Ductility design analysis

The dynamic analysis has been performed for the seismic parameters, defined by geotechnical investigation as different types of earthquake with defined maximum expected input acceleration for the corresponding return period. Obtained as results from the dynamic analysis are the storey displacement and the ductility, required by the earthquake, that has to comply with the design seismic safety criteria (Sect. 8.3.4). The results from this analysis are given in Sects. 8.4.1, 8.4.2 and 8.4.3 for each of the analysed monument structures, respectively. 

Dynamic analysis With the masses lumped at two characteristic levels, a nonlinear dynamic analysis has been performed with storey hysteretic model obtained by summing up the elastoplastic characteristics of each of the bearing walls, whereas the load-bearing capacity of each of them has been limited to the lower value of bending and shear capacity (according to Sect. 8.3.3). To obtain the dynamic response, three different types of earthquake (Petrovac 1979, Ulcinj 1979 and El Centro 1940) with maximum input acceleration of 0.24g and return period of 1,000 years have been applied. Obtained as the results from the dynamic analysis are the storey displacements and ductility ratios required by the earthquake that have to comply with the design criteria defined in Sect. 8.3.4. 

By comparative analysis of the dynamic responses, it can be concluded that the behavior of the structure constmcted of confined masonry is considerably more favourable in respect to the other two variants (Fig. 8.24). Despite the strict design criteria, the demanded ductility of the stmcture strengthened by horizontal and vertical elements for aU the analysed earthquakes is within the limits of the allowed ductility. It is only that the response of the fourth level in the longitudinal direction is more intensive than that allowed (p > 1.5 for amax = 0.16g, p > 2 for a ax = 0.22g) despite this, the stmcture possesses the demanded ductility capacity. A drastic improvement of response is characteristic for the transverse direction, particularly for the first, the most critical level. While the first level in the case of the designed stmcture is deep in the nonlinear range under the maximum expected earthquakes (p = 3-6 for different earthquakes), in the conditions of a strengthened stmcture, it is in the elastic range of behavior. 

Two basic theories of failure are used in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section I, Section IV, Section 111 Division 1 (Subsections NC, ND, and NE), and Section VIII Division 1 use the maximum principal stress theory. Section ni Division 1 (Subsection NB and the optional part of NC) and Section VIII Division 2 use the maximum shear stress theory or the Tresca criterion. The maximum principal stress theory (sometimes called Rankine theory) is appropriate for materials such as cast iron at room temperature, and for mild steels at temperatures below the nil ductility transition (NDT) temperature (discussed in Section 3.7). Although this theory is used in some design codes (as mentioned previously) the reason is that of simplicity, in that it reduces the amount of analysis, although often necessitating large factors of safety. 

Engineers have known for some time that the maximum shear stress theory and the distortion energy theory predict yielding and fatigue failure in ductile materials better than does the maximum stress theory. However, the maximum stress theory is easier to apply, and with an adequate safety factor it gives satisfactory designs. But where a more exact analysis is desired, the maximum shear stress theory is used. 

Considerations based on a fracture mechanics analysis are necessary if the designer is to progress beyond the primary division of plastics into ductile or brittle , based on simple laboratory tests (see Chapter 2). 

Assessment of Existing Stmctures Using Response History Analysis Behavior Factor and Ductility Code-Based Design Seismic Isolation of Buildings... 

In terms of calculation, instead of performing an explicit inelastic structural analysis in design, the capacity of the structure to dissipate energy, through mainly ductile behavior of its elements, is taken into account by performing an elastic analysis based on a lateral force reduced by a factor R (Fig. 3). Thus, the behavior factor is an approximation of the ratio of the seismic forces that the structure would experience if its response was completely elastic to the seismic forces that may be used in the design, with a conventional elastic analysis model. 

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