PSI - Issue 78

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

1147

Table 1. Comparison between analytical total deflections and deflection measurements for each test execution day and related to the layout represented in Fig. 5 in Bonopera et al. (2018).

Age of concrete (days)

E aver

G aver

N crE,shear,1

N 0

N x

F

v 1

v 2

v 3

v 4

v 5

v 6

v 7

(MPa) (MPa)

(kN)

(kN) (kN) (kN)

(mm) (mm) (mm) (mm) (mm) (mm) (mm) 1.03 1.92 2.55 2.79 2.55 1.92 1.03 1.03 1.94 2.58 2.83 2.58 1.94 1.03 1.03 1.94 2.58 2.83 2.58 1.94 1.03 1.15 2.15 2.85 3.12 2.85 2.15 1.15 1.16 2.17 2.88 3.16 2.88 2.17 1.16 1.16 2.17 2.89 3.16 2.89 2.17 1.16 1.27 2.38 3.16 3.45 3.16 2.38 1.27 1.28 2.40 3.19 3.50 3.19 2.40 1.28 1.28 2.40 3.19 3.50 3.19 2.40 1.28 1.42 2.32 3.12 3.43 3.03 2.27 1.22 0.95 1.78 2.37 2.59 2.37 1.78 0.95 0.96 1.79 2.39 2.62 2.39 1.79 0.96 0.96 1.80 2.39 2.62 2.39 1.80 0.96 1.19 1.78 2.39 2.59 2.33 1.73 0.94 1.07 2.00 2.66 2.91 2.66 2.00 1.07 1.08 2.02 2.69 2.94 2.69 2.02 1.08 1.08 2.02 2.69 2.95 2.69 2.02 1.08 1.31 2.00 2.67 2.92 2.60 1.94 1.05 1.19 2.22 2.95 3.23 2.95 2.22 1.19 1.20 2.24 2.98 3.27 2.98 2.24 1.20 1.20 2.24 2.99 3.27 2.99 2.24 1.20 1.46 2.22 2.97 3.23 2.90 2.16 1.17 0.93 1.75 2.32 2.54 2.32 1.75 0.93 0.94 1.76 2.34 2.57 2.34 1.76 0.94 0.94 1.76 2.35 2.57 2.35 1.76 0.94 1.20 1.75 2.33 2.54 2.29 1.71 0.92 1.06 1.98 2.63 2.88 2.63 1.98 1.06 1.07 2.00 2.66 2.91 2.66 2.00 1.07 1.07 2.00 2.66 2.92 2.66 2.00 1.07 1.33 1.98 2.65 2.88 2.60 1.94 1.04 1.16 2.17 2.88 3.15 2.88 2.17 1.16 1.17 2.19 2.91 3.19 2.91 2.19 1.17 1.17 2.19 2.92 3.20 2.92 2.19 1.17 1.42 2.17 2.91 3.17 2.86 2.14 1.15 1.45 1.95 2.62 2.84 – 1.93 1.02 1.59 2.20 2.95 3.20 – 2.17 1.15

Analytical – E. – B.

Eq. (2) – Shear Eq. (5) – Shear

619 620 20.2

LVDT

Analytical – E. – B.

Eq. (2) – Shear Eq. (5) – Shear

426 34870 14529 10471

619 620 22.6

LVDT

Analytical – E. – B.

Eq. (2) – Shear Eq. (5) – Shear

615 617 25.0

LVDT

Analytical – E. – B.

Eq. (2) – Shear Eq. (5) – Shear

723 724 20.1

LVDT

Analytical – E. – B.

Eq. (2) – Shear Eq. (5) – Shear

427 37618 15674 11296

720 721 22.6

LVDT

Analytical – E. – B.

Eq. (2) – Shear Eq. (5) – Shear

720 721 25.1

LVDT

Analytical – E. – B.

Eq. (2) – Shear Eq. (5) – Shear

820 820 20.2

LVDT

Analytical – E. – B.

Eq. (2) – Shear Eq. (5) – Shear

433 38791 16163 11648

820 820 22.9

LVDT

Analytical – E. – B.

Eq. (2) – Shear Eq. (5) – Shear

820 820 25.1

LVDT

4. Estimation of the time-dependent elastic moduli of the high-strength concrete The time-dependent elastic moduli of the high-strength concrete was evaluated through compression tests at 28 days and at each execution day of the three-point bending tests, i.e., at 426, 427 and 433 days of concrete age (Table 2). Nine 150×300-mm 2 cylinders were concurrently cast with the concrete girder-bridge specimen. All the cylinders and the specimen were maintained under the same curing environmental conditions, i.e., close to each other and outdoor until the insertion of the PC girder-bridge specimen in the test rig [Fig. 4(a) in Bonopera et al. 2018]. The chord elastic modulus ( E ) of each cylinder was measured using Eq. (11) reported in Bonopera et al. (2018), according to the ASTM Standards C 469/C 469M – 14 (Annual Book of ASTM Standards 2016) and after executing compression tests by a universal machine. Particularly, the average chord elastic modulus ( E aver ) was determined at 28 days by testing three cylinders (Table 2). Conversely, two cylinders were tested at 426, 427 and 433 days respectively (Table 2). No crack or void was observed in the cylinders. Specifically, the average chord elastic modulus ( E aver ) exhibited progressive increments of 14.1, 23.1 and 26.9% with respect to the value gained at 28 days (30,560 MPa). Obviously,