PSI - Issue 78

Marco Bonopera et al. / Procedia Structural Integrity 78 (2026) 1143–1150

1149

values of the post – tensioning forces ( N a ,shear ) determined by the measured parameters of the chord elastic modulus ( E aver ) and quarter deflection measurements v 2 (Test 1), and 3/4 deflection measurements v 3 (Test 2) for each test combination (Table 1). Particularly, the deflection measurements ( v 2 and v 3 ) were computed as parameters for the total deflections v tot,shear ( x ) ( x ) [Eq. (6)]. N crE,shear,1 is the first-order critical buckling load [Eq. (4)] which was similarly calculated for each test execution day (Table 1). Moreover, within the procedure for the prestressing force identification, the first-order deflections v I,shear ( a ) ( x ) were instead determined by Eq. (1). The comparisons between the applied ( N x ) and the identified post – tensioning forces ( N a ,shear ) were expressed by the percentage errors Δ = ( N a ,shear − N x ) / N x . Specifically, more favorable correspondences were found when the 3/4 deflection measurements ( v 3 ) were taken into consideration (Test 2). Accurate identifications of post – tensioning forces ( N a ,shear ) , i.e., with errors Δ<1 2%, were obtained when the applied post – tensioning force N x ≥ 721 kN (Sec. 3). Higher experimental second-order shear effects in terms of deflections ( v 3 ) provide better post – tensioning force predictions ( N a ,shear ). Finally, the remaining percentage errors Δ (Table 3) were caused by the determination of the high-strength concrete elastic modulus (Section 4) which should generally be conducted through compression tests on a set of cores drilled along the PC girder-bridge because of the scattered elastic modulus values along its axis (Bonopera and Chang 2021; Bonopera et al. 2022). Table 3. Post – tensioning force identifications ( N a ,shear ) based on Eq. (6), and measured and estimated parameters for each test day obtained using deflection measurements v 2 (Test 1) and v 3 (Test 2). Test 1 — v 2 Test 2 — v 3 deflection at a quarter deflection at a 3/4

Age of post – tensioning

Age of concrete

Δ

Δ

E aver

G aver

N crE,shear,1

N x

F v I,2,shear

v 2

N a ,shear

v I,3,shear

v 3

N a ,shear

(days)

(days)

(MPa) (MPa)

(kN)

(kN) (kN)

(mm)

(mm)

(kN)

(%)

(mm)

(mm)

(kN)

(%)

620 20.2 1.82 1.95 698 12.6 620 22.6 2.04 2.20 762 22.9 617 25.0 2.26 2.32 271 – 56.1

2.43 2.62 759 22.4 2.71 2.95 852 37.4

426

1

34870 14529 10471

3.00 3.12 403 2.24 2.39 709 2.52 2.67 635 2.79 2.97 685 2.18 2.33 750 2.47 2.65 791 2.71 2.91 801

– 34.7

724 20.1 1.68 1.78 635 721 22.6 1.89 2.00 621 721 25.1 2.10 2.22 611 820 20.2 1.64 1.75 732 820 22.9 1.86 1.98 706 820 25.1 2.04 2.17 698

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

– 2.1

427

2

37618 15674 11296

– 11.9

– 5.0 – 8.5 – 3.5 – 2.3

433

8

38791 16163 11648

7. Conclusions This work analyzed the shear deformation in simply supported PC girder-bridges based on the small-deflection theory. Indeed, their shear deformation in terms of second-order effects is usually neglected. A reference solution and a FE model assuming geometric nonlinearities were implemented to investigate such an issue in a simply supported PC girder-bridge specimen with a significant slenderness ratio, composed of a high-strength concrete, and subjected to different values of post – tensioning. According to the comparison with three-point bending tests executed on the above specimen, and reported in literature, the shear deformation should strongly be considered for gaining more accurate structural simulations, even when the simply supported PC girder-bridge has an important length/height ratio, e.g., between the values 10 ~ 20. Similarly, the identification of the prestressing force in such members, based on small-deflection measurements, requires taking the shear deformation into account within the beam model. Therefore, the nondestructive method proposed by Bonopera and Chang (2021) was revised based on the Timoshenko beam theory. In conclusion, the compression-softening theory was validated for simply supported PC girder-bridges when the crack formation is precluded and the magnification factor of the second-order shear effects is lower than 1.10. 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).