Dynamic 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. 

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. 

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. 

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 ... 

In combinations 6, 7, and 8, the maximum values of Ta, i a, Tj, Yi, and Tm including an appropriate dynamic factor shall be used unless a time history analysis is performed to justify otherwise. 

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

The current trend in seismic design of dams is to conduct linear or nonlinear time-history analysis to obtain dynamic response of dam to earthquake loads. Time-history analysis of dam requires input ground motion time histories (acceleration, velocity, and displacement). 

Nonlinear dynamic analysis is undoubtedly the most realistic and accurate analysis method available. It is also referred as nonlinear time history analysis, nonlinear response history analysis, or according to ASCE 41-06 (2007) as nonlinear dynamic procedure (NDP). Earthquake loading is taken into consideration as a natural or a synthetic ground motion on a structural model... 

Slope displacement time history and dynamic stability analysis... 

One of the methods developed for the seismic risk evaluation of structures is the SAC-FEMA method, which enables probability assessment in closed form (Cornell et al. 2002), and represents a part of a broader PEER probabilistic framework (Deierlein 2004). Within the framework of SAC-FEMA method, the relationship between the seismic intensity measure and the engineering demand parameter is usually determined by Incremental Dynamic Analysis (IDA) developed by Vamvatsikos Cornell (2002). IDA is a powerful tool for estimation of seismic demand and capacity for multiple levels of intensity. However, it requires a large number of inelastic time-history analyses (and corresponding detailed data on ground motion time-histories and hysteretic behavior of structural elements) and is thus very time-consuming. Often it is possible to create summarized IDA curves with less input data, with less effort, but with still acceptable accuracy. One possible approach is to determine seismic demand for multiple levels... 

The treatment of uncertainties requires the use of probabilistic methods, estimating the probability of exceeding response targets for the different performance requirements, for example, on an annual basis. The dynamic structural responses are highly nonlinear, and their time history must be found by numerical (e.g., finite elements) analysis for the duration of the earthquake. In a thorough analysis, the nonlinearity of the response is further increased when the interactions between the structure and the foundations are included. It is not possible to establish an explicit relationship between the intervening variables and the dynamic responses, and results can only be obtained in a discrete manner, given specific values of the structural variables and a particular earthquake record. Reliability calculations depend on simulations... 

Numerical analysis and simulation of adaptronic systems can be performed in the time or in the frequency domain depending on the representation of the system in the state space or as a matrix of transfer functions. In addition to performance criteria, important goals are stability and robustness of an adaptronic system. In the case of adaptronic structures, performance criteria are often given in terms of allowable static and dynamic errors relating to structural shape if subjected to specified disturbances. Many applications also involve limits in energy consmnption and actuator stroke or force, which must be checked in time-history simulations. A comprehensive introduction on the different aspects and their interaction can be found in [14]. Current research in the field is for instance presented in [15] and [16]. 

Use the nonlinear time-history dynamic analysis to check the design performance of building structure under an ensemble of selected ground motions scaled to match the design response spectrum corresponding to 2 % probability of exceedance in 50 years (NBCC 2010). 

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