PSI - Issue 78

Noemi Di Rienzo et al. / Procedia Structural Integrity 78 (2026) 1474–1481

1478

b

a

Fig. 2. Relationship between span length and experimentally identified OMA frequencies: (a) first mode flexural frequency f 1 for simply and continuous supported bridges; (b) second mode flexural frequency f 2 for the same sample.

Generally, from a first analysis, the comparisons shown confirm that length span and static scheme are the two parameters that best explain the variability of natural frequencies in monitored reinforced concrete bridges. While for the first frequency Fig. 1a shows a remarkable consistency between simply supported and continuous bridges, the second one seems more affected by the static scheme. 3. Development of a simplified formulation for flexural frequencies It is well known (Chopra, 2007) that the n-th natural frequency of a simply supported beam of length with constant distributed mass and stiffness over the length is: = n 2 n EI f 2L m  In the context of bridge decks, the mass can be assumed to be proportional to the area of deck through an equivalent density also including the contribution of other non-structural components as pavement, sidewalks, curbs, and railings. It follows that: (1)

1 I E L A 

f

 n 2

(2)

As a first approximation, the ratio √ (E/ ρ ) could be assumed as constant, given the low variation range of the two parameters E and ρ for homogeneous types of bridge and the presence of the squared root. The parameter √ (I/A), the radius of gyration, is instead related to the depth of the deck h (beam + slab). Thus, a tentative simplified relationship for the natural frequencies of simply supported beams can be defined as: