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

Table 3. Vibration frequencies comparison Mode f exp [Hz]

f num [Hz]

Δ [%]

1 2 3 4 5

2.45 2.67 3.51 3.57 3.63

2.53 2.74 3.42 3.78 3.79

3% 3% 3% 4% 5%

3. Seismic safety check in linear analysis In the next, the safety checks in seismic conditions of the piers are shown, it has been conducted by performing a linear static analysis as the deck beams are simply supported and the effective mass of the piers do not exceed 1/5 of the deck total mass (NTC 2018, 7.9.4.1). First, the mass afferent to the piers in exam was calculated. For this purpose, the reactions at the supports due to permanent structural, non-structural and accidental traffic loads were first calculated using a finite element model of the deck only (frame type elements) implemented with SAP 2000 software. Regarding the variable traffic loads, reference was made to the load schemes given in Section 5.1.3.3.3 of NTC 2018 (Load Scheme 1) by arranging the load lanes on the in order to maximize the actions on the edge beam and thus also the vertical unloading of the beam on the supports. The reactions at the supports due to the moving loads were obtained through a "Moving Load Analysis" which allow to evaluate the vertical actions at the deck supports (three reaction, one for each constraint) due to permanent structural (G1k), nonstructural (G2k) and accidental traffic loads (Q1k) and resulting that the accidental vehicles load effect is bigger on the lateral beams.

Table 4. Seismic verification result Ex (transversal). N Ed M Ed M Rd

V Ed

V Rd

D/C

D/C

[kN]

[kNm]

[kN]

[kN]

[kNm]

2.76

Left column

1287

3105

1124

1859

632

2.94

1.61

Right column

4668

3025

1882

1801

662

2.72

Table 5. Seismic verification result Ey (longitudinal). N Ed M Ed M Rd

V Ed

V Rd

D/C

D/C

[kN]

[kNm]

[kN]

[kN]

[kNm]

1.65

Left column

2978

9200

3482

2447

1484

1.65

Right column 1.65 Out of a static analysis the stresses can be obtained as shown in Figure 5 where either the seismic load in the longitudinal and transversal direction are plotted. Verification results are reported in table 4. Those show how the piers are not verified in seismic load combination because of an original design which did not take into account any seismic load. 2978 9200 3482 1.65 2447 1484

4. Effect of the soil-structure interaction 4.1. Soil-structure interaction modelling

Structure displacements and strains during an earthquake are always affected by interaction between the same structure, foundation and soil. The methods generally used to model the SSI can be or “direct” methods or “sub structure” methods. The first ones model the structure, the foundation and the soil in one single FEM model and analyze them in one step, this result in such a difficult calculation. However, the “sub-structure” methods allow to uncouple the evaluation of the foundation motion (kinematics interaction effect) and the evaluation of the dynamic