Summary In this paper, the problem of underdetermined modal identification where the number of modes to be identified is larger than the available sensor measurements is addressed using parallel factor decomposition and blind source separation. Underdetermined situations not only arise when the number of sensors are limited but also when narrowband excitations are present in the measurements, for example, in pedestrian‐induced vibration of footbridges. The basic premise of the proposed algorithm is based on multiple‐rank parallel factor decomposition of covariance tensors constituted from vibration response measurements. Unlike conventional parallel factor decomposition using a single rank order, the proposed method utilizes multiple rank order decompositions. A stability chart constructed from identified sources through such multiple rank orders allows for the robust estimation of active modes. The statistical characteristics of the resulting modes are evaluated in order to delineate the sources corresponding to external disturbances versus inherent modes of the system. The proposed framework enables an automated selection of rank order, detection of external harmonics and an estimation of modal parameters that are relatively insensitive to the sensor configuration. The performance of the algorithm is illustrated using both numerical studies and an experimental study using pedestrian‐induced vibration measurements of a stress‐ribbon bridge located at the Technical University—Berlin, Germany. Copyright © 2014 John Wiley & Sons, Ltd.

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Cable-stayed and extra-dosed bridges are today widely used bridge types. Recently, saddles have been used to deviate strands of cables in the pylons. Up to now the mechanics of strands on saddles are not well understood. It was found, that typical longitudinal contact stress distributions between strand and saddle show a strong nonlinearity and a high peak value around the detachment point, where the strand meets the saddle. This paper presents a procedure to analyse the longitudinal contact stress distribution obtained by FEM calculations: This contact stress can be idealised as a constant contact stress according to the Barlow's formula and a contact force at the detachment point due to the flexural rigidity of the bent tension elements. An analytical model is provided to verify this contact force. Finally, a formula is presented to calculate the maximum contact stress. This study provides the basis for further research on saddle design and fatigue of strands.

<p>Saddle systems have been used in recent projects to support the cables in cable-stayed and extradosed bridge structures. With this approach, the cable is anchored to the bridge deck on one side of the pylon, extended over a “saddle” within the pylon, and then fixed on the other end to the deck on the opposite side. A major design consideration for this type of anchorage system, where several significant gaps in the current state-of-knowledge have recently been identified, is the in-service fretting fatigue behaviour of the cables within the pylon saddle. In order to begin to address these knowledge gaps, a research project was recently undertaken at Technische Universität Berlin, wherein analytical tools for understanding and calculating the displacements and contact forces were developed, fatigue tests were performed on large-scale test specimens of cables draped over a round saddle, and fretting fatigue analysis was performed using various models, including several employing multiaxial stress-based approaches. In this paper, these fatigue models are described, and the input parameters required for their application are discussed. Predictions made using the described models are then presented. The paper concludes by identifying the future work needed to further develop this modelling approach, so that it may serve as a useful tool for tasks such as: optimizing design parameters including the saddle radius and contact surface material, and developing improved, reliability-based design guidelines, which will enable the safe and economic design of this connection type, while at the same time reducing the number of large-scale proof tests required at the design stage by the current standards.</p>