PSI - Issue 84

Marco Bonopera et al. / Procedia Structural Integrity 84 (2026) 465–472

471

mesh size = 24.5×24.8×30 mm 3

[Bonopera and Chang (2021)]

Age of post– tensioning

Δ

Δ

E cm,aver G cm,aver N crE,shear,1,3D FE

N x 1

F v 2

v I,2,shear,3D FE

N a 1,shear,3D FE

N a 1

(days)

(MPa) (MPa)

(kN)

(kN) (kN) (mm)

(mm) 1.90 2.80 3.45 1.98 2.72 3.50 4.21 2.17 2.79 3.45 4.25

(kN) 1,059 1,117 1,198 1,021 1,090 1,226 1,205 1,085 1,148 1,198 1,266

(%) 98.7

(kN) 292 359 441 235 333 478 470 322 390 466 541

(%)

23.2 2.13 34.2 3.16 42.2 3.93 24.2 2.21 33.2 3.06 42.8 4.00 51.4 4.80 26.5 2.44 34.1 3.16 42.1 3.93 51.9 4.88

–45.2 –32.6 –17.3 –55.9 –37.5 –10.3 –11.8 –39.5 –26.7 –12.4

288

533

109.6 124.8 91.6 104.5 130.0 126.1 103.9 115.8 125.2 138.0

290

533

36,054 15,023

9,806

291

532

1.7

Table 4. Comparison between post–tensioning force identifications ( N a ,aver,shear,3D FE and N a ,aver ) and measured and estimated parameters obtained using midspan deflection measurements ( v 4 ) (Tests 3–4). Test 3 Test 4 deflection at the midspan ( v 4 ) Solid FE modeling “Euler–Bernoulli” beam model mesh size = 12.25×12.4×15 mm 3 [Bonopera and Chang (2021)] Age of post– tensioning N crE,shear,1,3D FE N x ,aver F v 4 v I,4,shear,3D FE N a ,aver,shear,3D FE Δ N a ,aver Δ (days) (kN) (kN) (kN) (mm) (mm) (kN) (%) (kN) (%) 288 516 23.2 3.15 2.97 560 8.5 466 –9.7 34.2 4.65 4.38 569 10.3 480 –7.0

42.2 5.75 24.2 3.26 33.2 4.50 42.8 5.85 51.4 7.04 26.5 3.55 34.1 4.59 42.1 5.72 51.9 7.12

5.40 3.09 4.25 5.47 6.58 3.39 4.36 5.39 6.64

597 511 545 637 641 442 491 566 661

15.7 –1.0 23.4 24.2 5.6

502 383 448 535 556 325 375 473 573

–2.7 –25.8 –13.2

290

516

9,806

3.7 7.8

–14.2 –4.7

–36.9 –27.2 –8.2 11.3

291

515

9.9

28.3

7. Conclusions In this second article, a solid FE model including a concrete girder-bridge, and post–tensioned by a parabolic tendon, was similarly developed. The reduced-scale member was subjected to time-dependent post–tensioning losses. The second-order shear deformation was highly recommended to be assumed in most structural analyses even when the PC girder-bridges have a significant L /h ratio (range:10~20) and a high stiffness. Besides, applying the solid FE approach for computing the parameters of the magnification factor formula, the long-term post–tensioning is properly identified when a high-mesh size resolution is considered. Therefore, sensitivity analyses will be developed to evaluate the influence of the mesh size resolution. Conventional FE models are still a good solution to employ the “static deflected shape” method in the laboratory. Thus, the validation of computational strategies against experimental data creates a strong basis for the structural assessment of PC bridges. In conclusion, experiments are required to study the effect of temperature and relative humidity on the long-term nonlinear statics of PC girder-bridges. Acknowledgements M.B. acknowledges the funding provided by the Ministry of University and Research of Italy within the research project “TRAILED-LAB: Un Laboratorio Mobile a Servizio dei Comuni del Cratere” (PNR 2021-2027 program).