**2.2. Analyses performed**

**Figure 5.** (a and b) Flow chart moment curvature according to Takeda and force-velocity law (*F* = *C* × *Vα*).

a high stiffness.

154 Structural Bridge Engineering

**Figure 6.** Restraint diagram.

**2.1. Design choices relating to restraint diagram**

The OT devices, with a dynamic restraint (shock transmitter), represent a very stiff restraint against a dynamic action, whereas they allow slow displacements of the structures (e.g. due to thermal changes). Owing to their features, they have been modelled as truss elements with

The restraint system is outlined in **Figure 6**. Longitudinally, the fixed piers (P7 and P8) absorb static stresses due to braking and play the role of a thermal centre point by means of a transversal one-way restraint; from a seismic point of view, the shorter piers (P–P3 and P14 with a height of less than 25 m) are free to oscillate, piers P3–P13 (about 30 m high) are provided with OTP-type dissipation devices, able to check the stress value, given by the deck; for the remaining piers (with height exceeding 35 m), the application of temporary-restraint devices (shock-transmitter OT) is provided. Transversally, the piers (P1–P4, P10, P13, P14) are provided with a multidirectional support, associated to an OP plastic hydraulic type device, whereas P5, P6, P9, P11, P12 are associated with a DEF\* (\*with shoes, able to accept longitudinal displacements) fixed type restraint; piers P7 and P8 are provided with a transversal one-way

The assessment of the actions, due to the earthquake, has been carried out by means of a nonlinear dynamic analysis with step-by-step integration. The masses associated to gravitational loads have been assessed as follows:

$$G\_1 + G\_2 + \Sigma\_{\neq} \wp\_{\geq} Q\_{\neq} \text{with } \wp\_{\geq} = 0.2 \tag{2}$$

where *G*1 is the weight of the structure; *G*2 is the permanent load; *Q*<sup>j</sup> is the traffic load.

The procedure adopted provides for

**-** Non-linear step-by-step dynamic analysis (three groups of accelerograms in the three directions applied simultaneously). The effects on the structure are represented by the most adverse values of the effects obtained by the analysis by using the three different groups of accelerograms for ULS.


For seismic purposes, the following parameters (referred to DM 14/01/2008 [2]) have been taken into account: rated life of the works, *VN* = 50 years; use coefficient of the works, *CU* = 2. The result is a reference period equal to *V*R = 100 years. The soil has been considered of class C: deposits of medium thickened soil, with layers of more than 30m where mechanical properties gradually increase with depth.
