PSI - Issue 84

Marco Bonopera et al. / Procedia Structural Integrity 84 (2026) 457–464

463

buckling loads ( N crE,shear,1,3D FE ) and quarter first-order small-deflections [ v I,2,shear,3D FE ] (Table 3). More detailed information on identification accurancies and parameter errors were described in Bonopera et al. (2018) and Bonopera and De Matteis (2026). Table 3. Comparison between post–tensioning force identifications ( N a ,shear,3D FE and N a ,shear ) and measured and estimated parameters for each test day obtained using quarter small-deflection measurements ( v 2 ) (Tests 1–2). Test 1 Test 2 deflection at a quarter ( v 2 ) Solid FE modeling Reference solution including shear deformation

Age of concrete

Δ

Δ

G aver

N crE,shear,1,3D FE

N x

F v 2

v I,2,shear,3D FE N a ,shear,3D FE

v I,2,shear (mm)

N a ,shear

E aver

(days) (MPa) (MPa)

(kN)

(kN) (kN) (mm) 620 20.2 1.95 620 22.6 2.20 617 25.0 2.32 724 20.1 1.78 721 22.6 2.00 721 25.1 2.22 820 20.2 1.75 820 22.9 1.98 820 25.1 2.17

(mm)

(kN)

(%)

(kN)

(%) 12.6 22.9

1.71 1.97 2.14 1.59 1.83 1.98 1.54 1.77 1.93

1,167 88.2 991 59.8 735 19.1 1,090 50.6 868 20.4 1,104 53.1 1,264 54.1 1,117 36.2 1,165 42.1

1.82 2.04 2.26 1.68 1.89 2.10 1.64 1.86 2.04

698 762 271 635 621 611 732 706 698

426 34,870 14,529

9,479

–56.1 –12.3 –13.9 –15.3 –10.7 –13.9 –14.9

427 37,618 15,674 10,216

433 38,791 16,163 10,531

7. Conclusions In this first article of this work, a high-fidelity solid FE model including a concrete girder-bridge specimen, post– tensioned by an eccentric straight tendon, was developed to analyze the second-order shear deformation in PC girder bridges. According to three-point bending tests executed on the above reduced-scale girder-bridge, reported in literature, and characterized by a significant slenderness ratio, high-strength concrete, and subjected to different post– tensioning, the second-order shear deformation should strongly be considered for obtaining better accuracies in most evaluation techniques. This should be done even when the simply supported PC girder-bridge has an important L /h ratio (i.e., between the range: 10 ~ 20) and a significant elastic modulus value (high stiffness). Furthermore, a reliable prestressing force identification in such members can be gained by computing the parameters of the magnification factor formula of the second-order shear effects through a solid FE modeling, and in accordance with the “static deflected shape” method. This choice requires assuming high-mesh size resolutions within the solid FE model of the girder–tendon system. Yet, with the goal to prove the feasibility of the “static deflected shape” method in a multi-span concrete girder-bridge, a solid FE modeling is highly recommended instead of a conventional FE approach. Indeed, such FE analyses can solve problems of PC bridges by involving complex geometries and/or boundary conditions. In the second article of this work, experimental results regarding a concrete specimen with parabolic tendon, and subjected to post–tensioning losses with time, were compared with a similar FE approach. 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). References Bagge, N., Popescu, C., Elfgern, L., 2018. Failure Tests on Concrete Bridges: Have We Learnt the Lessons? Structure and Infrastructure Engineering 14 (3), 292–319. Belletti, B., Rodriguez, J., Andrade, C., Franceschini, L., Sánchez Montero, J., Vecchi, F., 2020. Experimental Tests on Shear Capacity of Naturally Corroded Prestressed Beams. Structural Concrete 21 (5), 1777–1793. Bonopera, M., Chang, K.C., 2021. Novel Method for Identifying Residual Prestress Force in Simply Supported Concrete Girder-Bridges. Advances in Structural Engineering 24 (14), 3238–3251.