 

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