Model floor displacement

Three-control-point approach As discussed previously, instead of employing a rigid body motion assumption, beam shape functions are used for the calculation of the equivalent nodal displacements in the VecTorl model. In the above approach, the interface floor system is divided into two beams connected by three control points. In Figure 4(b), control points N, N2, and N3 form two beam members with lengths equal to half of the wall width. Cubic shape functions are used for the interpolation of continuum model nodal displacement loads [ y,from at these three... 

Jayakumar and Beck (1988) modeled an w-story shear building in 2-D by applying the Masing model to the relationship between story shear forces and the inter-story drifts. Consider a structural model where the vector of relative floor displacements x(t) is related to the ground acceleration y(t) as follows ... 

In a PsD test it is assumed that the response of a structure can be determined by a discrete model with a limited number of degrees of freedom (DoF). In this test campaign four DoFs were selected the horizontal displacements of each storey with the assumption that all the mass is concentrated at the selected DoFs (i.e., the floor slabs). The equations of motion for such an idealized system are second order differential equations which can be expressed in matrix form ... 

When the output of the numerical analysis is requested in terms of floor response spectra, maximum relative displacements, relative velocities, absolute accelerations and maximum stresses during an earthquake, linear dynamic analysis (e.g. direct time integration, modal analysis, frequency integration and response spectrum) is generally adequate for most models. Alternatively, non-hnear dynamic analysis should be used where appropriate or necessary (e.g. structural hft-off, non-linear load dependent support, properties of foundation materials in soil-structure interaction problems or interactions between solid parts). 

Another problem that arises when using fiber element has to do with the selection of the control point. The original N2 method was developed for shear frames and can be easily applied to frames with floor diaphragms which are rigid in their plane. When the beams are modeled with fiber elements, floor diaphragms cannot be used, because they introduce artificial compression due to the fact that the beams cannot freely extend. Because the beams are normally axially suffer, almost any point can be selected. However, in older buildings with few beams and thin slabs the floor can become quite flexible in its plane and thus some differences can be expected in the horizontal displacements over a floor. Also, slabs have to be modeled with either shell elements or with equivalent bar elements (which ignore the flexural stiffness of the slabs). 

It is the main objective of this example to show that some d5mamic characteristics of a structure with dampers, modelled using the above mentioned models is practically identical if both models possess approximately equal possibilities to dissipate energy. This conclusion is supported by the results presented in Table 4. This table contains logarithmic decrements of damping and the peak values of displacements and accelerations of the fourth-floor, calculated from the obtained solutions to the equations of motion for both damper models. 

Beam elements may easily be expanded forthe study of compensator systems (Li 2010). To all nodes we add 2 dof to the 6 dof of the beam node (Figure 5b). These 2 dof represent the displacement of the compensator s mass in the 2 plane directions of the floor. They are attached to the corresponding translational dof of the beam via the compensators stifihess and damping. The mass, stifihess and damping of the compensators are the free parameters for the optimization of a compensation system. At floors without compensators, small values of the compensators properties produce only negligible effects, so there is no need to use different element types for floors with and without compensator systems (Figure 5a). It is evident that such models allow for fast studies of the dynamic response of structures. 

Actively and Semi-actively Controlled Structures Under Seismic Actions Modeling and Analysis, Fig. 11 Displacement and acceleration of the controlled blue line) and uncontrolled red line) system for the third floor of the three-story building subjected to earthquake... 

If there is a diaphragm in the structure, as, for example, is the case with the composite slab of the loft in the prototype building, it is recommended to avoid the more complex option of modeling it with shell elements and instead create a master node that will be connected with all nodes of the diaphragm (Eig. 21). In this case, in order to account for uncertainties in the location of masses and in the spatial variation of the seismic motion, the calculated center of mass at each floor shall be considered as being displaced from its... 

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