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Railroad bridge engineers are interested in the displacement of railroadbridges when the train is crossing the bridge for engineering decision makingof their assets. Measuring displacements under train crossing events isdifficult. If simplified reference-free methods would be accurate andvalidated, owners would conduct objective performance assessment of theirbridge inventories under trains. Researchers have developed new sensingtechnologies (reference-free) to overcome the limitations of referencepoint-based displacement sensors. Reference-free methods use accelerometers toestimate displacements, by decomposing the total displacement in two parts: ahigh-frequency dynamic displacement component, and a low-frequencypseudo-static displacement component. In the past, researchers have used theEuler-Bernoulli beam theory formula to estimate the pseudo-static displacementassuming railroad bridge piles and columns can be simplified as cantileverbeams. However, according to railroad bridge managers, railroad bridges have adifferent degree of fixity for each pile of each bent. Displacements can beestimated assuming a similar degree of fixity for deep foundations, butinherent errors will affect the accuracy of displacement estimation. This papersolves this problem expanding the 1 Degree of Freedom (1DOF) solution to a new2 Degrees of Freedom (2DOF), to collect displacements under trains and enablecost-effective condition-based information related to bridge safety.Researchers developed a simplified beam to demonstrate the total displacementestimation using 2DOF and further conducted experimental results in thelaboratory. The estimated displacement of the 2DOF model is more accurate thanthat of the 1DOF model for ten train crossing events. With only one sensoradded to the ground of the pile, this method provides owners with approximately40% more accurate displacements.

Measuring Total Transverse Reference-free Displacements of Railroad Bridges using 2 Degrees of Freedom (2DOF): Experimental Validation