GNGTS 2015 - Atti del 34° Convegno Nazionale

GNGTS 2015 S essione 2.3 227 required the solution of a series of additional uncertainties and numerical instabilities. The occurrence of local deformations at the stays-girders connection systems, in particular, was fully prevented by taking into account the nominal geometry of the steel supporting device, including in it all the stiffening elements. Concerning the restraint supports, a preliminary assessment of the same modelling approach was carried out on small FE models representative of the bridge and tower restraints only. The optimized restraining devices were successively implemented in the full FE model of the bridge. The frequency of the first vibration mode of the bridge highlighted in fact a marked sensitivity to the deck and pylon base restraints, with variations in the estimated frequencies up to 25% the optimal value (Tab. 1). The presence of the RC pier, involving an asymmetry in the overall geometry, also highlighted the presence of vibration modes pairs (e.g., bending modes of the deck), characterized by comparable in-phase or out-of-phase motion of the deck and bending deformation of the RC pier, corresponding to almost identical natural frequencies. In all these circumstances, the correlation between EMA and FE modes was based on minimization of natural frequency discrepancy values and MAC factor. In some other circumstances, despite an optimal correlation between EMA and FE frequencies, rather scarce MAC values were found. This is the case of higher vibration modes (e.g., EMA mode 5 in Tab. 1) characterized by significant motion of the deck coupled with large deformation of the steel tower. Due to few available experimental measurements, modal correlation was undergone in this case by taking into account not only the natural frequency and the calculated MAC value, but also an additional visual correlation. The general good agreement between EMA and FE predictions obtained for the lower vibration modes of the Pietratagliata bridge, in conclusion, justified in fact the fundamental role of the sophisticated FE-OPT model, especially for future, possible diagnostic applications. Axial forces on the cables. Further validation of the FE-OPT model was in fact provided by comparison of experimental and numerical axial forces on the cables. The performed simulations highlighted in fact that the FE-model correctly estimates the effects of the applied permanent loads, hence suggesting the use of the same refined FE-model for further advanced sensitivity studies and diagnostic investigations. The close agreement was found especially in terms of total axial forces T total taken up by the cables system (Tab. 2). Whatever a good global symmetry of the cable system supporting the deck of the bridge was found, the experimental measurements highlighted important discrepancies, within each group of cables, and suggested further detailed investigations. Tab. 2 summarizes in fact the average axial force T group,EXP for each group of cables, but also the discrepancy ∆ C n ( n = 1,..4) Tab. 1 - Experimental Modal Analysis (EMA) results and correlation with FE calculations. Mean value of natural frequency fr and damping ratio ξ r , with corresponding maximum deviations (r= mode order). B = Bending; T = Torsional mode shapes. Frequency error: Δ = 100×( f r (FE-OPT) – f r (EMA) )/ f r (EMA) .       EMA       FE-OPT r Description f r ξ r r f r Δ MAC [%] [-] [Hz] [%] [-] [Hz] [%] [%] 0 1.619 - 1 1.599 1.2 98.5 1 1 st B 1.665 1.2 ± 0.5 2 1.619 2.8 99.5 2 1 st T 2.669 0.6 ± 0.1 3 2.691 -0.8 97.3 3 2 nd B 3.411 0.7 ± 0.2 5 3.234 5.2 96.0 4 2 nd T 4.750 0.4 ± 0.0 7 4.717 0.7 76.3 5 3 rd B 5.261 0.7 ± 0.2 8 5.295 -0.6 48.4 6 3 rd T 7.336 0.9 ± 0.2 13 7.371 -0.5 78.4