Chapter 9 Vibration-Based Approach for Identifying Closely Spaced Modes in Space Frame Structures and Derivation of Member Axial Force s Mena Abdelnour and Volkmar Zabel Abstrac t It has become evident that climate change is an escalating situation requiring societies to act to prevent a nearby climate crisis. Preservation of existing infrastructures to withstand material deterioration and the current increase in loadings does not lead only to reducing dismantling debris but also less consumption of resources, leading to the protection of the environment. Space frame structures were and are still a widely used structural solution for many infrastructures due to their considerable lightweight and ease of erection. The structural stress status of space frame structures is an important step in the preservation process. Assessing the load-bearing capacity of space frame structures gives an insight into the stress status, which is possible through identifying axial forces inside various members. The determination of axial forces of a single tension cable has been intensively investigated based on vibration methods. In addition, as a part of a two-dimensional truss, the identification of stress status in tension members has been studied. However, far less attention has been put so far on the consideration of compression members and more complex systems. This chapter adopts a previously developed methodology to identify tension forces in a two-dimensional truss and extends it to include compression forces identification and application to three-dimensional systems. The approach includes the identification of members’ axial forces based on a numerical model and experimentally determined modal parameters, particularly natural frequencies and mode shapes. This chapter uses a relatively simple space frame structure as a case study. Numerical models of the simple space frame structure give an insight into the natural frequencies and mode shapes to be expected from the physical model. The closely spaced local and global modes of vibration obtained from the numerical model are discussed and explained, and a criterion to distinguish between them is introduced. From the experimental side, applying parametric modal identification is a reliable tool to extract modal parameters by considering different model orders concerning the identification of local and global modes. With the help of experimental results, axial forces are derived based on a numerical model of the structure. The numerical model does not give only a priori information about the modal parameters but also about the minimal model order needed for the identification of global and local modes. Keyword s Force estimation · Local/global modes · Space truss 9.1 Introduction The determination of the actual load-bearing capacity of space frame structures is a challenging task. Because accurate information about external loads, characteristics of the structure skeleton, connections and supports are usually unknown. Over the past decades, space frame structures have been suitable as lightweight structural solutions especially for long-span roof structures. Not only due to their low weight-to-area ratio but also because of the production of standardized crosssections and connecting nodes, which promoted the ease of erection concerning cost and time, space frame structures can be found all over the world today. Due to the increase of design loads in previous years and the modification of further criteria, such as serviceability limits, in the codes of practice also existing structural systems have to be re-assessed by engineers with respect to their load-bearing capacity. In case that the proofs cannot be satisfied by means of common calculations, experimental investigations can be performed to identify the current stress state of structural members. A traditional method to obtain the actual load-bearing capacity of a space frame structure is static load tests. An alternative approach to determine the axial forces of single members of a truss system, which then gives information about the actual M. Abdelnour ( ) · V. Zabel Institute of Structural Mechanics, Faculty of Civil Engineering, Bauhaus-University, Weimar, Germany e-mail: mena.abdelnour@uni-weimar.de © The Society for Experimental Mechanics, Inc. 2024 B. J. Dilworth et al. (eds.), Topics in Modal Analysis & Parameter Identification, Volume 9 , Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-34942-3_9 83
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