PSI - Issue 84

Marco Pirrò et al. / Procedia Structural Integrity 84 (2026) 552–559

554

 (x) = a 1 n+1

x n+1 + a 2 n

(3)

x n +…+ a

n+1 x + a n

The unknown coefficients a i can be determined by solving Eqs. 1-3 with assigned values of rotations, curvatures or deflections. In this paper, measured rotations from inclinometers (and imposed curvatures and deflections corresponding to boundary conditions) are assigned. Of course, if the number of equations exceed the unknown quantities to be computed, a least square solution is obtained.

Fig. 1. Schematic of deflected shape of a multi-span beam.

The present paper proposes two distinct strategies for estimating the deflection curves by using measured rotations, with both strategies assuming to adopt biaxial inclinometers, that measure the rotation in both the orthogonal directions and are mounted along the two opposite sides of a bridge. The first methodology consists of interpolating the longitudinal rotations along each side through a polynomial function (see Eq. 1) and then integrating the polynomial function to define the vertical displacement (Eq. 3) of both sides of the bridge. Eventually, the boundary conditions at internal and external constraints can be imposed (e.g., by setting the displacements equal to zero at the supports). Afterwards, the deflection along the bridge axis is retrieved by averaging the estimated displacements of the two sides. The second approach involves using also the transverse rotations that are measured at the opposite sides of the bridge deck. Firstly, the longitudinal rotations measured at the two sides are averaged to evaluate the rotations at the mid-line, so that the related deflections are retrieved from (Eq. 1). To estimate the deflection curve of the two sides, the measured transverse rotations are used: in more details, the average transverse rotation is computed for each instrumented cross-section and the vertical displacement associated with this transverse rotation is added, with the The previously described methodology has been applied to bridge shown Fig. 2. The investigated infrastructure, denoted to as Dolo overpass (Gentile et al., 2023), is a steel-concrete bridge that crosses the A4 Milan-Venice highway in the municipality of Dolo (VE). The overpass has an overall length of 108 m and consists of three spans of different lengths: the largest, crossing the A4, has a span of 48 m while the side ones have a span of 30 m. The continuous deck, housing a roadway of 12 m and two pavements with a width of 1.7 m each, consists of a trapezoidal box girder, exhibiting variable height and composite with a r.c. slab. The connection between the steel box girder and the r.c. slab is made through Nelson-type welded connectors. From geometric point of view, the trapezoidal box girder has a lower base of 2.6 m and a variable height between 0.8 m and 1.8 m. The variability of the height of the central beam is due to the longitudinal profile of the road surface, which is characterized by a slight curvature with a radius of about 1500 m. As shown in Fig. 2a, the central span is supported by elastic constraints consisting of inclined steel struts resting on squat r.c. piers. 30 bi-axial inclinometers were installed in the Dolo overpass: as shown in Fig. 3, five inclinometers are mounted at each side of each span, with the instrumented cross-sections corresponding to the supports, mid-span and quarter spans. All the inclinometers are synchronized, and the sampling frequency of 20 Hz is adopted to measure the longitudinal and transverse rotations, so that when peak rotation is attained at some point, it is possible to retrieve the rotations of all instrumented points at the corresponding time sample to evaluate the displacement distribution along the bridge. proper sign, to the deflection evaluated at mid-line. 3. Description of the bridge and sensors layout