PSI - Issue 44

Marco Gallo et al. / Procedia Structural Integrity 44 (2023) 618–625

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Marco Gallo et al./ Structural Integrity Procedia 00 (2022) 000–000

5. Non-linear static analysis for the definition of the behavior factor All verifications have been carried out by considering the stresses from a design spectrum obtained by the elastic one divided for the behaviour factor q . As usual for existing structures, the behaviour factor is assumed to be in the range 1.5-3.0 for the check of ductile mechanisms, while for the check of brittle mechanisms, as the shear, a value of q =1.5 must be used. For this reason, a non-linear static analysis was performed to justify the possibility to take into account in the calculation a greater value of q . The non-linear behaviour of piers was modelled via plastic hinges which allow the element to act as linear, then cracked and finally in plastic range. The following equation (Circ. N.7 21/01/2019) are useful in order to evaluate the yielding and failure rotation of the cross-section: . = / ! ) " 0 + 0.0013 '1 + % ) .-1 " ( + 0.13 / ! 2 ! 3 #$ 42 % (2) 5 = 6 % &$ . . + / 5 − . 2 78 '1 − *.-* ) '$ ) " (4 (3) Out of the non-linear static analysis the push-over curve is available and useful to define the bi-linear capacity curve which can be used to evaluate the behaviour factor by using the Eq. (4). = ( : − 1) ; ( ; + 1 = 4.85 (4) The q results to be equal . meanings that the system pier-pulvinus supporting the deck have a good ductility. Anyway, the maximum value, allowed from technical references, that can be used for the analysis is q=3.0. In this way the safety check can be updated. As the analysis carried out is linear the effect on terms of capacity-to-demand ratio is easily assessable by multiplying the previous value for the ratio between the two different behaviour factors used. The Figure 6, show then the comparing between the bending moment verification for each behaviour factor and any restrain (fixed or SSI) case.

Fig. 5. Push-over curve.

0.00 1.00 2.00 3.00

Fixed base transversal direction Fixed base longitudinal direction

D/C

bending moment q=1,5

bending moment q=3,0

Fig. 6. Behaviour factor value effect on demand-to-capacity ratios.

6. Effect of SSI varying piers slenderness and type of soil To better underline the soil-structure interaction effect, a parametric analysis was performed by considering more slender piers. The existing piers have a rectangular cross-section (70x150cm) and they are 3.0 height. With this aim the piers height was assumed equal to 3.0m (original), 4.5m and 6.0m respectively. As usual that effect can be