SUMMARY Numerous structures uplift under the influence of strong ground motion. Although many researchers have investigated the effects of base uplift on very stiff (ideally rigid) structures, the rocking response of flexible structures has received less attention. Related practical analysis methods treat these structures with simplified ‘equivalent’ oscillators without directly addressing the interaction between elasticity and rocking. This paper addresses the fundamental dynamics of flexible rocking structures. The nonlinear equations of motion, derived using a Lagrangian formulation for large rotations, are presented for an idealized structural model. Particular attention is devoted to the transition between successive phases; a physically consistent classical impact framework is utilized alongside an energy approach. The fundamental dynamic properties of the flexible rocking system are compared with those of similar linear elastic oscillators and rigid rocking structures, revealing the distinct characteristics of flexible rocking structures. In particular, parametric analysis is performed to quantify the effect of elasticity on uplift, overturning instability, and harmonic response, from which an uplifted resonance emerges. The contribution of stability and strength to the collapse of flexible rocking structures is discussed. Copyright © 2012 John Wiley & Sons, Ltd.

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SUMMARYThis paper presents a new analytical model for describing the large rocking response of an elastic multi-mass structure resting on ideally rigid ground. Using the experimental results from a rocking steel column, the ability of the proposed analytical model to estimate the rocking and translational acceleration response under free vibration, pulse and earthquake excitations is evaluated. It is observed that the classical treatment of impact may result in an unrealistically large transfer of energy to vibrations. Therefore a new Dirac-delta type impact model that spreads the effects of impact over time and space is proposed. The use of a Dirac-delta model and accurate restitution factors play a pivotal role in prediction of rocking and acceleration responses. In order to characterize the nonlinear response better, a modal analysis of the linearized system is proposed. With this approach, the vibration mode frequencies and shapes during rocking action were determined. A comparison of analytical and experimental modal estimations suggests good agreement. The results emphasize that the vibration characteristics of several vibration modes are affected by rocking action, and these modes may be excited at impact.

SummaryDynamic displacement measurements provide useful information for the assessment of masonry rail bridges, which constitute a significant part of the bridge stock in the United Kingdom and Europe. Commercial 2D digital image correlation (DIC) techniques are well suited for this purpose. These systems provide precise noncontact displacement measurements simultaneously at many locations of the bridge with an easily configured camera set-up. However, various sources of errors can affect the resolution, repeatability, and accuracy of DIC field measurements. Typically, these errors are application specific and are not automatically corrected by commercial software. To address this limitation, this paper presents a survey of relevant DIC errors and discusses methods to minimise the influence of these errors during equipment set-up and data processing. A case study application of DIC for multipoint displacement measurement of a masonry viaduct in Leeds is then described, where potential errors due to lighting changes, image texture, and camera movements are minimised with an appropriate set-up. Pixel-metric scaling errors are kept to a minimum with the use of a calibration method, which utilises vanishing points in the image. However, comparisons of DIC relative displacement measurements to complementary strain measurements from the bridge demonstrate that other errors may have significant influence on the DIC measurement accuracy. Therefore, the influence of measurement errors due to lens radial distortion and out-of-plane movements is quantified theoretically with pinhole camera and division distortion models. A method to correct for errors due to potential out-of-plane movements is then proposed. KEYWORDSdigital image correlation, field testing and monitoring, masonry arch bridge, measurement error, out-of-plane movement, pinhole camera | INTRODUCTIONAccording to a recent survey, there are approximately 18,000 masonry rail bridges in the United Kingdom, and this corresponds to 47% of the rail bridge stock. Most of the existing masonry bridges date back to the 19th century and haveThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.