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displacements (mm)

Figure 11. Reference case.

bell-tower and the clock-tower, they are not reported here for brevity's sake.

displacements (mm)

Figure 10. Capacity curve (pushover, y-direction).

simplified schemes based on the limit analysis. The structure is considered as the assemblage of a certain number of components depending on the structural compound geometry and shape (e.g. the whole façade) and on the details (e.g. quality of existing connections) whose behavior is similar to the behavior of analogous macro-elements in other buildings, where the collapse mechanisms can be identified. In this study, several possible mechanisms have been taken into account (D'Ayala & Speranza 2003), mostly out-of-plane mechanisms. Next the results are reported with respect to the most diffused collapse mechanisms.

To this end, several elementary macro-elements have been identified in the church; applying the Theorem of Virtual Work (TVW) the collapse multipliers (a0) have been evaluated by eq. (3) that refers to the simple scheme illustrated in Figure 11. After the identification of the collapse mechanism a rigid-body system is considered in application of the TVW. The seismic load is assumed as an overturning force while the gravity load is assumed as a stabilization load.

Analyses of past events have permitted to select a group of mechanisms to analyze. These mechanism concerns partial of local overturning of the main façade, of the lateral bearing walls, of the apse. Other mechanisms take into account the behavior of the

After the evaluation of the collapse multiplier, the corresponding seismic spectral acceleration is evaluated by (where M* is the mass of the idealized SODF system and g is the acceleration of gravity):

The respect of the analyzed limit state is assured by the respect of the following inequality (where q is the behaviour factor assumed equal to 2.0, Z is the height of the mass above the level of application of the seismic action and H is the total height of the macro-element):

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